C.R. Woodcock · J.S. Mason Editors.
Bulk solids
handling :
an introduction to the practice and
technology
BULK SOLIDS HANDLING
An Introduction to the Practice and
Technology
Prepared by Thames Polytechnic Bulk Solids Handling Unit
and edited by
C.R.WOODCOCK, DipTech, MSc, PhD, CEng, MIMechE
Principal Lecturer, School of Engineering, Thames Polytechnic
and
J.S. MASON, BSc, PhD, CEng, FIMechE, FIMarE, MIMinE
Head of School of Engineering, Thames Polytechnic
Springer Science+Business Media, LLC
1987 Springer Science+Business Media New York
Originally published by Blackie & Son Ltd in 1987
~)
First published 1987
Al/ rights reserved.
No parc of chis puhlication may he reproduced.
stored in a retrieval system, or transmitted,
in anyform or hy any means,
electronic, mechanical, recording or otherwise,
without prior permission of the Puhlishers.
British Library Cataloguing in Publication Data
Bulk solids handling: an introduction to
the practice and technology.
1. Bulk solids handling
1. Woodcock, C.R. Il. Mason, J.S.
III. Thames Polytechnic. Bulk So/ids
Hand/ing Unit
621.8'6
TS180.8.B8
Library of Congress Cataloging-in-Publication Data
Woodcock, C.R.
Bulk solids handling.
Bibliography: p.
lncludes index.
1. Bulk solids handling. 1. Mason, J.S.
Il. Title.
TS180.8.B8W66 1987
629.04
85-29147
ISBN 978-1-4757-1360-2
DOI 10.1007/978-1-4757-1358-9
ISBN 978-1-4757-1358-9 (eBook)
Phototypesetting by Thomson Press (1) Ltd, New Delhi and
Preface
An understanding of the properties and the handling characteristics of liquids
and gases has long been regarded as an essential requirement for most
practising engineers. It is therefore not surprising that, over the years, there has
been a regular appearance of books dealing with the fundamentals of fluid
mechanics, fluid flow, hydraulics and related topics. What is surprising is that
there has been no parallel development of the related discipline of Bulk Solids
Handling, despite its increasing importance in modern industry across the
world. It is only very recently that a structured approach to the teaching, and
learning, of the subject has begun to evolve.
A reason for the slow emergence of Bulk Solids Handling as an accepted
topic of study in academic courses on mechanical, agricultural, chemical,
mining and civil engineering is perhaps that the practice is so often taken for
granted. Certainly the variety of materials being handled in bulk is almost
endless, ranging in size from fine dust to rocks, in value from refuse to gold, and
in temperature from deep-frozen peas to near-molten metal. Almost everyone
has seen a belt conveyor in operation-perhaps carrying grain on the local
farm, or stone and rock from a nearby quarry-but how many would know
that belt conveyors are now being developed to transport bulk solids at rates
in excess of 30 000 tonnes per hour? The domestic vacuum cleaner is a familiar
machine in which dust particles are conveyed through a pipe in a stream of air,
but few people would appreciate that large lumps of coal and rock, and even
fish, can be transported in a similar way. Examples of bulk solids handling can
be found in almost every kind of industry and the problems associated with the
design, installation and operation of plant for the storage and transport of
materials in bulk are many and varied. No book can be a substitute for the
technical skill acquired through long experience in the industry. Nevertheless,
we have attempted to present here a foundation of knowledge, generally with a
practical rather than an academic emphasis, upon which expertise in various
specialized aspects of bulk solids handling can be developed subsequently.
Governments of many nations are now recognizing that the education and
training of engineers in many fields should include some study of the
technology of bulk solids covering the properties, storage, flow and transport
of a wide range of materials in particulate or granular form. In the United
Kingdom, for example, recent initiatives emanating from the Department of
Industry have led to conferences, courses, and various publications aimed at
promoting a greater awareness of the unique features of bulk solids. The
School of Engineering at Thames Polytechnic, and in particular the staff of its
iv
PREFACE
Bulk Solids Handling Unit, have been deeply involved in these initiatives from
the outset and this book is the result of a clearly perceived need for an
introduction to the subject that would identify and set out a structure for the
area of study that is becoming known by the convenient, if not entirely
accurate, title 'Bulk Solids Handling'. Many specialist treatments are already
available: works on particle technology, hopper design, fluidization, dust
control, pneumatic conveying, and others, can be found on library shelves and
in most cases these are excellent and valuable works of reference for the
experienced engineer. However, for the student and for the engineer who
requires an overview of the emerging discipline of bulk solids handling,
supported by an adequate coverage of fundamentals, this book should
provide essential reading.
In common with most books of similar size and scope, this one should really
be regarded as the product of a team effort. We, as authors and editors, would
unhesitatingly acknowledge the contributions, both direct and indirect, of our
colleagues in the Bulk Solids Handling Unit at Thames Polytechnic, notably
Dr David Mills and Dr Alan Reed. In their various ways the academic and
technician staff of the School of Engineering, together with many of our
postgraduate and undergraduate students, have played some part in the
events leading up to the conception, preparation and, ultimately, the
production of this book. Although it is perhaps a little unfair to mention
individuals by name, we do gratefully acknowledge the patient and tolerant
efforts of Mrs Pam Colley in undertaking the massive task of typing the
manuscript. Finally, our sincere thanks and appreciation goes to our
respective families, especially to our wives Angela and Fran, for the patience,
understanding and considerable fortitude that they have shown during the
months that this book has been in preparation, and indeed during the many
years that we have both been so deeply involved in the multitude of activities
arising out of our interest in the fascinating subject of Bulk Solids Handling.
CRW
JSM
Contents
PART 1 CHARACTERIZATION, FLOW AND STORAGE
1 The nature of bulk solids
Introduction
Sampling
1.2.1 Obtaining a gross sample
1.2.2 Preparing laboratory and test samples
1.3 Voidage and bulk density
1.4 Particle density
1.5 Particle size
1.5.1 Definition of 'size' and 'size distribution'
1.5.2 Measurement of particle size
1.6 Particle shape
1.7 Surface area
1.8 Particle hardness
1.9 Cohesion and adhesion
1.9.1 Angle of repose
1.9.2 Shear strength
1.9.3 The shear cell as a means of determining shear strength
1.9.4 Wall friction
1.9.5 Measurement of wall friction
1.9.6 Arching phenomena
1.10 Moisture content
1.11 Explosiveness
1.12 Notation
References and bibliography
1.1
1.2
2 Gravity flow of bulk solids
2.1
2.2
2.3
2.4
2.5
2.6
Introduction
Pressure distribution in a bulk solid
2.2.1 Bulk solid at rest
2.2.2 The effect of flow on the pressure distribution
Flow of bulk solids from hoppers
2.3.1 Introduction
2.3.2 Core flow
2.3.3 Mass flow
2.3.4 Obstructions to gravity flow
2.3.5 Predicting the solids discharge rate
Flow of bulk solids in chutes
2.4.1 Introduction
2.4.2 Flow patterns in straight inclined chutes
2.4.3 Flow patterns in curved chutes
2.4.4 Chute design
Flow of bulk solids in vertical pipes
2.5.1 Introduction
2.5.2 Mode of flow
2.5.3 Flow control-J-valves and L-valves
Notation
References and bibliography
1
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VI
CONTENTS
3 Dynamics of fluid/solids systems
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
Introduction
Flow through beds of fixed particles
3.2.1 Characteristics of flow in porous media
3.2.2 The prediction of pressure-drop across a fixed particulate bed
Settling behaviour of particles
3.3.1 Motion of a spherical particle settling in a stationary fluid
3.3.2 The settling of non-spherical particles
3.3.3 The settling of concentrations of particles (hindered settling)
3.3.4 Classification and sorting of particles
Fluidization
3.4.1 The fluidization process
3.4.2 The prediction of minimum fluidizing velocity
3.4.3 Entrainment of particles from a fluidized bed
3.4.4 The porous membrane, or distributor
3.4.5 The influence of particle size and density
Spouted bed behaviour
Gas/solids flow in pipes
3.6.1 Introduction
3.6.2 The flow of gas/solids suspensions in horizontal pipes
3.6.3 The flow of gas/solids suspensions in vertical pipes
3.6.4 Flow around 90" bends
3.6.5 The prediction of pressure-drop in flowing gas/solids suspensions
Liquid/solids flow in pipes
3.7.1 Flow characteristics of liquid/solids mixtures (slurries)
3.7.2 Non-Newtonian flow models for homogeneous suspension
3.7.3 The modelling of heterogeneous suspensions
Notation
References and bibliography
4 The design of storage bins and hoppers
4.1
4.2
Introduction
Hopper geometry
4.2.1 Shape
4.2.2 Overall dimensions
4.3 Outlet size and cone angle
4.3.1 Jenike's 'flow-no flow' criterion
4.3.2 Flow Functions and flow factors
4.3.3 Outlet dimension and cone angle
4.4 Period of storage and time consolidation effects
4.4.1 Caking
4.4.2 Testing for time consolidation
4.4.3 Practical ways of minimizing time consolidation
4.5 The effect of moisture
4.6 Overcoming space limitations
4.6.1 The use of low-friction linings
4.6.2 Changing hopper shape
4.7 Structural design
4.8 Control and measurement of discharge rate
4.9 Feeders
4.9.1 Introduction
4.9.2 Belt feeders
4.9.3 Apron feeders and rotary feeders
4.9.4 Rotary table feeders
4.9.5 Screw feeders
4.9.6 Vibratory feeders
4.10 Discharge aids
4.10.1 Introduction
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CONTENTS
4.10.2 Pneumatic methods
4.1 0.3 Vibrational methods
4.10.4 Mechanical methods
4.11 Notation
References and bibliography
5 Dust control
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Introduction
Dust as a hazard to health
5.2.1 Dust particle size
5.2.2 Dust concentration limits
Dust suppression
5.3.1 Elimination of dust
5.3.2 Control of dust dispersion
Gravity and inertial separators
Air cleaners-cyclones
5.5.1 Principle of operation
5.5.2 Prediction of collecting efficiency
5.5.3 Prediction of pressure-drop
5.5.4 Cyclone selection
Air cleaners-wet washers or scrubbers
5.6.1 Principle of operation
5.6.2 Low pressure-drop wet washers
5.6.3 High pressure-drop wet washers
Air cleaners-filters
5.7.1 Mechanism of filtration
5.7.2 Filter media
5.7.3 Bag filters-design and selection
5.7.4 Filter cleaning
Air cleaners-electrostatic precipitators
Notation
References and bibliography
6 Explosion hazards
6.1
6.2
6.3
6.4
6.5
6.6
Introduction
Characteristics of dust explosions
6.2.1 Ignition
6.2.2 Explosibility limits
6.2.3 Expansion effects and explosion pressures
Measurement of explosion parameters
Explosion risks and system design
6.4.1 Minimizing sources of ignition and prevention of ignition
6.4.2 Containment
6.4.3 Explosion relief venting
6.4.4 Detection and suppression
Static electricity
Conclusion
References and bibliography
vu
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258
PART 2 MECHANICAL HANDLING
7 Belt conveyors
7.1
7.2
Introduction
Features of belt conveyors
7.2.1 Belt construction
7.2.2 Idlers
7.2.3 Drive arrangements
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261
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CONTENTS
V111
7.2.4 The power unit
7.2.5 Loading and discharge arrangements
7.2.6 Belt cleaners
7.3 Belt conveyor design
7.3.1 The bulk solid to be transported
7.3.2 Belt speed
7.3.3 Belt width
7.3.4 Belt tension
7.3.5 Idler spacing
7.3.6 Power requirements
7.4 Belt conveyor variants
7.4.1 The cable belt conveyor
7.4.2 Belt conveyors without idlers
7.4.3 Closed-belt or pipe conveyors
7.4.4 Sandwich belts
7.5. Notation
References and bibliography
8 Bucket elevators
8.1
8.2
8.3
8.4
Introduction
Principal types of bucket elevator
8.2.1 Centrifugal discharge elevators
8.2.2 Continuous bucket elevators
8.2.3 Pivoted buckets
8.2.4 Profiled-belt elevators
Design and selection of bucket elevators
8.3.1 Design features
8.3.2 Loading
8.3.3 Discharge
8.3.4 Capacity
8.3.5 Driving power
Notation
References and bibliography
9 Chain and flight conveyors
9.1
9.2
9.3
9.4
9.5
9.6
9.7
Introduction
Drag conveyors
En-masse conveyors
9.3.1 Design features
9.3.2 Performance calculations
9.3.3 Applications of en-masse conveying
Tubular drag conveyors
Apron conveyors
Aerial ropeways
Notation
References and bibliography
10 Screw conveying
10.1
10.2
10.3
10.4
Introduction
Principle of operation of screw conveyors
The enclosed screw or 'auger' conveyor
I0.3.1 Constructional features
10.3.2 Prediction of the performance of an auger conveyor
The industrial screw conveyor or 'U-trough' conveyor
10.4.1 Constructional features
10.4.2 The conveyed product
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CONTENTS
I 0.5
10.6
10.7
10.4.3 Conveyor selection
10.4.4 Conveyor power
10.4.5 Inclined screw conveyors
Vertical screw conveyors
Conclusion
Notation
References and bibliography
11 Vibratory conveyors
11.1
11.2
11.3
11.4
11.5
11.6
Introduction
Movement of a bulk solid in a vibrating trough
11.2.1 The motion of the trough
11.2.2 The motion of bulk material in the trough
11.2.3 Average conveying velocity
11.2.4 The influence of the design parameters
11.2.5 Two-phase trough motion
Design features
11.3.1 Drive mechanism
11.3.2 Mounting systems
Applications of vibratory conveying
Spiral elevators
Notation
References and bibliography
IX
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379
PART 3 PNEUMATIC AND HYDRAULIC TRANSPORT
12 Basic pneumatic conveying systems
12.1
12.2
12.3
12.4
12.5
Introduction
Modes of conveying-dilute-phase and dense-phase
Low-pressure pneumatic conveying systems
12.3.1 Positive-pressure systems
12.3.2 Negative-pressure (vacuum) systems
12.3.3 Combined negative/positive pressure systems
High-pressure systems
12.4.1 General features
12.4.2 Single blow tank systems
12.4.3 Twin blow tanks and continuously operating systems
12.4.4 Long-distance conveying
Low-velocity conveying and the use of supplementary air feeds
12.5.1 General features
12.5.2 Plug-forming systems
12.5.3 Plug-limiting systems
12.5.4 Air-injection and booster systems
References and bibliography
13 Components of pneumatic conveying systems
13.1
13.2
Introduction
The air supply
13.2.1 General requirements
13.2.2 Fans and turbo-blowers
13.2.3 Roots-type blowers
13.2.4 Sliding-vane rotary compressors
13.2.5 Screw compressors
13.2.6 Reciprocating compressors
13.2.7 Vacuum pumps
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CONTENTS
X
13.3
13.4
13.5
13.6
Feeding devices
13.3.1 Rotary valves
13.3.2 Screw feeders
13.3.3 Venturi feeders
13.3.4 Gate Jock valves
13.3.5 Blow tanks
13.3.6 Entrainment devices for vacuum systems
The pipeline
Disengaging and collecting devices
Notation
References and bibliography
14 Pneumatic conveyor design
14.1
14.2
14.3
14.4
14.5
Introduction
General design procedure
14.2.1 Conveying velocity and volumetric air flow rate
14.2.2 Solids mass flowrate and solids loading ratio
14.2.3 Pipeline diameter
14.2.4 Pressure-drop
14.2.5 Stepped pipelines
14.2.6 Selection of the air mover
Summary of preliminary design procedure for dilute-phase systems
Designing from available test data
14.4.1 Conveying characteristics
14.4.2 Scaling for pipe size and conveying distance
Notation
References and bibliography
15 Air-assisted gravity conveying
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
Introduction
The flow of fluidised solids
Practical air-assisted gravity conveying
Design parameters for air-gravity conveyors
15.4.1 Slope of channel
15.4.2 Conveying distance
15.4.3 Width of conveying channel
15.4.4 Air requirement
Properties of bulk solids for air-gravity conveying
Air-float conveyors for horizontal and upward transport
Energy consumption of air-gravity conveyors
Notation
References and bibliography
16 Hydraulic conveying
16.1
16.2
16.3
16.4
Introduction
Components of a hydraulic conveying system
16.2.1 Pumps
16.2.2 Slurry preparation plant
16.2.3 The pipeline
16.2.4 De-watering equipment
System design
16.3.1 General design approach
16.3.2 Flow characreristics and pressure-drop
Recent development
References and bibliography
17 Capsule transport
17.1
Introduction
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CONTENTS
17.2
17.3
17.4
17.5
Index
Capsule transport in a pneumatic pipeline
17.2.1 General features of a pneumo-capsule system
17.2.2 The capsules
17.2.3 The pipeline
17.2.4 The air supply
17.2.5 Loading and unloading stations
Capsule transport in a hydraulic pipeline
17.3.1 General features of a hydro-capsule system
17.3.2 The capsules
17.3.3 The pipeline
17.3.4 The water supply and pump system
17.3.5 Injection and ejection of capsules
Size of capsule fleet
Notation
References
xi
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... when you can measure what you are speaking about, and express it in numbers, you know
something about it; but when you cannot measure it, when you cannot express it in numbers, your
knowledge is of a meagre and unsatisfactory kind: it may be the beginning of knowledge, but you
have scarcely, in your thoughts, advanced to the state of SCIENCE, whatever the matter may be.
(Lord Kelvin, as Sir William Thomson, speaking on 'Electrical Units of Measurement' at the
Institution of Civil Engineers, London, 3 May 1883.)
(Arab proverb, freely translated as: 'Experience without learning is better than learning without
experience'.)
1
The nature of bulk solids
1.1 Introduction
A bulk solid consists essentially of many particles or granules of different sizes
(and possibly different chemical compositions and densities) randomly
grouped together to form of a bulk. The 'nature' of such a material-that is, its
appearance, its 'feel', the way it behaves in various circumstances, and so onis thus dependent upon many factors, but principally upon the size, shape and
density of the constituent particles.
The nature of a bulk solid, described in terms of appropriate characteristics,
is an essential consideration when designing or selecting equipment for its
handling or storage. There are innumerable examples in industry of problems
that have been attributable to insufficient attention being paid to the
properties of the bulk solid involved. Failure of a material to discharge from a
storage hopper, blockage of a pneumatic conveying line and uncontrollable
flushing of material through a weigh-feeder are typical of such problems. In
this chapter some of the principal parameters that are used to describe bulk
solids and their behaviour will be introduced.
When attempting to describe a bulk solid it is important to understand that
the characterization can be on two levels:
(i) By means of features descriptive of the behaviour of the material in its
normal bulk form; for example, the way in which it compacts, its flow
properties, the influence of moisture and electrostatic charging
(ii) By means of features of the constituent particles such as their size, density,
hardness, shape and surface texture.
At the present time our level of knowledge is not sufficient to enable a
reliable prediction to be made of the behaviour of a bulk solid solely from the
characteristics of its constituent particles. Nevertheless, research in this field is
progressing, and by continually seeking correlations between the observed
behaviour of various materials in the bulk form and measured particle
characteristics, a valuable database is being compiled for the benefit of
designers and users of bulk handling equipment.
There are many descriptive terms and numerical parameters that can be
used in the characterization of particulate and granular bulk solids, and these
may refer both to the appearance of the material and to its behaviour in
various circumstances. A first step in determining the characteristics of an
unfamiliar material is to consider its behaviour in very general terms; for
2
BULK SOLIDS HANDLING
Table 1.1 A 'materials personality test' helps to establish the behavioural features of a bulk solid
'Neurotic' materials
}
have poor flowability
have too much flowability
are sticky or tacky
tend to pack or bridge
'Sadistic' materials are
}
abrasive
corrosive
toxic
explosive
hot
'Masochistic' materials are
friable
degradable
contaminable
'Schizophrenic' materials are
hygroscopic
susceptible to electrostatic
charge
}
}
they move awkwardly
they attack their
surroundings
they suffer from
their surroundings
they change their
behaviour pattern
example, does it 'flow' easily or is it 'sticky'? Is it fragile? Is it abrasive?
Corrosive? Explosive? And so on. The 'Materials Personality Test' (Table 1.1 ),
which is believed to have appeared originally in an Australian publication,
conveniently summarizes these features of bulk solids behaviour.
Although purely descriptive terms are essential when communicating
information on bulk solids, they are unlikely to be sufficient on their own.
Numerical parameters are required to characterize a bulk solid in a
quantitative manner and so to enable the designer of a handling system, in the
light of his past experience, to match the system to the product and to assess
the likelihood of problems occurring. Some of the more important of these
parameters will be considered in more detail in this chapter. Attention will
then be turned to some of the measurable characteristics of the constituent
particles. Useful particle properties include size, shape, surface area, density
and hardness, whilst more esoteric features such as surface texture may also
have some value when attempting to predict the behaviour of a bulk material
from a study of its particles.
In this book an attempt is made to define the common usage of various
properties of particles and bulk solids and to describe briefly examples of
currently available equipment and techniques for their measurement. A very
large amount of literature has been published on this aspect of particle
technology and for further information the reader would be well advised to
begin with one of the recent specialist guides or textbooks such as references
[1] or [2]. Much useful information on the sampling, testing and description
of very coarse materials such as mineral aggregates, which are generally
beyond the scope of this book, can be found in the series of British Standards
under the overall classification of BS 812 [3].
THE NATURE OF BULK SOLIDS
3
Before proceeding, some discussion will be undertaken on the essential need
for reliable methods of obtaining representative samples of material for
testing.
1.2 Sampling
The majority oflaboratory techniques for determining the properties of a bulk
solid and of its constituent particles naturally require only a very small sample,
usually to be taken from a large amount of material. Even a minute sample
may contain many thousands of individual particles and in order to appreciate
the difficulties of guaranteeing a representative sample, one needs only to
imagine trying to collect from, say, a one-tonne load of material, a few hundred
particles for analysis by microscope! There is little point in going to a great
deal of trouble to determine accurately the size distribution or the flow
properties, for example, of a bulk solid, if the sample used is not truly
representative of the larger mass of material from which it was taken.
In many processes involving the movement of a bulk solid, such as flow into
a hopper or on to a heap on a flat surface, significant segregation by size and/or
density can occur (Figure 1.1). Thus, there must be immediate doubt cast on
any sample taken by scoop or similar device from a large quantity of stationary
material. Where possible the sample should always be taken from a moving
stream of the material in question by diverting the whole stream for a series of
short intervals of time spaced over the period of flow of the complete batch.
Once a 'gross sample' (perhaps a few kg) has been obtained in this way it will be
necessary in the laboratory to further reduce it to a size suitable for whatever
measurement technique is to be used.
1.2.1 Obtaining a gross sample
Typical situations where it is necessary to take a sample from a large quantity
of a bulk material include:
(i) A moving stream of material; e.g. quality control of a product during a
continuous process
(ii) A static batch of material; e.g. in bags, in a bin or in a lorry or rail-wagon.
Figure 1.1
Segregation in a poured heap.
4
BULK SOLIDS HANDLING
It is almost always better to sample from a moving stream of material than
from a static batch, where this is possible, in order to minimize the influence of
segregation of particles during previous handling. In general, a careful
consideration of where segregation (and other spurious influences on the
homogeneity of the material, such as moisture) would be most likely to occur
can be of great help when deciding on the most appropriate sampling
technique. Thus, for example, when obtaining a sample from a moving
conveyor belt, care must be taken to avoid the effects of segregation of the
material as it was fed on to the belt. Sampling only part of the cross-section of
the moving stream could well be misleading, although taking a vertical 'slice'
out of the conveyed material would probably be better than 'skimming off' a
sample from the top. The best approach, however, is to sample the whole
stream for a short period of time. Even then, the possibility of variation of the
stream with time should not be overlooked, so that the sampling technique
finally adopted may be to divert the whole stream for a series of short intervals
during the conveying of a complete batch of material. Usually the easiest place
to carry out such sampling is at the discharge end of the conveyor.
Sampling from a static batch of bulk solid should always be regarded as a
poor alternative to sampling from a moving stream. Procedures can be
developed so that the worst potential errors are avoided. Thus, for instance, no
material should be taken from anywhere near a free surface. Various designs of
sampling probe are available commercially and, where one of these is used, a
number of samples should be taken from different regions within the batch of
material and mixed to form the gross sample.
Once the gross sample has been obtained, preferably from a moving stream
of the bulk solid, it will have to be 'divided' by one of the following methods to
yield a smaller sample suitable for laboratory use.
1.2.2 Preparing laboratory and test samples
As mentioned previously, a gross sample would typically be several kilograms.
For laboratory use it must be reduced in such a way that the final sample has
the same size distribution as the gross sample and is in all respects
Figure 1.2 'Cone-and-quartering'.
THE NATURE OF BULK SOLIDS
5
representative of the bulk material originally sampled. When reducing the
gross sample the main difficulty is again to avoid the effects of segregation.
A widely adopted method of preparing a laboratory sample is by 'cone-andquartering' (Figure 1.2) in which a conical heap of material is carefully divided
into four equal parts, two of these being re-mixed and formed into a smaller
conical heap which is again divided into four, and so on. Although this method
does reduce the effects of segregation it is still very sensitive to operator skill
and, where possible, some form of mechanical sample divider is preferable.
Many types of sample divider are available, such as chute splitters (Figure 1.3)
and table samplers (Figure 1.4), but perhaps the most reliable is the rotary
sample divider or 'spinning riffier' (Figure 1.5) which is capable of reducing a
gross sample of material down to several (typically eight or sixteen) 'equal'
samples for laboratory use, with minimum dependence on operator skill.
In many laboratory techniques for characterizing a bulk solid, the test
sample required is extremely small and further reduction of the laboratory
sample is necessary. For a free-flowing powder the spinning riffier should give
an acceptable sample down to one gram, but for cohesive materials, obtaining
a final test sample even of this size is not easy. One approach is to make up
paste of the laboratory sample in a suitable liquid and then to use a modified
cone-and-quartering technique. An alternative method, especially with very
fine powders, is to carefully mix the laboratory sample into a liquid dispersant
to form a suspension, a small quantity of which can then be extracted with a
pipette. Commercial models of suspension sampler are available which are
claimed to give more consistent samples than simple pipetting.
Figure 1.3
Sample divider (riffier).
6
BULK SOLIDS HANDLING
Figure 1.4 Table sampler.
mass flow hopper_
16-way dividing
head
Figure 1.5
Rotary sample divider (or 'spinning riffier').
7
THE NATURE OF BULK SOLIDS
1.3 Voidage and bulk density
The shape of particles constituting a bulk solid obviously depends upon the
manner of their production but, irrespective of whether they are of regular or
irregular shape, when they are packed together in random orientation there
will be a certain amount of free space between them. Thus a bulk solid is really
a combination of particles and space, the percentage of the total volume not
occupied by the particles usually being referred to as the 'voidage' or 'void
fraction'.
Thus
volume of voids
voidage, s = ----,--c-------=-----=-:----:---:--:total volume of particles and voids
or
vvoids
(1.1)
s=-----'-'-''--Vsolids
+ Vvoids
and, in a bed of material having unit volume, the actual volume of solid
particles, or 'fractional solids content', is (1 - s).
Sometimes the term 'porosity' is applied to bulk solids to mean the same as
'voidage'. However, it is probably advisable to reserve this term as a
description of the structure of individual constituent particles. Thus we can
define the particle porosity as the ratio of the volume of pores within a particle
to the volume of the particle (inclusive of pores). When quantifying either the
voidage of a bulk solid or the porosity of its constituent particles, it might be
necessary to avoid ambiguity by stating whether the values quoted are
inclusive or exclusive of closed pores.
Typical values of the voidage in static bulk materials consisting of
monosized spheres would range from 0.26 (that is, 26%) for regular hexagonal
packing, to 0.48 for regular cubic packing (Figure 1.6). For closely graded
irregular particles in random packing arrangements the voidage would
normally lie between these extremes, a high voidage corresponding to a loose
packing. A reasonable average figure would be around 0.4 for spheroidal•
(a} regular hexagonal:
Figure 1.6
E
~ 0.26
(b} regular cubic:
f ~
Packing arrangements for monosized spheres.
0.48
8
BULK SOLIDS HANDLING
particles, but where a material consists of particles of extremely irregular
shape, especially if they are also of very small size (i.e. fine cohesive products),
the voidage could be much higher.
A quantity ofparticulate or granular material will have an apparent density,
usually termed 'bulk density', which can be defined as the mass of the material
divided by its total volume (particles and voids).
Thus
b ulk d ensI.ty,
Ph =
+
+
msolids
mvoids
--"'='----___;_=
vsolids
vvoids
(1.2)
Writing pP as the 'true' density of the solid particles and Pr as the density of
the fluid in the void spaces, it can be shown that an expression for the bulk
density is
Pb =(pp- PrHl- t:) + Pr
(1.3)
For dry bulk solids the void spaces would, of course, usually contain air, and
thus the density Pr would be negligible compared with pP so that the
relationship between bulk density and particle density becomes
(1.4)
Clearly a knowledge of the bulk density of a product is essential in order to
design storage vessels, conveying systems and the like. Determination of this
parameter from a sample of the material concerned involves measurement of
the mass of the sample and its total volume. The measurements are essentially
straightforward, the problems arising more from the need to decide the
conditions under which the volume should be measured than from the actual
measuring techniques. It has been mentioned that the voidage (and therefore
the bulk density) of a particulate material depends upon the packing
arrangement. Therefore it is necessary to qualify any stated value of bulk
density with an indication of the condition of the material concerned. For
example, 'loose' or 'poured' bulk density might refer to a measurement for
which the sample of product was carefully poured into a measuring cylinder to
determine its volume. Alternatively, adopting a technique in which the sample
was packed by dropping the cylinder vertically a number of times from a
height of one or two centimetres on to a table could yield a value of'packed' or
'tapped' bulk density.
Note that the bulk density of a mixture of particles of different sizes will
depend upon the extent to which the smaller particles are able to fit into the
spaces amongst the larger ones.
Determination of voidage involves the separate measurements of the total
volume of the sample and the volume of the solid particles alone. The most
direct method of measuring the total volume is by pouring the sample into a
calibrated measuring cylinder and reading the volume from the scale, but note
the need to specify the condition of the product, as explained previously. The
THE NATURE OF BULK SOLIDS
9
determination of the volume of the particles will be discussed more fully in the
next section, but usually involves some form of fluid displacement technique
using a standard density bottle or a more sophisticated instrument such as an
air-comparison pycnometer. Difficulties arise with particles that are porous or
have internal voids (such as coke), since the definition of particle volume
becomes uncertain.
1.4 Particle density
It is important that the distinction between the bulk density of a particulate
solid and the 'true' particle density is clearly understood. For a single particle
the density is defined as the mass of the particle divided by its volume, so that
for a bulk material the average particle density can be determined by dividing
the mass of material by the true volume occupied by the particles (not including
the voids).
The determination of particle density thus involves the measurement of the
mass of a quantity of bulk solid and of the volume occupied by its constituent
particles, the latter measurement usually presenting the greatest difficulty. For
products oflarge particle size the density can be determined simply by noting
the volume ofliquid displaced by a known mass of particles in a partially filled
measuring cylinder. Fine powders require the use of a specific-gravity bottle or
air-comparison pycnometer.
The specific-gravity bottle (or density bottle) is a small flask fitted with a
ground-glass stopper which has a capillary hole running axially through it to
permit excess fluid to escape as the stopper is inserted into the bottle. The
normal procedure for use of the bottle begins with the determination of its
volume by carefully measuring the mass of distilled water to just fill it. A
sample of particulate material of known mass is then placed in the bottle and,
by weighing, the volume of distilled water required to just fill the bottle is
determined. Subtraction of this volume from the previously found volume of
the empty bottle thus allows the volume of the particle sample to be calculated.
Precautions should of course be taken against errors resulting from incomplete dispersion of the sample, moisture on the outside of the bottle,
temperature variations and dissolving of the particles! A more detailed
description of this method can be found in [4], Part 2.
For products that are soluble, fragile or very light, the air-comparison
pycnometer is almost essential. This commercially available instrument
consists basically of two identical cylinders connected through a valve and
each containing a piston, a differential pressure indicator and an output scale
reading volume in cm 3 (Figure 1.7). With the connecting valve closed, any
movement of the reference piston must be duplicated by an identical
movement of the measuring piston in order to maintain a null reading on the
differential pressure indicator. After setting the zero (tare) on the instrument,
the volume of any material placed in the measuring cylinder will be shown by
10
BULK SOLIDS HANDLING
top
reference
piston
measuring
piston
zero V
(tare)
Figure 1.7
scale
The principle of the Beckman air-comparison pycnometer.
the position of the measuring piston for a null reading of the differential
pressure indicator.
It should be noted that all these methods yield the average particle density of
the bulk solid. The densities of different constituent particles in a blended
product can only be determined with any certainty by measuring them before
blending.
it also should be noted that values of particle density obtained by an air
displacement method (such as the air-comparison pycnometer) may differ
slightly from those obtained by liquid displacement when the particles
involved have open pores, formed, for example, by air occlusion during crystal
growth. In general, the density determined for a porous material would be an
'apparent density' which could be defined as the mass of a particle divided by
its volume including closed pores but excluding open pores. If the particles are
immersed in a viscous fluid their average effective density would be the mass of
the particles divided by their volume including both open and closed pores
(that is, considering the boundary of the particle to be its external surface). The
'true density' of a porous particle should thus be defined as its mass divided by
its volume excluding both open and closed pores.
1.5 Particle size
1.5.1 Definition of'size' and 'size distribution'
Various terms are used to give a qualitative indication of the size of particles
constituting a bulk solid, the word 'size' here being used loosely to mean some
sort of average dimension across the particle. Naturally such terms are not
precise and tend to vary in usage from one industry to another. Nevertheless, it
helps to introduce the subject of particle characterization if the typical ranges
THE NATURE OF BULK SOLIDS
11
Table 1.2 Qualitative terms used to describe the size of bulk solids
Descriptive term
Typical
size range
Coarse (or broken) solid
Granular solid
5-IOOmm
0.3-5mm
Particulate solid:
coarse powder
fine powder
superfine powder
ultrafine powder
Coal, aggregates, etc.
Granulated sugar (0.3-0.Smm);
rice (2-3 mm).
100-300/lm
10-100/lm
1-10/lm
< lJlm
Table salt (200- 300 /lm)
Icing sugar ( ~ 45 Jlm)
Face powder
Paint pigments
Examples
of size covered by terms such as 'granular material', 'fine powder', and so on,
are appreciated. Table 1.2 sets out approximate ranges and, in order to assist
the reader to visualize these, some familiar bulk solid materials are quoted as
examples.
A mass of monosized, spherical particles can be described by a single
dimension-the particle diameter-and a mass of spherical particles of
varying size can be described by an 'average' particle diameter together with
some information on the distribution of sizes about that average value.
However, where the particles are non-spherical it becomes necessary to define
more carefully the parameters used for size and shape. (It may be remarked
that 'size distribution' is more a property of the bulk solid than of its
constituent particles. However, it is obviously convenient and relevant to
discuss the term at this stage along with characteristics of individual particles
such as size, shape, hardness, etc.)
In order to represent the size of an irregularly shaped particle by a single
quantity it is customary to use an 'equivalent diameter', corresponding to the
diameter of a sphere that exhibits the same behaviour as the particle under
certain conditions or that has the same value of some other descriptive
characteristics.
Thus, for example, a 'volume diameter', d., can be defined as the diameter of
a sphere having the same volume as the particle.
That is to say,
(1.5)
where vp is the volume of the particle.
(It may be noted that for a cube of unit side, the 'volume diameter' is 1.241,
compared with the maximum dimension of the cube, which is 1.732.)
In general, the manner of describing the particle size depends upon the
method of measurement, and it follows that the type of particle 'diameter' used
should depend upon the reason for specifying it! For instance, if a particulate
solid is to be used as a catalyst, the surface area of the particles is the significant
12
BULK SOLIDS HANDLING
quantity and therefore it is the 'surface diameter' that should be used for
particle size:
A
ds = ( ~
n
)112 = 0 564A
.
(1.6)
1 2
sp1
where Asp is the surface area of the particle.
(Again, note that for the cube of unit side, the 'surface diameter' is 1.382, so
that the ratio djd. is 0.898.)
In general industrial practice it is of course likely that the equivalent
diameter used would correspond to the diameter of a sphere that exhibits the
same behaviour when subjected to a specified sizing technique. For instance,
the diameter used could be that of a sphere which just passes through the same
square sieve aperture, or which falls at the same velocity in a fluid
(sedimentation-the 'Stokes diameter'), or which has the same projected area
(microscopy). Indeed, the definition of particle diameter may be so specific to a
method of size analysis that it has little meaning when applied to a single
particle; for example, Feret's diameter, used in microscopy, is the distance
between parallel tangents on opposite sides of the particle. Many other
'equivalent diameters' may be defined and further examples are listed in [2].
The ratio of any pair of the listed 'diameters' (often known as a 'shape
factor') is found to be fairly constant over quite wide size ranges for any one
material which has been produced in the same way or derived from the same
source. Thus it is possible, for instance, to correlate analyses in which the
coarser fraction of a material has been subjected to a sieve analysis and the
sub-sieve fraction has been sized in some other way. Typical values of these
ratios, quoted in [5], are given in Table 1.3, but it should be emphasized that
caution is required in the use of these figures, especially where the particles of
the material are of extreme shapes.
In an industrial situation it is probable that bulk solids comprising a large
number of particles of non-uniform size would be encountered. In order to
describe such materials completely, it is necessary to determine the particle size
distribution. This information may be presented in tabular form, but it is
generally more convenient to present it graphically as a histogram or as a
fractional percentage plot.
Table 1.3 Particle diameter conversion factors [5, Parts 3, 4]
To convert
Multiply by
Sieve diameter to projected area diameter
Sieve diameter to Stokes diameter
Projected area diameter to sieve diameter
Projected area diameter to Stokes diameter
Stokes diameter to sieve diameter
Stokes diameter to projected area diameter
1.40
0.94
0.71
0.67
1.07
1.50
13
THE NATURE OF BULK SOLIDS
(f)
(f)
"'u-<=
c
Ql
g
"0
"ji:
~
c~ 0"'
Q;
Q.
particle size
100
Ql
Ol
"'c
~ .....
80
··~
I\
·- .
Ql
u
Q;
Q.
60
(f)
(f)
"'
E
~~~-
~~
~r--·
20
E
::J
u
'
-~ ~
1/
>
::J
'undersize
0
V
V
I
I
I
--
-~-~
40
Ql
ro
/
I\
~
·-1~
oversize
/
I
' .......
~mern
particle size
---~
Figure 1.8 Graphical methods of presenting particle size distribution.
(Top) Relative percentage frequency distribution by mass.
(Bottom) Plots of cumulative percentage under- and over-size.
Once the size distribution has been measured (for example, using one of the
methods described in the next section), it is relatively simple to develop a
suitable histogram by constructing rectangles over each class interval, the
widths of which would usually be chosen in geometric progression. The area
under each rectangle is proportional to the percentage of particles in that class
so that a smooth curve through the histogram would yield a frequency
distribution (Figure 1.8). An alternative, and often more useful approach is to
present the data as a cumulative graph in which particle size is plotted along
the horizontal axis and the ordinate represents cumulative percentage
undersize or oversize (Figure 1.8). The principal advantage of this latter type of
graph is that values not determined experimentally are reliably predicted.
14
BULK SOLIDS HANDLING
surface - mean
diameter
volume - surface
mean diameter
......
0
........
0
\
I
r
same volume
same
surface area
-0
volume - mean
diameter
same volume
~~
/_
/
~
CJO
=oonoooooooo~aOO O
average surface area
for the mixture
average volume
for the mixture
Figure 1.9 Three examples of definitions of 'mean particle size' for a mixture of non-uniform
non-spherical particles.
Also, the 'median size' (that is, the 50% size, or mid-point of the distribution)
can be read off directly.
The mass median mentioned above is probably the most commonly used
method of indicating the 'average size' of particles constituting a bulk solid,
since for the majority of materials it is the easiest to determine. However, it
may happen that the median is not the most appropriate parameter and a
number of alternative definitions of average particle size could be used. The
one chosen would normally be dictated by its relevance to the situation
concerned. Three examples will be considered; definitions are illustrated in
Figure 1.9.
(i) Surface mean diameter is defined as the diameter of a particle having a
surface area equal to the average for all the particles in the mixture. This
parameter is clearly relevant to processes in which the surface area of the bulk
solid is a critical factor. The average surface area of a number of particles can
be expressed as
1
2
Asm = N "L(nds)
(1. 7)
where d. is the diameter of a sphere having the same surface area as the
corresponding particle. Thus the diameter of this particle of average surface
area (the 'surface mean diameter') is given by
A
dsm = ( ~
1t
)112 = (-"Ld
1
)112
N
2
s
(1.8)
(ii) Volume-mean diameter is defined as the diameter of a particle having the
THE NATURE OF BULK SOLIDS
15
average volume for the mixture. By similar argument to the above, the
'volume-mean diameter' is given by
6V
dvm = ( ____lllll
1!
)1/3 = (-1 "Ld 3)1/3
N
v
(1.9)
where dv is the diameter of a sphere having the same volume as the
corresponding particle.
(iii) Volume-surface mean diameter is defined as the diameter of a particle
having a ratio of volume to surface equal to the average for the mixture (that is,
the diameter of a sphere having the same volume as the particle of average
surface area for the mixture). Although the definition is somewhat unwieldy,
this parameter tends to be biased towards the lower end of the size range and
therefore offers a useful advantage over the more commonly used median size
in situations where the finer fraction of particles has disproportionate
influence on the behaviour of the bulk solid (e.g. fluidization, gravity flow from
hoppers and in chutes, etc.). From the above definition it can be seen that the
volume-surface mean diameter is given by
dvsm =
"Ld3
"Ld:
d:m
d;m
(1.10)
A very convenient approximation that allows the volume-surface mean
diameter to be determined easily from a sieve analysis on a bulk solid is
dv•m
~
(
r.
:.r
1
(1.11)
where x is the mass fraction of particles passing through sieve aperture of size
d•.
1.5.2 Measurement of particle size
There are many methods of determining the particle size distribution of bulk
solids. British Standards exist for a number of these [5], [6] and the underlying
principles of a wide variety of sizing methods are discussed in depth in [2]. A
summary of the approximate range of application of the more familiar
techniques and equipment is given in Table 1.4.
Sieve analysis. The most popular (and cheapest) method of particle size
analysis, especially with relatively coarse materials, is sieving. A test sieve
generally consists of a woven wire screen (with square apertures) rigidly
mounted in a shallow frame (Figure l.lOa), but for coarse materials the sieve
screen is more usually a perforated plate with either round or square holes.
Traditionally the sieve size is specified by the number of apertures per unit
length (the 'mesh'), but current practice is to quote the actual dimension of the
16
BULK SOLIDS HANDLING
Table 1.4 Some familiar methods of size analysis and their approximate
range of application
Approximate useful range
Method
Sieving:
dry
wet
Electrical sensing zone
(Coulter counter)
Laser diffraction
spectrometry
Sedimentation and
elutriation
Optical microscopy
Electron microscopy
50 Jlm-100 mm
10 jlm-100 mm
I Jlm-800 Jlm
2 Jlm-75 Jlm
I Jlm-150 Jlm
O.QI Jlm-1 Jlm
aperture in J.lm (Table 1.5). The sieve sizes used in an analysis should be
selected to conform to a
series, or for more accurate work, a ~ series.
A wide variety of types of sieve is available commercially. Apart from the
standard woven mesh sieves and the perforated plate sieves for coarser
materials, a range of electro-formed sieves is manufactured for the size analysis
of very fine products (less than about 45 J.lm). Specially designed sieves have
been produced for specific applications, such as the measurement of flakiness
index [7] and grain size of cereals (Figure 1.1 Ob).
The lower size limit for material on a wire mesh sieve is around 50 J.lm,
although with special techniques sieving down to about 10 J.lm is possible. The
recommended mass of sample to be used on standard 200 mm (8-inch)
diameter sieves is 50 g for materials of particle density between 1200 and
3000 kg/m 3 , and 100 g for materials of density greater than 3000 kg/m 3 .
The test procedure involves introducing the sample to the top of a stack,
typically consisting of up to eight sieves which are graduated from the coarsest
at the top to the finest at the bottom. The stack is then shaken or vibrated
(manually or mechanically) for a set period of time in order to distribute the
material through the sieves. Finally, the mass of material retained on each
sieve is determined by careful weighing. A detailed procedure for manual
sieving is set out in a British Standard [6], but it is now far more usual to make
use of automatic sieve shakers (Figure 1.1 Oc). For materials that are cohesive
or susceptible to electrostatic charging, or that prove for any other reason to
be difficult to distribute through the sieve stack, 'wet sieving' is possible. In this
system water or other liquid is introduced via a spray header into the top sieve,
and washes the product downwards before being extracted from a drain in the
pan at the bottom of the stack.
The overall size range of the sample can be specified by stating two sieve
sizes; one through which the whole sample passed and the other on which the
whole sample would be retained. Information could also be quoted on the
proportion of the sample between any two sieve sizes, or the full size
J2
THE NATURE OF BULK SOLIDS
17
b
Figure 1.10 Bulk solids characterization by sieving. (a) A selection of standard woven mesh
sieves. (b) Grain sieves for agricultural use. (Sieves for flakiness measurement are similar). (c) A
variable-speed electromagnetic sieve shaker in use. (Photos by courtesy of Endecotts Ltd.)
distribution could be plotted as illustrated in Figure 1.8. Further guidance on
sieve analysis techniques may be found in [1], (2], [6] and [8].
Sedimentation and e/utriation. Various methods of size analysis have been
developed which rely on observation of the sedimentation rate of a suspension
of particulate material in a suitable liquid. Elutriation methods are somewhat
18
BULK SOLIDS HANDLING
Table 1.5 Relationship between standard sieve numbers and Jlm
Size of
sperture
(Jlm)
44
45
53
60
62
63
74
75
88
90
100
105
120
125
140
149
150
170
177
180
200
210
250
297
300
350
355
360
385
BS Fine Mesh
(BS 410;
Table I)
350
300
240
200
170
US Bureau
of Standards
270
200
120
60
52
44
200
170
120
72
(DIN 4188)
100
230
140
85
German
Standard
325
150
100
American Society
for Testing of
Materials
100
80
80
70
60
50
100
80
40
30
70
60
50
24
20
45
40
16
similar but are based on the measurement of the proportion of the product
which is carried off by an upward flow of gas (usually air) in a vertical column
at a known velocity. For small particles having the same density, the rate of
settling is approximately proportional to the square of the particle diameter,
and consequently the concentration at a fixed depth in a sedimenting
suspension will vary with time in a manner that depends upon the size
distribution of the particulate material (Figure 1.11). For a discussion relevant
to sedimentation analysis of the theory of particles settling in a gravitational
field, the reader is referred to Chapter 3.
One of the most convenient and reliable commercially available instruments using this principle of size measurement is the photosedimentometer.
For this instrument a suspension of the material to be sized is prepared in a
suitable liquid dispersant. This suspension, contained in a tall tank of opticalquality glass, is placed into the photosedimentometer and a narrow beam of
light of pre-set intensity passed through it on to a photocell. The attenuation of
19
THE NATURE OF BULK SOLIDS
Table 1.5 (Contd.)
Size of
sperture
(Jlm)
420
430
490
500
540
590
600
700
710
750
835
840
850
1000
1005
1020
1190
1200
1400
1405
1500
1680
2000
2380
2400
2800
2820
3350
3355
4760
BS Fine Mesh
(BS 410;
Table I)
36
US Bureau
of Standards
American Society
for Testing of
Materials
German
Standard
(DIN 4188)
40
14
12
30
35
11
30
25
10
25
22
8
20
20
18
16
18
6
16
14
12
5
14
4
10
8
12
10
10
8
7
6
7
5
6
4
this beam of light is continuously recorded and will initially indicate a high
concentration for the homogeneous suspension. The intensity of the light
falling on the photocell will begin to increase from the moment that the largest
particles, falling from the free surface, pass through the beam, and will tend
towards a maximum as the finest particles reach the level of the light beam. The
variation of the photocell output with time thus allows the size distribution to
be determined, provided that the particle density and the viscosity and density
of the liquid dispersant are known.
A refinement of this instrument is a scanning device which speeds up the
analysis by allowing the light beam to scan the suspension vertically at a rate of
10 mm/min. The wide-angle scanning photosedimentometer (WASP), which
gives a readout in the form of a pen-recorder trace showing the variation of the
optical density of the suspension with time, is illustrated in Figure 1.12.
Sedimentation techniques generally are appropriate for bulk solids that are
too fine to be analysed by sieving but not so fine that they take an inordinately
20
BULK SOLIDS HANDLING
-1
H
. •. ··:· .·:
. ·.·.:·.· .·
.. · .....
--Xl· ;_;:.:;;: :,
(c)
Figure 1.11
sensitivity controls
•
•
•
0
•
::
••
0
•••
:
-x-
Concentration at
XX begins to
decrease: largest
particles have
settled distance
H in time since
sedimentation
started.
Sedimenting
suspension:
largest particles
settling at fastest
rate.
Concentration at
XX still
unchanged.
Homogeneous
suspension.
Sedimentation
begins.
\1$~,~~
::: ~- ....... :
-X
(d)
Concentration at
level XX continuing
to decrease. Time
period since start
allows determination
of smallest particle
size to fall to XX
from the free
surface.
Differential sedimentation of a polydisperse material.
-"'--m~-~-----i~~o
~-----=--~--
~f----
pen recorder
-
stirring rod --------1f----.l4.1L-~
sedimentation tank --;--..oo 11
zero adjustment
~
Lk~W===~JI~Hl:i~lt:~-::::ilfrUI~
F--r---photocell
i t - - - l(.iil
photocell ----------"1-----11 1 \
_1
-i:i
1....___ _ _ _ _ _
time clock
1
I
1
I
I
1
:: 0'
' :~+--\l,----------......------11
J.l -: / :-
;=~1\
:
1
I II
11
\light source
'
I
~~:
lr----1
scanning motor
'
I I
Ill
---H+-- 1: :
l,-<~
lA .-,
~ I
1
n
""
'
I
1
I
I
I
I
1
I
IL---:;tw-=------111
11
\bench
neutral density filters
(for setting sensitivity)
r------
manual scan/return
L.J-+------+
L---~,---j
Figure 1.12 The wide-angle scanning photosedimentometer ('WASP').
21
THE NATURE OF BULK SOLIDS
Table 1.6 Approximate upper size limits for particles in sedimentation analysis
Critical diameter (Jlm)
Material
Sand (pP = 2700 kg/m 3)
PVC (pp= 1400kg/m 3)
Settling in
air
Settling in
water
Settling in
ethylene glycol
31.6
39.4
60
97.2
560
1000
long time to settle under gravity in the selected dispersant. The exact size range
that can be determined by photosedimentation depends principally upon the
dispersant used and the density of the particles but, as an example, for sand
settling in water, measurement over the range 2-60 .urn should be possible. The
upper end of this range could be extended considerably if a more viscous
dispersant such as ethylene glycol were to be used (Table 1.6).
Optical microscopy. As a technique for size analysis of particulate solids,
optical microscopy has become well established for particles ranging in size
from about 0.8 .urn up to 150 .urn. It has the advantage of allowing examination
and measurement of individual particles of the material in question, and the
method can often be used where other techniques fail.
Disadvantages may be summarized as:
(i) Difficulty of obtaining a very small representative sample for study
(ii) Small depth of focus
(iii) Time-consuming procedure for counting particles.
The basic procedure for size analysis uses a microscope fitted with a
micrometer stage, and an eyepiece in which a glass disc engraved with a
suitable scale is positioned against the field stop. This ocular scale is calibrated
against a linear scale engraved on a microscope slide by bringing the two
images into sharp coincidence, and the engraved slide is then replaced by a
slide carrying the prepared powder sample. The sample is scanned in strips,
each particle being sized and counted as its image passes over the scale.
A linear scale in the eyepiece gives Feret's diameters of the particles
examined, but a number of alternative forms of graticule have been developed
which enable the particle images to be compared with engraved circles, thus
giving projected area diameters. One of these, shown with its relative
dimensions in Figure 1.13, has been adopted as the British Standard graticule
([5], Part 4).
The full procedure to be followed when carrying out a size analysis can be
found in various publications, for example, [5] Part 4; [9], but a summary is
given below.
(i) With the graticule in place in the microscope eyepiece, adjust the
B
22
BULK SOLIDS HANDLING
Relative dimensions of British Standard Graticule
Numerical value
(units)
~
0 os 0
7
1
T
~
Grid length
Grid breadth
Distance between
calibration marks
Diameter of circle I
2
5
0 4 o3 o2
grid length (mm)
o'
3
4
5
6
7
Figure 1.13
(ii)
(iii)
(iv)
(v)
64
45.3
60.4
1.00
1.41
2.00
2.83
4.00
5.66
8.00
British Standard graticule (BS 3625: 1963) (Ref. 2, Part 4).
magnification so that the diameters of the reference circles correspond to
the size range of the particles to be examined
Select a suitable regular pattern of sample fields in order to cover the
whole sample of powder on the slide (this step is simplified by using a
suitably engraved slide or counting cell)
Adjust the micrometer stage to position the graticule in the centre of the
first sample field
For particles within the graticule area (and on the boundary lines on two
adjacent sides) count the number within each size class by visual
comparison with the graticule circles
Repeat the counting of particles in this way with the graticule positioned
at the centre of each field area in turn until the whole sample of powder on
the slide has been scanned.
The Coulter counter. The Coulter counter, the best known commercially
available instrument for size analysis of particulate materials by the electrical
sensing zone technique, was originally developed by W.H. Coulter for
counting blood cells. A recent British Standard ([5], Part 5) describes the
method in detail and gives useful information on suitable electrolytes.
The Coulter technique enables the number and size of particles suspended in
an electrically conductive liquid to be determined by making the suspension
flow through a small orifice on either side of which is immersed an electrode.
As any particle passes through the orifice it increases the resistance between
the electrodes momentarily and thus generates a voltage pulse, the magnitude
of which is a function of the volume of the particle. These pulses are
electronically scaled and counted and from the resulting data the size
distribution of the suspended particulate material can be determined. For
23
THE NATURE OF BULK SOLIDS
particles of diameter within the range 2-40% of the orifice diameter it is found
that the magnitude of the voltage pulse is directly proportional to the particle
volume and it is on this principle that the reliability of the Coulter counter
depends.
A range of orifice sizes is available, so that the Coulter counter is well suited
to the measurement of particle sizes in the sub-sieve range (less than 75 ,urn)
down to about 1 ,urn. With special techniques this range can be extended up to
800 ,urn and down to 0.6 ,urn or even less. Almost any kind of material may be
analysed using the Coulter technique (except for some organic compounds
that are too soluble in any electrolyte), although the use of dispersants is often
required.
Figure 1.14 shows diagrammatically the basic components of a Coulter
counter. In operation the stopcock A is opened so that the action of the
vacuum pump causes the electrolyte to flow from the beaker through the
orifice and also draws mercury up into the siphon. The stopcock is then closed,
but the effect of the mercury siphon restoring its balance causes the flow of
electrolyte through the orifice to continue. Electrical contact of the advancing
mercury column with probes mounted in the glass tubing causes counting of
the voltage pulses to begin automatically and to stop after a pre-determined
volume of electrolyte (typically 0.5 ml) has passed through the orifice.
The voltage pulses are amplified and fed to a threshold circuit having an
Orifice
to vacuum pump
+
Voltage pulse generated
as particle passes
through IS directly
proportional to the
volume ol the part1cle
for particles having
diameters in the
range 2-40% of
the orifice diameter
counter 'start'
counter 'stop'
Figure 1.14 Diagrammatic representation of a basic Coulter counter.
24
BULK SOLIDS HANDLING
adjustable threshold level. If this level is reached or exceeded by a pulse, the
pulse is counted. By taking a series of counts at selected threshold levels, data
are directly obtained for plotting cumulative frequency (larger than stated size)
against particle size.
Laser diffraction spectrometry. During the early 1970s methods were described
for determining the size distribution of a sample of fine particulate material by
measuring the diffraction that occurs as a beam of light passes through a
suspension of the sample. Since that time the technique has been improved to
the point where the laser diffraction spectrometer (LDS) is commercially
available from several manufacturers in a form that allows a reliable size
analysis to be made by a semi-skilled operative in just a few minutes. Although
very costly, these instruments offer significant advantages in that special
electrolytes are not required and calibration is unnecessary. However, there
have been doubts expressed about discrepancies between analyses carried out
on the LDS and results from other size-measurement techniques.
The principle of laser diffraction spectroscopy is quite complex and only a
simplified explanation can be given here. The angle of diffraction of a beam of
light passing through a suspension of particles depends essentially upon the
wavelength of the light and the size of the particles. Thus a beam of
monochromatic light (from a laser source) passing through a suspension of
monosized particles would be diffracted through a specific angle (Figure 1.15a)
which is not dependent on the position or movement of the particles. If this
light then passes through a lens it will be drawn to a focus in the form of an
annular ring on the focal plane (Figure 1.15b ). For a mixture of particles the
0
(a) Laser light diffracted by
uniform-sized particles
focal plane
laser light _ . ,_ _i-"-2'
~
so' lid
particles
(b) Light patterns formed at
focal plane of lens
Figure I. IS
The principle of laser diffraction spectrometry.
25
THE NATURE OF BULK SOLIDS
measuring cell
laser
suspension (ultrasonically
and/or mechanically
stirred)
-
photodetector
and processor
output (VDU
and/or printer)
- --- -
Figure 1.16
The elements of a laser diffraction particle sizer.
incident light beam will be diffracted in a complex manner, but the result will
be a radially symmetrical pattern of light on the focal plane of the lens, the
intensity of this light at any radius being a function of the proportion of
particles of a corresponding size. Electronic analysis of the light pattern on the
focal plane can thus yield a size distribution of particles in the suspension. The
smallest particle size that can be measured is generally about 1 Jlm, since the
particles must be larger than the wavelength of the incident light, which is
0.63 Jlm for a He-Ne gas laser. The top size limit is set by the smallest
diffraction angle that can be detected (the diffraction angle being inversely
proportional to particle size) and in practice is usually around 200 Jlm.
Figure 1.16 illustrates the essential components of a typical commercial
LDS system. The instrument may be used directly on-line or may incorporate
a vessel in which the suspension is prepared and maintained in a dispersed
state by, for example, an ultrasonic oscillator. The particles are carried in the
suspension through a measuring cell where they are illuminated by a laser
beam. The diffracted light is collected by a system which may consist of a lens
and some kind of photosensitive detector, the electrical output from which is
analysed by a microprocessor. Finally the output data may be displayed on a
VDU screen or provided as hard copy from a printer.
1.6 Particle shape
Experience has shown that the shape of the constituent particles in a bulk solid
is an important characteristic as it has a significant influence on their packing
and flow behaviour. Some means of describing the shape of a non-spherical
particle is therefore necessary. Various terms such as acicular, flaky, nodular,
and so on, have been used to give a qualitative indication of the general shape
of particles; indeed, such terms have been defined in a British Standard [10].
For example, particles may be described as 'flaky' when they have a thickness
(smallest dimension) of less than 0.6 of their mean sieve size. A 'flakiness index'
can be measured using special sieves having elongated slots [7]. Defining the
shape of non-spherical particles in mathematical terms is not easy, but many
26
BULK SOLIDS HANDLING
attempts have been made to established the use of shape factors to indicate the
extent to which particles differ from the spherical.
Probably the most commonly used of these shape factors is the 'sphericity'
f/1., defined as the reciprocal of the ratio of the surface area of a particle to that
of a sphere of the same volume:
fjJ =
•
surface area of sphere } f h
o t e same vo1ume
surface area of particle
It will be noted that f/1. must be less than unity and that
f/Js =
nd;
=
(dv) 2
(1.12)
d5
Asp
where Asp is the surface area of the particle. Thus the 'volume diameter' dv is
always less than the 'surface diameter' d. for a non-spherical particle.
Also, from equations (1.5) and (1.6),
1241 V p113 )
112
0· 564A sp
fjJ = ( .
s
2
=
V 2 13
4 838-p.
A sp
(1.13)
Clearly the determination of sphericity requires the measurement of the
volume and the surface area of particles. Such measurements are not easy and
must normally be carried out by separate and indirect means which yield
average values for a group of particles. It follows that the resulting value of f/J.
will also be an average, but this gives little useful information about a bulk
solid that comprises particles differing widely in shape.
Although in certain chemical processes, for example, it might be essential to
have a knowledge of the shape of particles constituting a bulk solid, for the
majority of bulk handling systems such detailed information is not necessary.
Indeed, most storage vessels and conveyors would be designed without any
consideration of the particle shape of the bulk material concerned. The
difficulty in obtaining (and interpreting) quantitative data on particle shape is
discouraging, but a valuable alternative approach involves the use of a lowpower microscope with suitable photographic attachments. Micrographs
(Figure 1.17) can convey information which could alert the designer at an early
stage to potential problems. For instance, the structure of the particles might
appear to be fragile, indicating that degradation of the product during
conveying could be a significant problem; a fibrous appearance could warn of
a tendency of the particles to lock together, causing flow problems from
hoppers; or sharp, angular particles could be the cause of excessive wear
damage to the pipeline and the components.
1.7 Surface area
The surface area of certain finely divided bulk materials, such as catalysts and
paint pigments, is of considerable importance during the processing and use of
27
THE NATURE OF BULK SOLIDS
c:
lOO~m
d
500
~m
Figure 1.17 Micrographs of a few typical bulk solids showing a range of particle shapes. (a) Dry
sand. (b) Polypropylene powder. (c) Wheat flour. (d) Hardboard fluff.
these materials and various techniques have therefore been devised to measure
this property. In general, these techniques yield the 'specific surface' of the
material, which is usually defined as the surface area per unit volume, but may
be defined as surface area per unit mass.
For a single particle the volume specific surface is thus given by
sp = (nd;) / (~d?)
from which
6
sp =A-d
(1.14)
'f's v
but measurements on samples of a bulk solid would of course yield an average
value for the material.
An indication ofthe specific surface can be deduced from a knowledge of the
particle size distribution and other known characteristics ([4], Part 3).
Indeed, because the specific surface is inversely proportional to particle size,
this parameter is sometimes used to indicate the 'fineness' of a powder.
The most common type of instrument for measuring the surface area of
powders and particulate materials is the permeameter. This actually yields the
28
BULK SOLIDS HANDLING
specific surface of the material, and surface area is readily determined by
dividing the result by the particle density. Various designs of permeameter are
available, but their general principle of operation involves passing a known
quantity of air through a prepared plug of powder and the specific surface
calculated from the measured pressure-drop across the plug. The best known
models of permeameter, all of which are described in [2] and [ 4], Part 2, are
the Lea and Nurse constant flowrate instrument, the Fisher sub-sieve sizer, the
Rigden constant-volume apparatus and the Blaine constant-volume
apparatus.
Various other instruments are available for the determination of the specific
surface of powders, involving, for example, gas adsorption techniques ([4],
Part 1).
1.8 Particle hardness
A knowledge of the hardness of the particles constituting a bulk solid is
valuable when a handling installation is being designed since it will give an
indication of the need to take steps to avoid undue erosive wear of the system
components. Generally speaking, the harder the particles, the more abrasive
the product will be on the materials from which the handling installation is
constructed.
In common with many other characteristics of bulk solids and their
constituent particles, the problem with particle hardness is one of measurement. Static indenters of the Vickers, Rock well or Brinell type are oflittle or no
use for the determination of hardness of small particles, and current practice is
usually to make comparative measurements of hardness by simple scratch
tests. A semi-quantitative 'scale of hardness' was first proposed in 1822 by
Table 1.7 Mobs scale of hardness
Mobs scale
hardness
Material
Chemical
formula
Talc
Mg 3 (0Hh·(Si20sh
2
Gypsum
CaS0 4 ·2H 20
3
Calcite
Fluorite
Apatite
CaC0 3
CaF 2
Ca 5 (P0 4 lJ(Cl, F)
Feldspar
Quartz
Topaz
KA1Si 3 0 8
Si0 2
Al 2F 2 Si0 4
Corundum
Diamond
c
4
5
6
7
8
9
10
Al 2 0
3
Explanation
Very soft, can be powdered
with the finger
Moderately soft, can
scratch lead
Can sera tch fingernail
Can scratch a copper coin
Can scratch a knife blade
with difficulty
Can scratch a knife blade
All products harder than
6 will scratch window glass
29
THE NATURE OF BULK SOLIDS
hardness nos.
u
Qi
~
.><
()
0
a:
Qi
c
~
~
Q)
.><
()
>
0
10 4
E
()
C1l
70
750
50
500
30
10
250
100
103
::>
~
a.
()
Ol
()
(J)
>-
C1l
~
·.::
0
~
10 2
~
C1l
a.
C1l
10 1
2
3
~
E
::>
a.
(J)
N
"0
~
Q)
5
4
6
Mohs number
"0
N
C1l
a.
er
.s
7
8
::>
c
::>
~
0
()
9
"0
c
0
E
C1l
'6
10
Figure 1.18 The relationship between the M ohs scale of hardness and the Vickers, Brinell and
Rockwell C scales.
F. Mohs, who selected ten mineral standards beginning with the softest, talc
(M ohs hardness 1), and ending with the hardest, diamond (M ohs hardness 10).
Table 1. 7 lists the M ohs hardness standards and indicates the type of simple
scratch tests that can be used to give a guide to the hardness of a particulate
bulk solid.
Since the M ohs scale proved to be too coarse and, with the original natural
materials, insufficiently reproducible to form the basis of a standard measurement of the hardness of general engineering materials, alternative tests were
developed. These were mostly of the static indentation type (such as Vickers
and Brinell) and consequently, metal hardness came to be specified in terms of
the value indicated by either of these methods; e.g. 400 Vickers Pyramid (VPN),
380 Brinell Hardness Number (BHN). Fortunately, sufficient research has
been undertaken to relate the various values of the hardness parameters to the
Mohs scale, and vice versa (Figure 1.18).
1.9 Cohesion and adhesion
One of the first features to become apparent when handling a bulk solid may
be described in one word as its 'flowability'. This can be regarded as the
summation of a number of different effects, but is essentially concerned with
30
a
BULK SOLIDS HANDLING
500
~m
b
500~m
Figure 1.19 PVC powder showing the effect of electrostatic charging. (a) Uncharged.
(b) Charged.
the forces of attraction or 'cohesion' between constituent particles. Thus,
when these forces of attraction are low, the bulk material can be made to flow
easily under the influence of gravity with the particles moving as individuals
relative to one another. Dry sand and granulated sugar are familiar examples
offree-flowing bulk solids. However, high interparticle cohesive forces, which
may be caused by moisture or electrostatic charging, and are especially
pronounced in very fine materials, result in a tendency for agglomerates to
form so that the material flows in an erratic manner as 'lumps', if indeed it flows
at all (Figure 1.19). Examples of familiar cohesive bulk solids which usually
exhibit this sort of behaviour are wheat flour, cocoa powder and icing sugar.
The general term 'flowability' has been used in a qualitative sense to describe
whether a bulk solid is free-flowing or cohesive. The assessment of the
probable flow behaviour of a bulk solid is very much a matter of judgement
based on experience, but there are various tests which can be carried out to
provide quantitative evidence to assist this judgement. Thus, for example,
'cohesion' can be formally defined as the resistance of a bulk solid to shear at
zero compressive normal stress, and a test can be designed to determine this
quantity.
When designing systems involving the flow of bulk solids from hoppers or in
chutes, or in fact in any situation where a bulk solid slides in contact with a
fixed boundary surface, the property of adhesion is important. Whereas
cohesion is defined in terms of interparticle attractive forces, adhesion
describes the tendency of solid particles to 'stick' to a containing surface, such
as a wall of a hopper or the side and bottom surfaces of a channel or chute.
Quantitative measurements of adhesion between a bulk solid and any desired
type of wall material can be made in similar tests to those used for sliding under
specified conditions.
A measurement that is often used, incorrectly, as an indication of flow
behaviour is the 'angle of repose' that the free surface of a bulk material takes
up when the gravitational slippage occurs. Certainly, this is a convenient and
THE NATURE OF BULK SOLIDS
31
usually reproducible characteristic of bulk solids, but for the determination of
flow behaviour of such materials the appropriate tests are those involving the
use of some kind of shear cell, as described later in this chapter.
1.9.1 Angle of repose
When a quantity of bulk solid is allowed to form a heap, or when slippage of
material occurs so that a sloping surface is exhibited, the angle of the free
surface may take any value up to some maximum which depends principally
upon the nature of the bulk solid concerned. To some extent the value of this
maximum angle also depends upon the way that the sloping surface is formed,
but with a standardized test procedure it is found to be reasonably consistent
for a given bulk solid. Thus it is possible to define an 'angle of repose' as the
limiting natural slope of the free surface of a bulk solid observed during a
specified test procedure, and this can be regarded as a property of the material
concerned.
Many methods have been devised for measuring the angle of repose of bulk
solids, but it is important to recognize that the value determined will depend
not only upon the condition of the bulk solid (for example its moisture content
or level of electrostatic charge) but also upon the test procedure adopted and
the skill of the operator. Several different methods are illustrated in
Figure 1.20. The most commonly used method yields a value of'poured' angle
of repose, which is the angle between the horizontal and the sloping side of a
heap of the material poured gently from a funnel on to a flat surface
(Figure 1.20a). The technique probably giving the best repeatability is that
illustrated in Figure 1.20f, in which a circular platform of known diameter
(typically around 75 mm; 3 inches) is supported over a circular hole in a flat
base plate and surrounded by a cylinder of suitable diameter and height. After
carefully filling the cylinder with the bulk solid to be tested, the operator
unplugs the hole beneath the circular platform and, when flow through the
hole has ceased, removes the cylinder. Measurement of the height of the cone
of material remaining on the platform then allows the 'drained' angle of
repose to be calculated.
It is reasonable to regard the angle of repose of a bulk solid as crude
evidence of its likely flow behaviour, as follows:
Angle of repose
25-30°
30-38°
38-45°
45-55°
> 55°
Very free-flowing
Free-flowing
Fair flowing
Cohesive
Very cohesive
However, whilst it is true that this gives a useful qualitative guide to the flow
properties of a bulk solid, the approach should certainly not be relied upon
32
BULK SOLIDS HANDLING
(a) Heap poured on flat surface
(c) Rotating cylinder
(e) Cylinder with hole in base
(b) Tilting table
(d) Box with removable side
(f) Heap on circular platform
Figure 1.20 Methods of measurement of angle of repose.
where more appropriate tests are available. In fact, it is generally safer to treat
angle of repose only as an indicator of the contours of heaps of the material.
Thus, for example, the angle of repose of a bulk solid is required in order to
determine the ullage space in hoppers or bins, the cross-sectional area of
material transported on a belt conveyor, the surface topography of stockpiles,
and so on.
33
THE NATURE OF BULK SOLIDS
1.9.2 Shear strength
As with continuous material, the application of any force to a bulk solid
tending to cause shear deformation will result in an opposing resistive force. As
the magnitude of the applied force is increased, a point will be reached where
the bulk solid begins to deform with the constituent particles sliding relative to
one another (Figure 1.21). The limiting value of the resistive shear stress (when
the bulk solid is on the point of sliding) may be termed the 'shear strength' of
the material. Naturally the magnitude of the consolidating force on the bulk
solid will have a major influence on the shear strength, and other factors
having an effect will include the nature of the particles themselves, the packing
arrangement and the prior history of the material.
A plot ofthe relationship between the normal compressive force, F N• and the
shear strength, Sr, is commonly called the 'yield locus' for the bulk solid
concerned. A simple and convenient model of the yield locus, illustrated in
Figure 1.22, is
(1.15)
.1('
shear plane
Figure 1.21
Crushing of compacted, but unsupported, column of powder.
typical cohesive
material
free-flowing (non-cohesive) material
compressive (or consolidating) force, FN
Figure 1.22 The linear or Coulomb model for shear strength of a particulate material.
34
BULK SOLIDS HANDLING
"X
~~"2
""1
"1
(a] Compressive and shear stresses
Figure 1.23
"2
(b] principal stresses
Stresses on an element of material.
in which p is the coefficient of internal friction and T. is an 'apparent tensile
strength', i.e. the value ofFN (negative) for which the shear strength is zero. The
limiting value of Sr for F N equal to zero ( = p T.) is often used as the definition of
the 'cohesion' ofthe bulk solid. Thus for a non-cohesive (free-flowing) material,
pT. = 0 and the yield locus is the straight line
(1.16)
which passes through the origin.
A convenient graphical treatment of the relationships between the shear and
normal (consolidating) stresses in bulk solids involves the use of the Mohr
circle of stress. To illustrate the application of the Mohr circle, consider an
element of bulk solid subjected to consolidating and shear stresses as shown in
Figure 1.23a. The principal stresses are rr 1 and rr 2 acting on planes inclined at
angles e and e + 90° to the plane of (J" X as shown in Figure 1.23b, where
(1.17)
and
( 1.18)
Figure 1.24 illustrates the manner in which these stresses can be represented
by the use of the Mohr stress circle. Note that changing the consolidating or
the shear stresses on the element of bulk solid will result in changes in the
radius and/or centre of the Mohr circle. Thus, for example, increasing the
applied stresses to the point of sliding of the bulk solid will result in a 'limiting'
stress circle, and a series of such limiting circles at different combinations of
consolidating and shear stresses will have an envelope that corresponds to the
so-called 'yield locus' (Figure 1.25). Note that the limiting Mohr stress circle
passing through the origin defines the 'unconfined yield stress', rrc,
which represents the strength of the material at the free surface. Referring to
35
THE NATURE OF BULK SOLIDS
p
Figure 1.24 The Mohr circle of stress.
general Mohr
stress circle
normal stress,
Figure 1.25
a
Yield locus for a consolidated bulk solid.
Figure 1.21, the unconfined yield stress can be regarded as the force per unit
area applied to the top of the column of powder at the point of collapse.
1.9.3 The shear cell as a means of determining shear strength
More than one type of shear-testing device has been proposed but probably
the most familiar is the translational 'shear cell' developed by Jenike [11]. The
Jenike shear cell (Figure 1.26) consists of a circular base of 95.3 mm (3iinch)
diameter, a shearing ring which rests on top of the base, and a cover which has
a loading bracket attached to it. For tests at higher consolidating pressures a
smaller cell is used (63.5 mm; 21 inch diameter).
It has been mentioned previously that the shear strength of a bulk solid
is a function of its prior history. For this reason it is important that a
36
BULK SOLIDS HANDLING
normal load, FNt
shear plane
(area A)
Figure 1.26 The Jenike shear cell.
normal load, FN
Figure 1.27 A typical yield locus, as obtained from tests using a shear cell.
consistent procedure is adopted for preparation of the sample to be tested.
A detailed description of this setting-up procedure may be found in textbooks
such as [12], but basically it involves filling the cell with material and
consolidating it with a combination of vertical loading and horizontal
shearing using a special mould ring and twisting top cover. Once prepared, the
shear cell (Figure 1.21) is fitted with the test cover and the required vertical
load applied. A horizontal thrust is then applied by means of an electromechanically driven loading stem at a constant strain-rate of 2.3 mm/min
(0.09 inchjmin), and the shearing force is continuously recorded. This procedure is repeated for several different values of the applied normal force so that
a graph can be plotted of the maximum (yield) shear stress recorded against the
normal load (Figure 1.27). This graph is the 'yield locus' for the bulk solid at
the tested condition.
Various data can be determined from the yield locus plot of Figure 1.27.
Drawing a Mohr circle tangential to the measured yield locus and passing
through point M, which corresponds to the initial consolidating load (when
preparing the specimen in the shear cell), gives the major consolidating
principal stress
FN(G)
(Jmc=~
(1.19)
THE NATURE OF BULK SOLIDS
37
where A is the area of the shear cell and F N(GJ is the value of the normal load at
the point G on Figure 1.27.
Again, a Mohr circle drawn through the origin gives the unconfined yield
stress as
=
(J
c
FN(F)
(1.20)
A
Both of these parameters are of importance when designing for solids flow,
as will be explained in Chapters 2 and 4.
The slope of the yield locus at any point defines the dynamic 'angle of
internal friction', cp, at that condition. (Note that in practice there is usually
found to be some variation of cjJ with the consolidating load, shown by a slight
curvature of the yield locus.) On Figure 1.27 the 'effective yield locus' is also
shown. This is a straight line tangential to the Mohr circle for the initial
consolidating load and passing through the origin. The slope of this line
defines the 'effective angle of internal friction'. For a full investigation of the
flow properties of a bulk solid, graphs such as Figure 1.27 should be prepared
for a range of initial consolidating loads, resulting in a series of yield loci.
The influence of the time of storage on the flow behaviour of a bulk solid can
be studied by applying the initial consolidating load to the specimen in the
shear cell for a set duration before carrying out the test procedure. The
resulting plot of shearing force against normal load is then termed the 'time
yield locus'.
The translational type of shear tester, such as the Jenike shear cell, is subject
to a number of limitations, the most serious of which is that it is only suitable
for use with fine particulate materials. The maximum shear displacement
obtainable with a translational cell is about 6 mm and the top size of particles
that can be allowed is therefore around 3 mm. In order to achieve unlimited
strains, rotational shear testers have been developed, such as the torsional cell
(Figure 1.28a) used especially in studies of soil mechanics, and, more recently,
the annular or ring shear cell (Figure 1.28b). The torsional shear tester itself
suffers from the major disadvantage that the stress distribution within the
sheared material is undefinable, and the annular shear cell would therefore
appear to be the most reliable means of investigating the flow characteristics of
bulk materials.
-
I
(a) Torsional
Figure 1.28
(b) Annular (ring)
Principle of torsional and annular shear testers.
38
BULK SOLIDS HANDLING
(+1------------,~-
r-'
l
counterweight(s)
~~-=v
additional weight(s)
__ /_ ___ _
calibration
Figure 1.29 The Portishead ring shear cell.
Figure 1.29 illustrates in detail the arrangement ofthe Portishead ring shear
cell as originally devised by Walker [13, 14]. It consists essentially of an
annular trough having an inner diameter of 152mm (6 inches) and an outer
diameter of254mm (10 inches). An annular shoe fits inside the trough, centred
on an axial spindle and having a minimum radial clearance of about 3 mm.
Radial vanes integral with the underside of the shoe ensure that the bulk
material sample is held while material in the slowly rotating trough shears
against it. The speed of rotation ofthe trough is about 1.5 revolutions per hour,
and the compaction pressure on the bulk sample in the trough can be adjusted
by adding weights to the shoe or to the counterbalance hanger. A force
transducer bearing against a radial torque arm fitted to the shoe allows the
shear stress on the bulk sample to be continuously monitored.
Details have been published [15] of tests undertaken with a much larger
shear cell, having a diameter of approximately one metre, which allows the
flow properties of materials having particles of up to 50 mm to be investigated.
The procedure for carrying out shear tests begins by loosely packing the test
sample into the trough and then shearing it under the selected normal load in
order to achieve the required state of compaction. The total torque required
to just shear the material can then be measured for number of different normal
loads (Figure 1.30). Since the total shear torque is given by
f
Ro
~otal
shear
=
(1
R · 2rr: RdR
R;
(1.21)
39
THE NATURE OF BULK SOLIDS
~-f--
----
~-~-
I
.8
c;;
c
0
:;::;
0
a.
0
a.
QJ
c;;
u
UJ
~1
-
-~
r---
i
v--
~---
I-
f---· -
I
er
,
bi
a
\
v
I
v--
\
\
--
d.r/'
··-
r--
\ 1
scale proportional to displacement-
Figure 1.30 Typical output record from load transducer as a sample is sheared at a series of
increasing normal pressures from the same consolidating pressure. (Points a, b, c and d indicate the
yield strength in each case).
values of the yield stresses can be readily calculated and used to plot yield loci
and flow functions as previously described.
Two recently published papers [16, 17] attempt to compare data on bulk
solids flow behaviour obtained from a translational (Jenike) shear cell and an
annular (Portishead) shear cell. These suggest that, although there is a broad
agreement between the flow functions obtained from the two test procedures,
there is also evidence that the correlation of results may be to some extent
machine- and/or material-dependent.
1.9.4 Wall friction
A similar linear model to that suggested for the internal friction of bulk solids
(equation 1.15) can be used to represent the relationship between the normal
force, F N• pressing a particulate material against a constraining surface, and
the shear force, Sw, required to cause the material to slide along that surface.
Thus
(1.22)
where f-Lw is the 'coefficient of wall friction' and the constant Cw is a parameter
defining the adhesion between the bulk solid and the containing surface or wall
(Figure 1.31). The line represented by equation (1.22) is termed the 'wall yield
locus' and for most bulk solids is found to be below the yield locus for the same
material. Also, the angle of wall friction (tan- 1 f-Lw) is generally less than the
angle of internal friction (tan- 1 f-L).
The linear model of equation (1.22) is found to be a reliable representation of
the behaviour of dry bulk solids on dry surfaces, and for such cases the value of
the constant Cw approaches zero.
40
BULK SOLIDS HANDLING
//
yield locus
'y
/
//
-wall yield locus (slope llw )
//
//
angle of wall friction
- tan" 1 11 w
1£--.....l....-
normal load, FN
Figure 1.31 'Wall yield locus' for a bulk solid in contact with a plane surface.
1.9.5 Measurement of wall friction
Tilting plate method. In this method a thin layer of the bulk solid concerned is
carefully laid on to a horizontal plate made of the required wall material. The
plate is then slowly tilted and the angle recorded at which the layer of bulk
solid slides off. In contrast to conventional solid friction, the angle of the plate
is a function of the weight of the powder bed, increasing as the weight of
the bed decreases. An appropriate test procedure is therefore to adjust the
thickness of the layer of bulk solid on the plate until the sliding angle is in the
range 40-90°. It should be ensured, however, that the layer of material is not so
thick that internal collapse occurs before the layer slides.
Writing equation (1.22) as
mg
mg .
(1.23)
A Sin IX= JlwACOSIX + Cw
where m is the mass of the bulk solid on the plate, A is the nominal contact area
and IX is the angle at which sliding occurs, it can be seen that a plot of
(mg/A) COSIX ( = FN) against (mg/A) sin IX ( = Sw) should give a straight line of
slope Jlw and intercept Cw. The angle of wall friction, </Jw, is equal to tan - l Jlw·
Shear cell method. An alternative to the tilting plate is an adapted shear cell in
which the base of the cell is replaced by a flat plate made of the wall material
under investigation (Figure 1.32).
The recommended procedure is to load the top cover up to the maximum
required value of the consolidating force and decrease the load in a series of
steps, recording the maximum shear force (to initiate sliding) at each step. The
wall yield locus can then be plotted as a graph of normal load F N against shear
force Sr as described above for the tilting plate method.
THE NATURE OF BULK SOLIDS
normal load, FN
t
41
twisting cover
shear load, S f
~ =:::::;::ll·------d-~
Figure 1.32 Jenike-type shear cell set up for determination of wall yield locus.
1.9.6 Arching phenomena
One of the most important practical consequences of the cohesiveness of a
bulk solid is that the material can develop sufficient 'strength' to form a stable
'arch' (or 'bridge' or 'dome') over an opening, even when the opening is very
large in comparison to the particle size of the bulk solid concerned. It is for this
reason that a knowledge of the flow behaviour of bulk solids is essential when
designing storage containers and other components of bulk handling installations. One of the main purposes of the test procedures described in the
previous sections is to establish the conditions under which arching can occur,
in order, for example, to design a hopper which will discharge its contents
under gravity without the flow becoming obstructed.
As explained earlier, the main factors contributing to the tendency of a bulk
solid to form a stable arch across an opening are the presence of very fine
particles or of moisture, both of which increase the cohesiveness of the
material. Compaction during storage also tends to increase the strength of the
material and so aggravate the flow situation.
It is important to understand that two forms of stable arch can occur across
an opening. A simple 'mechanical arch' can develop directly as a result of
interlocking of particles that are of large size compared with the opening
(Figure 1.33a). However, this problem can usually be avoided by ensP.-ing that
the hopper outlet is at least ten times the largest particle size. A 'cohesive arch'
(Figure 1.33b) is somewhat more difficult to predict as it forms as a result ofthe
consolidation and strength of a cohesive bulk solid and can therefore occur
even with materials of very fine particle size. Much of the research undertaken
in the field of bulk solids handling has been aimed at gaining an insight to the
conditions necessary for a stable cohesive arch to occur so that reliable
techniques for the design of bins, hoppers and other components could be
developed.
In section 1.9.2 it was explained how the shear strength of a particulate bulk
solid is a function of the consolidating pressure. Of special significance to the
42
BULK SOLIDS HANDLING
(a) Mechanical arch
(b) Cohesive arch
Figure 1.33 Arching phenomena in bulk solids.
material C, showing
typical effect of
material C
~
Q)
·;;,
l
r 'instantaneous'
material 8 , flow functions
"0
Q)
c
c0
()
c
::l
material A (free-flowing)
major consolidating stress
~
Figure 1.34 Typical Flow Functions for bulk solids.
ability of a bulk solid to form a cohesive arch is the 'unconfined yield stress'
which represents the strength of the material at the free surface. For a freeflowing (non-cohesive) material, such as dry sand, the unconfined yield stress is
zero and therefore a cohesive arch could not occur. The flow behaviour of a
cohesive bulk solid can be conveniently illustrated by a plot of unconfined
yield stress against the major consolidating (normal) stress, this plot being
termed the 'Flow Function' of the material. In order to plot a Flow Function a
series of yield loci must first be drawn, using results obtained from a shear
tester as outlined in section 1.9.3. Each yield locus determines one point on the
flow function. Thus, on Figure 1.27, a Mohr circle tangential to the yield locus
and passing through the origin gives the unconfined yield stress (point F) and a
second Mohr circle tangential to the yield locus at M, corresponding to the
initial consolidating load, gives the major consolidating stress (point G).
THE NATURE OF BULK SOLIDS
43
Figure 1.34 illustrates Flow Functions for three typical bulk particulate
solids. Material A is free-flowing, therefore having no cohesion, and the Flow
Function coincides with the horizontal axis. Material B is slightly cohesive and
material C is more cohesive still; both of these materials acquiring greater
strength as the consolidating stress is increased. Note that other factors such as
moisture content, storage time and vibration can influence the strength of the
materials, effectively moving the Flow Function either up or down.
Although the tests described for the determination of flow properties of bulk
solids are relatively straightforward, the interpretation of the test data is not
easy. It is beyond the scope of this book to deal with the real intricacies of bulk
solids flow behaviour, but some further discussion on gravity flow will be
undertaken in Chapter 2 and the application of these various concepts and
measurements to the design of storage hoppers will be further developed in
Chapter 4.
1.10 Moisture content
In the large and varied industry concerned with the handling, processing and
storage of bulk solids there can be few areas where the moisture levels of these
materials are not important. In addition to causing effects such as chemical
change, deterioration of quality and so on, moisture can have a dramatic
influence on the flow behaviour of bulk solids, and therefore moisture analysis
is one of the most frequently performed tasks in their characterization.
It is usual to express the moisture content in terms of the percentage of water
to dry solids. Thus
.
mass of water
mOisture content=
fd
I'd ( x 100%)
(1.24)
mass o ry so 1 s
However, an alternative definition gives moisture content in terms of the
percentage of water to wet solids:
.
mOisture content=
mass of water
( x 100%)
total mass of solids and water
(1.25)
A simple method for determining the moisture content of a bulk solid is to
weigh a sample of the material and then place the sample in an oven for an
appropriate length of time to dry it thoroughly. The decrease in the mass of the
sample should correspond to the mass of water originally in the sample so that,
by the first definition above, the moisture content can be calculated from:
.
initial mass of sample- final mass of sample
f
( x I 00%)
mOisture content=
fi 1
ma mass o samp1e
( 1.26)
Where the moisture content is low it matters little which of the above
definitions is used.
44
BULK SOLIDS HANDLING
It should be noted that water may be present in a bulk solid in two forms:
(i) 'Surface moisture', which is present only on the surfaces of the particles
(ii) 'Inherent moisture', which exists as water of crystallization within the
structure of the particles.
When the surface moisture has increased to the point where all the
interparticle voids are filled with water, the bulk solid is said to be 'saturated'.
The method of oven-drying suffers from the disadvantage of taking several
hours to perform, and a number of faster methods of moisture measurement
have been developed. These rely upon a number of different techniques such as
infrared absorption, microwave absorption, nuclear magnetic resonance,
ultrasonics, conductivity, gas evolution and chemical methods.
Probably the most widely used methods are still those based on heating the
sample to drive off the moisture, as in the oven technique described above. A
refinement that has recently become popular is the 'moisture balance' which
consists essentially of a conventional electronic top-pan balance adapted so
that the pan is contained in an enclosed chamber. The sample of material on
the pan is subjected to infrared radiation and its mass continually monitored
as the moisture is driven off. The time taken to dry a sample of bulk solid for a
moisture analysis can be greatly reduced by using a fluid bed dryer in place of
an oven. This method is particularly suited to heat-sensitive products as it
offers a relatively short residence time and a uniform temperature distribution
with an absence of 'hot-spots'.
1.11 Explosiveness
Many bulk particulate solids, when dispersed in air to form a dust cloud,
constitute a potentially explosive mixture which may be ignited by a naked
flame, a hot surface or an electrical discharge. The range of products that are
hazardous in this respect is quite wide and includes common foodstuffs such as
sugar, flour and cocoa; synthetic materials such as plastics, chemicals and
pharmaceuticals; metals such as aluminium and magnesium; and traditional
fuels such as coal and wood. Other products such as sand, alumina and certain
paint pigments are non-combustible and therefore present no danger. Of those
products that are combustible, research has shown that it is only the fraction of
the bulk having a particle size less than about 200 11m that causes the existence
of an explosion hazard. The picture is further complicated by the fact that the
risk of an explosion occurring depends upon parameters such as product-toair concentration and minimum ignition temperature and energy. Tests have
been devised to determine the 'explosiveness' of a bulk solid in terms of these
parameters, and for many products the results are freely available-see, for
example, [18]. The whole subject of explosion hazards existing during the
handling of bulk solids is covered in more detail in Chapter 7 and some
THE NATURE OF BULK SOLIDS
45
guidance is given on the precautions that can be taken to reduce the risk
associated with dust explosions.
1.12 Notation
A
Asm
Asp
Cw
da
d.
dsm
d.
dvm
dvsm
FN
g
N
m
msolids
mvoids
Sr
sp
SW
Ta
vp
Vpm
V.olids
vvoids
X
IX
E
e
J.1
J.lw
Pb
Pc
Pp
al,a2
ac
a me
ax,ay
r
Area
Average surface area of one particle in a group
Surface area of a single particle
Adhesion parameter (equation 1.22)
Sieve aperture dimension
'Surface diameter' of a particle
'Surface mean diameter' of one particle in a group
'Volume diameter' of a particle
'Volume mean diameter' of one particle in a group
'Volume-surface mean diameter' of one particle in a group
Normal compressive force
Gravitational acceleration (specific gravitational force)
Number of particles
Mass
Total mass of particles in a bulk solid
Mass of fluid in void space in a bulk solid
Shear strength
Specific surface (surface area per unit volume)
Shear force at wall
Apparent tensile strength
Volume of a single particle
Average volume of one particle in a group
Total volume of particles in a bulk solid
Volume of void space in a bulk solid
Mass fraction
Angle
Voidage or void fraction
Angle of plane of a 2 to vertical
Coefficient of internal friction
Coefficient of wall friction
Bulk density
Density of fluid
Density of solid particles
Principal stresses
U nconfined yield stress
Major consolidating principal stress
Compressive stresses in x and y directions
Shear stress
BULK SOLIDS HANDLING
Angle of internal friction
Sphericity of a particle
Angle of wall friction
References and bibliography
References
1. The Bulk Solids Physical Property Test Guide, British Materials Handling Board (1983).
2. Alien, T. (1981) Particle Size Measurement, 3rd edn., Chapman and Hall, London.
3. BS 812: 1975, 1976, Sampling and testing of mineral aggregates, sands and fillers. British
Standards Institution, London.
4. BS 4359, Methods for the determination of the specific surface area of powders
Part 1: 1985. Nitrogen adsorption (BET method).
Part 2: 1982. Air permeability methods.
Part 3: 1979. Calculation from particle size distribution. (Withdrawn 1985). British Standards
Institution, London.
5. BS 3406, Methods for determination of particle size distribution.
Part 1: 1986. Guide to powder sampling.
Part 2: 1984. Gravitational liquid sedimentation methods for powders and suspensions.
Part 3: 1963. Air elutriation methods.
Part 4: 1963. Optical microscope method.
Part 5: 1983. Electrical sensing zone method (the Coulter principle).
Part 6: 1985. Centrifugal liquid sedimentation methods for powders and suspensions. British
Standards Institution, London.
6. BS 1796: 1976, Methods for the use of BS fine-mesh test sieves. British Standards Institution,
London.
7. BS 812, Section 105. 1: 1985, Flakiness index. British Standards Institution, London.
8. Test Sieving Manual, Endecotts Ltd., London (1977).
9. Pharmaceutical Society of Great Britain ( 1967) Characterisation and Manipulation of
Powders, Pharmaceutical Press, London.
10. BS 2955: 1958, Glossary of terms relating to powders. British Standards Institution, London.
11. Jenike, A.W. (1964) Storage and Flow ofSolids, Bull. No. 123, Utah Engg. Exp. Station, Univ of
Utah.
12. Brown, R.L. and Richards, J.C. (1970) Principles of Powder Mechanics, Pergamon, Oxford.
13. Walker, D.M. (1967) A basis for bunker design. Powder Technol. 1, 228-236.
14. Carr, J.F. and Walker, D. M. (1967/68) An annular shear cell for granular materials. Powder
Technol. 1, 369-373.
15. Bagster, D. F. (1981) Tests on a very large shear cell. Bulk Solids Handling I (4), 743-746,742.
16. Wilms, H. and Schwedes, J. ( 1985) Interpretation of ring shear tests. Bulk Solids Handling 5 (5),
1017-1020.
17. Reed, A.R. and Arnold, P.C. (1985) A comparison between techniques for measuring the flow
properties of ordinary portland cement. Zement-Kalk-Gips 38 (11), 671-674.
18. Palmer, K.N. (1973) Dust Explosions and Fires, Chapman and Hall, London.
Recommended further reading
Alien, T. (1981) Particle Size Measurement, 3rd edn., Chapman and Hall, London.
The Bulk Solids Physical Property Test Guide, British Materials Handling Board (1983).
Brown, R.L. and Richards, J.C. (1970) Principles of Powder Mechanics, Pergamon, Oxford.
2
Gravity flow of bulk solids
2.1 Introduction
A good understanding of the nature of bulk solids flow is an essential
prerequisite to the design of virtually any system involving the storage or
handling of such materials. Observation of a bulk material discharging from a
hopper or flowing under gravity along a steeply inclined channel will
immediately suggest similarities to the behaviour of liquids. Whilst there are
certainly some similarities between the flow characteristics of bulk solids and
liquids, the analogy is one that it is unwise to pursue. In general it is more
appropriate to model a bulk solid as a plastic solid than as a fluid continuum.
The main features of liquids which are not shared by bulk solids are as
follows:
(i) At rest, liquids cannot sustain shearing stresses. This is most clearly
demonstrated by the fact that bulk solids can be formed into a stable heap
whereas liquids at rest always have a horizontal free surface.
(ii) Changes of pressure in a liquid at rest are transmitted uniformly to all
other points in the liquid.
(iii) Shear stresses that occur in a flowing liquid are dependent upon the rate of
shear and independent of the mean pressure of the liquid.
In contrast, bulk solids at rest can transfer shearing stresses and, in many cases,
possess sufficient cohesive strength after consolidation to retain their shape
under pressure. Furthermore, when a bulk solid 'flows' slowly the shearing
stresses within it are dependent upon the mean pressure to a much greater
extent than the rate of shear.
These distinctive features of liquids and bulk solids can be illustrated and
compared by considering the distributions of pressure on the internal surfaces
of two identical cylindrical containers; one filled with a bulk solid, the other
filled with a liquid having the same (bulk) density. In Figure 2.la the pressure
distributions due to the bulk solid and the liquid are shown and the much
greater stresses that exist in the liquid near the bottom of the container are
immediately apparent. The reason for this difference lies in the fact that there is
no shearing stress at the walls of the liquid container, and therefore the whole
weight of the liquid is taken on the horizontal base, whereas a significant
proportion of the weight of the bulk solid is carried on the vertical walls.
The manner in which internal stresses are transmitted through the bulk
solid and the liquid are illustrated in Figure 2.1 b in which the effect of
48
BULK SOLIDS HANDLING
liquid
bulk
solid
(a) Pressure distributions due to weight alone
bulk
solid
liquid
(b) Excess pressures due to additional free surface loading
Figure 2.1
Pressure distributions in liquids and bulk solids.
increasing the loading on the free surfaces of each are shown. In the case of the
liquid, the excess load is transmitted uniformly throughout, so that all of this
excess load is, in fact, actually carried on the base of the container. However, at
the base of the bulk solid container there is no change as a result of the
additional loading on the free surface.
As explained in Chapter 1, the ability of a bulk solid to flow may be regarded
GRAVITY FLOW OF BULK SOLIDS
49
as the summation of a number of different effects, but it is essentially concerned
with the forces of attraction between constituent particles. Thus, when these
forces of attraction are low, the bulk material can easily be made to flow under
the influence of gravity with the particles moving as individuals relative to one
another. Dry sand and granulated sugar are familiar examples of free-flowing
materials. However, the high interparticle forces, which may be caused by such
effects as moisture or electrostatic charging and are especially pronounced in
very fine materials, result in a tendency for agglomerates to form so that the
material flows in an erratic manner as 'lumps', if indeed it flows at all.
Examples of cohesive materials which usually exhibit this sort of behaviour are
flour and cocoa powder.
The assessment of the flow characteristics of a bulk solid (i.e. whether it is
'free-flowing' or 'cohesive') is very much a matter of judgement based on
experience, but some of the various tests that can be undertaken to provide
evidence to assist this judgement have been described in Chapter 1. Having
established a method of predicting whether a bulk solid is likely to flow or not,
it is now helpful to gain some insight into the patterns of flow behaviour that
might be observed in various situations. In this chapter, therefore, attention is
given firstly to the usual form of pressure distribution that would exist in a bulk
material at rest (for example in a storage hopper or silo) and to the changes
that occur in that pressure distribution at the start of, and during, flow.
Descriptions are given of the types of flow pattern that may be seen in
gravity discharge of a product from hoppers of different configuration, and
also in gravity flow in inclined chutes and channels. Discussion of the
somewhat intractable problem of predicting the flow rate in such circumstances is considered to be largely beyond the scope of this book and only a
brief introduction will be attempted. In fact, although prediction of flow rate is
important, it is likely to be secondary to the task of ensuring unobstructed
flow, since in many cases the actual rate is controlled independently by a valve
or feeder downstream of the chute or hopper outlet.
The flow behaviour of bulk materials suspended in a stream of air, or at least
under the dominant influence of air or some other fluid medium, is dealt with
as a separate topic (in Chapter 3) and provides an essential foundation to the
understanding of the pneumatic conveying systems described in detail in
Chapters 12-17 of this book.
2.2 Pressure distribution in a bulk solid
2.2.1 Bulk solid at rest
The pressure distribution that would exist within a quantity of bulk solid
contained in a hopper or bin is of interest when designing the container for
strength, but does not have a direct influence on the pattern of flow from the
container. Nevertheless, a good understanding of the pressure distribution
50
BULK SOLIDS HANDLING
T
~
llw Pr 1rD dh
Figure 2.2 Analysis of forces on an elemental 'slice' of bulk solid in a cylindrical bin.
under storage and flow can prove to be a valuable aid when assessing the
likelihood of obstructions to flow occurring.
It has already been explained that the pressure distribution within a bulk
solid is different from that within a liquid in a similar container. The main
cause of this is the frictional forces between the solid particles and the walls of
the containing vessel which means, in effect, that these walls are supporting
part of the weight of the bulk material. Also as a result of this frictional effect,
the lateral pressure on the containing walls is generally less than the
'hydrostatic' pressure due to the head of material (Figure 2.1 ).
In order to develop a model for the pressure distribution existing within a
column of particulate material contained in a cylindrical vessel, consider first
the equilibrium of a thin horizontal 'slice' as shown in Figure 2.2.
At distance h below the free surface of the bulk solid, the lateral pressure is p,
and the vertical pressure, due to the overlying head of material, is Pv· In
general, for particulate materials, the ratio of p, to Pv is found to be
approximately constant, so that
(2.1)
Pr = kpv
where k is a constant less than unity.
Now for the elemental slice of material, of diameter D and thickness dh
(Figure 2.2), the vertical forces acting are those resulting from
pressure (difference)= ~D 2 dpv
n
gravity
= pbg4.D 2 dh
wall friction
=
J.lwp,nDdh
GRAVITY FLOW OF BULK SOLIDS
51
where Pb is the bulk density of the particulate material and f.lw is the coefficient
of friction at the walls.
Then for equilibrium of this element
n
2
n
2
pbg4D dh- 4D dp.- f.lwp,nDdh = 0
Pbgdh - dpv - 4f.1;Pr dh = 0
4f.1wkPv) dh -dp.=O
( pbg--D-
from which
Integration then gives
where C is a constant of integration.
Now Pv = 0 for h = 0, so that
and
from which
l _ 4f.1wkP. = exp( _ 4f.1wkh)
D
pbgD
Rearranging this to give an expression for p, leads to
Pr =
P;:~ ( 1 -
exp ( -
4 f.1~kh))
(2.2)
This is one form of the well-known Janssen formula for radial pressure on
the vertical wall of a cylindrical bin containing a bulk solid.
It may be noted that for tall bins h is large compared with D, so that
pbgD
p,max=-4f.lw
(2.3)
52
BULK SOLIDS HANDLING
=
"'3:
increasing
bin diameter
Q)
-o
<fl-
eet
oo. c
c:.a
gtii'-'
ro~
~~
:>>-
<f)
rJl
'-'
~
Cl.
height of bulk solid above point p (h]
Figure 2.3 Relationship between the pressure at a point on the wall of a cylindrical bin and the
height of material above that point, from equation (2.2).
and
(2.4)
Figure 2.3 illustrates the relationship between the pressure at a point on the
wall of a cylindrical bin and the height of material above that point, as
predicted by equation (2.2).
2.2.2 The effect of flow on the pressure distribution
There are many records of serious mechanical damage occurring to bulk solids
storage vessels, notably grain silos, as a result of an apparent physical
weakness of the vertical walls. Investigations subsequently showed that the
problem was basically due to the failure of the designer to appreciate that
during discharge of the material from the bin or silo the lateral pressures
developed could be considerably greater than existed with the material at rest.
Tests on models have suggested that the so-called 'overpressure' on the side
wall may be as much as three or four times the static pressures. The maximum
possible lateral pressure during flow is a function of the height of the bulk solid
in the bin, being given simply by Prmax = pbgh, where Pb is the bulk density of
the material. The transient pressures occurring on the sloping and vertical
sides of storage vessels during emptying are a complex phenomenon and it is
only in relatively recent years that progress has been made towards a
satisfactory explanation. The following description of the varying pressure
53
GRAVITY FLOW OF BULK SOLIDS
'peaked' field
-'switched' field
(a} Static
Figure 2.4
(b} Dynamic
Static and dynamic stress fields in a bulk solid contained in a storage bin.
distribution within a bulk solid discharging from a storage vessel is
attributable to Jenike and Johanson.
During the filling of a bin an active state of pressure exists, as the material
tends to settle and thus contract vertically under the increasing load. The lines
of principal stress are almost vertical and form a 'peaked' or 'static' stress field
as shown in Figure 2.4a. When the bin outlet is opened and flow begins, the
material expands in the vertical direction, but it must contract laterally in
order for flow to continue through the converging hopper section. The
principal stresses now tend to align themselves with the lateral contractions of
the bulk material, becoming almost horizontal across the outlet of the hopper
and forming an 'arched' or 'dynamic' stress field in this region. The change
from a static to a dynamic stress field occurs quite rapidly, the effect travelling
upwards through the bulk solid as a shock disturbance or 'switch' which may
appear on the side wall as a narrow band of higher pressure (Figure 2.4b). This
'overpressure' is necessary to maintain equilibrium, since the dynamic
pressures existing below the level of the switch are less than the static pressures
that existed initially. The switch, with its associated band of higher pressure,
travels upwards at least to the transition where the conical and cylindrical
sections of the bin intersect, reaching a higher level in a free-flowing material
than it will in a cohesive one. Where there is a considerable height of bulk
material in a bin, the peak pressure occurring at the transition can be very
large. Above the level of the switch the material is undisturbed and a static
stress field still exists.
54
BULK SOLIDS HANDLING
2.3 Flow of bulk solids from hoppers
2.3.1 Introduction
The flow patterns occurring as a bulk particulate material discharges under
gravity from a hopper have been investigated by many research workers using
a number of different experimental techniques. One common approach has
been to carefully fill the hopper with layers of differently coloured particles so
that changes in the stratification could be observed during the flow. Such work
helped to give an insight to the nature of gravity flow of free-flowing and of
cohesive materials and allowed the influence of the wall angle and the outlet
size to be determined. It became evident that the flow patterns could be
conveniently classified into two groups which are now generally known as
'core flow' (alternatively 'funnel flow' or 'plug flow') and 'mass flow'.
2.3.2 Core flow
In core flow from a bin, the discharge of the bulk solid is essentially irregular,
with material sloughing off the free surface and falling through a vertical
channel which forms within the bin (Figure 2.5). The material around this
central channel is stationary. Core flow bins tend to be relatively short with
rather more shallow wall slopes than would usually be associated with mass
flow. Such bins are sometimes deliberately designed for situations where the
headroom is severely limited, but often they are the result of ignorance about
the advantages of mass flow. The main characteristics of core flow, most of
which are generally regarded as undesirable, may be listed as follows:
(i) First-in, last-out sequence of flow
Figure 2.5
Patterns of discharge from hoppers.
GRAVITY FLOW OF BULK SOLIDS
55
(ii) If the bulk solid has a tendency to spoil, cake or degrade with time, this will
happen in the non-flowing region
(iii) For materials which segregate on charging, there is no re-mixing in the
hopper
(iv) Flow rate tends to be erratic with a widely varying density of the feed
(v) The erratic flow rate may cause fine powders to become aerated and
'flood'
(vi) 'Rat-holing' (described in section 2.3.4) will occur if the non-flowing
material consolidates sufficiently to remain stable after the flow channel
has emptied out.
Nevertheless, core flow may be acceptable in situations where segregation is
unimportant, deterioration of stored material is not likely to be a problem and
the outlet is sufficiently large to ensure flow without the help of a discharge aid
(Chapter 4).
2.3.3 M ass flow
The most important single distinguishing characteristic of so-called 'mass
flow' is that every particle of the bulk material in the hopper begins to move
when the outlet is opened (Figure 2.5). A hopper designed for mass flow
would generally be recognized by the steep wall slopes of the converging
section, the absence of sharp transitions and the relatively large outlet to the
feeder or flow control valve.
For most purposes mass flow is regarded as the ideal, or at least the
preferable, flow pattern. The beneficial properties of mass flow may be listed as
follows:
(i) Channelling, hang-ups, surging and flooding are absent
(ii) Flow is uniform, and steady flow (independent of the head of material in
the bin) can be closely approached
(iii) The bulk density of the drawn solid is constant, and practically
independent of the head of material in the bin
(iv) Pressures are relatively uniform across any horizontal section of the bin
(v) There are no dead regions within the bin
(vi) A first-in first-out flow pattern can be obtained
(vii) Segregation of the bulk solid is kept to a minimum.
2.3.4 Obstructions to gravity flow
The two principal types of flow obstruction encountered in practice are
(i) A 'rat-hole' or 'pipe' (Figure 2.6a), and
(ii) A cohesive arch or bridge (Figure 2.6b).
A third type of obstruction, which can occur when the size of the bulk solid is
56
BULK SOLIDS HANDLING
(a) 'Rathole' or 'pipe'
Figure 2.6
(b) Cohesive arch
Obstructions to flow from hoppers.
large in comparison to the outlet of the hopper, is a 'mechanical arch' formed
simply by the particles or lumps of material becoming interlocked across the
converging section above the outlet.
Both the rat-hole and the cohesive arch are characteristic of cohesive
materials, the former generally occurring in core-flow hoppers and the latter in
the mass-flow type. These obstructions occur when the bulk solid has gained,
within the constraints of the bin, enough strength to support itself, and
therefore both are impossible in free-flowing (non-cohesive) materials.
Arching can also occur in a core-flow bin, forming at the top of a cylindrical
void extending from the hopper outlet upwards into the bulk solid.
When designing storage vessels for bulk solids the primary aim is usually to
ensure that a reliable steady flow of the material will be maintained when the
outlet is opened. With most materials this aim can be achieved by correct
design, particularly with regard to the slope of the converging walls and the
size of the outlet, as explained in Chapter 4, but with very cohesive materials
the use of some form of discharge aid may be advisable, or indeed essential.
2.3.5 Predicting the solids discharge rate
An important step in the process of designing a bin or silo for the storage of a
bulk material is the estimation of the unrestricted rate of discharge, under
gravity, ofthe material when the outlet is opened. It is necessary thus to ensure
that the material is capable of being discharged at a rate in excess of the
required rate, as it is then a relatively simple matter to install some kind of
feeder beneath the outlet port in order to exercise control over the flow rate.
Because of the complex nature of the gravity flow of bulk solids there is as
GRA VJTY FLOW OF BULK SOLIDS
57
yet no single convenient method that will lead to a consistently reliable
prediction of discharge rates for the full range of materials and various designs
of bins and hoppers. Indeed, for materials of a fine cohesive nature no method
has yet been developed that could be confidently recommended to the designer
of storage vessels.
As gravity flow takes place in the converging hopper towards the outlet
opening, the bulk material is in dynamic equilibrium and a force balance on an
element of material in this region should lead to an expression for the rate of
discharge. There are various effects that will influence the solids flow rate,
including the cohesive forces amongst the particles, the frictional effects
between the moving particles and the hopper surfaces, the pressure gradients
in the interstitial air and, consequently, the local air flow patterns and
resulting drag forces on individual particles. An adverse pressure gradient
across the outlet opening can cause a significant reduction in the solids
discharge rate, and thus the actual flow rate obtained may depend upon
whether the top of the storage vessel is open or closed and also upon the depth
of bulk material above the outlet opening. In some cases it may be beneficial to
modify the pressure gradient in the vicinity of the hopper outlet by injecting air
into the hopper during discharge. However, it should be noted that excessive
air injected into fine materials could well cause fluidization and uncontrollable
flooding from the outlet. Some examples of techniques that can be applied to
the gravity flow from conical hoppers of non-cohesive materials and, to some
extent, of coarse cohesive materials, will now be introduced. However, as
mentioned previously, the underlying theory is often extremely complex and
beyond the scope of this book. The reader wishing to pursue this subject is
recommended to begin with references [ 1- 3].
Relatively simple equations, for rough order-of-magnitude assessment of
the discharge rate of coarse, free-flowing materials from circular and
rectangular outlets are recommended in a recently published British code of
practice [ 4]. These are as follows.
For a circular orifice:
ms = 0. 58p g 0 · 5(D c b
k pp
d )0 · 25 kp
(2.5)
For a rectangular orifice:
m.= 1.03ppg 0 · 5 (L- kPdP)(DP- kPDP)1. 5 kp
(2.6)
where Pb is the bulk density of the discharging material, De is the diameter of
the outlet (or, for a plane-flow hopper, DP is the width of the outlet and Lis its
length), dP is the particle diameter, kP is a shape factor (with values of 1.6 for
spherical particles up to about 2.4 for non spherical ones) and kp is a factor
equal to (tan {3)- 0 · 35 for {3 < 45o or equal to unity for {3 > 45°.
Of the various approaches to be found in the literature dealing with the
gravity flow of bulk solids from storage hoppers, only four will be discussed
here: Carleton [5], Williams [6] and Johanson [7] for mass flow and Zanker
58
BULK SOLIDS HANDLING
Table 2.1 Summary of methods for predicting discharge rates from hoppers
Method(s)
Application
Non-cohesive
materials - coarse
( > 500 I'm approx.)
(Mass flow)
Remarks
{i) British Code of
Practice [ 4]
Simple to use-circular
and rectangular orfices
(ii) Williams [6]
Most widely applicable
since wall friction
effects are allowed for
(Significant for flow
through small orifices)
Simple to use-graphical
solution available
(iii) Carleton [ 5]
Non-cohesive
materials - fine
(Mass flow)
Carleton [ 5]
Suitable for cases where
the bin surcharge is
small
Non-cohesive
materials
(Core flow)
Zanker [8]
Core flow: discharge
from circular orifice
Cohesive materialscoarse
Johanson [7]
Requires shear test data
Cohesive materialsfine
No reliable method yet
available
[8] for core flow. Table 2.1 summanzes the applications of each of these
prediction techniques.
Carleton method. The expression derived by Carleton [5] relates the linear
velocity u0 of particles in the discharge stream to the properties of the particles
and of the interstitial fluid, and the geometry of the hopper outlet (Figure 2.7).
This expression can be written in the form
4pPd5f3 sin fJ(u513)3
+ !Opf13 111!3 Dc(u513)2- g = 0
(2.7)
which is seen to be a cubic equation in u5 13 . Although an iterative solution of
this equation should not be particularly difficult, it will clearly be useful to
have a simple graphical technique for the determination of u0 from a specified
set of independent variables. Since the interstitial fluid is likely to be air under
normal atmospheric conditions, the relevant parameters are the diameter d
and density pP of the particles, the diameter De of the hopper outlet and the
angle fJ that the hopper wall makes the vertical. Figure 2.8 is a line chart
developed from equation (2.7) and from which values of u 0 can be readily
determined.
The procedure to be followed when using the Carleton method to estimate
the discharge rate of free-flowing particles from a hopper can be summarized
as follows:
59
GRA VJTY FLOW OF BULK SOLIDS
Figure 2.7 Parameters used in the Carleton method for estimating the discharge rate of freeflowing particles from a conical hopper. Properties of particles: d, average diameter; pP, density.
Properties of interstitial fluid: p,, density; Jl.r, viscosity.
0
0
C\J
1000
---------
Pp
(kg;m')
Uo
0
(cm;s)
9
8
7
6
Figure 2.8
Line chart for the solution of the Carleton equation, equation 2.7, from [5].
(i) Note the parameters defining the hopper geometry, i.e. the diameter of the
outlet opening and the angle of the wall to the vertical.
(ii) Determine, for the bulk material, the average particle diameter and the
density of the particles.
(iii) Use the line chart (Figure 2.8) to determine a value for the linear velocity of
the material in the outlet opening. (Note that if the hopper is not
60
BULK SOLIDS HANDLING
discharging into air at normal atmospheric conditions, the line chart will
not be valid and an iterative solution of equation (2.7) will be needed.)
(iv) Calculate the mass flow rate of the bulk material from
(2.8)
where pb is the bulk density of the discharging material.
Although this method is relatively easy to use it does appear to suffer from
some drawbacks. Probably the principal source of inaccuracy in the Carleton
method is its failure to take into account wall friction effects which could have
a significant influence where the discharge takes place through a small orifice.
In such situations the Williams method, described below, is likely to be more
reliable.
Another weakness in the Carleton model is that no allowance is made for
interstitial air flows resulting from adverse pressure gradients that develop
during the emptying of a hopper. This may not cause a great error when the
hopper surcharge is small, but for large surcharges the flow rate of material
may be substantially overestimated. A more complex modelling approach,
such as that proposed by Arnold et al. [I] should be adopted in such cases.
Williams method. This approach [6] takes into account the friction effects
between the flowing material and the hopper wall, and is therefore likely to
give a more reliable prediction for cases in which the outlet opening is small
(less than about 20 mm). However, no allowance is made for the influence of
interstitial air flows on the discharging particles. The model proposed by
Williams is thus based on the mass flow of homogeneous material consisting of
relatively large particles which offer no appreciable resistance to air flow.
Analysis of this model does not lead to a single unique value of discharge rate,
the result being instead in the form of upper and lower limits of the solids mass
flow rate. The upper limit in fact corresponds to zero wall friction and the
lower limit to the specified value of the angle of friction at the sloping wall of
the hopper. The difference between these limits is said to be sufficiently small
that their mean gives an estimate of the discharge rate which is accurate
enough for practical design purposes.
For the full analysis leading to expressions from which these upper and
lower limits can be computed the reader should consult [6], but for
convenience the data are presented here in a simplified form, using charts for
materials having angles of internal friction of 20-50°.
An expression for the solids mass flow rate is
(2.9)
where Pb is the bulk density of the material, De is the diameter of the hopper
opening and Kh is a coefficient which is a function of the wall slope of the
hopper, the angle of internal friction of the bulk solid and the angle of friction
61
GRAVITY FLOW OF BULK SOLIDS
3.0
1
1'
2.0
\~ 1---- upper limit
\
c
~ f</
Ql
~
1--~~~J----__::'"......~~ 0
Q;
0
2
(,)
0
;;:::
~----1----+----+--
-.!
c:
.g
10.~~
~---1----="'""'-=c.:;-~~:::-_ 5
;::
-= ~
=<1>
~g
0.5
~-+--
-
///lower limits
~"0
o~
<1>
~ If\..
~ ~~
.r::
c .
:,.::: 1 0
Ql
~
Q;
0
(,)
;::
0
0>
.;:
~ ~ t--......;;;::::: r--"::::::1
I---
-
tO
·-·
0
20
40
30
10
wall slope {3 (degrees)
wall slope {3 (degrees)
(b)
(a) Angle of internal friction, <t>- 20°
<t>
=
30°
2.0~-~-~----r-----.
.r::
:,.:::
c
Ql
~
.r::
:,.:::
Q;
0
~
(,)
(/)
;::
<1>
Ql
0
(;,
Ql
3
0
c)
q:,
40
30
20
wall slope {3 (degrees)
10
~ 40°
;::
-G-
c<1>
·c::;
;;::
Q;
0
(,)
;::
0
0
10
20
30
40
wall slope {3 (degrees)
(d)
<t> = 50°
Figure 2.9 Charts giving upper and lower limit values of flow coefficient Kh in equation 2.9 [6].
at the wall. Values of Kh giving upper and lower limits of the solids mass
flowrate can be determined from the appropriate charts in Figure 2.9.
Zanker's nomograph. A very convenient method of obtaining a rapid estimate
of the rate of discharge of a granular or particulate bulk solid from a circular
62
BULK SOLIDS HANDLING
mean particle diameter, d (mm)
.t:::.
U1
0)
N
W
!,,,,j,,,,j,,,,j,l!!l!!lll!l!jl!!lll;;,,!,,,,],,,,j,,,,(,, ,(
,)'-/
/
//
/angle of internal friction. <P (degre:)
g;
c;Ni5.g
I\
'')<1~,),,, I I
~
~
I
I
I
I
I
\,,I
I
I
I
I
I
I
C3
l
I
I
t
I
I
1""1 I II I 1/1 I I I 11 11 I11 "I I I I I I 11 I!
. . . 0 0w 0 0 0
w (Jl/
0
0 00
0
0.:'
.b.
::;
0
.t::>.
J'\)
001
g
_.
(J1
8 g gg
\particle density p0
\
1
11 11 I
I' I ill
I
<.n
<.n
0
II II I
\
0
0
0\\:1 l
(J)
o
o
(Jl
o
o
I I I
I 11
3 )
l
11 11
I
g g
m \ (tonnes/hou~)
& g
I j l l l l l l l l l l l 11111 I I
-"{OCO-.J
° (kg/ni
w
solids flowrate
oooo
gooo
.
g
.p.
a
o
II I I I II I I I I I
0w
0
"'
<.n
0
"'
0
0
<.n
I
0
0
0
0
0
0
0
I
<.n
0
0
0
I
"'0
diametor of outlet opening, D (mm)
Figure 2.10 Zanker's line chart for estimating the discharge rate of a granular bulk material in
core flow through a circular orifice [8].
GRAVITY FLOW OF BULK SOLIDS
63
orifice has been presented by Zanker [8] in the form of a line chart or
nomograph. It is based on an empirical relationship, proposed initially by
Franklin and Johanson, which can be written
.
PvD~
m=-------'------(6.288 tan fJ + 23.16)(dv + 1.889)
s
(2.10)
where Dc is the diameter of the orifice, fJ is the angle made by the hopper wall to
the vertical, dv is the mean particle diameter and n is an exponent. For angular
particles the value of n is about 2.5, ranging up to 3.3 for spheres, and it is
suggested that, in the absence of more reliable information, the value of the
angle of friction should be taken as 10% greater than the angle of repose of the
material concerned.
The Zanker line chart is reproduced (replotted in SI units) as Figure 2.10
and its use is summarized as follows:
(i) On the left -hand scales, join the values for particle diameter dv and angle
of internal friction c/J, and extend the line to the first pivot line.
(ii) Move to the second pivot line in the direction indicated by the oblique tielines.
(iii) Join the resulting point to the appropriate value of particle density and
extend this line to the third tie-line.
(iv) On the right-hand scales, join the values for orifice diameter and index n,
and extend the line to pivot line 4.
(v) Join the points on pivot line 3 and pivot line 4, and where the resulting line
crosses the scale of solids flow rate read off the value required.
Johanson method. For the discharge of a fine cohesive bulk solid from a
hopper the model proposed by Johanson [7] is based on a continuously failing
arch that is in dynamic equilibrium. In order for the arch to fail, the strength of
the material in the arch, caused by the consolidation stress in the vicinity of the
hopper opening, must be overcome. In Chapter 4 it is shown that the
condition for continuous, unobstructed flow of material from a hopper is that
the ratio of major consolidating stress to the unconfined yield strength (<J 1/<JJ
is less than a certain critical value which depends upon the geometry of the
hopper in addition to the flow properties of the bulk solid. These ratios are
termed 'flow factors' (JJ) so that for ff.ctuai > ffcritic•'' flow will occur because a
stable cohesive arch cannot be sustained.
Johanson's method of analysis leads to the expression
m_ p
-
nD 2 [___!!__cl!_( 1 _ ffcrit )] 112
b
4
4 tan fJ
ffactual
(2.11)
for the mass flow rate of material from a conical hopper, where Dc is the outlet
diameter of the hopper and fJ is the slope that the wall makes with the vertical,
64
BULK SOLIDS HANDLING
0.55~------r-----~------~------~------~
c
Q)
·c;
Qi
0
0
10
20
30
40
50
angle of hopper wall to vertical {3 (degrees)
Figure 2.11
Chart for coefficient Kp in equation (2.12) [7].
Pb is the bulk density of the discharging material and g is the specific
gravitational force.
The method of Johanson for estimating the rate of discharge of a cohesive
bulk solid can be summarized as follows:
(i) Determine the critical flow factor (ffcrit) for the hopper (see Chapter 4).
(ii) Determine the value of the bulk density of the discharging material at the
consolidating stress a 1 existing at the hopper opening. An approximate
value of bulk density may be used initially in order to determine the
consolidating stress from
(2.12)
where the coefficient K Pis a function of the ratio of the volume of the arch
to its perimeter and can be determined from Figure 2.11. Materials flow
property graphs will then need to be consulted for the actual value of bulk
density at the consolidating stress given by equation (2.12).
(iii) From the instantaneous Flow Function (FF) of the material (see section
1.9.6), determine the yield strength a c associated with the consolidating
stress a 1 and then calculate the actual flow factor ffactua 1(adac).
(iv) Use equation (2.11) with the values offfcrit• ab and ffactual> obtained from
the steps above, to calculate the discharge rate m.
2.4 Flow of bulk solids in chutes
2.4.1 Introduction
There are many instances in bulk solids handling installations of gravity flow
of a particulate or granular material along an inclined channel or chute. For
GRAVITY FLOW OF BULK SOLIDS
65
example, where a bulk solid is to be discharged at a point below and to the side
of a hopper outlet, it would be common practice to rely on gravity flow
through a simple transfer chute. In such situations both straight and curved
chutes are used but, unfortunately, failure to understand the fundamental
principles of bulk solids flow often results in unsatisfactory chute
performance.
Amongst common applications of transfer chutes for bulk materials, perhaps
the most familiar occurs at the loading point of a belt conveyor. In this case it is
important that the horizontal velocity component of the material leaving the
chute is matched to the velocity of the belt in order to minimize the
acceleration of this material and so effect reductions in power consumption
and belt wear. Other situations may require that the exit velocity is as large as
possible and of a direction to obtain the maximum possible 'throw' of the
flowing material. Thus it is important that the design of gravity-flow chutes
and channels is undertaken in the light of a clear appreciation of the
characteristics of flow in such situations if the desired performance is to be
achieved.
In this section attention is directed to the characteristics of steady flow of
non-cohesive bulk solids in straight and curved chutes. Patterns, or modes, of
flow are described and an introduction is given to the complex problem of
modelling the flow in order to design chutes for specific purposes. Much of the
presently available information on flow in chutes and channels has been
presented by Roberts and his colleagues, for example [9], and by Savage [10],
and readers wishing to undertake a more detailed study are directed to these
sources. Little has been published on the flow behaviour of fine powders and
cohesive bulk solids, although Roberts and Scott [9] have drawn attention to
the characteristically different motion of such materials when compared with
cohesionless products. They report that alumina moves in a series ofblockwise
shears with each block elongating and decreasing in thickness as the velocity
along the channel increased. Similar types of flow have been observed by
Woodcock and Mason [11] in air-assisted gravity conveyors, which are
described in Chapter 15.
Gravity flow in vertical channels and pipes is regarded as a special case and
will be discussed in section 2.5.
2.4.2 Flow patterns in straight inclined chutes
As for liquids flowing along inclined channels, bulk solids in gravity flow may
be expected to exhibit two possible modes: varied flow or uniform flow.
However, the analogy between liquids and bulk solids must not be taken too
far. The terms 'fast' and 'slow' have been used to describe flow conditions that
are observed to occur in enclosed chutes [9] but these terms do not correspond
exactly to 'rapid' and 'tranquil' flow, used conventionally to describe liquid flow
in channels.
66
BULK SOLIDS HANDLING
e
slope lies
between the angle
of repose and
the angle of
internal friction
(b) 'Slow flow'
Figure 2.12
Modes of flow in a straight inclined chute [9).
If a particulate bulk solid is fed into a steeply inclined straight chute or
channel of constant width, 'fast flow' occurs, with the material accelerating,
and consequently the depth of the flowing bed decreasing, until some steady
condition is achieved at which the downward component of the gravity force is
balanced by the various drag forces on the particles (Figure 2.12a). If the slope
of the channel is decreased the rate of acceleration will also decrease, since the
component of the gravity force on the material must be smaller. As the slope of
the channel approaches the angle of internal friction (cp) of the bulk solid, the
flow tends to become uniform. This condition of fully-developed flow at
67
GRAVITY FLOW OF BULK SOLIDS
constant depth (or 'slow flow') is observed in straight chutes or channels at
relatively shallow inclinations, normally only in the very restricted range
between the angle of repose (a) and the angle of internal friction (c/J) of the bulk
solid concerned (Figure 2.12b).
free fall zone due to
'vena contracta' effect
ideal case
,;~~\-~
I
surge wave
(c) Transition from fast to slow flow
(d) Slow flow
angle of repose
(e) Choked flow condition:
Oc too large
Figure 2.13 Modes of flow in a circularly curved chute [9]. 0,, chute cut-offangle; 0, 0 , optimum
value of cut-ofT angle; Or, limiting value of 0, for 'fast' flow.
68
BULK SOLIDS HANDLING
Placing an obstruction near the downstream end of a chute in which a bulk
solid is flowing in the fast mode can cause a surge wave or stationary jump
(sometimes called a 'granular jump') to occur in much the same way as a
hydraulic jump occurs in a flowing liquid.
2.4.3 Flow patterns in curved chutes
The general flow patterns that may be observed when a bulk solid flows
through a curved, enclosed chute are illustrated in Figure 2.13 [9]. As with
straight inclined chutes, two modes of flow have been observed to occur,
termed 'fast flow' and 'slow flow' according to whether the stream of material is
accelerating or travelling at a uniform (slow) velocity.
Figure 2.13a shows the general case of fast flow in which the particulate
material first accelerates as it falls freely from a hopper into the chute, but then
decelerates as a result of the curvature of the channel and the decreasing slope
of the bottom surface. It should be noted that there exists an 'optimum cut-off
angle' (Bco in Figure 2.13b) at which the velocity of the stream is a maximum
and the stream thickness is a minimum. Ideally the chute should be terminated
at this optimum cut-off angle, since any additional length of chute will result in
an increase of stream thickness, frequently leading to an unstable flow
condition (Figure 2.13a).
Where the cut-off angle exceeds the optimum value, it is quite possible for
the thickness of the stream at the lower end of the chute to increase to the point
where the flowing material comes into contact with the top surface of the
chute.
The velocity ofthe stream of bulk material will then be considerably reduced
and a surge wave travels upstream as illustrated in Figure 2.13c. This surge
wave indicates a change from 'fast' to 'slow' flow as the channel becomes
completely full of the bulk solid which is then in contact with all four internal
surfaces (Figure 2.12d).
It should be noted that even a temporary obstruction to fast flow in a
chute having a cut-off angle greater than the optimum value can be sufficient
to initiate a change to slow flow. Indeed, if the cut-off angle is too large
(Figure 2.12e) the chute may become choked and flow cease altogether, or
flood over the sides if the chute is not enclosed. In order to ensure that fast flow
is maintained in a curved chute, the cut-off angle should not exceed some
limiting value ef which depends upon the sliding friction between the
particulate material and the internal surfaces of the chute.
Figure 2.14 shows the typical form of relationship between the solids
flowrate and the cut-off angle for the two modes of flow. When the flow in the
chute is 'fast', the rate is governed by the size and type of the outlet from the bin
or hopper feeding the chute. However, in slow flow the chute itself restricts the
rate, behaving effectively as an extension of the bin or hopper.
69
GRAVITY FlOW OF BULK SOLIDS
Ql
2'
C1l
£
u
(/)
"0
fast flow
Figure 2.14
[9].
ef ~I
slow flow
cut-off
1 angle,
Oc
Typical discharge graph for a circularly curved chute fitted to a flat-bottomed bin
2.4.4 Chute design
There is relatively little published information on the modelling of gravity flow
in inclined channels and the design of transfer chutes for bulk solids. The
following approach is a simplified form of that presented by Roberts and Scott
[9].
It is generally recommended that transfer chutes should be designed to
ensure a stable 'fast' flow condition throughout the length of the chute and
therefore the analytical model of the flow should enable the designer to predict
the variation along the chute of the velocity and cross-sectional area of the
bulk solids stream. The main features of the model are:
(i)
(ii)
(iii)
(iv)
The flow is steady with the material behaving as a continuum
There is no drag on the free surface of the flowing bed
The flow is not affected by interparticle effects within the bed
The bulk density is uniform throughout the flowing bed.
For the general case of gravity flow in a curved chute Figure 2.15 illustrates
the forces that would affect the motion of an element of the flowing bulk
material.
Now for steady flow
ms = pbAu =constant
(2.13)
where Pb is the bulk density of the flowing stream, A is its cross-sectional area
and u is its velocity along the chute. Then since any variation in the bulk
density is to be ignored, we can write
(2.14)
70
Figure 2.15
BULK SOLIDS HANDLING
Forces acting on an elemental mass of bulk solid flowing under gravity in a curved
chute [9].
where A 0 is the cross-sectional area of the flowing stream as it enters the chute
and u0 is the velocity at this point.
Also, for the direction perpendicular to a radius of curvature (i.e. along the
chute), the equation of motion for the elemental mass is
!5m g cos() - F 0
=
du
!5mdt
(2.15)
For this simplified model the drag force F 0 comprises only the wall friction
effect and therefore it can be written as
(2.16)
where 11E is an effective friction coefficient and F N is the normal force on the
element.
For a chute of rectangular cross-section, taking the pressure distribution to
be of the simple form shown in Figure 2.16a, an expression for f.1E is
JlE =
f.lw( 1 + k ~)
(2.17)
where f.lw is the coefficient of friction at the wall, k is the ratio of the lateral
pressure to the major normal pressure at the wall, B is the width of the chute
and H is the depth of the flowing bed.
Experimental work carried out by Roberts and others using a variety of
bulk materials showed that a more reliable model is obtained by replacing the
coefficient k with the expression
(2.18)
71
GRAVITY FLOW OF BULK SOLIDS
1--
8
H
H
(a) Rectangular cross·sect10n
Figure 2.16
(b) C1rcular cross-section
Distributions of pressure on the interior surfaces of chutes (Roberts' model).
where K Eo is the effective linear pressure gradient down the wall surface at zero
velocity and C is an 'intergranular stress constant'.
Noting also that H = (u 0 /u)H 0 , equation (2.17) becomes
(2.19)
If the chute is of circular cross-section a similar approach, based on the
pressure distribution shown in Figure 2.16b and supported by experimental
work, suggests that equation (2.19) can be used, with B equal to the diameter of
the chute and suitable values taken for the parameters kEo and C.
Now referring to Figure 2.15, the normal force on the flowing element of
bulk solid is given by
FN = bm(gsin8+
~)
(2.20)
and combining with equation (2.16) gives
F 0 =,uEbm(gsin8+
~)
(2.21)
Substituting for F 0 in equation (2.15) and rearranging leads to
~~ = g (COS 8 -
.UE Sin 8)
(2.22)
If .UE is taken to be constant (for example, at a value corresponding to the
average stream thickness along the chute) equation (2.22) can be solved for the
cases of straight inclined chutes (for which R = oo) and circularly curved
chutes (R =constant).
72
BULK SOLIDS HANDLING
Thus, for straight inclined chutes, noting that
du
du
dt
ds
-=U-
where s is the distance measured along the chute from the entry point,
equation (2.22) becomes
udu = g(cos (}- f-LE sin (J)ds
(2.23)
and integration then yields a velocity distribution as
u = [u6 + 2gs(cos (}- f.LEsin (})] 112
(2.24)
The solution of the corresponding equation for circularly curved chutes is
much more difficult, but Roberts and Scott [9] give
u=[ 2iR
4f.LE + l
{sin(J(l-2f.l~)+3f.LECOS(J}
+ exp(- 2f.LE(J) ( u6 -
6f.l Rg
1
4/-l~E+
)]112
(2.25)
Using equations (2.24) or (2.25) together with the continuity equation (2.14),
the variation of the stream thickness along the chute can be investigated.
Allowance can be made for the curvature (concave or convex) of the free
surface of the flowing stream by using an appropriate value of the surcharge
angle when developing expressions relating the depth H of the flowing bed to
its cross-sectional area.
For a chute of rectangular cross-section (Figure 2.17a) in which the
surcharge surface is parabolic, the cross-sectional area of the bed is given by
B
H
(a) Rectangular cro ss-section
(b] Circular cross-sectio n
Figure 2.17 Calculation of cross-sectional area of bulk solids stream in transfer chute.
GRAVITY FLOW OF BULK SOLIDS
73
and since
H 1 = H -Btan.?c
we have
A .?c-1
H=-+--Btan.?c
B
(2.26)
.le
In the case of a circular cross-section, again with a parabolic surcharge, the
cross-sectional area is
B2 [
A=4
tan~~.1
(1-cosc:)) + (c:5-sinc:5)]
3
2
(2.27)
where the angle c:) defines the contact perimeter. Also, an expression for the
depth of the bed is
(2.28)
The following general guidelines can then be given for the design of transfer
chutes in order to ensure stable 'fast' flow conditions.
(i) Identify the requirements in terms of direction and magnitude of the exit
velocity. (The overall cross-sectional dimensions of the chute (B and H 0 )
are likely to be dictated by the upstream feed arrangement, which would
also fix the bulk solid mass flowrate and therefore the entry velocity u 0 ).
(ii) Estimate, from equation (2.17) or (2.19), an average value of J.iE· Values of
the unknown parameters should be determined experimentally if possible,
but failing this, a preliminary assessment of chute performance may be
made with J.lw = 0.46 and k = 0.3 in equation (2.17).
(iii) (a) For a straight inclined chute, equation (2.24) is used to determine the
longitudinal velocity profile, and then equation (2.26) allows the variation
of the bed thickness to be determined.
(b) For a circularly curved chute the cut-off angle should normally be
designed to correspond to the optimum value for minimum thickness and
maximum velocity. The value, which is principally influenced by the
radius of curvature of the chute, the initial velocity of the bulk· solids
stream and the effective wall friction J.iE, can be determined from equation
(2.25) by setting the derivative dujde equal to zero and solving fore [12].
Typical data for the variation of cut-off angle and stream velocities at cutoff with radius of curvature, initial velocity and effective wall friction are
shown in Figure 2.18. As explained in section 2.4.3 the maximum cut-off
angle should not exceed the limiting slope angle Or which is given
approximately by ef =tan- l J.iE at exit.
Note that for a chute of circular cross-section it is recommended that
the flow is restricted to ensure that the chute fullness at any point in the
deceleration zone does not exceed half [9].
74
BULK SOLIDS HANDLING
~
en
Q)
Q)
60
60
0,
Q)
3
0
50
""'()
Q)
c;,
c
"'
40
?::;
()
E 30
:J
E
c.0
radius of curvature R (m)
initial velocity u0 (m/s)
(a) Optimum cut-off angle
~
en
~
0
()
:J
::= 2 .41---+---+-H'--I't.f---1------1
?
::;
()
E
E2.2
c.
0
o;
::-
2.0 1---+--H-H----+--j.....------1
·c::;
0
Qi
>
1. 8 0
1. 0
radius of curvature R (m)
1. 80!::--J-..L-L..L~--L...Ll+.l-1.--'-~--LJ.J
initial velocity u0 (m/s)
(b) Velocities at optimum cut-off
Figure 2.18 Charts showing typical optimum cut-off data for flow in circularly curved chutes
[12].
Typical predicted performance curves for straight inclined and circularlycurved chutes are illustrated as Figures 2.19 and 2.20.
2.5 Flow of bulk solids in vertical pipes
2.5.1 Introduction
Very little information is available on the flow of particulate bulk solids under
gravity through vertical pipes. It has been suggested [3] that dry material can
75
GRAVITY FLOW OF BULK SOLIDS
distance down chute, s (m)
Figure 2.19 Typical predicted performance curves for straight inclined chutes [12].
0.6
I
(/)
(/)
(])
ICD
~
(])
0.5
u
E
(])
--o
E <l>
eo-
<I>::::>
.:::{i
0.3
0.2
~\
I
m = 2.87
.............. f..,.
~~
I
----
!
Oco
0.1
10
20
I
30
40
50
position along chute,
§
a:
0.25
/ 0.5
0.75
_,--:::::;. ~ 1.0
'o,
I
(/)
0
I
tonnes/hour
u 0 = 0.315 m/s
flb; 1000 kg/m'
~
0.4
c-"'
:.c.~
I
"'~B 0 .651
60
70
80
(])
:;
(U
>
:;
u
0
(/)
::::>
'6
~
90
0 (degrees)
Figure 2.20 Typical predicted performance curves for circularly curved chutes of circular crosssection [9].
discharge from a filled open-ended vertical pipe two or three times faster than
through a circular aperture of the same size positioned in the centre of a flatbottomed bin. Consequently it would not be possible to obtain steady plug
flow through a vertical pipe fitted to the base of a flat-bottomed container
because the pipe could not be filled at a rate to match the potential maximum
outflow. Nevertheless, it seems likely that the discharge from a hopper or flatbottomed container could be increased by fitting a vertical stem to the outlet
76
BULK SOLIDS HANDLING
and evidence suggests that, especially with fine particulate materials, the rate
of discharge rises as the length of the stem is increased.
2.5.2 M ode of flow
Observations of a fine cohesionless bulk solid flowing under gravity in a
vertical tube show a number of quite distinctive features. Figure 2.21a
Figure 2.21 Gravity flow of a fine cohesionless bulk solid in a vertical pipe from a flat-bottomed
container [9].
77
GRAVITY FLOW OF BULK SOLIDS
illustrates the entry region to a vertical pipe from a flat-bottomed container.
Within the container the movement of the bulk material is likely to follow the
'tulip' pattern first reported by Brown and Hawksley [3], but once the
particles enter the discharge zone they are able to fall under gravity through
the orifice into the pipe as a smooth stream. The cross-section of this stream
initially decreases as it accelerates but, after a short distance, particles begin to
come into contact with the pipe wall and soon a condition of more or less stable
plug flow will be attained. At this point there may be observed what appear to
be 'bubbles' rising up the pipe through the downward flowing material. This
effect is probably due to 'free fall surfaces' developing within the flow.
The existence and motion of a free fall surface can be readily demonstrated
by filling vertical tube with fine sand, sealing the top end and allowing the sand
to discharge from the lower end (Figure 2.22). Immediately sand particles will
fall from the lower surface of the plug and as a result this 'free fall surface'
moves slowly upwards (Figure 2.22b). At the same time the whole plug of sand
begins to slide downwards, the upper free surface and the lower free surface
approaching each other until they meet (Figure 2.22d). This behaviour occurs
only because of the low-pressure region existing at the top of the pipe; any air
entering this region (for example if the closing seal is removed) will cause the
sand plug immediately to fall out of the pipe. It is thus evident that, where a
container discharges through a vertical pipe, the flow behaviour in the pipe
will be greatly influenced by interstitial air flows and therefore by the size and
density of the particles, the length and diameter of the pipe and the conditions
existing in the exit region of the feed container.
pipe filled
with sand
sand 'plug' moves
slowly down the pipe
(d)
(a)
'free-fall surface'
moves up the pipe
Figure 2.22 'Free-fall surface' in a cohesionless bulk solid discharging under gravity from a
vertical pipe.
78
BULK SOLIDS HANDLING
2Q)
E
ro
}19
u
Q)
o_
0.
}13
--~-
-___
-
--== . .
--
0.0 2 ~-~~~-[-~-ll~lllll!lll-1-ll-~-~-~-~-~-1-1
,_0.01-- -
~----=:
1.5
0.5
2
pipe length (m)
Figure 2.23 Experimental data for the flow of two different sizes of sand particles through
vertical pipes fitted to a flat-bottomed container [13]. Mean particle size of sand:--206 Jlm,
--- l12J1m.
Tests carried out at Thames Polytechnic [13] seem to confirm that the rate
of discharge from a circular aperture in the centre of a flat-bottomed bin can be
substantially increased if a vertical downpipe is fitted, the amount of the
increase being mainly a function of the length of the pipe and its diameter. The
effect is particularly marked for very fine free-flowing products in smalldiameter downpipes. Figure 2.23 shows, for example, the results for two
different sizes of fine sand discharging from a flat-bottomed container through
vertical pipes of various sizes and lengths.
It has been suggested, from observations of downward flow in relatively
large standpipes [14], that the maximum flow rate that can be attained will
depend upon the extent to which the flowing bulk solid can become
compacted. Aeration of the material needs to be undertaken with care in order
to reduce the chance of flow-obstructing 'pseudo-bridges' developing in the
standpipe.
Some measure of flow control can be exercised by allowing an influx of air
near the top of the vertical pipe, but a more effective method, allowing
79
GRAVITY FLOW OF BULK SOLIDS
complete shut-off of the flow, involves the use of a non-mechanical valve, such
as a 'J-valve' or 'L-valve' at the lower end of the pipe.
2.5.3 Flow control: ]-valves and L-valves
Essentially these types of so-called 'non-mechanical valve' rely on the natural
angle of response of a bulk solid which prevents it from flowing under gravity
past a bend, or a series of bends, in a pipe. Thus, an obstruction develops and
the flow stops (Figure 2.24a). In order to re-start the flow, air is introduced to
(a)
::. -_
~.-
air in
(b)
Figure 2.24 Non-mechanical valves (L-valve and J-valve) for the flow control of bulk solids in
vertical pipes.
(a) The valves in the 'closed' condition.
(b) The addition of air reduces the angle of repose of the bulk solid and effectively 'opens' the valve.
80
BULK SOLIDS HANDLING
the static material in the vicinity of the bend, reducing its angle of repose and so
permitting it to negotiate the bend. The flow of the bulk solid should then
continue smoothly until the air supply to the valve is stopped, and when this
occurs the bulk solid flow will also cease. It should be noted, however, that
whether the flow ceases initially or not will be very much dependent upon the
capacity of the bulk solid to retain air in its interstices and so maintain, for a
time, a 'fluid' state. A typical application of 1- or L-valves is to feed directly into
a dense-phase (fluidized-bed) environment, but they are also suitable for
feeding into a dilute-phase system such as a pneumatic conveying line or the
freeboard above a fluidized bed.
Much of the work on the development and performance of non-mechanical
valves has been undertaken by Knowlton and Hirsan [15, 16], who state that
the maximum flow rate obtainable is a function of the length of the vertical
downcomer above the L-valve or J-valve, and suggest techniques for
determining the length of downcomer needed in order to achieve a specified
flow rate.
Some insight to the operation of the device can be gained by recognizing
that, in a steady-flow condition in (for example) an L-valve, the pressure-drop
over the downcomer must be equal to the pressure in the L-valve plus that in
the outlet pipe since both the inlet to the system and the outlet are open to
L'::.p downcomer
Figure 2.25
Pressure-drops in an L-valve controlled system.
81
GRAVITY FLOW OF BULK SOLIDS
atmosphere (Figure 2.25). However, the pressure that can be sustained at the
bottom of the downcomer will be limited, its maximum value depending upon
the fluidization characteristics of the material in the downcomer. Up to this
maximum value the pressure-drop in the downcomer will adjust itself until it
exactly balances the pressure-drop in the L-valve and outlet pipe. Increasing
the air supply to the aeration point on the L-valve will tend to increase the
solids flow rate until either the limiting pressure in the downcomer is reached
or the maximum discharge rate into the top of the downcomer is reached. In
the latter case the flow in the downcomer becomes dilute and free-falling
occurs. Excessive aeration to the L-valve will result in 'bubbling' of the
material in the downcomer which, in extreme cases, can cause complete
stoppage of the flow~a situation known as 'gassing up'.
A design procedure, based on the work of Knowlton and Hirsan, can be
summarized as follows:
(i) Select a suitable horizontal length to stop the flow. In order to keep the
pressure-drop in the valve as low as possible, this length must be a
minimum, which can be calculated by simple trigonometry based on the
pipe diameter and the angle of repose of the bulk solid.
(ii) Using experimental data, or an appropriate correlation, estimate the
pressure-drop in the valve and outlet pipe at the desired solids flow rate.
(iii) Using fluidization data for the bulk solid, estimate the maximum
permissible pressure-drop per unit length in the downcomer (Ap/Llmax·
(iv) Calculate the minimum length of the downcomer from the expression
L . = Ap(L valve+ outlet
mm
(Ap/L)max
pipe)
(2.27)
(v) Determine from experimental tests the required flow rate of air to the
aeration tap, which should be positioned about 75-100 mm above the
centre line of the horizontal section of the valve.
2.6 Notation
A
Ao
B
c
Cross-section of flowing stream in chute
Cross-section of flowing stream in chute at entry
Width of channel
Constant of integration; 'intergranular stress constant' in
equation (2.18)
Diameter of storage container or pipe
Diameter of outlet (circular-section hoppers)
Width of outlet (rectangular-section hoppers)
Particle diameter
Drag force on element of bulk solids stream
82
m.
n
Pr
Pv
R
s
u
Uo
IX
f3
(j
e
BULK SOLIDS HANDLING
Normal force on element of bulk solids stream
Flow factor
Gravitational acceleration (specific gravitational force)
Depth of flowing bed in channel
Vertical distance
Coefficient in equation (2.12)
Hopper factor in equation (2.9)
Constant in equation (2.1); ratio of lateral to normal
pressure on an element in a flow bulk solids stream
Effective linear pressure gradient, normal to flow direction,
of flowing bulk solids stream
Hopper factor in equations (2.5), (2.6)
Particle shape factor in equations (2.5), (2.6)
Length of outlet (rectangular section hoppers)
Solids mass flow rate
Exponent in equation (2.10)
Lateral (radial) pressure
Vertical pressure
Radius of curvature of channel
Distance measured along chute
Velocity of flowing stream in chute
Velocity of solids; velocity of flowing stream at entry to chute
Angle of repose of a bulk solid
Angle of hopper wall to vertical (i.e. half-included angle)
Angle of arc of contact of bulk solids stream in channel
Angle of inclination of straight channel; radial angle
of curved (measured from horizontal)
Chute cut-off angle
Optimum value of chute cut-off angle
Limiting value of (Jc for 'fast flow'
Surcharge angle of bulk solids stream in channel
Effective friction coefficient
Viscosity of fluid
Coefficient of wall friction
Bulk density
Density of fluid
Angle of internal friction of a bulk solid
References and bibliography
References
1. Arnold, P.C., McLean, A.G., Roberts, A.W. (1979) Bulk Solids: Storage. Flow and Handling,
TUNRA Ltd, Univ. of Newcastle, New South Wales, Australia.
2. Jenike, A.W. (1964) Storage and Flow of Solids, Bull. No. 123, Utah Engg. Exp. Station, Univ.
of Utah.
GRAVITY FLOW OF BULK SOLIDS
83
3. Richards, J.C. ( 1966) 'Bulk solids in motion', in The Storage and Recovery o(Particulate Solids,
IChemE Working Party Report, Institution of Chemical Engineers, London.
4. Draft Code o( Practice for the Design of Silos, Bins, Bunkers and Hoppers, 2nd edn., British
Materials Handling Board (1985) edn.
5. Carleton, A.J. (1972) The effect of fluid drag forces on the discharge of free flowing solids from
hoppers. Powder Technol. 6, 91--96.
6. Williams, J.C. ( 1977) The rate of discharge of coarse granular materials from conical massflow hoppers. Chem. Engg. Sci. 32, 247-255.
7. Johanson, J.R. (1965) Method of calculating rate of discharge from hoppers and bins. Trans.
Min. Engrs AIME 232,69-80.
8. Zanker, A. (1975) Estimating the flow of solids through openings. Process Engg (July) 66-67.
9. Roberts, A.W. and Scott, O.J. ( 1981) Flow of bulk solids through transfer chutes of variable
geometry and profile. Bulk solids Handling 1 (4) 715-727.
I 0. Savage, S.B. ( 1979) Gravity flow of cohesion less granular materials in chutes and channels. J.
Fluid Mechanics 92 (I) 53-96.
11. Woodcock, C.R. and Mason, J.S. (1977) The flow characteristics of a fluidised PVC powder in an
inclined channel, in Proc. Int. Powder and Bulk Solids Handling and Processing Conf,
Chicago, May 1977, 466--475.
12. Roberts, A.W. and Arnold, P.C. (1971) Discharge-chute design for free-flowing granular
material. Trans. ASAE 14 (2), 304-308, 312.
13. Bishop, A.W. ( 1982) A study of the flow of bulk solids through vertical downpipes and the
effect of downpipes on the discharge rate of hoppers. Unpublished report, Thames
Polytechnic, London.
14. Dries, H.W.A. (1980) Packed-bed solids downflow in a cat. cracker standpipe: solids
compaction effects and flow instabilities, in Proc. Powder Europa Con{, Wiesbaden, January
1980.
15. Knowlton, T.M. and Hirsan, I. ( 1978) L-valves characterised for solids flow. Hydrocarbon
Processing 57, 149-156.
16. Knowlton, T.M. and Hirsan, I. (1980) The effect of system parameters on the operation of
dense-phase vertical lift lines and J-va1ves, in Proc. Pneumotransport 5, BHRA Con f., London,
1980, Paper E3.
Recommended further reading
Brown, R.L. and Richards, J.C. (1970) Principles o( Powder Mechanics, Pergamon, Oxford.
Arnold, P.C., McLean A.G. and Roberts, A.W. (1979) Bulk Solids: Storage, Flow and Handling,
TUNRA Ltd., Univ. of Newcastle, New South Wales, Australia.
3
Dynamics of fluid/solids systems
3.1 Introduction
In modern industry there is an increasing number of situations where
particulate and granular materials are handled in bulk, and there is a greater
awareness than ever before of the importance of safety and efficiency in
processing and handling such materials. Designers and plant operators,
perhaps schooled in traditional fluid mechanics involving only liquids and
gases, thus have a considerable task in understanding and predicting the
unfamiliar flow characteristics of bulk solids.
Chapter 2 dealt with the flow behaviour of dry bulk solids under gravity.
Although there is inevitably a considerable overlap, it is convenient to make a
distinction between gravity flow and the motion of two-phase (gas/solids or
liquid/solids) systems. In this chapter, therefore, attention is given to the
modelling of a number of readily identifiable flow situations involving the
relative motion of solid particles and fluids: flow through beds of fixed
particles, particles settling in fluids, fluidization and spouting, and finally twophase flow in pipes. Each of these is directly relevant to some practical
measuring, handling or processing operation involving particulate or granular
materials, and an attempt has been made to present the models in a way that
will be immediately useful to a practising engineer. The mathematics
underlying these models has been deliberately kept to the minimum consistent
with providing a satisfactory prediction of flow behaviour but, for students
and research workers who wish to attempt to unravel the mysteries of, for
example, pneumatic conveying, references are given to more specialized
works.
3.2 Flow through beds of fixed particles
3.2.1 Characteristics of flow in porous media
The flow of fluids through beds composed of stationary granular particles
frequently occurs in industry (especially the chemical industry) and in the
design of process plant there is often a need for the prediction of pressure drop
as a fluid flows through such a bed. Examples of fluid flow through fixed
particulate beds include catalysis and filtration. One method of determining
the specific surface of a fine particulate material involves an investigation of
the resistance of a fixed bed of the powder to fluid flow. Petroleum engineers
DYNAMICS OF FLUID/SOLIDS SYSTEMS
85
and civil engineers have an interest in the flow of water and oil through soils
and porous rock formations. The mechanical engineer might find himself
involved in any of these problems, and an awareness of the approach to
investigating fluid flow through porous media could often prove to be useful.
It could be suggested that the permeation of a fluid through a bed of packed
particles can be regarded either as an 'internal flow' of fluid in the
interconnecting channels between the particles, or as an 'external flow' around
the particles. The majority of authors writing on the subject have chosen to
regard permeation as an internal flow problem, probably because the
approach is then valid for both 'consolidated' porous media (solid materials
with holes) and 'unconsolidated' porous media (consisting of separate particles
packed together).
Various attempts have been made to develop theoretical and semi-empirical
formulae which would enable the pressure-drop across a fixed particulate bed
to be predicted. The work that seems to have achieved the greatest acceptance
is that of Carman [1] whose extensive study has more recently been
augmented by Ergun [2]. Upon their work is based much of the analytical
modelling subsequently proposed by various authors and leading to expressions for the pressure-drop across a fixed particulate bed in terms of the
properties of the flowing fluid and of the solid particles within the bed.
3.2.2 The prediction of pressure-drop across a fixed particulate bed
The principal variables influencing flow behaviour in packed beds are the rate
of fluid flow, the density and viscosity of the fluid, the closeness and orientation
of packing, and the size, shape and surface of the particles. The variables
concerning the packed solids are the voidage ~: 0 , and the size and shape of the
particles, which are conveniently characterized by the parameters volume
diameter dv and sphericity <Ps· The specific surface of the bed Sb can be
expressed in terms of the other parameters as
(3.1)
but note that this expression assumes that negligible surface area is lost due to
contact between the surfaces of particles in the bed.
In general, the particles in a bed would not be of uniform size. Although this
analysis is developed on the basis of monosized particles, the more usual case
of particles of similar shape but non-uniform size could be covered by the use
of a volume-surface mean diameter dvsm in place of dv.
For a cylindrical bed of solid particles (or a bed of any other uniform crosssection) the voidage, or porosity, can be written
D
86
BULK SOLIDS HANDLING
where A is the total cross-sectional area of the bed and Ae is the average
effective cross-sectional flow area of the voids.
If the total volumetric flow rate of fluid through the bed is V, the effective
mean axial component of velocity in the voids (called the 'interstitial velocity')
will be
v v1
u
u =-=-·-=e Ae A ~>o eo
where u is the mean approach velocity, or 'superficial velocity', of fluid.
Now the effective length le of a fluid path through the interstices of the bed
(the actual distance that the fluid travels) will be greater than the height of the
bed H. If the bed is modelled as a set of discrete flow passages, each oflength le,
the velocity of the fluid in them will necessarily be greater, and can be
expressed as
,
U =U
/e
U le
-=-·eH e0 H
(3.2)
Furthermore, if the flow in these passages is laminar, we can write an
expression for the pressure-drop based on the Poiseuille equation for laminar
flow in circular pipes, thus
(3.3)
where A is a hydraulic radius of the void passages, f.1 is the viscosity of the fluid
and k is a constant.
Now hydraulic radius is defined as
A=
flow area
wetted perimeter
and multiplying by the length of the void passages this could become
.
A=
volume of fluid in bed
wetted surface
---------:c------:c---
total volume of bed - volume of solid particles
wetted surface
That is,
,
eo
Sb
(3.4)
A=-
Substituting for u~, from equation (3.2), and for A in equation (3.3), we have
/e) (Sb)
e
Apb = kf.l ( -u ·- /e -
e0 H
0
2
DYNAMICS OF FLUID/SOLIDS SYSTEMS
87
and writing
this expression becomes
(3.5)
or
(3.6)
where sp is the specific surface of the particles within the bed.
Equations (3.5) and (3.6) are forms of the generally accepted CarmanKozeny equation for fluid flow in packed beds.
The quantity k' may be regarded as an empirical coefficient, the value of
which depends mainly upon the particle shape and size distribution. From
many practical investigations it has been found that k' normally lies within the
range 3.5-5.5.
It may be useful to eliminate Sb from equation (3.5) using equation (3.1).
Thus
or, writing k"
=
36 k',
(3.7)
Again, k" is an empirical coefficient whose value is normally about 130-200.
The value given by Ergun [2] from correlations of his own experimental data
and that of other researchers is 150.
The foregoing analysis is based on laminar flow through the bed, but as the
velocity of the fluid is increased the nature of the flow between the particles
changes gradually from laminar to turbulent. (Turbulence is likely to occur
initially in the larger channels, extending eventually to the smaller ones.) A
modelling approach will be therefore required to extend the validity of
equation (3.7) into the turbulent-flow regime.
An alternative approach leads to an expression for pressure-drop in terms of
the kinetic energy of the flowing fluid, which is thus analogous to the familiar
Darcy formula for head loss in closed conduits (see section 3.5).
A force balance across a bed of fixed particles gives
ApbAe = RbSb Vb = Rb(l - s 0 )Sp Vb
88
BULK SOLIDS HANDLING
where Rb is the resistance per unit area of the bed surface and Vb is the volume
of the bed.
Now Ae x (depth of bed)= volume of voids= e0 x (volume of bed)
0
• .
A =e 0
e
volume of bed eo vb
=-depth of bed
H
and thus
(3.8)
It is convenient now to define a 'friction coefficient' for the void passages, by
drawing an analogy between the wall shear stress in circular pipes and Rb for
the packed bed; thus
(3.9)
Now SP = 6/d.tf;, so that from equation (3.8)
!!pb
eo
d.tf;,
Rb=~·--·-H 1-e 0 6
and substituting for Rb and for
u~
(from equation 3.2) in equation (3.9) we get
kc=~· tf;,e6
3 1 - e0
(H)z!!Pb.
le
H
d.2
PrU
(3.1 0)
It might be expected that kc would be a function of a Reynolds number of the
form 4A.pru~/J.l, and such a Reynolds number can be derived by substituting for
)._and u~ from equations (3.4) and (3.2) and combining with equation (3.1) as
Re - 2. if;, . le . Prd.u
3 1- e0 H
J.1
b-----~-
(3.11)
For most practical examples of beds of fixed particles, it is found that the
ratio le/H is effectively constant and is usually dropped from the dimensionless Reynolds number and friction coefficient terms.
Thus, we have the definitions
Reb =
2 if;, Prd.u
3 1- e0 J.l
-·--·~-
(3.12)
and
(3.13)
DYNAMICS OF FLUID/SOLIDS SYSTEMS
89
Rearranging equation (3.13) we have
Ll
- 3k 1 Pb- r ,~,
Bo .PrHu2
3
d
'1-'sBo
(3.14)
v
and since this expression has been developed from a general analysis of the
flow through a packed bed, it should be applicable whether the flow is laminar
or turbulent, provided that an appropriate value of the coefficient kc is used.
For the case of laminar flow the pressure-drop can be expressed by the
Carman-Kozeny equation,
(3.7)
and an expression for kc can then be developed by combining the
equations (3.14) and (3.7) to eliminate Llpb/H.
Thus,
from which
1- £ 0 . J1
kr_- -1 k" -3
cf>s Pcdvu
(3.15)
As mentioned previously, a typical value of k" for many real particulate or
porous beds would be about 150, giving
kr-- 100
3Reb
(3.16)
As might be expected, for highly turbulent flow the value of kc tends to
become constant (the pressure-drop becoming proportional to u2 ) and an
empirical relationship has been proposed by Ergun [2] which seems to
correlate with available experimental data quite well:
100
kc =3-Reb
+ 0.58
(3.17)
This expression is shown in Figure 3.1, plotted to a log-log scale indicating
that the transition from laminar to turbulent flow in the packed bed
occurs over a range of values of Reb given approximately by 10 < Reb <
1000.
Substituting equation (3.17) into equation (3.14), we get a general equation
90
BULK SOLIDS HANDLING
I"
kt = 100
3 Reb
~
""
10
0.58
~
""
~
-,
' ::-::-'
0.1
0.1
+
10
Reb
Figure 3.1 Dimensionless plot of friction coefficient, k,, against Reynolds number, Reb, for flow
through a packed bed, as defined by equations (3.13) and (3.12). After Ergun [2].
for pressure drop as
!!pb = 1- ~ 0 . PrU 2 ( 100
H
rP.E~o
dv
Reb
+ 1. 75 )
(3.18)
which on expanding becomes the full Ergun equation
+ 1 751- Eo .PrUz
----
!!pb = 150(1- £o)2 .f.1U
H
r/J;~:6
a;
viscous effect
. r/J.e6 dv
________.....
(3.19)
kinetic energy effect
It will be noted that this expression represents the pressure-drop as the sum
of the viscous effect (as modelled by the Carman~Kozeny equation) and the
kinetic energy effect.
As mentioned previously, the pressure-drop across a bed of particles of nonuniform size could be predicted with this equation ifthe volume diameter dv is
replaced by the volume-surface mean diameter dvsm·
One of the major difficulties in the prediction of pressure-drops in flow
through particulate beds is the variability of the voidage with particle size,
shape, packing arrangement and, possibly, surface texture. Variation of
density in gas flow also causes difficulties in the analysis. The Ergun equation
DYNAMICS OF FLUID/SOLIDS SYSTEMS
91
(equation 3.19) is just one of many correlating expressions that have been
proposed. In most, if not all, of these expressions information is required on the
sphericity </J. and the voidage e0 of the particulate bed. If this information is not
available for the material concerned, it must be determined experimentally or
estimated. For fine particles the voidage is most easily determined from a
knowledge of the particle density and the bulk density:
1 - Pb
(3.20)
Pp
but for large particles it should be noted that the effective voidage may be
considerably higher than the value determined in this way in situations where
the average diameter of the particles is more than a few percent ofthe diameter
of the containing vessel. The reason for this is, of course, the relatively large
interstices adjacent to the wall of the vessel.
The determination of sphericity is more difficult and the reader is referred to
Chapter 1 for further information.
B0
=
3.3 Settling behaviour of particles
There are many processes of industrial relevance in which solid particles are in
relative motion within a fluid environment and settling or sedimentation is one
of the most important. In this section some of the simplest analytical models of
sedimentation are introduced in order that the rates at which particles of
specified characteristics would settle in a fluid can be predicted. It should be
noted that most of the models available actually relate to a single particle in
an infinite expanse of fluid and thus ignore the possible influence of other
particles or nearby containing walls. In situations where the concentration of
particles is fairly low such effects are likely to be minimal and the 'single
particle models' should give a reasonable estimate of the settling velocity.
However, at high levels of solids concentration the motion of any particle will
inevitably be influenced by the presence of others, and the condition known as
'hindered settling' exists, in which the settling rates may be significantly
reduced.
3.3.1 Motion of a spherical particle settling in a stationary fluid
At any instant, following its release from rest, a particle falling under gravity in
a stationary fluid will be acted upon by three forces (Figure 3.2). These are the
gravitational force, F G (=mass of particle x g); the buoyancy force or
upthrust, F u (=mass of displaced fluid x g); and the drag force, F 0 .
The general equation of motion can then be written as
du
F G - F u - F 0 = mP dt
(3.21)
where
mP
is the mass of the particle and du/dt is its acceleration.
92
BULK SOLIDS HANDLING
Figure 3.2
Forces on a falling particle.
Provided that the particle is completely surrounded by the fluid, the gravity
force and the buoyancy force will remain constant, but the drag force F 0 will
change, increasing as the particle accelerates from rest. It is clear from
equation (3.21) that as F 0 increases the acceleration of the particle will
decrease until a condition is achieved in which the net downward force on the
particle (Fa- F u) is exactly balanced by the drag force F 0 . The acceleration of
the particle will then be zero and the steady velocity so reached is called its
'terminal velocity' or 'free-fall velocity'. Although for large objects, and for
smaller bodies of extremely low density, the time taken to reach terminal
velocity may be significant, in the majority of situations involving particulate
materials the acceleration period is virtually zero and for most models of
settling behaviour it is ignored.
For a particle falling at its terminal (steady) velocity, the drag force can be
expressed as
Fo=Fa-Fv
(3.22)
and if the particle is spherical with diameter d and density pP
(3.23)
where Pr is the density of the surrounding fluid.
It is convenient to express the drag on a settling particle in terms of its
velocity, and dimensional analysis can be used to set up an appropriate
equation in the form
F o = C 0 Ap!PrU 2
(3.24)
where AP is the projected area of the particle (which for a sphere is nd 2 /4)
and C 0 is a 'drag coefficient'. The dimensional analysis will have shown that C 0
is a function of the particle Reynolds number, defined by ReP= udjv, where v
is the kinematic viscosity of the surrounding fluid. The form of the relationship between these two dimensionless parameters has been the subject of
much experimental investigation.
Combining equations (3.23) and (3.24) and rearranging leads to an
DYNAMICS OF FLUID/SOLIDS SYSTEMS
93
expression for the terminal velocity of a spherical particle settling in a fluid as
_ [4gd(pp- Pr)J 112
Ut-
3prCD
(3.25)
Clearly the usefulness of this expression for the prediction of settling rates
depends upon a knowledge of the drag coefficient C0 . Where the particles are
very fine, and especially if the viscosity ofthe fluid is relatively high, the motion
of the particle will be predominantly influenced by viscous effects. Under these
conditions the drag force on the particle is conveniently modelled by Stokes's
law as
F0
=
3ndprvu
(3.26)
and combining equations (3.24) and (3.26) then leads to
24
Co=ReP
(3.27)
Substitution for C 0 in equation (3.25) yields the expression
Ut=
gd 2 (Pp- Pr)
18pr v
(3.28)
which gives an accurate indication of the terminal velocity of a fine spherical
particle settling under gravity in a viscous fluid. The error in this predicted
value of ut increases as the particle Reynolds number ReP increases and inertial
effects begin to be significant. This is illustrated in a dimensionless plot of C 0
against ReP (Figure 3.3) which shows the result of experimental investigations
covering a full range of flow conditions involving spheres moving in
incompressible fluids. It is unlikely that Reynolds numbers above 10 5 would
be encountered in practical bulk solids handling situations, but this is still
much greater than the range of validity of Stokes's law, corresponding to the
straight line C 0 = 24/ReP shown in Figure 3.3. The usually accepted limit for
Stokes's law in ReP= 0.2 which, for example, would be the value for a 60 J.lm
diameter grain of sand settling in water or a 30 11m grain settling in air, and
would give an error of about 5% in the predicted value of terminal velocity.
The form of the full relationship between C 0 and ReP for spheres is not easily
modelled mathematically, and the usual approach is to adopt one of a number
of expressions each covering a range of values of ReP (Figure 3.4). For
ReP< 1000, the Schiller and Naumann model
C 0 = 24 (1
ReP
+ 0.15Re~· 687 )
(3.29)
seems to be generally preferred, although it does suffer from the disadvantage
that it cannot be used to derive an explicit expression for the terminal
velocity ut.
94
BULK SOLIDS HANDLING
1\
0
102
I'\
(.)
1'\
c:ii
-o"'
0
c
Ql
~t\.
10
Stokes law .,.
c 0 =24Rep 1 '
"()
~0
(.)
~"'-t-...
-1-0.01
0.1
10
Reynolds number, Rep
Figure 3.3 Dimensionless plot, from experimental data, of drag coefficient against Reynolds
number for spheres moving in incompressible fluids.
~
~
~
Stokes law
c0 =24 Rep-1
~ VCD = _g±_(1 +0.15Rep ·
~' Rep
0 687)
',
'~
-o 6
/Co=18.5Rep ·
0.01
0.1
'
c 0 =0.44
/
~' ............
'
....
10
Reynolds number, Rep
Figure 3.4 Some mathematical models of the relationship between C 0 and ReP.
DYNAMICS OF FLUID/SOLIDS SYSTEMS
95
From the set of equations
C 0 -- 24
ReP
tor ReP < 0 .2
(3.30)
l'
Co=~
Re 0 · 6
for0.2 <ReP< 500
(3.31)
for 500 < ReP < 2 x 10 5
(3.32)
p
and
C0 = 0.44
the following expressions for terminal velocity can be derived having, of
course, the same ranges of validity:
ut=
gd2(pp-pf)
18 PrV
l'
d1.14[g(pp-Pr)J0.71
_
ut - 0.153 043
v ·
Pc
ut= 1.73 [
(3.33)
tor ReP< 0.2
dg(p - Pr)
~r
Jo.5
for 0.2 < ReP < 500
for 500 <ReP< 2 x 10 5
(3.34)
(3.35)
In order to use the above approach it is necessary first to estimate the
particle Reynolds number ReP in order to determine which of the equations is
the more appropriate. Since the terminal velocity ut appears in the Reynolds
number as well as in the drag coefficient, the method becomes somewhat
inconvenient, and this has resulted in the development of an alternative
technique involving plots of ReP against C 0 Re; and C0 /ReP. The significance
of these combinations of dimensionless parameters is that
3
C R 2 _ 4d g(pp- Pr)
o eP3 2
PrV
(3.36)
which is independent of the terminal velocity and
C0
4g(pp- Pr)v
ReP=
3pru~
(3.37)
which is independent of the particle diameter.
The chart (Figure 3.5) thus allows the terminal velocity to be determined for
a spherical particle of known size, or the size of a particle to be estimated when
its terminal velocity is known.
3.3.2 The settling of non-spherical particles
Where the terminal velocity of a non-spherical particle is known, as for
example in the results of a sedimentation analysis, the equations given in the
96
BULK SOLIDS HANDLING
\
\
1\
/
I\
\
V
\
\.
eo
/
V
10
/
1
0.1
V
/
10
V
Rep
/
I\. V
/V
;/
/
/
1\
c 0 Rep2
/
/
a.
()Cll a:Q)
1\
\
/
V
'\
"'\
'\
V
'\
\
'\
'\.
"'
'\
0.4
4
10
Reynolds number, Rep
40
100
10-3
400
Figure 3.5 Chart for the determination of terminal velocities of spherical particles of known
diameter, or the diameter of particles settling at a known velocity.
previous section can be used to determine an 'equivalent diameter' of the
particle. In the case of fine particles settling in a viscous fluid this approach
would yield the so-called Stokes diameter, which is defined as the diameter of a
spherical particle of the same density as the measured particle and which
would settle at the same terminal velocity in the same fluid.
Comparatively little has been published on the terminal velocities of nonspherical particles, and virtually nothing on such particles falling in air. The
main work on the subject is probably that of Pettyjohn and Christiansen [3].
Their extensive experimental study dealt only with isometric particles having
cfJ. > 0.67, but covering a wide range of particle size and density, and resulted in
the suggestion that in the laminar flow region the terminal velocity could be
97
DYNAMICS OF FLUID/SOLIDS SYSTEMS
given by multiplying the value for spherical particles by a factor K, where
K,
0.366loge
=
o.b~s
(3.38)
Some caution should be exercised when applying this result to particles
settling in gases, since Pettyjohn and Christiansen worked only with liquids,
and also there is likely to have been a significant wall effect. At Reynolds
numbers above about 2, orientation effects may be significant and the
influence of sphericity predicted by equation (3.38) appears to become
increasingly unreliable.
A proposal by Hawksley [4] was that the C 0 v. ReP relationship for
spherical particles could be used for irregularly shaped particles provided that
C 0 and ReP are redefined as follows:
C' = cp 4gd(pp- Pr)
D
(3.39)
3prU~
s
and
1
du,
#.
(3.40)
Re'=--·P
V
The scarcity of recent experimental data on terminal velocities of irregular
particles, especially in gases, is very evident, but the chart reproduced as
Figure 3.6, based on Hawksley's approach using equations (3.39) and (3.40)
gives some indication of the behaviour of non-spherical particles.
I .1.
sphenctty, 4> 5
105
Q)
Cl
(.)
<
103
c:
~
o/
/. ~V
/;~
102
//. ~
en
Q)
~~
y ~
/:::
I:?P
"0
Q)
E
:<:(.) 10
<
v~
~ ... ....:"""~
~y
~
/,
Gi
::J
--;~
~
1.~~~y
.0
E
/
o.~~LL
104
<'>IV
-!!..
//:
o.i~V/' ;?"'"
0.4
0.6
C\Jo.
a:
/'
I
...._~
~,::.P~
0.1
0.2
0.5
2
5
10
20
50
100
200
Reynolds number, Rep
Figure 3.6 Terminal velocity correlation for non-spherical particles [ 4].
500
98
BULK SOLIDS HANDLING
3.3.3 The settling of concentrations of particles (hindered settling)
Where a concentration of particles is settling in a stationary fluid It IS
inevitable that the motion of any individual particle will be affected by its near
neighbours. The terminal velocity of the particle, as previously defined, will be
reduced to an extent that it is a function of the voidage fraction of the
suspension. In spite of the different conditions, it is not unreasonable to
suggest that the models for free settling could be applied if suitably modified to
take account of the lower actual settling velocities that would normally occur.
Thus, writing the density of the suspension as p its apparent kinematic
viscosity as v., and the reduced settling velocity as u" the coefficient of drag and
the Reynolds number become
5,
C _ 4gd(pp - Ps}
0 3psu?
(3.41)
and
usd
Re=P
Vs
(3.42)
Most of the experimental investigations into hindered settling seem to have
been concerned particularly with the change in sedimentation rate that occurs,
and the relationship between this change (decrease or increase) and the
voidage of the suspension. Alien [5] gives a detailed discussion of concentration effects, but a typical form [ 6] of the correlation for settling velocity
IS
(3.43)
where ~>s is the voidage of the suspension and n is an index which is a function of
ReP and has a value of 4.65 for ReP < 0.2.
3.3.4 Classification and sorting of particles
Reference has been made in Chapter 1 to the use of the sedimentation
technique, and also of elutriation, in the determination of the size distribution
of a particulate bulk solid. Clearly these methods could be adapted to provide
a means of classifying particles by size, or sorting them by density. If the
particles are introduced into an upward-flowing fluid, those for which the
terminal velocity is identical to the velocity of the fluid should be held
stationary whilst larger (or more dense) particles will fall and smaller (lighter)
particles will rise.
Adjusting the fluid velocity to a suitable value can thus allow, for example,
two different minerals to be 'un-mixed'. The major practical difficulty lies in
ensuring that the velocity of the upward-flowing fluid is reasonably uniform,
but if this can be achieved it is possible to separate particles that are quite close
99
DYNAMICS OF FLUID/SOLIDS SYSTEMS
bulk solid A
bulk solid B
a;
(ij
()
(/)
"'
0
v
-
:::J
particle diameter, d (log scale)
Figure 3.7
Separation of two bulk solids from a mixture using an upward-flowing fluid stream.
in size and/or density. Figure 3. 7 illustrates the relationship between terminal
velocity and particle size for two bulk solids, denoted A and B, the material A
having the higher value of density. If a mixture of these two materials is being
sorted in a fluid stream having a uniform velocity u, all particles of material A
having diameter greater than dA will fall whilst those of material B with
diameter less than d 8 will rise. Thus, for satisfactory separation into two pure
fractions it would be necessary to prepare the mixture so that all the particles
are between the size limits dA and d 8 . In order to sort materials A and B having
particle sizes outside this range, it would be necessary to increase or decrease
the velocity of the upward-flowing fluid, or to use a fluid of higher or lower
density.
3.4 Fluidization
3.4.1 The fluidization process
As described in section 3.2, if a fluid is passed upwards through a supported
bed of solid particles or granules at a relatively low flow rate, it will merely
filter through the interstitial voids without disturbing the packing arrangement of the bed. As the superficial velocity (that is, the volume flow rate per
unit cross-sectional area of the fluidizing vessel when empty) of the fluid
upwards through the stationary bed is gradually increased, the pressure-drop
across the bed increases (Figure 3.8a). For a given bed, the pressure-drop
across it would depend only on the flow rate of the fluid, in most cases the
100
BULK SOLIDS HANDLING
transition
''"' bod
"''m~ I
fluidized bed regime
;-~--~------~~-----
~
c:0
-o
Ql
3
"'"'
~
c.
Umf
superficial gas velocity
(a) The varia lion of pressure drop across the bed
'-~
(b) 'Fixed' bed
t
(cl Incipient fluidization
,_~
t
(d) Bubbling bed
Figure 3.8 The fluidization behaviour of an 'idealized' bed of uniformly-sized spherical particles.
relationship being approximately proportional. This system is termed a 'fixed'
or 'packed' bed (Figure 3.8b), and corresponds to the case discussed in
section 3.2.
As the superficial velocity continues slowly to increase, a stage will be
reached at which the pressure-drop approaches the magnitude of the
downward gravity force per unit cross-sectional area of the bed of particles. If
the bed is not restrained on its upper surface, there will be a slight expansion of
DYNAMICS OF FLUID/SOLIDS SYSTEMS
101
the bed accompanied by a rearrangement of the particles as each one tends to
'float' separately in the upward flow of fluid. This rearrangement brings the
particles towards a state corresponding to the loosest possible packing in the
bed, which is now on the point of becoming 'fluidized'. Further increase in
the superficial velocity of the fluidizing agent will cause little, if any, change
in the pressure-drop across the bed, but will cause the bed to expand, thus
allowing additional spaces between the particles through which the fluid can
pass (Figure 3.8c). At still greater superficial velocities the excess fluid tends to
pass through the bed as a series of voids or bubbles (Figure 3.8d) until
eventually a stage is reached where the interstitial velocity of the upward
flowing fluid approaches the terminal velocity of individual solid particles.
These particles then tend to become entrained in the flow, being carried
upwards from the surface of the bed, and the system approaches a condition
equivalent to that of pneumatic transport.
At the point where the individual particles or granules first become
buoyantly supported in the flow the bed is said to be in a condition of
'incipient' or 'minimum' fluidization. In this condition the bed exhibits many
fluid-like characteristics; for example, it will flow from a hole in the side of the
containing vessel, light objects can be 'floated' on its surface whereas heavier
objects will sink, and the surface will remain horizontal if the vessel is tilted.
The fluidization technique has found widespread acceptance in industry as a
means of ensuring continuous contacting between a particulate or granular
solid and a stream of gas or liquid, one of the first applications being for the
gasification of powdered coal. Fuel requirements in World War II provided
the impetus for a rapid development in the petroleum industry of the fluid
catalytic cracking process, and the knowledge gained during such development, combined with the results of technological research, led to a considerable improvement in the understanding of fluidized-bed behaviour. Many
other processes making use of the advantageous properties of fluidized beds
have been developed in industry, including drying, mixing, plastic coating,
fluidized combustion and bulk solids transport. For a review of some of these
applications see, for example, [7].
The onset of fluidization is conventionally illustrated on a plot of the
pressure-drop across the bed against the superficial velocity of the fluidizing
agent, and for an 'ideal' bed of uniformly sized spherical particles the
relationship between the pressure drop Ap and the superficial velocity u might
be expected to follow linear paths as shown in Figure 3.8a. Note that at a given
superficial velocity the pressure-drop across the bed may be significantly
different when increasing the flow from zero than when decreasing from a
fluidized state, because of the looser packing of the particles in the latter case.
The 'minimum fluidizing velocity', umr• is defined as the point at which the bed
of particles becomes fully supported, from this loosest packing arrangement.
Particulate bulk solids that might typically be encountered in industrial
situations generally do not behave in this idealized manner, but may show a
102
BULK SOLIDS HANDLING
"--~
[a) Incomplete fluidization
caused by non-uniform
air distribution
'-~
t
,_~
(c) Intermediate channelling
Figure 3.9
t
(b) Channelling, resulting
from poor air distribution
or cohesive powder
[d) Slugging
t
Behaviour of poorly-fluidized beds.
variety of characteristics depending upon factors such as particle size and size
distribution, particle shape, degree of cohesiveness, and so on. Some kinds of
'imperfect fluidization' are illustrated in Figure 3.9 including partial fluidization, where a portion of the bed remains unfluidized (Figure 3.9a), channelling (Figure 3.9b), intermediate channelling (Figure 3.9c) and slugging
(Figure 3.9d). The type of plot that might be obtained of pressure-drop against
superficial velocity in each of these cases is shown in Figure 3.1 0. Note that
Figure 3.10 f represents the form of plot that would usually be obtained with
materials that fluidize reasonably well, the length of the smooth curve joining
the 'packed-bed' and 'fluidized-bed' regimes depending largely upon the range
103
DYNAMICS OF FLUID/SOLIDS SYSTEMS
L:.p
17
L:.p
:;
"ml
u
(a)
L:.p
u
(b)
L:.p
u
(cl
/
L:.p
u
(d)
/
L:.p
I
I
I
I
I
I
I
(e)
u
Ufs
:/
(f)
u
Figure 3.10 Pressure variation in fluidized beds. (a) Ideally fluidizing materials; (h) materials
exhibiting moderate channelling; (c), (d) more severely channelling materials; (e) cohesive
materials exhibiting 'slugging' behaviour; (f) materials having wide size distribution.
of particle sizes present in the material. Where the particle size distribution is
very wide, or where the material consists essentially of a mixture of two or
three powders of relatively uniform size, segregation may occur as a result of
the finer particles becoming fluidized before the coarser ones. Such behaviour
can cause several peaks to occur on the plot of pressure-drop against
superficial velocity.
104
BULK SOLIDS HANDLING
3.4.2 The prediction of minimum fluidizing velocity
Many different correlations have been proposed to enable the minimum
fluidizing velocity for a given bulk solid to be predicted. None of these is
entirely satisfactory since there are a number of variables, such as particle
shape and size distribution, and (especially with very fine particles) interparticle forces that are virtually impossible to take adequately into account.
Perhaps it could be said that as direct measurement of umc for a given sample of
bulk solid is not usually difficult, there is little need to be excessively concerned
with methods of predicting it. Nevertheless, a quick indication of a probable
value of umc is often useful and a considerable amount of energy has been
expended by a number of workers in searching for a reliable correlation.
Figure 3.8c illustrates the bulk solid in the condition described as 'incipient
fluidization': the bed of particles is in an expanded state with each particle
notionally 'floating' in the fluid stream and separate from its fellows. A
particulate solid in this fluidized state exhibits a number of fluid-like
characteristics including, for example, the ability to flow through a hole in a
retaining wall. Naturally, the tendency for a bulk solid when aerated to flow in
the manner of a fluid has resulted in the widespread use of aeration as a 'flow
aid', for example, to assist 'difficult' materials to discharge from hoppers. An
interesting refinement of this technique is the continuous aeration of a bulk
solid in an inclined channel which allows the material to 'flow' steadily along
the channel even when its slope is as little as two or three degrees, as described
in Chapter 15.
The behaviour of a bulk solid in various flow situations is strongly
dependent upon what may loosely be called the 'nature' of the material.
Fluidization is one such flow situation, and the 'quality' of fluidization
obtainable, or indeed, whether the fluidized state can be achieved at all, is
dependent on several characteristics of the bulk solid, notably particle size and
density, and cohesiveness. In the following section the phenomenon of
fluidization is modelled as a bed of monosized spherical particles subjected to
an upward flow of fluid. In this way correlations are introduced to allow
prediction of the lowest fluid velocity required to ensure that a material
becomes fluidized, i.e. the so-called 'minimum fluidizing velocity'.
One of the simplest approaches involves extending the model for fluid flow
through a bed of fixed particles, considered in section 3.2, by allowing the fluid
flow rate to increase to the point where the bed becomes fluidized. When this
condition has just been attained, the bed of solid particles will be fully
supported by the upward-flowing fluid, and the total gravity force can then be
expressed as
Wb =(pp- Pc)gAH(1- c)
(3.44)
where pP and Pc are the densities of the solid particles and of the fluidizing
medium respectively, A is the cross-sectional area of the fluidized bed, and H
and B are the depth and voidage of the bed.
105
DYNAMICS OF FLUID/SOLIDS SYSTEMS
The term H(l -e) remains constant irrespective of the expansion of the bed,
so that the equation can be written in terms of the conditions at the onset of
fluidization as
(3.45)
If the gravity force per unit area of the fully supported bed is regarded as
being balanced by the pressure drop across the bed, that is, without any
supporting contribution from either the distributor surface or the walls of the
vessel, we can write
(3.46)
At the condition where the bed is on the point of becoming fluidized it is not
unreasonable to suppose that the expressions developed for flow through a
packed bed might still be valid. Thus !lpb could be expressed in terms of one of
the correlations developed in section 3.2.
For example, using the Ergun model, we have from equation (3.19)
(3.4 7)
Combining with equation (3.46) and rearranging, we get
Pr(Pp- Pr)gd; = 150 ( 1 - Emr)Prdvumf
112
</J; E~r
J1
+ 1.
75 (~1
3 )
</J,Emr
(Prdvumf )
J1
2
(3.48)
Now the left-hand side of this equation is a form of Archimedes number for
the bed:
A rb
=
Pr(Pp - Pr)gd;
J1
2
(3.49)
and the right-hand side is a function of the bed Reynolds number at the
minimum fluidization condition:
Prdvumf
Remr=--/1
(3.50)
Thus equation (3.48) can be simplified to a relationship between these two
dimensionless parameters as
(3.51)
106
BULK SOLIDS HANDLING
This expression tends to be inconvenient to use in this form because of the
shortage of readily available information relating to the sphericity 4J. and the
voidage Bmr· However, Wen and Yu [8] have pointed out that smr increases as
4J. decreases, and also smr is nearly independent of the particle diameter, and
they go on to show that available experimental data correlates reasonably well
with the expressions
(3.52)
and
(3.53)
It has subsequently been suggested that this approach is not entirely
satisfactory [9]; nevertheless, substitution of these values into equation (3.51)
does lead to a very convenient correlation between the Archimedes and
Reynolds numbers for the bed at the minimum fluidizing condition.
Thus
Re~r + 67.3Remr- 0.0408Arb = 0
(3.54)
For approximately spherical particles, Richardson [9] suggests a value of
0.4 for Bmr and arrives at a similar expression relating Remr and Arb as
Re~r
+ 51.4Remr- 0.0366Arb =
0
(3.55)
In order to apply this correlation to non-spherical particles, Richardson
comments that the 'diameter' used must be that of a sphere with the same
specific surface as the particles, that is, 4J.dv. This means effectively multiplying
the Archimedes and Reynolds numbers for spherical particles by 4J; and 4J.
respectively, so that, for example, equation (3.55) would become
(3.56)
However, this appears to result in a very considerable underestimate of Umr
for non-spherical particles.
It is clearly not easy to predict the behaviour at incipient fluidization of
irregular particles. A decrease in the sphericity of an isolated particle would
cause an increase in the drag exerted on it at a given velocity. However, in a bed
of particles a decrease in sphericity would normally be accompanied by an
increase in the bed voidage, which in turn would cause a reduction in the
interstitial velocity. The effects might be expected to oppose each other to
some extent so that particles of the same size and density should in general
become fluidized at around the same value of superficial fluid velocity. There is
thus good justification in using a correlation, such as equation (3.54) or (3.55),
that is independent of 4ls and smr·
107
DYNAMICS OF FLUID/SOLIDS SYSTEMS
~
.,,,~
t-
.....,..,
t-
~ '7/
~-
't-
~/. /
~/. / /
t-
r10
entrainment
r-
~/ /
A~//
-
Q)
a:
'E
A~'
~-,/
'/ / /
r-
ci
.Q
:::J
c 10- 1
<J)
"0
~/.
///,//
-
I!
'/.~~
0
c
>-
Q)
a:
//'
6 //
~'l-,. /
t-
E
/
/
~/ /
tt-
a:
//
~-/ /
r-
Q)
~~
~'/
t-
c.
le'///
_,1 -;.-//
10- 2 '/ /
~
-
f-
r-
~//
'// /
~/
/V
/
V
/
14
/
,.. .
/
/
/
""(. 'o.6
7
/
V
I
..
. ..
m1mmum
flu1d1zat1on
10 3
V
f-
4
f-
f-
I I
I
I
I I
I
I
I I
I
I
I I
10
Archimedes number, Ar
Figure 3.11 Correlations of Reynolds number against Archimedes number for isolated particles
at terminal velocity, and for a bed of particles at a condition of minimum fluidization.
An empirical correlation rather similar to these two, but which is perhaps a
little more reliable, has been proposed by Baeyens and Geldart [10] as
Arb = 1823Re~r
+ 21.7Re!r
(3.57)
This expression is shown in Figure 3.11 as a plot of Remr against Arb, and
whilst some caution should be exercised because of the unreliable correlation
between cp, and Emr• a fairly quick assessment of the minimum fluidizing
108
BULK SOLIDS HANDLING
velocity of a material may be made from this graph by first calculating Ar b' and
then reading off a value of Remr and from this estimating umr·
The foregoing analysis is a general one, endeavouring to cover the whole
range of flow behaviour from laminar through transitional to turbulent.
However, at normal atmospheric pressures and temperature the fluid flow
through a bed of solid particles tends to be laminar for particles having
diameters less than about 500 ,urn. For such relatively fine particles, viscous
effects predominate and the expressions for minimum fluidizing velocity can
therefore be simplified by ignoring the kinetic energy term.
Thus, for example equation (3.47) reduces to
(3.58)
and combining with equation (3.46) gives
a;
</J;c~r Pp-Pr g
Umr=-·---·---·150 1 - Emr
Pr
V
(3.59)
Following Wen and Yu [8] in eliminating </J. and Emr using equation (3.52),
we find
- 61
Umr-.
X
to-4d;g
Pp- Pr
---V
Pr
(3.60)
The same form of equation is easily derived from Stokes's Law for the drag
force on an isolated particle in a laminar flow region, writing k as the ratio of
the drag force on a single particle in a packed array to the drag force on a single
isolated particle, so that
(3.61)
which on rearranging gives
(3.62)
Comparison with equation (3.60) suggests that the value of k would be
around 90.
Recent experimental work suggests that the numerical constant in
equation (3.60) is too low and a better prediction of minimum fluidizing
velocity is given by
Umr = 8
X
10_4d;g .PP- Pr
V
Pr
(3.63)
although in general this form of equation is inclined to overestimate umr for
DYNAMICS OF FLUID/SOLIDS SYSTEMS
109
bulk solids having a very fine particle size, and to underestimate umc for coarser
materials.
For fluidization with air at normal ambient pressure and temperature, /1 can
be taken into the numerical constant along with g, and noting that Pc« pP, the
expression becomes
(3.64)
A value of C' of 420 seems to give the most reliable prediction of umc for a
range of different powders from around 50 Jlm to around 500 Jlm.
Thus
(3.65)
giving umc in m/s with pP in kg/m 3 and din metres, and this expression serves as
a useful rule of thumb to estimate minimum fluidizing velocity.
3.4.3 Entrainment of particles from a fluidized bed
Where the upward velocity of a gas through a fluidized bed exceeds the
terminal velocity of the particles (that is, the velocity of free fall of the particles
in the gas) it is likely that these particles will tend to become entrained in the
gas stream leaving the surface of the bed. In order to predict the occurrence of
entrainment it is therefore helpful to be able to estimate the terminal velocity of
the particles, and modelling techniques for this purpose have been discussed in
section 3.3.
The curves shown in Figure 3.11 for predicting the entrainment of particles
from the free surface of a fluidized bed are plotted from the equation
0 344
_ 18ReP [
ArrPs 1 + 0.15 (Re~)
rPs · ]
J
(3.66)
which is derived by combining equations (3.29), (3.36), (3.39) and (3.40), noting
that Ar = ~C 0 Re~.
Although it may happen that entrainment of particles from the bed surface
does not become significant until the bed is fluidized at velocities well in excess
of the terminal velocity of a single particle, at higher velocities the quantity of
material entrained can increase rapidly.
3.4.4 The porous membrane, or distributor
In all processes involving the fluidization of a bed of solid particles some form
of distribution device is needed to introduce the fluidizing agent to the bed.
Although it would be possible to use a pipe grid at the base of the bed, for gas
fluidization the more widely used method is to construct the vessel with some
form of gas plenum chamber at the bottom, separated from the main container
by a porous or perforated plate. The design of this distributor plate,
110
BULK SOLIDS HANDLING
particularly with regard to the material from which it is constructed and the
pressure-drop across it, can vary over a wide range. For example, some
applications are suited to the use of metal plates perforated with a small
number of relatively large holes across which the pressure-drop would be very
small, whilst at the other end of the scale (that is, high pressure-drop) would be
found porous distributors such as ceramics, sintered metal and plastics, and
woven cotton and polyester materials.
Considerable interest surrounds the influence of the pressure-drop across
the distributor, or more specifically, the ratio of this pressure-drop to that
across the fluidized bed, on the 'quality' of fluidization. Clearly the stability of
the fluid bed system is an important criterion, and it is worth considering how
this might be defined and how it depends upon the ratio of the distributor
resistance to the bed resistance.
Suppose that a disturbance occurs, in the nature of a localized increase in
gas velocity, in a uniform bed of dry particles in a condition of incipient
fluidization. This disturbance will cause the bed in this region to expand,
resulting in a fall in the local pressure-drop through the bed, and consequent
rise in pressure-drop through the distributor as more gas tries to force its way
through the potential 'channel'. The system is stable if the combined pressuredrop across the bed and distributor rises with an increase in the local gas
velocity in the bed. However, if this combined pressure-drop were to fall, there
would be a further increase in the local gas velocity, tending to establish a
channel through which most of the fluidizing gas could flow, causing the rest of
the bed to defluidize. In general it may be said that the resistance to gas flow
offered by the distributor should be great enough to ensure stability of the
fluidized bed system without being so high that blower power becomes
excessive. Although there appears to be some disagreement as to how the
optimum pressure-drop should be determined, the consensus suggests that the
pressure-drop through the distributor should be at least 15% ofthat across the
particle bed. In fact the stability of the fluidized bed may also be influenced by
the size and density of the particles in it, and, although very little experimental
data is available, Figure 3.12 gives an indication of the way in which the
minimum required distributor pressure-drop would vary with these
properties.
3.4.5 The influence of particle size and density
It has long been accepted that the size and density of particles, and also the size
distribution, can have a significant influence on the behaviour of a bed of
fluidized material, and it is well established that, in general, the minimum
fluidizing velocity decreases and the bed expansion ratio increases with
decreasing particle size and density. It should, however, be noted that the
apparent influence of particle size can be distorted by the method of
determining the mean size. Thus, for example, the use of the median size,
111
DYNAMICS OF FLUID/SOLIDS SYSTEMS
"'
Q)
.0
Cl
0
-o.;,
:;20
Cl)
Cl)
~
Cl
0
~16
c:"'
Q)
0
Q;
Cl
"'12
Cl)
1000
"'0
~
~ B
Cl)
Cl)
0
t
"'
Cl
~ 4 1----
--r----- -t-----t ---
0,
:;
Cl)
Cl)
Q)
a.
200
300
500
mean particle diameter d v ( 11mJ
Figure 3.12 Minimum pressure drop required across distributor for bed of spheroidal particles
fluidized with air at a condition close to normal ambient, based on an equation by Siegel [11].
defined by
(3.67)
where da is the particle size from sieve analysis and x is the mass fraction of
particles of that size, tends to under-emphasize the influence of the fine
particles, which may in fact have a pronounced effect on the particle surface
area per unit volume of the bed, and therefore on its fluidization behaviour. A
more relevant size is the volume surface mean diameter, which is conveniently
(though not exactly) expressed as
dvsm
~( L
;J 1
(3.68)
Probably the most useful recent work dealing with fluidization characteristics
of different types of particulate bulk solids has been that of Gel dart [ 12] who
112
BULK SOLIDS HANDLING
showed that the behaviour of a fluidized particulate material can generally be
classified into one of four recognizable groups. These groups are characterized
by the difference in the densities of the solid and the fluidizing medium, and by
the mean particle size; and the salient features of the groups may be
summarized as follows.
Group A. Generally includes materials of small particle size and/or low
particle density (less than about 1400 kg/m 3 ). Powders in this group show
considerable expansion of the bed between the minimum fluidizing velocity
umc and the 'minimum bubbling velocity' umb• and relatively slow settling of the
bed when the flow of the fluidizing medium is shut off. At velocities above umb
the bed bubbles freely and at higher velocities axisymmetric slugging tends to
occur. At velocities higher still, the slugging movement is continually
collapsing so that the upward flowing fluid is forced to track upwards through
angled crevices to the top surface of the vigorously turbulent bed.
Group B. Including most materials in the mean particle size and density
ranges 40-500 Jlm and 1400-4000 kg/m 3 , this group would typify the
generally accepted model of fluidized bed behaviour. At fluid velocities above
umc the expansion of the bed is small and bubbling occurs at or just above this
minimum fluidizing velocity. Collapse of the bed is rapid when the fluid flow is
shut off. As the velocity is increased the bed bubbles freely, and eventually
tends to a form of asymmetric slug flow.
Group C. This includes cohesive powders that are difficult to fluidize satisfactorily because of high interparticle forces resulting from very small particle
size, electrostatic effects or high moisture content. Attempts to fluidize such
materials usually result in the formation of stable channels or in the whole bed
rising as a plug, although some success may be achieved with the aid of
mechanical vibrators or stirrers.
Group D. Including materials having large mean particle size and/or high
particle density. Fluidization behaviour is in some respects similar to powders
in Group B, but beds of Group D materials can generally be made to exhibit
the phenomenon known as 'spouting' (see section 3.5) if the gas is admitted
centrally.
These zones of behaviour are conveniently illustrated on a plot of (pp- Pc)
against d (Figure 3.13). The empirical boundary between materials of
Groups A and C is indistinct as there are many factors that can influence the
cohesiveness of these fine powders, including electrostatic charging, moisture
content and particle shape.
From a knowledge of the mean particle size and particle density of a bulk
solid it is possible to make a reasonably reliable estimate of the minimum
DYNAMICS OF FLUID/SOLIDS SYSTEMS
M
113
2000
E
Cl
25
1000
Cl
Q.
<I)
0
500
c
<I)
~
i5
?:
<ii
c
200
<I)
"C
100
500
1000
5000
mean particle diameter (,m)
Figure 3.13 Geldart's classification of fluidization behaviour according to size and density of the
particulate material: for fluidization with ambient air [12].
fluidizing velocity using one of the correlations presented in this chapter.
However, it should be recognized that, although these two properties
generally have the major influence on the fluidization characteristics of the
material, there are other variables which may also have a significant effect.
Thus, for materials that are cohesive, have a very wide size distribution, or are
prone to electrostatic charging, especially those of very fine particle size, the
use of simplified mathematical models to predict umr could be quite misleading.
There are many commercial applications of fluidization, and a useful
discussion of some of these is given in [7]. In the case of air-float conveying
(described in Chapter 15) the direct part played by the phenomenon of
fluidization is evident. In pneumatic conveying by pipeline, especially in
dense- and medium-phase, fluidization is still involved, although the exact
mechanism is less clearly defined.
3.5 Spouted bed behaviour
The phenomenon known as 'spouting' can occur in a bed of granular material
when an upward flowing jet of air is admitted centrally at the bottom ofthe bed
(Figure 3.14). It can be regarded as a combination of two distinct regimes of
gas/solids flow: a central core moving upward at relatively high velocity in
which the solid particles are widely dispersed, and the surrounding main part
of the bed in which the densely packed particles move slowly downwards. The
whole mass of bulk solid is constantly in motion and the spouted bed thus
114
BULK SOLIDS HANDLING
fountain
_ level ol natural
free surface
spout
(high velocity)
annular bed
(low velocity)
Figure 3.14 A typical arrangement of spouted bed.
fixed bed flow
----·~1---- spout developing - -
varying degrees ol
initial compaction
/
/
/
/
/
~"""'
/
/
/
-
..,..,...--
-
........
'
--
--,
minimum spouting
\
I
I
'- -~
steady-sta(spouting
superficial air velocity
Figure 3.15 Typical relationship between pressure-drop and air flow rate for a spouted bed.
DYNAMICS OF FLUID/SOLIDS SYSTEMS
115
provides an alternative to fluidization for contacting fluids with a coarse
granular material.
Various applications of the spouting phenomenon occur in industry, the
commonest involving the drying of granular bulk solids such as grain and
wood chips. As with fluidization, the most important single factor in the design
of a spouted bed system is ensuring that the flow rate of fluid supplied to the
bed is correct. Various correlations for minimum spouting velocity have been
proposed and some of these are introduced here. Other important design
considerations relate to the geometry of the spouting vessel, the pressure-drop
across the bed, and so on, and for further information on these aspects the
interested reader is referred first to the work of Mathur and Epstein [13, 14].
Figure 3.15 shows the typical form of relationship between the pressuredrop and air flow rate for a spouted bed as the flow rate is increased from zero
to the condition of steady-state spouting. As with a conventional fluidized bed
the system initially corresponds to flow through a bed of fixed particles and the
pressure-drop is nearly proportional to the flow rate. Eventually a point will
be reached at which the particles at the apex of the conical base of the vessel
(where the velocity is greatest) begin to rise. Further increase of the air flow rate
will cause the channel or spout formed at the bottom of the vessel to extend
upward into the bed and, since the concentration of particles in this spout is
much lower than in the rest of the bed, there will be a decrease in the overall
pressure-drop. Continuing to increase the air flow rate will result in further
upward extension of the internal spout although, because of the increase in the
depth of the bed caused by displacement of particles from the central region,
the fall in overall pressure-drop could be less marked. When the air flow rate is
sufficient to cause the spout to break through the surface of the bed there will
be a sudden decrease in the overall pressure-drop to the value corresponding
to steady-state spouting and this value will be more or less unaffected by
further increases in airflow.
It should be noted that the peak value of pressure-drop reached will be
largely dependent upon the packing of the granular bed so that for the most
loosely packed bed there may be virtually no observable peak at all in the plot
of l'lp against air flow rate.
The usually accepted correlation for the prediction of minimum spouting
velocity urns is an empirical equation involving the densities of the flowing fluid
and the particles, together with relevant dimensions of the spouting vessel:
d
(D· )n ·2gH{(pp-pr)/pr}
Ums=D · D~
0
(3.69)
where d is the effective diameter of the granules, Di and D0 are the diameters of
the inlet and the main vessel, H is the height of the bed surface above the inlet,
and Pv• Pr are respectively the densities of the granules and the fluid. Leva [15]
gives the following values of the index n: for D0 = 150 mm, n = 0.33
(independent of cone angle); for D 0 = 600 mm, n = 0.23 (for 45o cone) n = 0.13
(for 85° cone).
116
BULK SOLIDS HANDLING
3.6 Gas/solids flow in pipes
3.6.1 Introduction
The entrainment of solid particles in a high-velocity flow of gas is such a
familiar concept, with examples ranging from sandstorms to domestic vacuum
cleaners, that no-one is surprised that a pneumatic conveying system works.
Yet, in order to design and construct an installation that will be reliable and
efficient, it is necessary to have some appreciation of the mechanism of flow of
gasjsolids suspensions in pipes.
Despite considerable study and research into various aspects of gas/solids
flow, the subject remains very much an art, and the successful design and
installation of pneumatic handling plant owes a great deal to practical
experience. It is becoming increasingly evident that only limited progress can
be made in scientific studies of gas/solids flow because of the very large number
of variables that are involved, variables that include, for example, velocities of
conveying gas and of solid particles, pressure and temperature of the
conveying gas, size, shape and density of solid particles, and so on. Even the
study of the flow of homogeneous (single-phase) fluids is largely empirically
based and clearly there can be little hope of developing a set of practical and
reliable mathematical formulae to describe completely the flow behaviour of
two-phase gas/solids suspensions.
Such progress as can be made towards an understanding of the flow of
gas/solids suspensions will be through observation and analysis of actual
working pneumatic conveying systems, in industry as well as in research
laboratories. With the accumulation of a sufficient store of practical knowledge, techniques are being developed for the interpolation and extrapolation
of relevant data to enable the behaviour of a gas/solids suspension to be
predicted with reasonable confidence. As more experience is gained in
handling a wider range of materials, the level of understanding of the
interrelationships amongst the relevant parameters will increase. For this
reason, publication of accurate performance figures for industrial pneumatic
conveying plant is as important as that of the results of academic research into
the flow behaviour of gas/solids suspensions.
However, in order to make the best use of such data to design and
commission an installation that will be reliable and efficient, it is obviously
necessary to have some understanding of what is happening inside a pipeline
carrying a flowing gas/solids suspension. In this section the nature of twophase, gas/solids flow in pipes is described in the light of actually observed
behaviour, and some of the suggested mechanisms of flow that have been
proposed to explain this observed behaviour are discussed. Finally, the
important but difficult matter of predicting the pressure-drop occurring as a
gas/solids suspension flows along a pipe is considered in some detail.
Because of the increasing industrial importance of pneumatic conveying as a
DYNAMICS OF FLUID/SOLIDS SYSTEMS
117
means of transporting bulk solids a large proportion of this book is devoted to
the design and operation of practical pneumatic conveying systems (p. 380).
3.6.2 The flow of gas/solids suspensions in horizontal pipes
Flow patterns existing in two-phase, gas/solids suspensions travelling along
horizontal pipes tend to be very complex and are principally dependent upon
the velocity of the gaseous phase, the ratio of the mass flow rate of solids to the
mass flow rate of gas (i.e. the 'solids loading ratio', sometimes rather
misleadingly called 'phase density') and the nature of the particulate solid
material being conveyed. From visual observation of gas/solids flow in a glass
pipe, Wen [16] described the manner in which the flow pattern changed as the
solids loading ratio increased (see Figure 3.16).1t seems reasonable to suggest
that three principal categories of stable gas/solids flow may be encountered in
horizontal pneumatic transport:
(i) When the solid particles are conveyed in a uniformly dispersed phase.
(ii) When the conveyed material mainly occupies the lower part of the
conveying line and assumes the form of a moving layer, or moving 'dunes'
of solid particles.
(iii) When the density of the flowing suspension approaches the bulk density of
the conveyed material. This would represent a true 'mass-flow' situation
somewhat reminiscent of the 'extruded flow' of a soft plastic material.
The transition from (i) to (ii) and from (ii) to (iii) occurs as the gas velocity is
decreased or the solids flow rate is increased, and is due to the continued
deposition of solid particles from the flowing suspension. Actual values of the
solids loading ratio for these three categories of stable flow cannot, of course,
be exactly specified since they are influenced by a number of other factors, but
dispersed- or dilute-phase flow would typically be observed with solids
loading ratios of less than five whilst the characteristics of dense-phase flow
would tend to be seen when the solids loading ratio ranges from about 25 up to
a value of several hundreds.
Methods of prediction of pressure-drop will be discussed in a later section,
but it may be emphasized at this stage that the tendency for the solid material
to be concentrated in the lower part of a horizontal pipeline makes it unwise to
compare pressure-drop data for suspension flow in horizontal pipes with
corresponding data obtained in vertical flow, except perhaps at very high
conveying velocities where the particles would be widely dispersed. Also,
pressure-drop correlations proposed by various investigators must be used
with caution and only for the limited region of the experimental programme
upon which the correlation is based. If extrapolation is absolutely necessary,
careful analysis of the actual flow conditions to be encountered must be carried
out.
It should, at this stage, be understood that the different flow patterns
E
118
BULK SOLIDS HANDLING
immature slug flow
homogeneous flow
slug flow
degenerate homogeneous flow
.. . . .
2
.~·..:,;; :'.::..<;·;·. ~:.;; ,:·.: ·.":·;.;:,::;<•::.::,.)
degenerate slug flow
immature dune flow
• • • • • ••
3
••
0
•
j;.~k;;;~.;;;
•
-~
~-
.:. . . :·...;·:;;;;;,~
• • • ••
: •
. ' ·• •· : : ·
:·:
dune flow
ripple flow
degenerate dune flow
pipe plugged
flow direction
Figure 3.16
Flow patterns in horizontal pipelines [16].
illustrated in Figure 3.16 may be observed at different points along the same
pipeline. Changes in the cross-sectional area of the pipe will affect the velocity
and therefore may change the flow pattern. However, even in a pipe of uniform
cross-section, the decreasing pressure of the conveying gas will cause its
velocity to increase so that, in an extreme case, the flow could change from
dense-phase (at low velocity) at the entry to the pipe, to a very dilute phase,
with widely dispersed particles travelling at high velocity at the outlet end.
A useful qualitative presentation of dilute-phase gas/solids flow in a
horizontal pipeline has been given by Zenz and Othmer [17] in the form of a
so-called 'phase-diagram' which is a log-log plot of the average pressure
gradient along the pipe against the superficial gas velocity (based on the total
119
DYNAMICS OF FLUID/SOLIDS SYSTEMS
a;
(ij
Cl
<f)
0>
0
D
~mp=o
(gas flow in
empty pipe)
saltation
velocity us
for solids
flow rate
p1
m
Wmp
~I
IL
[+--- L__.:
--~----------------
mg
average superficial velocity of gas, ug in pipe length L (log scale)
Figure 3.17
'Phase diagram' for horizontal gas/solids flow.
cross-sectional area of the pipe) for various solids concentrations. This
approach is developed in Figure 3.17 which illustrates the fundamental fact
that for any bulk particulate material being transported along a pipeline the
value of the pressure gradient at any point must be somewhere between the
values for the same air flow rate, (i) through the empty pipe, and (ii) through the
pipe when plugged with the bulk solid. The first of these two conditions is quite
easily modelled as the flow of a single-phase compressible fluid, as described in
section 3.6.5, and the second corresponds to flow in a packed bed, which was
discussed in section 3.2. The two lines of Figure 3.17 marked as mP = 0 are for
the flow of gas in an empty pipe and through a packed bed of the bulk solid
120
BULK SOLIDS HANDLING
concerned, and thus represent two boundaries of the area within which any
actual flow condition ofthe product must lie. It should be noted, however, that
this does not imply that the area defines flow conditions that could actually be
achieved, as whether a certain flow condition is possible or not depends upon
the properties of the bulk solid in a manner that is not easily modelled or
predicted.
The two lines denoted mP = 0 therefore represent the flow of gas alone,
whilst mP 1 , mP 2 , ... represent increasing solids mass flow rates. Thus, for
example, suppose the solid particles are introduced at a rate mP 1 into a gas
flowing along a pipeline at a superficial velocity uH. The increase in frictional
resistance due to the particles causes the pressure-drop per unit length to
increase from point B to point C 1 . If the superficial gas velocity is now reduced
(effectively increasing the solids loading ratio) the concentration of particles
per unit length of the pipe will increase until eventually a point will be reached
(D tl where the particles begin to settle out at the bottom of the pipe. This
phenomenon is known as 'saltation' and the value of the superficial gas
velocity at this point (u,) is known as the 'saltation velocity'. Note, however,
that this saltation velocity may be a function of the mass flow rate of solids, so
that points D 2 , D 3 ••. correspond to saltation velocities for solids mass flow
rates mP 2 , mP 3 ... Further reduction of the gas velocity will cause more solid
material to settle out until a substantial non-moving layer develops on the
bottom of the pipe. Transport will continue above this deposited layer, with
the actual gas velocity significantly greater than the superficial velocity
because of the reduced area, but there will be a sharp increase in the pressuredrop (from D to E). After passing through the various intermediate stages
illustrated in Figure 3.16 as the amount of deposited material increases, the
pipe eventually becomes full of particles and a condition of true mass flow may
be attained, with the pressure-drop approaching that corresponding to the
value for packed-bed flow.
The actual mechanism of two-phase gas/solids flow at high solids loading
ratios and low velocities (i.e. below the saltation velocity) is still far from being
fully understood, although recently reported experimental investigations,
particularly at Thames Polytechnic in the UK [18-20] have done much to
improve this situation.
The proposal of Geldart [ 12] for characterizing the fluidization behaviour
of bulk solids, which was described in section 3.4.5, is now well established and
it is hardly surprising that various research workers, notably Dixon [21, 22],
remarking on certain similarities between gas fluidization and dense-phase
gas/solids flow, have attempted a similar classification for pneumatically
conveyed materials. Although originally based on empirical formulae relating
to flow in vertical pipes, Dixon's so-called 'slugging diagrams' may well have
relevance to non-suspension gas/solids flow generally. Figure 3.18 shows the
slugging diagram for flow in a 2-inch (50 .urn) diameter pipe. Group A
materials (powders) and Group D materials (granules) both tend to convey
"0
·u;
cQ)
~
'5
£
Q)
g
Q)
~
Q
la.
~
Ci
E
C'1
500
1000
I
c
20
\ \
\ \
500
,,,,
\\,,
,,,,
,,
,,,,
mean particle size d ( flml
100
\\
'
\
\
\
1000
\
''
\\
\
,,
\
\
\
\
\
\
\
'
\
D
\
\
\
'
\
'\
strong
axisymmetric slugs
Figure 3.18 Slugging diagram for 50-mm (2-inch) pipe.
50
//
//
///
//
//
//
//
//
weak asymmetric
slugs (dunes)
,,,,
,,,,
,,,,
,,,,
,,,,
,,,, 8
,,,,
,,,,
\\,,
A
,,
,,,,
,,,,
\ \
pressure (bars)
no slugging
~
'/
'/
~
~
~
~
~
/
~
~
:/.
24
\
\
\
'\
' '
'\
-<:
n
N
-
"'
::
"'
"'...,-<:
"'m
t""
8
-----"'0
t""
c
8
'T1
'T1
"'0
::
z
>
0
122
BULK SOLIDS HANDLING
well in dense-phase, but their mode of flow is very different. The significant
feature of Group A materials is that they have the capability of retaining air in
the void spaces for some time after the supply of air has been discontinued.
This means that, once aerated, these products have a persisting fluid-like
quality which enables them to 'flow' very readily along a pipeline without
slugging. The granular bulk solids of Group D usually exhibit a natural
tendency to form slugs of up to a metre or so in length which travel along the
conveying line shedding material from the back of the slug and picking up
material at the front. Materials falling into Group B do not retain air and in
general can only be conveyed in dense phase at relatively high velocities if
unstable slugging behaviour is to be avoided. Finally, there are the Group C
powders to be considered: these are likely to be cohesive and therefore
unsuitable for simple dense-phase conveying, although it may be possible to
transport such materials in special systems which are designed to provide
additional air at successive points along the conveying line. For descriptions of
various types of pneumatic conveying systems with 'air addition' see
Chapter 12.
3.6.3 The flow of gas/solids suspensions in vertical pipes
At high values of the superficial gas velocity and low solids loading ratios it
could reasonably be expected that the flow of a gas/solids suspension would be
essentially the same in horizontal and in vertical pipelines, with the solids
having an approximately uniform dispersion throughout the flowing gas.
There would be no significant difference in the pressure gradient in these two
situations. Likewise, if the pipeline were to be packed with stationary particles
with the gas flowing through the interstitial voids, the pressure-drops for
horizontal and vertical orientation would not be discernibly different.
A useful qualitative representation of vertical gas/solids flow, similar to that
described previously for horizontal flow, is shown in Figure 3.19. As before,
the line AB (rhp = 0) represents the flow of gas in an empty pipe, line A' B' (also
having mP = 0) represents the flow of gas through a stationary bed of particles
in the pipe, and mP 1 , mP 2 ... represent increasing solids mass flow rates. The
Upper partS Of the lineS mPl' mp2 ... COrrespond tO fully dispersed flOW at
relatively high gas velocities in which the flow conditions are similar to those
for horizontal flow. As the gas velocity is reduced the frictional resistance at the
pipe wall decreases. Also, the solids concentration increases, causing the static
head to increase. From point C to point D the decreasing wall friction is the
predominant effect and the net result is to decrease the total pressure-drop.
Further reduction in the superficial gas velocity causes a sharp rise in the total
pressure-drop as the increasing static head now predominates over the
decreasing wall friction. As the solids concentration increases towards point E
the bulk density of the suspension becomes so great that the particles can no
longer be supported by the drag effect of the upward-flowing gas and the
DYNAMICS OF FLUID/SOLIDS SYSTEMS
''
(j)
(ij
u
''
''
'
123
E2
<ll
Cl
0
0
_J
.<:
0>
c:
~
())
c.
·a.
.S
c.
0
u
())
5
<ll
<ll
())
a.
)/''"""
choking velocity for
A
average superficial velocity of gas. ug in pipe length L (log scale)
Figure 3.19 'Phase diagram' for vertical gas/solids flow.
suspension then collapses into a slogging state. This phenomenon is called
'choking' and the superficial gas velocity at which it occurs (u.h) is described as
the 'choking velocity'.
The choking velocity represents the condition in which the gas stream is
carrying the maximum concentration of solids in dilute-phase flow for a given
solids loading ratio and therefore is analogous to the saltation velocity in
horizontal transport. At gas velocities below the choking velocity the solid
material tends to settle towards the lowest point in the pipeline and
continuous conveying ceases.
Before leaving this discussion on the so-called 'phase diagrams', it is perhaps
worth commenting upon the interpretation of such diagrams. Firstly, it should
be clearly understood that the diagrams represent relationships between
average conditions over a specified length L of the pipe: they do not represent
124
BULK SOLIDS HANDLING
the varying instantaneous conditions existing at successive points along the
pipe. Nevertheless, it is important to appreciate that the flow along the pipe is
changing as a result of the frictional pressure drop which causes a decrease in
density and consequently an increase in velocity. This means that although a
point on the phase diagram might appear to suggest a satisfactory flow
condition, the actual flow giving this average point could vary from an
impossibly low velocity at the feed point to an excessively high value at
discharge. In a practical pneumatic conveying line it is perfectly possible,
although generally undesirable, for the mode of flow to change from low
velocity dense-phase to a dilute-phase suspension flow as the velocity
increases.
3.6.4 Flow around 90° bends
The previous discussion has centred on fully-accelerated flow where the solid
particles have reached an equilibrium velocity close to, but slightly less than,
the velocity of the conveying gas. (Note, however, that in dense-phase flow the
particle velocity may be very much smaller than the conveying gas velocity.)
Where the particles have been slowed down by some kind of obstruction, the
commonest of which is a bend in the pipe, there will be an unstable flow as they
are 'picked up' again and re-accelerated to their equilibrium velocity.
Visual observation of the motion of solid particles in bends indicates that
there are two basic categories of flow: (i) that in which the solid particles slide
around the outer radius of the bend at a much slower velocity than the
conveying gas; and (ii) that in which the solid particles suffer a number of
collisions in traversing the bend, the particle trajectories between the particlewall impacts sometimes being reported as straight lines and frequently as
distinct curves. This latter flow behaviour is usually restricted to large
particles.
Extensive studies by Miihle (unpublished) into the paths followed by coarse
particles indicate that the particles travel rectilinearly along the straight pipe
preceding a bend until they impinge upon the outer wall of the bend. The
particles lose momentum on impact, but are speeded up after reflection by the
flow medium. This sequence is repeated and, for a low initial velocity, the
collisions may result in the particles eventually remaining in contact with
the wall along which they slide at a decelerating rate.
The flow pattern in a bend is further complicated by the secondary motion of
the carrier gas which is induced by centrifugal effects. That is, twin eddies are
formed in the radial plane and in association with the main flow produce a
double spiral motion downstream. To make progress with a rigorous
mathematical analysis of this two-phase motion it is necessary to make
simplifying assumptions, such as laminar flow and a perfect fluid; it is thus very
unpromising owing to practical considerations.
Flow visualization experiments carried out by Mason [23] for 15 Jlm
DYNAMICS OF FLUID/SOLIDS SYSTEMS
125
alumina particles flowing around vertical-to-horizontal 90° bends of 75 mm
diameter and a curvature ratio (curvature diameter/pipe diameter) of 20,
generally substantiated the work of Miihle, even though fine particles were
used. Deviating flow was not evident at a solids loading ratio of 1.8 and mean
gas velocity of 16 mjs. This suspension was influenced by the bend curvature
and a large proportion of the particles was well distributed across the entire
flow area, although there was a thin layer of particles which had migrated to
the inner wall and become deposited. When the flow conditions were changed
to a solids loading ratio of 7.5 and a mean gas velocity of 13 mjs, the particles
impacting on the outer wall were reflected and 'cut across' the main stream to
impinge on the inner surface. The material was then deflected towards the
outer wall but with insufficient energy to penetrate the fast-flowing main
stream of particles. The deviating flow gradually became less severe, but its
influence was still apparent when the flow entered the downstream horizontal
pipeline.
Having accepted that large particles may bounce around a bend at higher
velocities or slide at lower velocities, and that a particle may first bounce and
then slide the rest of the way, it will be evident that an analysis which assumed
the physical model of particles sliding the whole way around a bend will
produce doubtful correlations.
3.6.5 The prediction of pressure-drop in flowing gas/solids suspensions
It will have become clear from the preceding discussion that the reliable
prediction of pressure-drop in a gasjsolids suspension flowing along a pipeline
is one of the major difficulties facing the designers of pneumatic conveying
systems. In recent years a considerable amount of literature has been
published on the characteristics of two-phase gas/solids flow, but there is, as
yet, no technique for predicting pressure-drop that is both reliable and
convenient. Techniques that are simple enough to be readily used (such as socalled 'rule-of-thumb' methods) tend to be rather uncertain, and, at the other
extreme, high-level mathematical models that are claimed to give accurate
predictions of pressure-drop are usually complex and inconvenient, often
requiring data on the particulate material that would not ordinarily be
available. In any case, it should be recognised that because of the extreme
complexity of two-phase gas/solids flow, a direct mathematical approach is
never likely to be successful. The most satisfactory results should be obtained
through modelling techniques which will give sufficient insight to the nature of
gas/solids flow to allow available data (for example, from existing pneumatic
conveying systems and from academic and industrial research work) to be
extended. In this way it should become possible to predict pressure-drops, flow
rates, and so on, for a proposed pneumatic conveying system from data
determined on a system of different configuration and, perhaps, carrying a
material of different particle and bulk characteristics.
126
BULK SOLIDS HANDLING
The usual starting point in any discussion of pressure-drops in gas/solids
flows is to regard the total pressure-drop as comprising that due to the flowing
gas alone plus the additional pressure-drop caused by the presence of the solid
particles. Thus
(3.70)
where !'J.p. is the total pressure-drop in the suspension, !'J.pg is the pressure-drop
due to the gas alone and /':,.pP is the additional pressure-drop attributable to the
solid particles.
Each of these components of pressure-drop will now be considered
separately, attention being given to the influence of bends, valves and other
fittings in addition to the frictional resistance of the pipe walls. Reliable
methods are available for the prediction of the pressure-drop due to the gas
alone and a typical approach is given here in outline. Except in the case of
pneumatic conveying at very low solids loading ratios, especially in longdistance pipelines, the 'gas-only' pressure drop is likely to represent the
smaller, and often insignificant, component of the total pressure-drop.
Nevertheless, a clear understanding of the variation of density and velocity
along the line is a valuable asset when it comes to designing such systems.
Pressure-drop in a gas .flowing along a pipe. As a gas flows along a pipeline, the
decreasing pressure resulting from the frictional resistance to the flow causes
the gas to expand. That is, the density of the gas decreases, and consequently
the average velocity of the gas across a section of the pipe must increase in the
direction of flow. These changes of density and velocity may not be very great
and, if the velocity at the upstream end of the pipe is not high and the pipe is
relatively short, it is usually safe to determine the pressure-drop by treating the
flow as one of constant density.
Thus, using the familiar Darcy formula, the pressure-drop !'J.pg in a gas of
density Pg flowing along a pipeline of diameter D and length L would be given
by
!'J.p
=
g
4'~pgu:
'1
D
2
(3. 71)
where ug is the average velocity of the flowing gas and f is the 'pipe friction
factor'.
A more reliable prediction of the pressure-drop, and a useful indication of
the variation in velocity along the pipeline, may be obtained by using one of
several possible analytical models that take account of the varying density.
The most convenient of these is perhaps the isothermal model in which the
pressure gradient along the pipe is expressed as
dpg 32 frn: RT
dL = n 2 . D 5 ·-,;;
(3.72)
DYNAMICS OF FLUID/SOLIDS SYSTEMS
127
where mg is the gas mass flow rate, T is the (constant) temperature of the gas
and R is the characteristic gas constant.
Provided that the velocity of the gas remains well below the sonic velocity
(so that variation of kinetic energy is insignificant), integration of
equation (3.72) allows a reliable value of the pressure-drop (pg 1 - pg 2 ) over
pipe length L to be determined from
_ [
2 _
Pg2 Pg1
64fm;RTLJ 112
n2
Ds
(3.73)
The gas velocity at the upstream end of a pneumatic pipeline is usually an
important parameter ('pick-up velocity') and it is likely to be useful to
introduce this into the expression for pressures.
Noting that
equation (3.73) becomes
(3.74)
and rearranging
Pg1 = [
u;2 J
1 - 4fL.
D RT
(3.75)
1/2
Thus, in a situation where the downstream pressure is known and the
velocity at the upstream end of the pipe (pick-up velocity) is specified, this
expression allows the pressure required at the upstream end, for gas alone, to
be estimated.
Note that the value of the pipe friction factor f may be taken to be 0.005 for a
preliminary calculation, but should then be checked from the Moody chart
(Figure 3.20) using an appropriate value of the pipe roughness e and the value
of Reynolds number at the upstream end of the pipe, calculated from
Re
= Pg1 . ug1 D
1
RT
(3.76)
J1
where J1 is the viscosity of the air at temperature T.
Alternatively (and this is a more satisfactory approach when preparing
computer software), a value off can be calculated using one of the empirical or
semi-empirical correlations such as the Colebrook formula
l
JJ
=
-
( ejD
l.?2loge 3.71
1.255 )
+ ReJf
(3.77)
E
t5
0
c:
~
u
c5
0.002
0.003
0.004
0.005
0.01
0.012
0.02
\
1Q3
I
Cast iron
0.25
Commercial steel 0.045
Drawn tubing
0.0015
I
~~
1'-
t-- 1-- t-.
104
I'
,...~
1Q5
r-;:
f;::: t-ot-.
f-.
~ F:::
r-.... ~ r-.1--t--
t-- r- !-.
~ t:- r-
~ ..........
~
.._
I-~ ~~ 1'--t-- t-- t-
Reynolds number, Re
'~
t- f-.t--;....
R 8 t::-- !--..
;....
"!'-.... . . . 8:: t--....
~'-t-----
'~ t'~
I~ r--r-.
t-....
Approximate roughness of internal
surfaces of pipes, <(mm)
\
'1\ '
'\
Re cri(
\
'\
turbulent flow
Figure 3.20 Moody chart for the determination of friction factors for the flow of fluids in pipes of
circular cross-section.
r--
r--
I'
laminar flow (critica~)
f =16/Re
flow,
laminar
~
106
0.00001
f=:::: ~ smooth
0.0001
0.00005
r-- 0.0002
t:::: t--
t-.
0.0005
0.001
0.002
0.005
•
~
~
>
Q)
2
Ol
:l
.<:
Q)
en
"'c:
';:;
0
......
z
Cl
r
Vl
:r:
>
zt)
s
r
0
Vl
~
tc
c::r
N
00
129
DYNAMICS OF FLUID/SOLIDS SYSTEMS
or the more convenient Churchill formula [24]
f
=
[(
]1/12
1
8 )12
+(A+ B)t.s
Re
(3. 78)
where
1
A= [ 2.457loge ( (7/Re)0.9 +0.27ejD
and
B = (37530/Re)
)]16
16
It is also likely to be necessary to know the gas velocity at the downstream
end of the pipe. This can be easily predicted using the same isothermal model
since, for this model, the gas velocity is inversely proportional to the absolute
pressure in the line.
Thus
Pg1
ug2 = ug1Pg2
(3.79)
Naturally an actual installation is likely to include bends in the pipeline, and
also valves and other fittings. These will increase the frictional pressure loss
and are best dealt with by considering them as 'equivalent lengths' of pipe of
the same diameter as the main pipeline, which are then added to the valve of L
in the preceding equations. Values of equivalent lengths of pipe for various
fittings may be conveniently estimated from a nomograph (Figure 3.21).
Additional pressure-drop due to solids: fully accelerated suspension flow. As
mentioned previously, the complex nature of two-phase gas/solids flow in
pipes means that it is not amenable to a rigorous mathematical treatment and
the best approach to the development of a reliable design technique is
therefore through interpolation and extrapolation of experimental data.
Many correlating equations have been proposed by various authors for the
additional frictional pressure-drop in a flowing suspension that can be
attributed to the presence of dispersed solid particles. The most sensible
approach would appear to be to express this additional pressure-drop in terms
of the 'gas-only' pressure-drop 11pg, giving the total pressure-drop as
(3.80)
where IX is a 'pressure loss factor' that may be a function of a number of different
variables. Whilst IX would normally be positive, some cases have been reported
of the pressure-drop in a flowing gas/solids suspension falling below that for
gas alone. These examples of 'drag reduction' apparently occur when the
suspension consists of fine particles at low solids loading ratios [25].
The dependence ofthe pressure loss factor IX on the various system variables
130
BULK SOLIDS HANDLING
Gate valve, 1/4 open
Diaphragm valve, 1/4 open
Butterfly valve, 8=40°
EQuivalent length
of straight pipe (m)
1000
Gate valve, 1/2 open
Diaphragm valve, 1/2 open
500
Diaphragm valve, 3/4 open
200
Diaphragm valve, open
Check valve, swing type
100
800
Butterfly valve,8=20°
Bend, 180° close return
50
600
300
Inside diameter
of pipe (mm)
1000
30
Gate valve, 3/4 open
20
Bend, 90° standard
10
Enlargement, d/D=1/4
Butterfly valve, 8=1 oo
Bend, 90° long radius
500
400
300
200
3
Bend, 45° standard(•
Enlargement, d/D=1!21
100
Butterfly valve, 8=50
80
Bend, 45° long radius
Gate valve, open
0.5
60
50
Enlargement, d/D=3/4
0.3
40
0.2
30
0.1
0.05
20
Figure 3.21
has been the subject of considerable research effort. Most authors seem to
agree that rx will be directly proportional to the solids loading ratio c/J, but there
is clearly some substantial inconsistency in the suggestions concerning the
influence of particle characteristics such as size, shape and density.
Clearly, any correlation involving the large number of relevant variables
will be complex. However, test results reported for a large number of different
products demonstrate the general trend illustrated in Figure 3.22; that is, the
frictional pressure-drop attributable to the presence of solid particles in the gas
stream increases as solids loading increases, and also as the conveying velocity
is decreased. The very sharp rise in frictional pressure-drop that is seen in
(])
c.
"'"'
5
(])
"'"'
.2
~
C3
c5
~
2
5
10
20
50
100
~ 2::::::::::
..........
......
30
conveying velocity (m/s)
20
' -
-------..._
r
40
I
Figure 3.22 Approximate values of the solids pressure-loss factor in equation (3.80).
..........
r-...
10
~
_\ '\." ~"' ~
-...__:::
.......
~" ~
........
'·"'"'
~~ ~
\\.'\.~
~\.
\\.~
.\.
50
I
I
4
6
8
g
~
"'
.2
"'
s
12 ;;,
10 ,g
w
--
~
~
t)
enc0Sl
fl
"l
0
?A
~
~
>
16 0
14 ~
18 -e-
20
t)
132
BULK SOLIDS HANDLING
Figure 3.22 occurs as the conveying velocity approaches the mm1mum
transport velocity. Again it should be noted that as a gas/solids suspension
flows along a pipe the velocity, and therefore the factor a, will be changing. For
dilute-phase flow in a long pipe a first approximation to the pressure-drop can
be obtained from equation (3.80) by simply setting a equal to the solids loading
ratio 4J. Several authors have noted the influence of pipe diameter on the value
of the factor a, and the approximate method outlined in this paragraph may
give a somewhat high prediction of pressure-drop for gas/solids flow in smalldiameter pipes.
A few examples of reported correlations for a will serve to illustrate the
variety of approach, and from these the reader may work out a routine that
will predict the pressure-drop reliably for his or her specific purpose. A useful
comparison of published correlations for dilute-phase suspensions has been
given by Arastoopour et al. [26]. These may be summarized as follows.
Rose and Barnacle [27] suggest that a can be correlated by the expression
a=r:_[_p_(pP) 112 ·4J
8Jg Pg
(3.81)
where Jg and JP are respectively pipe friction factors for the flow of gas alone
and for the flow of solids, pg and pP are the densities of the gas and the solid
particles and 4J is the solids loading ratio. Information given by Rose and
Barnacle suggests that an acceptable value of JP would be given by
for 1.104 <Re< 5.104 , where Re is the Reynolds number for the gas phase.
If the friction factor for gas is now expressed in terms of Reynolds number by
the Blasius formula
Jg =
0.08 Re- 0 · 25
equation (3.81) can be simplified to
a= K 1 (pp/pg)lf24J
(3.82)
where K 1 = (0.325 Re- 0 · 60 ) + (0.0425 Re- 0 · 35 ).
A very similar correlation, having a a function of slip ratio instead of density
ratio, has been proposed by Hinkle and referred to subsequently by several
authors, for example, Leva [15] and Dixon [22]. This correlation can be
expressed as
~ u
a=...E._..P..4J
Jg
Ug
(3.83)
where uP is the solids velocity and u8 is the gas velocity.
The use of an empirical 'solids friction factor' JP in this and the previous
DYNAMICS OF FLUID/SOLIDS SYSTEMS
133
correlations is interesting. That of Rose and Barnacle is said to be a function of
the gas-phase Reynolds number, whereas Leva gives an expression for the
solids friction factor as
(3.84)
in which C0 is the drag coefficient for a particle and is a function of the particle
Reynolds number, ReP= dpgutlf-l, as shown in Figure 3.3.
Another somewhat similar correlation is that ofRichardson and McLeman
who suggested [28]
(3.85)
where ut is the terminal velocity of the solids particles (in free fall) and K 2 is a
factor that depends on the diameter of the conveying pipe.
Yet another correlation, quoted by Boothroyd [29], is that of Vogt and
White who give
rx
=
K 3 ~(!!_) 2 Pp
Re
d
Pg
(3.86)
where d/ D is the ratio of particle size to pipe size, Re is the gas-phase Reynolds
number and K 3 is a constant.
There are many such correlations, often unfortunately showing significant
lack of agreement. A useful summary of the influence of different variables,
such as solids loading ratio, Reynolds number, particle and conveying-pipe
size and particle/gas density ratio, has been given by Boothroyd [29]. He
follows this with a theoretical discussion which leads to the result that
(3.87)
where K 4 is a constant, and this agrees quite closely with some of the empirical
correlations, notably that of Richardson and McLeman, equation (3.85).
There appears to be fairly general agreement that the pressure loss factor rx is
likely to be proportional to the solids loading ratio </> and the conveying-pipe
diameter D, and inversely proportional to the solids velocity uP. The particle
size of the conveyed solids also has an influence on rx and this may be taken into
account by including in the correlation the particle diameter d, the terminal
velocity ut or the drag coefficient C 0 .
For most of the above approaches it is necessary to know the actual
conveying velocity of the solid particles and their terminal velocity in free fall.
Again, various correlations have been proposed for these quantities. For
example, Arastoopour et al. [26] give for the particle velocity
uP=
ug(l - 6.98 x 10- 4 d 0 · 3 p~· 5 )
(3.88)
134
BULK SOLIDS HANDLING
1.0 r - - . - - - - - - - - - r - - - - - - - - r - - - - - - , - - - - - - - - - ,
Cl
:::l
0.9
c.
:::l
'U)
"'
Cl
0 0.8
1?:'
'(3
0
--g
Qi
>
particle density
Q)
(kgfm3J
~
c. 0.7
0
1?:'
'(3
0
Qi
>
J1
.Q
5000
0.6
'§
.Q.
u;
0.5
20
50
100
200
500
particle diameter, d (I'm)
Figure 3.23 Correlation of slip ratio (u 0 /u 0 ) with particle size and particle density. Based on
equation (3.88) [26].
where d is the particle diameter in Jl.m and pP is its density in kg/m 3 . This
correlation is shown plotted as Figure 3.23 and gives a convenient indication
of the relationship between the velocities of the conveying gas stream and of
the solid particles entrained in it.
Many correlations are also available for the terminal velocity in free-fall of
particles of specified size and density, and some methods of predicting the
terminal velocity have been discussed in section 3.3.
The majority of the previously mentioned correlations for pressure-drop in
two-phase gas/solids flow relate to flow in horizontal pipes, and where vertical
flow is involved it is necessary to incorporate an additional term to account for
the solids head.
DYNAMICS OF FLUID/SOLIDS SYSTEMS
135
Thus, for example, we could write
f..p, = f..pg(l +et)+ f..ph
(3.89)
where
(3.90)
This approach should give a reasonably reliable prediction of the pressuredrop in a system comprising a large proportion of vertical pipe runs, since the
influence of the doubtful parameter et is less than for horizontal flow.
Additional pressure-drop due to solids: bends andfittings. A useful discussion of
the influence of pipe bends, divertcr valves and feeding devices is given by Scott
[30]. He suggests that the simplest approach is to treat the whole length of the
system as fully-accelerated flow and then to add on an appropriate extra
pressure-drop for each obstruction. This extra pressure-drop arises essentially
from the need to re-accelerate the solid particles after they have been slowed
down by the obstruction.
For the additional pressure-drop caused by the acceleration of the solid
particles from the pick-up point Scott gives
(3.91)
for a horizontal line, where A is the pipe cross-sectional area. The prediction of
additional pressure-drop resulting from a pick-up in a vertical riser would be
somewhat more difficult due to the added effect of solids hold-up in the
accelerating length.
The flow of gas/solids suspensions around pipe bends has been discussed
elsewhere (section 3.6.4) and from that discussion it was evident that the
peculiar sliding/bouncing motion of the particles through the bend must
render the reliable prediction of pressure-drop all but impossible. A reasonable approach to the estimation of the bend pressure-drops would be through
the use of'equivalent lengths' of pipe, using factors derived from experimental
work, or based on past experience. Thus, if the pressure-drop in a bend is
expressed as
2
A
-
upb-
k PsUg
b
2
(3.92)
where Ps is the density of the gas/solids suspension and kb is a coefficient,
comparison with the Darcy formula equation (3. 71 ), shows that the equivalent
length of straight pipe would be given by
L b_- kb . f.!_. Ps
4 f Pg
136
BULK SOLIDS HANDLING
Table 3.1 Bend pressure-drop factors in equations (3.92),
(3.93)
Bend ratio
(
=
Bend pressure-drop
factor kb
2 x radius of bend)
diameter of pipe
4
8
12
1.50
0.75
0.50
or
Lb =
kb D
47(1 + c/>)
(3.93)
Values of kb in equations (3.92) and (3.93) [31] are given in Table 3.1.
Additional pressure-drop due to solids: dense-phase flow. Because of the
extreme complexity of non-suspension gas/solids flows, and indeed the wide
variation in modes of such flows, it has proved virtually impossible to develop
a reliable mathematical model that would allow the designer of a dense-phase
pneumatic conveying system to predict the pressure-drop with confidence.
Recourse must be made to empirical correlations which, inevitably, will be
valid for a very restricted range of conveying conditions and usually for a
specific bulk solid. Commonly such information will be in the form of test
results obtained from conveying trials on the product concerned in a pilot
plant, and frequently this approach of carrying out actual trials proves to be
the only way of ensuring a reliable design of conveying system for a product for
which the benefit of previous handling experience is unavailable. This design
approach will be discussed in detail elsewhere in this book.
One of the simpler published correlations for pressure-drop in dense-phase
flow is that of Wen and Si mons [32]. Their correlation was developed from the
results of tests on glass beads (70 ,urn to 280 ,urn particle diameter) and coal
(110 ,urn to 750 ,urn) conveyed in pipes of up to one inch (25.4 mm) maximum
diameter. In consistent SI units, the equation of Wen and Simons which gives
the total pressure-drop along a pipeline of length L and diameter D can be
written
11p, = 4.27 Lpd,u~· 45 (
d
)0.25
D
(3.94)
where d is the average particle diameter, uP is the particle velocity and Pcts is the
dispersed solids density (defined as the mass of solids trapped in a short length
DYNAMICS OF FLUID/SOLIDS SYSTEMS
137
of conveying line by the instantaneous closure of two valves, divided by the
volume of the line between the two valves).
The work of Muschelknautz and Krambrock [33] yielded different
correlating expressions according to whether the mode of the dense-phase flow
was 'stratified' or 'dune/slug'. The analysis leading to these expressions is
interesting, but quite complex, and the reader is directed to [33] for full details.
For stratified flow, the form of the expression for pressure-drop in a pipe of
length Lis
(3.95)
where re is the steady-state cross-section ratio, p, is the bulk density of the
stratified flow and fd is a frictional coefficient for the sliding and rolling
product.
In general, if stratified flow is to be maintained the ratio of the crosssectional area of the suspension flow should be at least 40 percent of the total
flow cross-section, and this is likely to correspond to a solids loading ratio of
10-100 with gas-phase velocity of 6-20m/s and solids velocity of 0.1 to 0.3
times the gas velocity. The frictional coefficient fd would be typically around
0.6 to 0.8.
Dune and plug conveyance can occur over much the same range of solids
loading ratios as stratified flow but the gas velocity is likely to be slightly lower
and the solids velocity slightly higher. The form of the Muschelknautz and
Krambrock equation for this mode of dense-phase flow, which is also
discussed by Dixon [22], is
Ap = p 0 (e'- 1)
(3.96)
for horizontal pipes, where
ug
RT uP
j~cjJL
z=~-·~
(3.97)
The probable value of the friction coefficient fd is in this case 0.4 to 0.8. The
velocity ratio, up/ug, would normally be in the range 0.3 to 1.0, with high
loadings of fine products giving the higher values of velocity ratio.
It is clear that, especially for dense-phase flow, the techniques available for
the prediction of pressure-drops in two-phase gas/solids flows is not sufficiently reliable for the engineer to design, with confidence, systems for the
pneumatic transport of bulk solids. The use of test results from suitable pilot
plant is essential, but the models and correlations discussed in this chapter can
be invaluable in scaling and otherwise manipulating such results in order to
understand fully the behaviour of the bulk solid concerned, when it is
pneumatically conveyed. Detailed descriptions of pneumatic conveying
systems and full recommended design methods are given in Chapters 12-14.
138
BULK SOLIDS HANDLING
3.7 Liquid/solids flow in pipes
3.7.1 Flow characteristics of liquid/solids mixtures ( slurries)
Hydraulic conveying is now a well-established mode of transportation of bulk
solids, especially where the requirement is for high tonnages to be conveyed
over long distances. Coal, phosphates and mineral ores represent just a few of
the materials that are carried hydraulically in 'slurry pipelines' at many
different locations around the world. An elementary study of hydraulic
conveying technology, beginning with a description of a number of actual
working installations and going on to describe features and components of
typical systems, will be undertaken in Chapter 16. However, in order that the
reader should be able to make informed decisions on the practical and
economic feasibility of potential systems it is essential to have a general
understanding of the flow characteristics of two-phase liquid/solids mixtures.
For this reason the possible modes of flow are discussed here in some detail
and then mathematical modelling techniques will be introduced.
It is convenient to make a broad distinction between two types of flow.
(i) Homogeneous flow (non-settling suspensions). Very fine particles at high
concentration tending to remain in suspension irrespective of the conditions under which flow is taking place.
(ii) Heterogeneous flow (settling slurries). This classification of flow behaviour
can range from fully suspended fine particles exhibiting a significant
concentration gradient, to relatively large particles transported by a
combination of carrying and rolling at the bottom of the pipe or channel.
The distinguishing feature of heterogeneous flow is that the liquid phase
remains separate from the solid particles, with its character (and its flow
properties) essentially unchanged.
The so-called 'homogeneous slurry' is usually the result of high concentrations (generally greater than 80% by volume) of very fine particles which
tend to have such low rates of sedimentation that the mixture becomes
effectively a single-phase one, but having flow characteristics that may be
markedly different from those of the original uncontaminated liquid. In fact,
the flow behaviour of homogeneous slurries may exhibit distinctly nonNewtonian features, the extent of the deviation from Newtonian flow
depending principally on the tendency of the suspended particles to flocculate.
Where significant flocculation occurs the suspension is likely to display shearthinning (pseudoplastic) properties, but there are many other factors, such as
solids concentration, particle size distribution, temperature, additives/
contaminants, pH levels and so on, which can affect the flow behaviour of a
slurry.
Various non-Newtonian models may be considered to represent the flow of
homogeneous slurries, in order to predict pressure-drops, for example, and
selection of these models will be discussed in section 3. 7.2.
DYNAMICS OF FLUID/SOLIDS SYSTEMS
139
Where the concentration is less than about 40 per cent (the actual figure
being much influenced by the size and density of the particles, and the density,
viscosity and turbulence of the carrying liquid) the particles will tend to settle
so that there is a distinct concentration gradient over a cross-section of the
flow channel. If the flow velocity is relatively high it is still possible for the
particles to be fully suspended, but at lower velocities a situation is likely to
exist in which suspended flow occurs over a sediment of particles moving more
or less steadily along the bottom of the pipe or channel. This describes the
typical behaviour of a heterogeneous or settling slurry flowing horizontally.
Vertical flow of heterogeneous slurries is less well documented, although it is
clear that the effects of hindered settling, varying terminal velocities according
to the particle size distribution, and the radial variation of flow velocity, will
cause the flow behaviour to be quite complex.
The prediction of pressure-drops and deposition velocities in flows of
heterogeneous slurries in both horizontal and vertical pipes is discussed in
section 3.7.3.
3.7.2 Non-Newtonianflow models for homogeneous suspension
A fluid flowing in a pipe loses energy as a result of friction at the pipe wall. This
friction loss can be expressed in general terms as a pressure-drop:
(3.98)
where r 0 is the shear stress existing at the pipe wall, Lis the pipe length over
which !lp occurs and D is the diameter of the pipe. Naturally, if there is a
change of elevation this will also have to be taken into account in order to
determine pumping requirements.
In the familiar case of Newtonian fluid behaviour the local shear stress is
given by
du
dr
!=Jl-
(3.99)
where 11 is the coefficient of (dynamic) viscosity and du/dr is the velocity
gradient.
More generally, however, the local shear stress r could be regarded as a
function of the rate of shear y and the time t, and a considerable number of
non-Newtonian fluid models have been proposed, described variously as
'time-independent', 'time-dependent' and 'visco-elastic'. Although some slurries may exhibit time-dependent behaviour, this is relatively uncommon, and
in this book only the first group of models-those in which the shear stress is a
function only of the shear rate-will be considered.
The time-independent fluid models are defined by the relationship
r =function (Y]
140
BULK SOLIDS HANDLING
- - Herschei-Bulkley
-
Bingham plastic
-
Newtonian
-dilatant
"'
(])
.<:
Vl
shear rate,
Figure 3.24
'Y
Models of time-independent non-Newtonian fluids.
and it may be noted that the Newtonian fluid is merely a special case of this
general model in which the function is a linear one.
Since for this model of time-independent fluid there is a unique relationship
between rand y, the function may be plotted as a single line on a graph of shear
stress against shear rate. Various types of behaviour have been observed and
the most important of these are represented in Figure 3.24.
Pseudo plastic and dilatant fluids. These types of behaviour are characterized
by curved lines on the plot of r against y, showing that as the shear rate is
increased the liquid is tending either to become 'thinner' (pseudoplastic fluids)
or to become 'thicker' (dilatant fluids). It is convenient to define an 'apparent
viscosity' Jlavv in the same way as dynamic viscosity is defined for a Newtonian
fluid; i.e.
r
Jlapp
= ~
r
However, it must be noted that Jlavv• which is represented by the slope of a
line from the origin to a point on the curve of r v.y, is not constant, but is a
function of y. Thus the term 'viscosity' has no meaning for a non-Newtonian
fluid unless it is related to a particular shear rate.
The simplest mathematical model of the behaviour of pseudoplastic and
dilatant fluids (due to Ostwald) is the power law
r = k)"
(3. I 00)
DYNAMICS OF FLUID/SOLIDS SYSTEMS
141
loge Y
Figure 3.25
Power law models of non-Newtonian fluids.
where k and n are constants. The value of k gives an indication of the
consistency ofthe fluid and the index n indicates the amount of deviation from
Newtonian behaviour. Thus, for Newtonian fluids, n = 1, for pseudoplastics
n < 1 and for dilatant fluids n > 1. This can usefully be illustrated on a
logarithmic plot as
loge T
=
logek + nlogey
(3.101)
since the slope of the log plot is n and from the intercept the value of the
'consistency constant' k can be determined (Figure 3.25).
For the power law model the apparent viscosity is given by
T
J.lapp =-;- =
y
• n- I
ky
(3.102)
The power law model has a number of inherent limitations: (i) equation
(3.1 02) suggests that at zero rate of shear the apparent viscosity is infinite; (ii)
for most slurries n is not likely to be constant over the entire range of practical
flow conditions; and (iii) the consistency constant k has dimensions which
depend upon the value of the index n.
Various alternative mathematical models have been proposed in efforts to
overcome these limitations. Nevertheless, the simple power-law model is
adequate for the prediction of the behaviour of many real slurries and colloidal
suspensions, such as detergent slurries, mayonnaise, some paints and lacquers,
some mineral slurries and paper pulp suspensions, in a wide variety of flow
situations.
It is well known that Newtonian fluids exhibit a transition from laminar to
turbulent flow behaviour when the flow condition is such that the Reynolds
142
BULK SOLIDS HANDLING
number has a certain characteristic (or 'critical') value. Thus, for a Newtonian
fluid flowing in a pipe of circular cross-section, the mode of flow is likely to be
laminar if
PrDUav < 2000
J1.
(3.103)
where Pr and J1. are the density and viscosity of the fluid, uav is its mean velocity
and D is the diameter of the pipe.
Non-Newtonian fluids also exhibit this transition from laminar to turbulent
flow, but a problem arises over the definition of 'viscosity' as it appears in the
Reynolds number used to characterize the flow.
Now an analysis of the laminar flow of a power law fluid in a pipe of
diameter D leads to the following expression for the average velocity:
u = _n_.!!_(!. DAp )1/n
av
3n + 1 2 k 4L
(3.1 04)
from which the pressure-drop Ap in length L can be written
Ap
L
= 4k(3n + 1. 2uav )"
D
n-
D
(3.105)
Noting that the shear stress at the pipe wall is given by
DAp
ro= 4L
(3.106)
equation (3.105) gives the expression
(3.107)
in which the term 8uav/D can be identified as a flow characteristic that is
proportional to the shear rate y.
For a Newtonian fluid k = J1. and n = 1, so that equation (3.105) reduces to
Ap
I:
32Jl.Uav
---vz-
(3.108)
which is the familiar Poiseuille equation.
Now by rearranging equation (3.108) it can be seen that an expression for
the viscosity is
_ DAp /8uav
D
Jl.- 4L
(3.109)
and it is convenient to extend this expression to apply to non-Newtonian fluids
by defining an 'effective viscosity' Jl.e as the wall shear stress divided by the
143
DYNAMICS OF FLUID/SOLIDS SYSTEMS
2600
(;;
_o
E
:l
~ 2400
/V
1:l
0
............
V
c
>())
~ 2200
et!
-_;::;
()
~
1'---
..........
J
•t
2000
0
Figure 3.26
fluids [34].
I
I
i'....
............
---- ------- f--f--
0.2
OA
0.6
0.8
flow index, n
1.0
r--....
"""'
1.2
--
f---
~"-......
1.4
Relationship between critical Reynolds number and flow index (n) for power law
average shear rate at the boundary, i.e.
_ ;su.v
D
J.l.e-
To
(3.110)
Combining equations (3.1 07) and (3.11 0) it is seen that for a power-law fluid
the effective viscosity is given by
J.l.e
=
k
(~)"(8Uav)n-l
4n
D
(3.111)
Extensive experimental work on a wide variety ofnon-Newtonian fluids has
shown that the value of the Reynolds number (defined in terms of the effective
viscosity J.l.e) at which transition from laminar to turbulent flow occurs is a
function of the flow index n. Figure 3.26 [34] gives an approximate
relationship between Re and n so that, provided the non-Newtonian
characteristics k and n are known, it is possible to estimate the velocity at
which the transition from laminar to turbulent flow would occur for a slurry
flowing in a pipe of specified diameter.
If the flow is in the laminar region, the pressure-drop can then be estimated
using equation (3.1 05). The prediction of pressure-drop for power law fluids in
the turbulent region is neither straightforward nor reliable. Perhaps the
simplest approach is the one originally proposed by Dodge and Metzner [35]
based on the use of a generalized Reynolds number defined by
av
{J D"u2 -n
Re*= r
(3.112)
J.1.
Using this Reynolds number and the design chart of Figure 3.27 [35] a
144
BULK SOLIDS HANDLING
1'\
0.02
c5
u
t\
1=16/Re
-
)'\~'-/
'(
0.01
-- -
r-1-1 ..
...... ~--~---
"'
/
/
"V
2
c
g 0.005
.....
~
~
f.;;
!"""~
-r-r-- ....
...., f'.....
·,
-----
experimental regions
0.001
10 3
Figure 3.27
' f\.r-.
extrapolated regions
I Ill
I
...
r--~'
1...
·a.
0.002
-- - ---.. ..
..
t--- ........
'
Q)
Q.
.. ..- ...
1- ...
I I III
r--
... r...
...-~-.........._
.... ......
''
...
...
......... ...
...
2.0
r- 1--.
...
1.4
1.0
0.8 c
...... r-
-.. -
,;.
0.6
·--~--
''
r-
-~
0.4 3:
0.3
.... r-
10 4
generalized Reynolds number, Re*
0.2
10 5
Friction factor design chart (power law fluids) from [35].
r=
"y + l'pi'
(Bingham plastic)
slope= l'p
(coefficient of rigidity
or plastic viscosity)
t
yield stress, T y
I
shear rate, i'
Figure 3.28
Q)
"0
Bingham plastic and Herschel-Bulkley models of non-Newtonian fluid flow.
0
;;:::
DYNAMICS OF FLUID/SOLIDS SYSTEMS
145
value of the pipe friction factor can be estimated which allows the pressuredrop to be calculated in the usual way.
Bingham plastics and Herschel-Bulkley fluids. Some types of slurry at rest
exhibit a three-dimensional structure of sufficient rigidity to resist any stress
less than a certain 'yield' value. When this yield stress is exceeded the material
flows as a conventional liquid. This behaviour can be represented by a model
in which the slurry flows under an effective shear stress r- ry either as a
Newtonian fluid (the Bingham plastic model) or as a pseudoplastic having
power-law characteristics (the Herschel-Bulkley model). The features of these
models are illustrated in Figure 3.28 on a plot of r against y.
The Herschel-Bulkley model is very convenient, as it can be used to
describe all the types of fluid-flow behaviour illustrated in Figure 3.24. The
Bingham plastic, which can be regarded as a special case of the HerschelBulkley model, will be considered now in more detail.
Two parameters are required to characterize the Bingham plastic modelthe yield stress ry and the slope of the straight line Jlp, known as the 'plastic
viscosity' or 'coefficient of rigidity' (Figure 3.28). The plastic viscosity can thus
be defined as
r- ry
y
(3.113)
Jlp=--.-
and it is also possible to define an 'apparent viscosity' in the same way as for
the power law models, i.e.
r
Jlapp = -;- = Jlp
Y
ry
+ ---;y
(3.114)
The Bingham plastic model is found to be quite reliable for the prediction of
flow behaviour of a wide range of liquid/solid suspensions such as drilling
muds, thick mineral slurries, sewage sludge, and polymer solutions.
As with other models of fluid flow, it is necessary to be able to predict the
transition from laminar to turbulent behaviour. For Bingham plastics a useful
dimensionless parameter, from which the transition can be predicted with
reasonable confidence, is the Hedstrom number, defined as
He= PsryD2
Jl~
(3.115)
An empirical relationship between the critical Reynolds number (defined
now in terms of the plastic viscosity Jlp) and the Hedstrom number is given in
Figure 3.29 [34] allowing the average velocity of the slurry at transition to be
estimated.
In contrast to the velocity profiles associated with most models of fluid flow
in pipes, the velocity profile for a Bingham plastic is not a smooth curve. Since
146
BULK SOLIDS HANDLING
105
~
loo
1--l--
--
!""'
:;::;;-
....
...... ~~-""
-+""
105
Hedstrom number, He
Figure 3.29 Relationship between critical Reynolds number and Hedstrom number for
Bingham plastics [34].
...
flow
--- ----
!
~flowz one
f
(T>Ty )
plug zone
(T< Ty)
__....., ___l
Figure 3.30 Velocity distribution in a flowing Bingham plastic.
the shear stress in the flowing fluid decreases from a maximum at the pipe wall
towards the centre, there will be a point at which it becomes equal to the yield
stress
Between this radial position and the pipe centre-line the fluid shear
stress does not exceed the yield value and therefore there is a central core of
fluid which moves at a uniform velocity, effectively as a solid cylindrical 'plug'
(Figure 3.30).
Analysis of this model yields the following expression for the mean velocity
of the flow of a Bingham plastic in terms of the plastic viscosity Jl.p, the yield
stress and the shear stress at the pipe wall 0 :
ty.
ty
t
Uav=Dto[l-~·ty +~(ty)4]
8J1.p
3
t0
3
t 0
(3.116)
DYNAMICS OF FLUID/SOLIDS SYSTEMS
147
1.0
0 0. 1
0
~
c
.g
~
CD
·~ 0.01
Aeynolds number, Re
Figure 3.31
Friction factor design chart (Bingham plastics) from [36].
It can be shown that relatively little error is introduced by neglecting the
final term in the square bracket, if rJ r: 0 is small, and therefore an approximate
expression for the mean velocity is
D
Uav= -8
/).p
4
(ro-J!y)
(3.117)
Writing r 0 in terms of Ap and rearranging then gives an expression from
which the pressure-drop occurring in the laminar flow of a Bingham plastic
can be estimated:
Ap
L
(3.118)
The similarity to the Poiseuille equation (3.108) will be noted.
An alternative and perhaps more reliable approach, based on the method
developed by Hedstrom, involves the use of a chart relating the pipe friction
factor f to the Reynolds number (p.Duav!Jl.p) for various values of Hedstrom
number (Figure 3.31 ).
As with the power law model of non-Newtonian flow, the accurate
prediction of pressure-drops occurring in the turbulent regime is much more
difficult. However, a very convenient approximation that has been proposed
by a number of research workers is simply to use the conventional Moody
148
BULK SOLIDS HANDLING
saltation regime
heterogeneous regime
pseudo-heterogeneous
regime
::;
'0.
<l
Q)
Ol
.Q
"0
Q)
Ol
Ol
:J
0.
Q)
0.
·a.
"0
Q)
.0
"0
>-
.0
Ol
~
c
.9
Ei
<JJ
Q)
-~
>
0
E
c
0
c
0
I
I
I
I
I
I
·u;
I
I
I
I
·;::
·;::
E
E
E
E
<JJ
<JJ
c
Q)
0.
<JJ
:J
<JJ
()
a;
>-
"'
:/udc
·u;
c
Q)
0.
<JJ
:J
<JJ
()
a;
>-
loge Uav
Figure 3.32
Modes of flow occurring in heterogeneous slurries.
diagram (Figure 3.20) for the determination of the pipe friction factor f, but
with the Reynolds number defined in terms of the plastic viscosity /lp· For a
discussion of the error incurred in this approach the reader is referred to [34].
3.7.3 The modelling of heterogeneous suspensions
Whereas in homogeneous flows only laminar and turbulent regimes exist, in
the case of heterogeneous flows there are a number of possible flow patterns
that can occur, depending principally upon the velocity and concentration, as
described in section 3. 7.1.
It is convenient to illustrate these modes of flow on a log-log plot of
pressure-drop against mean velocity (Figure 3.32), somewhat similar to the
Zenz diagrams used previously to illustrate the flow behaviour of gas/solids
mixtures (Figures 3.17, 3.19). It can be seen that at relatively high velocities the
149
DYNAMICS OF FLUID/SOLIDS SYSTEMS
particles are carried in suspension and the flow pattern tends towards the
symmetrical, homogeneous mode. As the velocity is reduced, the conveyed
particles will show a greater tendency to settle, and the flow pattern becomes
asymmetrical. The minimum point on the pressure curve corresponds to the
so-called 'deposition critical velocity' udc· At lower velocities a sliding or
moving bed of deposited particles will exist and this can gradually build up
causing a steady increase in the pressure-drop.
Because of the need to avoid this unstable flow situation, in slurry transport
systems for example, the prediction of the critical deposition velocity is
important. The usual method is due to Durand and involves the definition of a
modified Froude number or 'deposition velocity parameter' F L as
F L -
udc (
fiii5
Pc )1/2
Pp -Pc
(3.119)
where pP, Pc are the densities of the solid particles and the liquid respectively.
It is found that F L is a function of the particle size and of the concentration
of solids in the suspension. Wasp [34] has extended the correlation to include
the influence of particle size, suggesting the expression
F~=~(-Pc )1/2(12)1/6
flii5
An approximate empirical correlation for
concentration is
F~ = 3.13 c~· 186
(3.120)
d
Pp - Pc
in terms of the solids
F~
and combining this with equation (3.120) and rearranging leads to
udc = 1.323 C?· 186 [
2gD(Pp ~Pc)
J (~ y
12
16
(3.121)
where Cv is the volume concentration of solids.
The point has been made previously that the distinctive feature of
heterogeneous flow is the minimal effect that the presence of solid particles has
on the flow properties of the carrying liquid. In practical slurry transport
systems the flow condition will inevitably be such that the liquid is in the
turbulent regime so that, for heterogeneous suspensions, the prediction of
pressure-drop is only concerned with turbulent flow.
Once again, an analysis of the turbulent flow condition is very difficult and
much reliance is placed on empirical correlations. The best known approach is
that of Durand [37] who proposed the following expression for the effective
pipe friction factor f, (for the slurry) in terms of the friction factor fc for the
liquid and the drag coefficient C0 for the particles:
_[
f, - fc 1 + K Cv
F
{gD.pp-Pc(_1 )
2
u.v
Pc
C
1 2
o
1 } 3 12 ]
(3.122)
150
BULK SOLIDS HANDLING
where K is a constant having a value in the range 80-150. A detailed discussion
and examples of the use of this correlation may be found in [34].
3.8 Notation
A
A.
AP
Ar
Co
CV
D
d
da
dv
dvsm
dwm
e
Fo
Fa
Fv
f
fd
fc
/g
JP
f.
H
Hmc
Kt
K2
K3
K,
k
k', k"
kb
kc
L
1.
mP
mg
mp
n
Cross-sectional area of a bed of particles
Average effective cross-sectional flow area of voids
Projected area of particle
Archimedes number
Drag coefficient
Volumetric concentration of solids in a suspension
Diameter of pipe
Diameter of a spherical particle
Sieve aperture size
Volume diameter of a particle
Volume-surface mean diameter of a particle
Median size of particles in a bulk solid
Pipe roughness
Drag force on particle
Gravitational force on particle
Buoyancy force on particle
Pipe friction factor (Darcy)
Friction factor for dense-phase flow
Pipe friction factor for a liquid
Pipe friction factor (gas phase)
Pipe friction factor (solids phase)
Pipe friction factor for a suspension of particles in a liquid
Depth of bed
Depth of bed at condition of incipient fluidization
Constant in equation (3.82)
Constant in equation (3.85)
Constant in equation (3.86)
Multiplying factor in equation (3.38)
Constant in equation (3.3); consistency constant for power-law
fluid
Coefficients in Carman-Kozeny/Ergun equations
Bend pressure loss factor
Friction coefficient for particulate bed
Length of pipe
Effective length of fluid path through bed
Mass of particle
Gas mass flow rate
Solids mass flow rate
Index in equation (3.43); index in equation (3.69); flow index for
power-law fluid
DYNAMICS OF FLUID/SOLIDS SYSTEMS
Pg
R
Rb
Reb
Re*
r
re
Sb
Sp
T
u
u.v
uch
udc
ue
u~
Urs
ug
umb
umr
urns
uP
us
u1
Vb
V
Wb
x
~
y
l'ip
l'ip.c
l'ipb
l'ipg
emr
~: 0
es
A.
J1
Jlapp
Jle
151
Pressure of gas
Characteristic gas constant
Flow resistance of particulate bed per unit area of free surface
Reynolds number for flow in a particulate bed
Generalized Reynolds number, equation (3.112)
Radial position
For stratified dense-phase gas/solids flow, the ratio of the
effective cross-section of the gas phase to that of the empty pipe
Specific surface of a particulate bed
Specific surface of particles within a bed
Absolute temperature
Time
Mean approach velocity of fluid (superficial velocity)
Mean velocity (over cross-section of flow)
Choking velocity
Deposition critical velocity for heterogeneous slurry
Effective mean axial component of velocity in voids (interstitial
velocity)
Corrected interstitial velocity
Minimum velocity at which fluidized bed is 'fully supported'
Velocity of gas
Minimum bubbling velocity of fluidized bed
Minimum fluidizing velocity
Minimum spouting velocity of granular bed
Velocity of solid particles
Saltation velocity
Terminal velocity of a particle
Volume of particulate bed
Volume flow rate
Total gravity force on bed of particles
Mass fraction
'Pressure loss factor,' equation (3.80)
Shear rate
Pressure drop
Acceleration pressure-drop
Pressure-drop across bed of particles; pressure-drop across pipe
bend
Pressure-drop for gas
Voidage of bed at condition of incipient fluidization
Voidage of a particulate bed
Voidage of a suspension of particles in a fluid
Hydraulic radius
Dynamic viscosity
Apparent viscosity
Effective viscosity of non-Newtonian fluid
152
J.lp
V
BULK SOLIDS HANDLING
Plastic viscosity of coefficient of rigidity (for Bingham plastic)
Kinematic viscosity
Effective kinematic viscosity of a suspension of particles in fluid
Density
Dispersed solids density, equation (3.94)
Density of fluid
Density of gas
Density of a particle
Density of a suspension of particles in fluid
Local shear stress
Shear stress at pipe wall
Yield shear stress (for Bingham plastic)
Solids loading ratio ( = rhp/rhg)
Sphericity
References and bibliography
References
1. Carman, P.C. (1937) Fluid flow through granular beds. Trans. Instn. Chem. Engrs. (London)
51 (1) 150-166.
2. Ergun, S. (1952) Fluid flow through packed columns. Chem. Engg. Progr. 48, 89-94.
3. Pettyjohn, E.S. and Christiansen, E. B. (1948) Effect of particle shape on free-settling rates of
isometric particles. Chem. Engg. Progr. 44 (2) 157-172.
4. Hawksley, P.G.W. (1951) The physics of particle size measurement. BCURA Bull. 15(4)
105-146.
5. Alien, T. (1981) Particle Size Measurement. 3rd edn., Chapman and Hall, London.
6. Richardson, J.F. and Zaki, W.N. (1954) Sedimentation and fluidisation: Part I. Trans. /nstn.
Chem. Engrs. 32, 35-53.
7. Kunii, D. and Levenspiel, 0. (1969) Fluidization Engineering. John Wiley, New York.
8. Wen, C.- Y. and Yu, Y.H. (1966) Mechanics of fluidization. Chem. Engg. Progr. Symp. Ser. 62
(62) 100-111.
9. Richardson, J.F. (1971) Incipient fluidization and particulate systems, in Fluidization, eds.
J.F. Davidson and D. Harrison, Academic Press, New York, 25-64.
10 Baeyens, J. and Geldart, D. Predictive calculations of flow parameters in gas fluidized beds
and fluidization behaviour of various powders, in Proc. Conf, La Fluidization et ses
Applications, Toulouse, October 1973, 263-273.
11. Siege!, R. (1976) Effect of distributor plate-to-bed resistance ratio on onset of fluidized bed
channelling. A/ChE J. 22 (3) 590-592.
12. Geldart, D. (1973) Types of gas fluidization. Powder Technol. 7, 285-292.
13. Mathur, K.B. and Epstein, N. (1974) Spouted Beds. Academic Press, New York.
14. Epstein, N., Lim. C.J. and Mathur, K.B. (1978) Data and models for flow distribution and
pressure drop in spouted beds. Can. J. Chem. Engg. 56, 436-447.
15. Leva, M. (1959) Fluidization. McGraw-Hill, New York.
16. Wen, C.-Y. (1971) Dilute and dense-phase pneumatic transport, in Bulk Materials Handling,
ed. M.C. Hawk, Vol. I, Univ. Pittsburg School of Mech. Engg., 258-287.
17. Zenz, F.A. and Othmer, D. F. (1960) Fluidization and Fluid Particle Systems. Reinhold, New
York.
18. Hitt, R.J., Reed, A.R. and Mason, J.S. An investigation into modes of slugging in horizontal
dense-phase pneumatic conveying, in Proc. Pneumatech I Conf., May 1982, Stratford-uponAvon, UK.
19. Hitt, R.J. (1984) An investigation into the low velocity pneumatic conveying of bulk solids.
PhD Thesis, Thames Polytechnic, London.
DYNAMICS OF FLUID/SOLIDS SYSTEMS
153
20. Mainwaring, N.J. and Reed, A.R. Mechanisms of gas-solids flows at low velocity in pneumatic
conveying pipelines, in Proc. 11th Powder and Bulk Solids Conf, Chicago, May 1986.
21. Dixon, G. The impact of powder properties on dense-phase flow, in Proc. Int. Conf on
Pneumatic Conveying, Cafe Royal, London, January 1979.
22. Dixon, G. (1981) Pneumatic conveying. In Plastics Pneumatic Conveying and Bulk Storage,
ed. G. Butters, Applied Science Publishers, Barking.
23. Mason, J.S. ( 1972) Pressure drop and flow characteristics for the pneumatic transport of fine
particles through curved and straight circular pipes. PhD Thesis, Liverpool Polytechnic.
24. Churchill, S.W. (1977) Friction factor equation spans all fluid-flow regimes. Chem. Engg., 7th
November, 91-92.
25. Marcus, R.D. A review of drag reduction and reduction in power consumption in pneumatic
conveying systems with special reference to actual experimental observations, in Proc. Int.
Powder and Bulk Solids Handling and Processing Conf, Philadelphia, May 1979, 315-326.
26. Arastoopour, H., Modi, M. V., Punwani, D. V. and Talwalkar, 'l'\.T. A review of design
equations for dilute-phase gas-solids horizontal conveying systems for coal and related
materials, in Proc. Int. Powder and Bulk Solids Handling and Processing Conf, Philadelphia,
May 1979, 339-355.
27. Rose, H.E. and Barnacle, H. E. (1957) Flow of suspensions of non-cohesive spherical part:cles
in pipes. The Engineer 203 (5290) 898-901, 939-941.
28. Richardson, J.F. and McLeman, M. (1960) Pneumatic Conveying: Part II. Solids velocities
and pressure gradients in a one-inch horizontal pipe. Trans. Instn. Chem. Engrs. 38, 257-266.
29. Boothroyd, R.G. (1971) Flowing Gas-Solids Suspensions. Chapman and Hall, London.
30. Scott, A.W. Pneumatic conveyor design-art or science, in Proc. 4th Int. Powder Tech. and
Bulk Solids Conf, Harrogate, February 1977, Heyden, Philadelphia, 10-17.
31. EEUA Handbook No. 15, Pneumatic Handling of Powdered Materials. Constable, London
(1963).
32. Wen, C.-Y. and Simons, H.P. (1959) Flow characteristics in horizontal fluidised solids
transport. A/ChE J. 5 (2), 263-267.
33. Muschelknautz, E. and Krambrock, W. (1969) Vereinfachte Berechnung horizontaler
pneumatischer Fiirderleitungen bei hoher Gutbeladung mit feinkiirnigen Produkten (Simplified calculations for horizontal pneumatic systems conveying fine products at high loadings)
Chemie Ing. Tech. 41 (21), 1164-1172. [In German.]
34. Wasp, E.J., Kenny, J.P. and Gandhi, R.L. (1979) Solid-Liquid Flow Slurry Pipeline
Transportation. Gulf Publishing Co., Houston.
35. Dodge, D.W. and Metzner, A. B. (1959) Turbulent flow ofnon-Newtonian systems. A/ChE J.
5 (2), 189-204.
36. Baker, P.J. and Jacobs, B.E.A. (1979) A Guide to Slurry Pipeline Systems, BHRA Fluid
Engineering.
37. Durand, R. (1952) The hydraulic transportation of coal and other material in pipes, Colloq.
National Coal Board, London.
Recommended further reading
Alien, T. (1981) Particle Size Measurement. 3rd edn., Chapman and Hall, London.
Massey, B. (1983) Mechanics of Fluids. 5th edn., Van Nostrand Reinhold.
Coulsen, J.M. and Richardson, J.F. (1980) Chemical Engineering. Vol. 2, Unit Operations. 3rd Edn.,
revised, Pergamon, Oxford.
Kunii, D. and Levenspiel, 0. (1969) Fluidization Engineering. John Wiley and Sons, New York.
Leva, M. (1959) Fluidization. McGraw-Hill, New York.
Zenz, F.A. and Othmer, D.F. (1960) Fluidization and Fluid Particle Systems. Reinhold, New York.
Mathur, K.B. and Epstein, N. (1974) Spouted Beds. Academic Press, New York.
Butters, G. (ed.) (1981) Plastics Pneumatic Conveying and Bulk Storage. Applied Science
Publishers, Barking.
Holland, F.A. (1973) Fluid Flow for Chemical Engineers. Edward Arnold, London.
Boothroyd, R.G. (1971) Flowing Gas-Solids Suspensions. Chapman and Hall, New York.
4
The design of storage bins and
hoppers
4.1 Introduction
The storage bin, silo or hopper is one of the most important items of
equipment in any bulk solids handling installation, since a poorly flowing
hopper can have repercussions extending throughout the plant. All too often
hoppers are 'squeezed in' after the remainder of the system has been designed,
and this can result in various flow problems, such as those described generally
as 'arching' or 'rat-holing' (section 2.3.4). Obviously, if this occurs, even the
most sophisticated and expensive equipment downstream of the hopper will
be unlikely to perform effectively because of the erratic supply of material. Part
of the problem is often a lack of appreciation by designers and operators that,
for a system to operate satisfactorily, bulk solid must flow from the hopper
when required and in a predictable manner. Thus, as with any other part of the
handling system, gravity-flow storage hoppers should be designed or selected
to handle the actual product under consideration.
With many free-flowing materials, lack of detailed attention to the design of
the storage facility is oflittle consequence, since the free-flow characteristics of
such materials enable discharge to be effected as and when required. For some
materials the flow/discharge pattern within the hopper is important. For
example, it is evident that for perishable foodstuffs a mass-flow pattern is more
desirable than core-flow, since the 'first-in first-out' discharge sequence
minimizes the residence time of the material in store. As indicated in
Chapter 2, for a given product it is the angle of the converging section of the
hopper that largely dictates the discharge pattern.
With materials that have a tendency to be cohesive (such as those having
fine particle size or high moisture content), the consolidating forces exerted
during storage in a hopper may result in the bulk acquiring sufficient strength to
obstruct the flow. This can happen either by the material arching (bridging)
across the opening, or by a stable 'rat-hole' developing from the opening up to
the free-surface of the bulk material. It is the size of this opening that
determines whether or not an obstruction will occur; above a critical size the
product will flow unobstructed, whereas below this size some kind of
obstruction to flow may be anticipated. If such obstructions are to be avoided
it is therefore necessary to be able to predict the critical dimensions of hopper
outlet for the product under consideration.
In this chapter is presented a simplified form of the procedure evolved by
Jenike [1] for determining (i) the outlet dimension(s) of the hopper to give
THE DESIGN OF STORAGE BINS AND HOPPERS
155
unimpeded gravity flow, and (ii) the cone angle to give the required flow
pattern. It is important to realize that the analytical work leading to Jenike's
design procedure is very complex. However, it has yet to be superseded by
anything of lesser complexity. A simplified form of the Jenike method will be
presented in this chapter after a discussion of the various factors which
influence the overall hopper geometry. For a much more rigorous treatment
the reader is directed to [2] or [3].
A detailed consideration of the structural design of storage vessels is beyond
the scope of this introductory textbook and therefore only a brief mention of
the topic will be made in this chapter. References are given, however, to enable
the interested reader to undertake further study on, for example, the
application of finite-element methods and computer-aided design techniques
to the design and construction of storage vessels.
The final sections of this chapter deal with the selection and use of feeders
and discharge aids. There are many occasions in industrial practice when it is
necessary to control the rate at which a bulk solid is fed from a storage bin or
hopper; for example, when filling bags or supplying product to a processing
plant. Two aspects of hopper discharge then become important:
(i) The flow of material from the hopper cannot usually be allowed to take
place freely but must be 'throttled' to the required rate by some type of
'feeder'.
(ii) Once an appropriate feeder has been selected, it must be ensured that
product flows from the hopper to the feeder continuously at an adequate
rate. The design of the hopper system must be undertaken with care if
problems of flow obstruction through arching or rat-holing are to be
avoided.
(Although these aspects of hopper discharge have been listed separately, it
cannot be over-emphasized that the hopper and the feeder must be designed to
work together as an integrated system.)
Attention has previously been given briefly to the matter of estimating the
discharge rate from a storage hopper. Although the method of designing
hoppers for unobstructed flow is now well-established and reliable, the
accurate prediction of the actual rate at which a bulk solid discharges still
represents a formidable challenge. A number of technical papers have been
published on this problem, and some simplified methods of estimating the flow
have been outlined in Chapter 2, but there is as yet no useful general approach
that could be considered within the scope of this book. Attention is therefore
focused upon the measurement and control of solids flow from storage
hoppers, and in section 4.9 descriptions will be given of a number of different
types of feeding device.
Whilst with many bulk solids the avoidance of flow problems is simply a
matter of ensuring that the angle of the sloping walls is sufficient and the size of
the outlet is large enough, other cases are frequently encountered where the use
156
BULK SOLIDS HANDLING
of some form of discharge aid is necessary. Examples of such discharge aids for
'awkward' products range from simple impact devices that are little better
than continuously beating the hopper wall with a hammer, to quite
sophisticated vibrating mechanisms that fit inside the hopper, and in the final
part of this chapter a selection of these will be described.
4.2 Hopper geometry
4.2.1 Shape
It is convenient to make a general classification of storage hoppers or bins as
'mass-flow', 'core-flow' or 'composite', although the actual pattern of flow
within the container may depend upon the nature of the bulk solid concerned
as well as on the shape of the hopper.
Typical mass-flow bins are shown in Figure 4.1. The two basic shapes are
conical and plane-flow, as illustrated in Figures 4.1a and 4.1b respectively. As
explained in Chapter 2, mass-flow hoppers are characterized by a shallow
angle of the converging section. For a given product, the hopper half-angle f3c
(a) Conical hopper
(d) Chisel,
plane-flow hopper
(b) Wedge, plane-flow hopper
(c) Transition
(f) Square opening
(e) Pyramid hopper
Figure 4.1
Mass-flow hoppers.
157
THE DESIGN OF STORAGE BINS AND HOPPERS
(a) Pyramid,
square opening
(b) Cylindrical,
flat-bottomed,
slot opening
De
(c) Conical
(d) Cylindrical,
flat-bottomed,
circular opening
Figure 4.2 Core flow hoppers.
will normally be smaller for a conical hopper than the half-angle {3P for a
corresponding wedge, plane-flow hopper. In addition the opening size or
diameter Dc for a conical hopper is typically twice as large as the minimum slot
width DP for a wedge hopper. Thus it is clear that a plane-flow hopper is more
efficient in terms of headroom required when a given quantity of material is to
be stored. The disadvantage of the plane-flow hopper is the need for the slot
length to be equal to the hopper width L; this makes for a long narrow
opening. The limiting (minimum) length of slot for plane-flow is L = 3DP.
There are several alternative shapes for mass-flow hoppers, as illustrated in
Figures 4.lc-f. The transition hopper has plane-flow sides and conical ends.
The chisel shape is simple and effective but has the disadvantage of in-flowing
valleys. The same is true of the pyramidal shape with a square opening.
Typical core-flow hoppers are shown in Figure 4.2. Such hoppers may have
flat or tapered bottoms, but in the case of the latter the inclusive angles are
larger than for mass-flow hoppers. Core-flow hoppers therefore tend to be of
more squat proportions than the mass-flow type, and may be used to good
effect in situations where headroom is limited. The outlet dimension of a core-
............--live (effective)
storage
dead storage
Figure 4.3 Reduction of the effective storage capacity of a core-flow hopper as a result of
'topping-up'.
158
BULK SOLIDS HANDLING
flow hopper is larger for a given product than that of a mass-flow hopper.
Although a core-flow hopper will maximize the storage volume for a given
headroom, it will do so only if the contents are completely emptied on a
batchwise basis. If the hopper is continually 'topped-up', the first-in last-out
sequence of a core-flow hopper will mean that the effective storage volume can
be significantly less than the potential capacity, as illustrated in Figure 4.3.
Composite hoppers are a combination of both core- and mass-flow
patterns: the upper section is designed for core-flow whilst the lower section is
designed for mass flow (Figure 4.4a). This is a useful way of increasing the
storage capacity whilst still maintaining mass flow, and therefore a greater
_._ __,.___ core flow
section
(a) Basic expanded-flow bin
(b) Multiple outlet bin
Figure 4.4 Composite hoppers.
THE DESIGN OF STORAGE BINS AND HOPPERS
159
uniformity of feed, at the outlet. This approach is also particularly suitable for
installations where numerous outlets are required for one storage facility
(Figure 4.4b).
4.2.2 Overall dimensions
Once the decision on whether to design for mass flow or core flow has been
taken, the overall dimensions of the hopper depend upon two factors: (i) its
shape, and (ii) the amount (that is, volume or mass) of product to be stored. It is
clear that these two factors are not unrelated, since it is often the constraints of
the site or the system (or both) that dictate the shape of a hopper that is
required to store a given quantity of product. For example, it has already been
mentioned that a plane mass-flow hopper is more effective than a corresponding conical hopper in terms of the quantity of material that can be stored for
a given headroom, and there are many instances where this fact has been used
to good advantage. It is useful for the engineer to be able to estimate the overall
dimensions of a hopper (i.e. height and cross-sectional size) at an early stage in
the design process, as he will then have a good indication of whether the
proposed shape, storing the required volume, can be accommodated within
the plant.
In order to estimate the cross-sectional dimension(s) and height of the bin
required to store a given quantity of product, it is convenient to imagine the
stored volume divided into three parts, as shown in Figure 4.5.
Thus,
v;otal =Vol. 1 +Vol. 2 +Vol. 3
:·: ·..... 0
H
. •. '
.•
·.·. ·.·
~ ·..· \::·:/:
. ·,,
: .. ::.~ ~:;~~·- ·.·. . .
.
Figure 4.5
.
.
. ..
Analysis of effective storage volume of a hopper.
160
BULK SOLIDS HANDLING
or, in general
stored
volume
volume of conical
section
volume of
+ parallel section
+ volume
resulting
from surcharge on
filling
(4.1)
In order to illustrate this approach a bin of cylindrical cross-section will be
considered. In this case the stored volume can be simply determined from the
geometry, so that
(4.2)
where D is the diameter of the bin, De is the diameter of the outlet, His the
height of the cylindrical section, {3 is the half-angle of the conical section and ()
is the surcharge angle of the 'free surface' of material in the hopper (which
corresponds to the poured angle of repose).
Suppose that, in order to estimate H for a given volume of stored material, {3
and () are both given a value of 30° and the volume of the space between the
outlet and the vertex of the conical section is neglected. Equation (4.2) can then
be rearranged to give
1.274V
H=---0385D
Dz
.
(4.3)
While it must be acknowledged that this equation strictly is valid only for
the chosen values of {3 and (), the error resulting from moderate changes in
these angles will be small. Similar equations can be developed for other shapes
of bin.
Often the specification for a bin or hopper requires that it should store a
given mass of product. Writing the volume V in terms of the mass m and bulk
density pb, equation (4.3) becomes
1.274m
Dzpb
H = - - - 0.385D
(4.4)
Clearly the accuracy of this expression depends upon the value of the bulk
density used, which itself depends upon the condition of the product.
Therefore it is evident that the value used should represent as closely as
possible the condition that will exist in the hopper.
It is useful to represent equation (4.3) in the form of a chart (Figure 4.6)
which yields a rapid, albeit approximate, indication of the relationship
161
THE DESIGN OF STORAGE BINS AND HOPPERS
volume, V
60 100 200 300
(m 3 )
500
f,. r"""',.- H·4D
18~-+--~4-~~~~~-~L+-~~~--+-~
1---1----11-t--+-1-1-t -++--fl--t\+t"- limits of
_
recommended
16 1---1----lt-t--t--t--H- --t--+t--t+- range of hopper _
proportions
f
\
l
2
4
6
8
10
diameter, D (m)
Figure 4.6 Recommended proportions of cylindrical mass-llow hoppers to store a given volume
of bulk solid.
between the height H and diameter D for a mass-flow hopper of fixed volume
V. Hoppers are generally manufactured to have a height H (of the parallel)
between one and four times the diameter; i.e.
D<H <4D
(4.5)
This range plotted on Figure 4.6 shows that for a hopper of given volume V
162
BULK SOLIDS HANDLING
there is a lower limit (D 1 ) and an upper limit (D 2 ) of diameter which, because of
the steepness of the constant volume lines, are not very different in magnitude.
The selection of an appropriate value of D is made considerably easier by the
fact that an increasing number of manufacturers are making bins and hoppers
in 'standard' diameters. Selection is then simply from the available diameter(s)
within the range D 1 < D < D2 , and a bin of the required volume can be easily
fabricated. The only part of the bin that needs to be manufactured to suit the
product is the converging section, and methods of determining the critical
dimensions of this item will be discussed in the following pages.
It may be noted in passing that, for the example being considered (i.e. a bin
filled with material such that = f3 = 30°), the overall height H 10131 , which
includes both the conical section and the surcharge space at the top, can be
expressed approximately as
e
or
H + 1.15D
1.274 V
= ~ + 0.765D
Htotal =
(4.6)
Htotal
(4.7)
4.3 Outlet size and cone angle
4.3.1 J enike's 'flow-no flow' criterion
Before the method of calculating the outlet size and cone angle can be
discussed, it is necessary to have an understanding of Jenike's philosophy for
determining these interrelated parameters [1]. Figure 4.7a shows a conical
mass-flow hopper in which a cohesive arch has formed at some point in the
converging section. In effect (as explained in Chapter 2) the bulk solid has
formed a structure which transfers the weight of the solid to the walls of the
hopper. The magnitude of the stress a. set up in such a stable arch has been
found to be approximately proportional to the span D. of the arch, and the
relationship between this stress and the position at which the arch forms can
therefore be illustrated graphically as shown in Figure 4. 7a.
In Chapter 1 the relationship between the shear strength of a particular bulk
solid and the consolidating stress (or pressure) a 1 was discussed and it was
explained that an increase in a 1 results in an approximately proportional
increase in the shear strength. Obviously, in order for a stable arch to become
established at any given position, the bulk solid must be capable of sustaining
the stress a. without failing. It is therefore necessary to examine the variation
within the bulk solid of the 'unconfined yield stress' a c• which represents the
strength of the material at the free surface. If values of a cat different positions
in the hopper can be determined and compared with Figure 4.7a, the position
at which a stable arch could become established is indicated by the point at
which ac =a •. Jenike's 'flow-no flow' criterion can be regarded as following
from this observation, and states that a 'bulk solid will flow provided that the
THE DESIGN OF STORAGE BINS AND HOPPERS
163
.s::
0
a;
0
c
.g
"(ij
0
0.
..
. :. :
stress set up
In stable arch, a a ~
(a) Relationship between the position of a stable arch in a hopper
and the stress required to support it
flowing •
element Ill a1
of solid
I
\/
consolidating stress
Cor pressure), a 1
(b) Variation of consolidating stress within a bulk solid
discharging from a hopper
Figure 4.7
Stress variation within a bulk solid in a hopper.
strength a c which it develops is less than the stress a. which would exist in a
stable obstruction to flow'.
In order to determine the variation of a c within the bulk solid it is necessary
first to understand the distribution of the consolidating stress a 1 . The bulk
material is unconsolidated when it is fed into the bin but becomes consolidated
as the filling process continues. In Chapter 2 it was explained how the change
164
BULK SOLIDS HANDLING
from a static to a dynamic stress field occurs as the hopper outlet is opened. In
the flowing condition, illustrated in Figure 4. 7b, the consolidating stress a 1
varies within the 'static' stress field from zero in the top layer of the bulk solid
towards a maximum near the junction of the cylindrical and conical hopper
sections. There is then an abrupt increase in stress to a peak value at the point
where the transition from the 'static' to the 'dynamic' stress field occurs (the
'switch'). Within the dynamic stress field, a 1 decreases linearly towards zero at
the virtual apex of the conical section.
As explained in Chapter 1, the flow behaviour of a cohesive bulk solid can
be conveniently illustrated by a plot of unconfined yield stress ac against the
major consolidating (normal) stress. This plot, termed the 'Flow Function'
(F F) of the material, can be determined by shear cell tests of the type described
in section 1.9.3.
Figure 4.8 illustrates the manner in which the unconfined yield stress a c•
generated by the consolidating stress a 1 , follows the same type of profile as a 1 .
Also on this diagram is re-plotted the stress a. that would exist in a stable arch,
and it is evident that the point of intersection (P) of these lines represents a
critical condition between 'flow' and 'no flow'. Above this point P, a.> ac, the
flow condition is satisfied and the product will flow. Below P, however, a c > a.
indicating that the bulk solid has enough strength to support a stable arch and
therefore may not flow without some form of discharge aid of the type
described in section 4.1 0. The dimension Dmin corresponding to the position in
the hopper where a.= ac is thus the 'critical outlet dimension' which has to be
exceeded if no arching is to occur.
flowing
element
of solid
Figure 4.8
I
•
al
Diagrammatic representation of the 'flow-no-flow· criterion in a hopper.
165
THE DESIGN OF STORAGE BINS AND HOPPERS
4.3.2 Flow Functions and flow factors
The derivation of the 'Flow Function' (FF) curve for a bulk material has been
described in Chapter 1, and Figure 4.9 shows a typical FF curve.
For a hopper of the type shown in Figure 4.8, both the stress in the stable
arch aa and the consolidating stress a 1 are linear functions of the horizontal
dimension Da. Furthermore, each of these stresses approaches zero at the
virtual apex of the conical section and it follows that the ratio of a a to a 1 is
constant for a given hopper. This ratio, commonly called the 'flow factor' (ff) is
an important parameter, since it characterizes the manner in which a given
hopper discharges its contents. Values of fJ have been computed by Jenike and
others for a wide range of hopper types and these are particularly valuable
when used in conjunction with an appropriate flow function to determine the
critical dimensions of a hopper for a given application.
If the flow factor (Jf) and the Flow Function (F F) are plotted on the same
axes, as shown in Figure 4.9, the condition for which the flow-no flow
criterion is satisfied can be clearly seen. Thus, the 'critical' condition
(represented in Figure 4.8) occurs at the intersection of the fJ and F F lines on
Figure 4.9 and the flow criterion is satisfied at all conditions for which F Flies
below ff. The value of a c corresponding to the intersection of these two lines
(acrit) can be used to compute a limiting value of the hopper outlet dimension
(Dmin).
Thus,
D . = (J"critJ
mm
(4.8)
pbg
where Pb is the bulk density of the stored material, g is the gravitational
acceleration and J is an empirical dimensionless factor which depends upon
consolidating stress, u i
Figure 4.9
Bulk solid Flow Function F F and hopper flow factor
ff.
166
BULK SOLIDS HANDLING
3.0
---.
circular
section
2.5
i\
Ul
(/)
<D
c0
2.0 ~
c
~
·c;;
<D
~
"
----
.............
.............
I'
_.... .... .-
-~
=
I =
~~ =
loo
~
~
"-~quare
I
~)-
I-=
section
E
§
-,
_.,.. ,.
rectangular
section
1.5
-
(L;;. 3Dp) ~
1.0
I
0
10
20
30
I
40
50
60
hopper half angle ~ (degrees)
Figure 4.10
Values of the empirical factor J in equation (4.8).
the shape of the hopper and the angle of the converging section (Figure 4.1 0).
Note that for a rectangular hopper having L < 3Dmin the value of J should be
interpolated between the curves on Figure 4.10 for square and rectangular
shapes.
When designing for core flow, it is necessary to ensure that the outlet is large
enough to prevent the occurrence of rat-holing. The design procedure is
similar to that outlined above, except that a different flow factor jJ would be
used, and the empirical factor J replaced by a term G which depends upon the
static angle of internal friction of the bulk solid. Typically, for the same
product, the outlet size for core flow will be two to three times that required for
mass flow.
4.3.3 Outlet dimension and cone angle
The foregoing discussion has been concerned mainly with the theory essential
to an understanding of the method of calculating the critical outlet
dimension(s) for mass flow and core flow hoppers. Little has been said about
the method of determining the angle of the converging section of the hopper
needed to give the desired flow pattern. This angle is related to the frictional
properties between the stored product and the wall material and, as discussed
in Chapter 1, can be estimated from the results of shear tests on representative
samples of these. The 'angle of wall friction' r/Jw found from the shear tests is
also used to determine the flow factor .ff, a knowledge of which is essential for
the calculation of acrit for use in equation (4.8).
167
THE DESIGN OF STORAGE BINS AND HOPPERS
hopper half angle
f3c
(degrees)
(a) Conical hoppers
3:
~ 30P.~--+--+~~'
c
.2
0
E 20~~~~~~~~~4-~
a;
3:
0
~
c
10~~~~~k--+~~~--
"'
10
20
30
40
50
60
hopper half angle {3p (degrees)
(b) Plane-flow hoppers
Figure 4.11 Flow factor (fJ) contours for conical and symmetrical plane-flow hoppers; effective
angle of internal friction <P = 50°.
Flow factor charts for various designs of hopper are presented in detail
elsewhere [1], [3] but, as an illustration, two typical charts are shown here
(Figure 4.11). These charts, for a product having an angle of internal friction cjJ
of 50° in a conical hopper (Figure 4.11a) and in a plane-flow hopper
(Figure 4.11 b), show the manner in which the flow factor fJ varies with the
angle of wall friction c/Jw and the hopper half-angle (J.
In the case of a conical hopper the transition from mass flow to core flow is
168
BULK SOLIDS HANDLING
quite distinct and is indicated by the 'critical line'. When designing for mass
flow in conical hoppers, it is usual to select a value of f3c some 4o to the left ofthe
critical line. In plane-flow hoppers the region for mass flow is much wider, and
experience suggests that it is better for {3P to be selected either on or very close
to the broken line marking the 'suggested limit for mass flow'. Thus, for a given
value of wall friction c/Jw, the flow factor if and hopper half-angle {3 can be
predicted. The value of if enables a line to be drawn to intersect the Flow
Function FF, giving a cri~> which can be substituted in equation (4.8), together
with the values of J (from Figure 4.10) and {3, to yield the critical outlet
dimension Dmin· A similar procedure would be followed, using appropriate
charts for if and G, when designing for core flow.
It is recommended that, in order to avoid instabilities of flow patterns, the
actual hopper outlet dimension should be about 20% greater than the
minimum determined for equation (4.8) [2].
4.4 Period of storage and time consolidation effects
It is clear that, with some products, consolidation of the material inside the
hopper with time can lead to a considerable increase in strength of the bulk.
For a particular product the extent of this increase in strength over that of the
material when the hopper is initially filled depends principally upon the period
of storage. Depending on process requirements, this may range from minutes
to days, weeks or even months. From the onset of storage time consolidation
effects (that is, increase in bulk strength of material with time) start due to loss
of entrained air, settling and re-orientation of the constituent particles within
the bulk. The natural de-aeration and rearrangement of particles tend to be
enhanced by the extraneous vibrations that are normally associated with any
bulk materials handling plant. These effects lead to closer packing of particles
which results in an increase in the strength of the bulk. In the case of freeflowing materials the gain in strength is likely to be negligible. This can also be
true of more cohesive materials but it should be remembered that these will be
much stronger initially. However, many materials exhibit the characteristic of
significantly increasing strength with the period of storage, an effect which can
be illustrated by a higher and sometimes steeper Flow Function compared
with that of the same material for instantaneous filling and discharge
conditions (Figure 4.12). In fact, there will be a range of Flow Functions
corresponding to different periods of storage. From these comments it is clear
that time consolidation effects result in higher values of acrit which in turn
results in a corresponding larger minimum outlet dimension, Dmin• necessary
to ensure unobstructed gravity flow.
Experience suggests that time consolidation effects do not increase linearly
with time and this may be illustrated by Figure 4.13, which is typical of the
results for many products. In this figure the minimum outlet dimension, Dmin•
as determined by the appropriate form of equation (4.8), is plotted against the
THE DESIGN OF STORAGE BINS AND HOPPERS
ff
.c
0.
c:
CD
!::
m
CD
>
·c;;
I-·------ //
acrit based on FFt
y
/
/
169
FFt - Row Function
resulting from specified
period of storage
-
,_~:::..-----"'1\~F=F~- Flow Function
m
CD
li
resulting from
Instantaneous discharge
E
0
CJ
consolidating stress
Figure 4.12
The effect of time consolidation on the Flow Function.
t
storage
time~
Figure 4.13 The effect of storage time on the minimum outlet dimension.
period of storage, and it is clear that, although the strength of the material and
hence Dmin are increasing with time, the rate of increase is diminishing.
Ultimately a stage is reached where further increases in the period of storage
have little or no effect on Dmin and the product is then considered to have
acquired maximum strength. This observation is significant and is put to use
when testing for consolidation effects.
4.4.1 Caking
It must be remembered that under normal circumstances an increase in
strength due to de-aeration and re-orientation of the constituent particles is a
reversible situation and thus, given space into which it can dilate or expand,
the bulk will revert to a weaker state. However, with some products, changes in
moisture level or chemical reactions can cause 'caking'. In this situation
particles are not just attached to adjacent particles by electrical or surface
170
BULK SOLIDS HANDLING
tension (moisture) effects but become more permanently bonded together.
Granulated sugar is a well-known product that, under certain conditions of
storage, exhibits this tendency. In the case where caking is a characteristic of
the product resulting from long-term storage, failure of the bulk probably will
not take place without external assistance, however large the outlet. With
regard to time consolidation the difficulty is then to determine how, on the
basis of test results, normal compaction effects can be differentiated from
caking. This point will be discussed in the next section.
4.4.2 Testing for time consolidation
With many bulk materials the effects of time consolidation can be substantial,
and it is important at an early stage to assess the likely period of storage of the
product and to calculate the outlet dimension from the Flow Function
corresponding to this time. One method of determining the appropriate Flow
Function, FF 1, would be to leave representative samples of material under
load for the required time before subjecting each sample in turn to shear tests,
thereby reproducing the strength the material will have acquired for the
corresponding period of storage in the hopper. This technique can be used
with the Jenike shear cell but it is time-consuming to generate the required
data. The approach is not suitable for the Walker shear cell. However, it has
proved acceptable to calculate the outlet size based on a knowledge of how the
material increases in strength with time for one point (i.e. one normal load) on
one yield locus. The material is left in the shear cell under the selected normal
load for different periods of time up to, say, one week. The values of the
measured shear strength are plotted against time (Figure 4.14) and from this
the percentage increase in shear strength of the material for the required period
of storage may be estimated. If a storage period longer than that tested is
required, it is possible to extrapolate the graph to the required time. The
justification for this is based on the observation, previously mentioned, that
the most significant consolidation effects occur in the relatively short term.
With materials that exhibit caking tendencies, the relationship between shear
time--~--
Figure 4.14
Typical relationship between shear strength and time (for constant normal load)
THE DESIGN OF STORAGE BINS AND HOPPERS
171
=
Cl
c
~
Cii
(U
CD
.t::.
Ill
time _ ___,._
Figure 4.15 Typical relationship between shear strength and time for a product exhibiting
caking tendencies
strength and time exhibits a significant upward turn, as shown in Figure 4.15.
Having estimated the percentage increase in shear strength resulting from
the required period of undisturbed storage over that for the 'instantaneous'
value, the instantaneous yield loci for the product are increased by the same
percentage. This then permits a new Flow Function, F F 1, corresponding to the
required storage period to be plotted (Figure 4.12). When the appropriate flow
factor, jJ, is superimposed on this figure, the intersection denotes acrit·
Substituting this value into equation (4.8) then yields the minimum outlet
dimension, Dmin• necessary to achieve gravity discharge after the specified
period of storage. It is not uncommon for the outlet dimension based on the
time consolidated Flow Function, F F 0 to be as much as twice that of the
instantaneous value.
4.4.3 Practical ways of minimizing time consolidation
The effects of time consolidation may be minimized by moving the bulk
regularly either by recycling or by transferring it to another hopper. In a massflow hopper, since all of the stored product moves on discharge, it is only
necessary to discharge a small amount to restore the material to its former,
weaker state. With core-flow hoppers, complete emptying will be necessary to
ensure movement of the material close to the walls and base of the hopper. In
this case simple recycling will not be effective as the recycled material will
simply be returned into the flowing core and will be immediately redischarged.
If the product has a wide particle size distribution it is almost certain that with
a core-flow hopper such recycling will also lead to significant segregation in
terms of fine and coarser size fractions.
4.5 The effect of moisture
It can be seen from equation (4.8) that the principal parameter influencing the
minimum outlet dimension Dmin is the Flow Function FF and hence acrit for
172
BULK SOLIDS HANDLING
the material concerned. As discussed in the previous section, the period of storage can have a significant effect on acrit and hence on Dmin· With many bulk
solids the moisture content of the material can also have a significant effect on
its flow behaviour. Any water present on the outer surfaces of the constituent
particles of the bulk (i.e. 'free moisture') can result in surface tension effects
which inhibit their movement relative to one another, rendering the bulk more
cohesive and, therefore, less free-flowing. The consequence of this is that a
hopper will generally require a larger value of minimum outlet dimension Dmin
if surface tension effects are present than for the same product free from
moisture. The effect that moisture has on the required minimum outlet
dimension can be quantified by determining the Flow Functions FF of the
material at different levels of moisture. Figure 4.16 illustrates, as an example,
the outcome of such tests for copper concentrate, and it is evident that, with this
particular product, moisture has a significant effect on the hopper design. The
form of Figure 4.16 is typical of the effect of moisture on outlet size, although
the actual values will obviously depend upon the material and the particle size
distribution. It should be noted that at moisture levels in excess of the
saturation value the product takes on slurry-like characteristics and therefore
can no longer be considered as a bulk solid. If moisture is a potential problem
information in the form of Figure 4.16 is useful since it permits the engineer to
balance the cost of a drier or filter, to render the product more free-flowing,
against that of the size of feeder necessary to handle the undried product from a
large outlet. Naturally, design should be based on the Flow Function F F ofthe
product at the highest moisture level that is expected in practice.
4.6 Overcoming space limitations
Following the procedures outlined in the previous sections should lead to an
'ideal' functional design of hopper to give reliable gravity discharge with a
specified discharge pattern. In this context 'ideal' refers to the geometry
(minimum outlet dimension and wall angle) necessary to ensure the correct
mode of discharge without taking into account any of the physical constraints
which may be imposed on the siting of the hopper. In the case of small hoppers,
say up to one tonne, the resulting geometry is usually acceptable, but, with
larger volumes, once the critical dimensions of an ideal hopper have been
determined, certain practical difficulties may become apparent. Examples of
the types of problem that are commonly encountered are (i) insufficient
headroom to accommodate the required storage volume; (ii) outlet too large
for feeder situated beneath hopper, and (iii) flow rate through the outlet
incompatible with the requirements of the system or process downstream of
the hopper. With regard to (i) and (ii), a change in the basic shape and/or wall
material of the hopper may yield an acceptable solution to the problem. If the
discharge rate through the outlet is likely to be too great, some form of feeder
will be required to 'choke' the flow (section 4.9).
173
THE DESIGN OF STORAGE BINS AND HOPPERS
4.0
I
3.6
.
3.2
.....
Gl
::::Gl
11)
2.8
i
E
......
c
·e 2.4
I
a
conical flow
hopper.'-.....
r£
0
·;;
c 2.0
Gl
E
'6
i
~ 1.6
0
·e
1.2
plane flow
hopper " '
0.8
0.4
,....
---
'/
~
~
V
~
4
~
6
.
IJJ \
V
E
:I
E
c
J
......
~
1
'\
/ I \,
!'V
.......
8
If
10
c
0
+=
I
Gl
~
"'-"'
... ·:I
:lje
-
12
0
-
\
~
14
" moisture content
Figure 4.16 Relationship between minimum outlet dimension and moisture content for copper
concentrate.
4.6.1 Use of low1riction linings
Where only a small increase in storage capacity is necessary in a mass-flow
hopper this may be achieved by decreasing the angle of the sloping wall,
incorporating a 'low-friction' lining material into the converging section to
ensure that reliable flow is maintained. Highly polished stainless steels, epoxycoated steels, glass-coated steels, glass and ultra-high molecular weight
polyethylene sheeting are all commonly used for this purpose. As illustrated in
174
BULK SOLIDS HANDLING
10r---,----,---,----,---,----,---,----,---~--~
N
E
.....
z
25
Ul
Ul
~
;;;
20
normal stress (kN/m2)
Figure 4.17 Frictional characteristics of brown flour against epoxy-coated mild steel and
stainless steel linings.
Conical channel
Effective angle of
internal friction et>= 50°
c
0
:;::
()
:E
hopper half angle {3 c (degrees)
Figure 4.18 The effect of decreasing cf>w on hopper half angle {J, and flow factor ff.
Figure 4.17 there is a significant difference between the wall friction angle for a
grade of brown flour on epoxy-coated mild steel compared with that for the
stainless steel. If this information is translated to the appropriate flow factor
(ff) contours, it will result in an increased hopper half-angle for the lower
friction wall material but a correspondingly higher value of JJ. Figure 4.18
illustrates this point. This in turn means that although the included angle of
the hopper is increased, thereby increasing the storage capacity, the corresponding value of acrit and hence outlet dimension Dmin are also increased.
175
THE DESIGN OF STORAGE BINS AND HOPPERS
4.6.2 Changing hopper shape
A relatively simple but effective way of increasing the storage volume of a
mass-flow hopper where headroom is a limitation is to change from a conical
to a pyramidal, square-outlet hopper. This will result in a slightly smaller
outlet dimension, that is, the length of the side of the square outlet will be less
than the diameter of the outlet of a circular hopper. However, it should be
remembered that the major consideration with this type of hopper is that to
ensure a mass-flow discharge pattern, the valley angles must conform to the
minimum angle for mass flow. This results in the walls being steeper than for
the corresponding circular hopper. The nomograph shown in Figure 4.19 will
assist in determining the relationship between the valley and wall angles and
can be used to determine the wall angles for hoppers with either square or
rectangular outlet openings.
Another approach to utilizing space more effectively is to use a wedgeshaped hopper. The reasoning behind this is based on the observation that if
the same basic data resulting from shear and wall friction tests is used to design
conical and plane mass-flow hoppers, it will be found that the latter has a
larger included angle and smaller outlet dimension. Both the increased
included angle and the more efficient utilization of floor area result in a
0 (vertical)
10
20
30
wall angle
(jp,
valley
angle
(jv
40
wall angle
(jp.
50
60
65
Figure 4.19
section.
Nomograph relating wall and valley angles for hoppers of square and rectangular
176
BULK SOLIDS HANDLING
considerably larger storage volume. The width of the slot outlet is typically
half that of the diameter of a conical hopper for the same product. However, it
should be remembered that the length of the slot outlet must be at least three
times greater than the width in order to achieve mass flow.
A more drastic step in attempting to increase capacity is to move from a
mass-flow to a core-flow hopper. The larger included angle of such a hopper
maximizes the storage volume for a given headroom. However, the disadvantage of this type of hopper is a non-uniform feed of material through the outlet.
If this is an important criterion, a composite hopper (Figure 4.4a) combining
both core-flow and mass-flow patterns may be more appropriate. As already
explained, such a hopper is designed for core flow in the upper section and
mass flow in the lower section. The dimension of the transition from core
flow to mass flow corresponds to Dmin for a core-flow hopper. This
approach has provided a useful way of increasing storage capacity while still
maintaining mass flow, and therefore a greater uniformity of feed, at the outlet.
4.7 Structural design
The foregoing discussion has been concerned with the design of storage
hoppers to discharge the stored product on demand and in a predictable
manner. It is clear that the mass-flow pattern of discharge has a number of
advantages over core-flow. However, a major disadvantage of mass flow is
that, since all of the material in any cross-section is flowing, it transmits the
lateral pressure within the material (which may be considerable) directly to the
hopper walls. This is less of a problem with core flow, since the stationary
material adjacent to the hopper walls serves to absorb the stress resulting from
flow in the central core. Thus, in addition to being designed for the required
mode of flow, the hopper must also be designed to withstand the stresses
generated by the material in both static and dynamic conditions. In Chapter 2
it was shown that the radial stress exerted on the walls in the static conditions
can be estimated by the well-established Janssen equation [ 4]. It was also
explained how, with mass-flow hoppers in the flowing (dynamic) condition, an
abrupt change in stress ('switch') can occur in the region of the transition from
the parallel to the converging section. The pioneering work of Walker [5] has
shown that this stress peak may be up to ten times that of the static condition
on which structural designs had previously been based. With hindsight, it is
not surprising that ignorance of this stress peak resulted in some catastrophic
failures. Such failures have tended to occur in the larger hoppers since smaller
ones are effectively much stronger for their relative size. Although Walker has
developed a procedure for estimating the stress in the region of the
parallel/convergent transition, many hopper manufacturers design on a
conservative basis by strengthening the hopper in this region so that it will
withstand up to at least ten times the calculated static pressure at the same
point.
THE DESIGN OF STORAGE BINS AND HOPPERS
177
There is an enormous variability in the type of silos made. They can be
constructed of steel, concrete, wood, or even plastic. They may be of round,
rectangular or non-uniform cross-section and can be used to store a vast
variety of material from fine powder to farm silage. In addition, inlets and
outlets may be single or multiple, symmetrically placed or eccentric. Most silos
are in the open and consequently they are subject to the full range of adverse
environmental conditions. A detailed and rigorous approach to the structural
design of silos and hoppers is therefore beyond the scope of this book, which is
restricted to a brief coverage of commonly used codes of practice. For further
information on this topic the interested reader is referred especially to [3], [5]
and [6].
Until recently three codes of practice were in most common use [7, 8, 9]. All
present methods for the design of silos using empirically based techniques
allow for over-pressures which occur during loading and unloading, and
which may be several times the static pressure.
Jenike [10] has summarized the causes of silo failure as uneven foundation
settlement, faulty construction and unanticipated loading conditions. The first
two are problems for the site engineer; the third cause, the responsibility of the
design engineer, can be further subdivided as follows.
(i) Shock loads: a silo may discharge material from the lower part of a hopper
but permit an arch to form over a void higher in the hopper. When the
arch collapses, a mass of solids falls into the hopper producing a shock
load. This is particularly dangerous when the void extends over the whole
cross-section of the hopper. Multiple-outlet silos are more prone to this
problem than those with single outlets.
(ii) Bending in cylinder walls: circular walls are generally designed to transfer
hoop tension and vertical compression only, on the presumption that wall
pressures are uniform along a circumference. Significant non-uniformities
in pressure can occur when a flow channel touches the cylinder wall. These
conditions occur in many core-flow and mass-flow silos. Horizontal
bending moments are generated in such conditions which produce inward
dents in metal silos and vertical cracks in concrete silos.
(iii) Overpressures: whenever a flow channel expanding upward from an
outlet reaches the vertical wall of a silo, there occurs a switch from
cylindrical to converging flow. At and below the switch an overpressure
acts on the wall. In a mass-flow silo with a single outlet, the location of the
switch coincides with the physical transition from the cylindrical section
to the conical section. In other silos the location of the switch depends
on the flow channel expansion angle and the geometry of the silo.
An understanding of how these factors (shock loads, bending and overpressures) relate to the various codes of practice is vital to the safe and economical
design and construction of bins and silos.
The American, German and French codes have already been mentioned. A
178
BULK SOLIDS HANDLING
new British code of practice has very recently been published, in draft form,
under the auspices of the British Materials Handling Board [2]. Even more
recent is the code prepared by the Institution of Engineers, Australia [11].
There is a great deal of detail in these codes, and the reader wishing to
undertake a serious exploration of the tortuous routes leading to the reliable
structural design of storage bins and silos is recommended to begin with [2]
and [11].
It would not be right to terminate this brief comment on structural design
without mentioning the recent advances in the computer-aided design of bins
and silos, especially the finite-element method, which can enable a complete
silo system to be analysed in a relatively short time. In the finite-element
method the 'system' of the silo material and the silo wall are treated as a
continuum discretized by a number of finite elements. Ideally this should be
done in three dimensions, although all of the studies to date have confined
themselves to a 2-D analysis.
A recent study of the silo/materials interaction for powdered coal shows the
potential of the finite element method [ 12]. The silo in question was a 30 m
diameter self-cleaning coal silo having seven draw-off points. On unloading,
pressures were generated due to eccentric draw-off. This is an area where the
available codes of practice provided little information. The flow channels were
established from functional design, the flowing and non-flowing regions
having different internal pressures (Figure 4.20a). Figure 4.20b shows a
quarter-section of the silo divided into finite elements and Figure 4.20c the
deformed shape of the silo due to the pressure exerted by the flowing material.
The advantages of this approach are, first, that eccentric loading conditions
can be simulated, and second, that the material and silo can be treated as a
single system.
4.8 Control and measurement of discharge rate
It was explained in the Introduction that often there will be a need for control
to be exercised over the rate at which bulk solids discharge from a hopper, and
this is usually achieved by incorporating in the design of the plant some form
of feeding device. Before making any attempt to select or design a feeder to
control the rate of flow of a bulk solid, it is necessary to study the application in
order to make an assessment of the accuracy required. Thus, for example, it
may be sufficient to exercise only a rough control in order to avoid overloading
subsequent items of plant, but if a product is being metered for sale the greatest
possible accuracy of feed control is likely to be needed.
A number of different techniques have been developed for controlling the
rate of flow of a bulk solid either by volume or by weight. In many cases these
techniques are based upon familiar conveying devices such as belts, screws or
vibrating troughs which can be adjusted in order to match the actual solids
l{)
"'
E
30.4m dia.
•
"
j
(c) Displaced shape
of silo (shown In
broken lines)
Finite element analysis of a coal silo.
pressure 31 kN/m 2
~ flowing material
static material
pressure 22 kN/m 2
Figure 4.20
(a) geometry and flow regime
I
7 draw-off hopper
channels
critical slice
static material
~flow
-
(b) Finite element mesh
of a quarter section
of the silo
~
0
:;.::
-.J
\0
......
"'
:;.::
m
'1:1
'1:1
5
0
z
"'>
tl:l
z
Cl
m
>
"'d
'Tl
0
a"'z
m
180
BULK SOLIDS HANDLING
storage
hopper
solids
flowmeter
feed rate
controller
to process
feedback signal
Figure 4.21
System for solids feed rate control.
flow rate to the desired rate. It follows, of course, that for accurate control it is
necessary to measure the flow rate either continuously or at suitable intervals
in order to provide the feedback signal to the flow control device. The problem
can be represented diagrammatically, as in Figure 4.21.
There are various methods of measuring solids flow rate, but probably the
commonest device used in this type of application is the belt weigher which can
be installed either on a main conveying belt or alternatively on a belt feeder.
Where the highest accuracy is not required, and provided that the physical
characteristics (especially bulk density) of the product do not vary, it may be
acceptable to rely on calibration of the feeder to give flow control over the
desired range. In the case of the screw feeder, for example, the solids mass flow
rate is approximately proportional to the rotational speed of the screw so that,
once calibrated, the device can provide a reasonably reliable control of the
flow. It must be remembered, however, that with products that do not flow
readily the problem is to ensure that a continuous feed is maintained to the
feed rate controller!
In the following pages are described a selection of different types of feeder,
but in the cases of belt, screw and vibratory feeders, which are obviously
similar to the corresponding conveyors, further information may be obtained
from Chapters 7, 8 and 9. Some additional information on feeders (notably
rotary valves) specifically applying to pneumatic conveying systems is to be
found in Chapter 13.
4.9 Feeders
4.9.1 Introduction
It has been explained previously that to ensure reliable operation of a
continuous weighing device it is usually necessary to provide a consistent
THE DESIGN OF STORAGE BINS AND HOPPERS
181
supply of the bulk solid concerned. Thus, for example, when a bulk solid is
required to be discharged from a hopper to a process at a controlled and
measured rate, a feeder of some kind would normally be installed at the hopper
outlet. It is essential to appreciate that a feeder used in this way can only
operate satisfactorily if the bulk material flows steadily and continuously into
it under gravity. The function of a feeder as a means of controlling the
discharge of bulk solids from bins or hoppers should not be confused with that
of a discharge aid which is specifically to prevent the flow being obstructed as a
result of the formation of arches or rat-holes. Feeders, and indeed discharge
aids, must be considered as an integral part of the complete storage and feed
system. There is little point, for instance, in attempting to select a feeder for a
system unless the hopper has been properly designed to prevent arching and
rat-holing and to provide the maximum discharge rate required.
The importance of the hopper-feeder interface cannot be over-emphasized,
and it is probably fair to say that more discharge problems arise through the
failure of the designer to understand the flow conditions existing in this region
than for any other reason.
It is necessary also to consider the vertical load exerted on a feeder mounted
directly beneath the opening of a hopper. Whilst this load would normally be
less than the 'hydrostatic head' of material in the hopper, it may become very
high during filling. However, various techniques may be used to ensure that
the feeder load does not become excessive, the most obvious being to locate the
feeder in an offset position from the hopper opening. Another approach is to
ensure that the bin is not completely emptied, but that a two- or three-metre
depth of product is still present when it is refilled, thus avoiding the impact of
fresh material directly over the bin opening. For a further discussion of this
aspect of feeder design see, for example, [ 13], [14].
4.9.2 Belt feeders
A belt feeder consists essentially of a continuous rubber or polymer belt
running between end pulleys and supported on a number of idler rollers
(Figure 4.22). In normal use it would be fitted beneath a hopper having a
rectangular opening which is often tapered in order to provide an even feed
along the length of the belt. Typically this taper is about 4-5%. A further
advantage of the tapered hopper opening is that it permits some movement of
the material in the hopper in the direction of the belt travel which helps to
reduce shearing conditions with consequent reduction of belt wear and driving
torque.
Belt feeders are typically 0.5-2 m wide and 2-3 m in length, and their
capacity, which obviously depends almost entirely upon the width and speed
of travel of the belt, may be anything from a few tonnes per hour up to more
than 2000 tonnes per hour. The maximum speed of travel of the belt on a belt
feeder is normally around 17 m/min, higher speeds tending to result in
G
182
BULK SOLIDS HANDLING
Figure 4.22
Belt feeder.
,-1
I variable
speed drive
i
1'
I
I
load
cell
to feeder
I
I
feed rate
metering
I
t
I
I
I
I
I
'------~----
feed rate
controller
Figure 4.23
------,
L~--~~~j
set feed rate
Weigh-feeding system.
('"'"'"' ) I
feed rate
indicator
THE DESIGN OF STORAGE BINS AND HOPPERS
183
excessive wear. Power requirements seem to be moderately high at 2-40 kw
[13], but the majority of this load occurs on start-up and under steady
operation the power usage is quite low.
Belt feeders are ideally suited to the transport of fine granular materials such
as small coal or ores, but can feed much finer materials satisfactorily provided
that the moisture content does not become too high. Problems may also arise
with materials that are very lumpy, hot, or sharp and abrasive. (The lump size
is obviously limited by the gate opening on to the belt, which should normally
be not more than three times the depth of the product on the belt.) A significant
advantage of belt feeders is their relatively simple construction, and therefore
moderate cost. Furthermore, they offer a degree of regulation of the discharged
material so that, used in conjunction with a belt weigher, they can provide the
basis for a reasonably reliable continuous weighing system (Figure 4.23).
4.9.3 Apron feeders and rotary feeders
These two devices operate on a similar principle insofar as they regulate the
discharge from a hopper by passing a continuous series of 'pockets' across the
hopper outlet at a controlled rate. Each pocket becomes filled with particulate
material and then moves on to discharge the material into an appropriate
receiving vessel or perhaps on to a conveying belt.
In the case of the apron feeder (Figure 4.24) the pockets or pans are linked
Figure 4.24 Apron feeder.
184
BULK SOLIDS HANDLING
together on a two- or three-strand chain and supported on a central rail.
Apron feeders are typically 0.6-3 m wide and 3-5 m long. At operating speeds
of 3-16m/min, capacities are about 100-2000 tonnes/h, although the exact
capacity obviously depends upon the bulk density of the product being
conveyed and the depth in the pans, in addition to the width and speed of the
feeder. An important advantage of the apron feeder is that it can operate on an
upward gradient. Amongst its disadvantages is the relatively high level of
maintenance required (resulting from the large number of moving parts and
susceptibility to spillage of fine materials). As with the belt feeder, some care
must be taken with the design of the interface between hopper and feeder. For
example, where the length of the rectangular outlet over the feeder is greater
than the width, flow problems may arise with mass flow from the hopper not
being properly achieved. An interesting method of overcoming this problem is
to use a wide apron feeding across the side of the rectangle [1].
Rotary feeders of various types are very widely used, the actual design
selected depending principally upon the nature of the bulk solid being
handled. The rotary drum feeder (which may be regarded as an extreme type
having zero pocket depth) tends to prevent product discharging freely from the
hopper (Figure 4.25a). For relatively free-flowing materials this device is cheap
and easy to maintain. For more general use, the drum is fitted with vanes
which then give a greater measure of control over the discharge rate of the
product (Figure 4.25b). In order to handle very free-flowing materials, which
may have a tendency to flood, the rotating vanes would normally be enclosed
in a casing (Figure 4.25c). This is the familiar rotary valve or star valve which is
commonly used to feed pneumatic conveying lines, and is therefore described
in more detail in Chapter 13.
4.9.4 Rotary table feeders
A hopper designed for the unobstructed discharge of poorly-flowing materials
is likely to have a large opening, and the rotary table feeder is a convenient
method of overcoming the resulting problem of unacceptably high flow rates.
(a) Drum type
(b) Vane type
Figure 4.25 Rotary feeders.
(c) Enclosed type
(rotary valve)
THE DESIGN OF STORAGE BINS AND HOPPERS
185
spiral
collar
hopper
outlet
Figure 4.26
Rotary table feeder.
Figure 4.27
Screw feeder.
The device consists basically of a horizontal circular table concentric with, and
just below the hopper opening (Figure 4.26). The diameter of the table is some
50% greater than the hopper outlet diameter. While the table rotates (typically
at 2-10 rev /min) a fixed blade ploughs off material from the column emerging
from the hopper outlet, the fixed spiral collar helping to ensure a uniform rate
of flow. It should be noted that most of the shearing resistance to the rotation
of the table results from the 'dead' conical mass of product in the centre
occupying a cross-sectional area of 40-50% of the hopper outlet and extending
to a height of around half the outlet diameter [ 13].
4.9.5 Screw feeders
The screw feeder (Figure 4.27) is perhaps the most common mechanical
method of discharging/extracting and feeding products from storage containers. Its advantage is that it can feed at a reliable rate whilst providing a
186
BULK SOLIDS HANDLING
suitable 'choke' to what might otherwise be an unacceptably high rate of flow
by uncontrolled gravity discharge. Because of its positive action a single- or
multiple-screw device can serve as a discharge 'aid', extracting difficult
materials at a consistent rate (section 4.1 0.4). Also, an enclosed screw can
provide a degree of sealing against a pressure gradient which renders it suitable
for feeding pneumatic conveying lines, as described in Chapter 13.
The screw feeder consists essentially of a helical screw, driven by an external
source, and mounted beneath the hopper outlet. The design of the screw itself,
particularly with regard to the arrangement of the flighting, depends mainly
upon the nature of the product to be handled, as explained in Chapter 10. The
main requirement for screw feeders is that there should be a uniform removal
of product from the hopper outlet, and in this respect screws with increasing
pitch and increasing diameter are likely to be the most successful (Figure 4.28).
Uniform pitch and uniform diameter
Graduated pitch and uniform diameter
Increasing pitch and increasing diameter
Figure 4.28 Approach flow patterns in screw feeders.
THE DESIGN OF STORAGE BINS AND HOPPERS
Figure 4.29
187
Vibratory feeder.
4.9.6 Vibratory feeders
The principle of operation of vibratory feeders is very similar to that of
vibratory conveyors and will therefore be mentioned only briefly at this point.
Detailed description, with an introduction to design and selection methods,
will be found in Chapter 11. The vibratory feeder is really no more than a short
conveyor (Figure 4.29) mounted directly beneath the hopper outlet. It does
not 'extract' material from the hopper and because of its lack of positive action
it is generally unsuitable for controlling feed rate to a high degree of accuracy.
Nevertheless, where a specification calls for a low cost, reliable device giving a
reasonably uniform feed rate, the vibratory feeder may be the ideal answer.
Tuned feeders can give some degree of control over the feed rate and are
readily linked to feedback systems such as belt-weighers, resulting in an
installation offering a very consistent feed.
4.10 Discharge aids
4.1 0.1 Introduction
It is worth re-emphasizing the comments made previously concerning the need
to regard discharge aids as an integral part of the complete storage and feed
system. Too frequently these useful devices are treated simply as a solution to
flow problems caused by poor design or incorrect use of a hopper. Whilst it is
certainly true that the installation of an appropriate discharge aid can provide
a satisfactory solution to the problem of a poorly-flowing hopper, it should
also be understood that the selection of an unsuitable device may have the
reverse effect and create more problems than it solves. In short, discharge aids
should not be used as a substitute for good design but should be selected, at the
design stage, if it becomes apparent that a simple gravity-flow hopper will not
188
BULK SOLIDS HANDLING
be suitable because of the nature of the product or other constraints within the
overall system.
The first step in the design of a storage/feed system for a bulk solid should
normally be concerned with the size and proportions of a hopper for gravity
flow. This should involve laboratory tests on a representative sample of the
bulk solid, as described in Chapter 1.
It may happen that the 'ideal' dimensions of a hopper of the required volume
that can be relied upon to discharge its contents without obstructions
developing render it impractical for the intended application. For example,
mass-flow hoppers are generally tall, and there may be insufficient headroom
to accommodate the required storage volume. Another common difficulty
with mass-flow hoppers, particularly where cohesive products are involved, is
that the outlet opening is generally large. The discharge rate is then likely to be
high and may prove to be incompatible with the feeder or with other
downstream plant components. It could be possible to overcome these
problems by modifying the hopper geometry, for example, by fitting stationary
conical inserts or providing a long slot outlet, but where such approaches are
impractical or insufficient it becomes necessary to adopt a more positive
method of assisting the flow of material from the hopper-the so-called
'discharge aid'.
Commercially available discharge aids have generally developed from
primitive practices such as beating the sides of the hopper with a convenient
'blunt instrument' and stirring or poking the material in the hopper with some
kind of rod. It is helpful to classify modern discharge aids as (i) pneumaticrelying on the application of air (or other gas) to the product; (ii) vibrationalrelying on mechanical vibration of the hopper and/or the product; and
(iii) mechanical-physically extracting the product from the hopper. The
advantages and limitations of a selection of devices from each of these groups
will now be considered.
4.1 0.2 Pneumatic methods
Pneumatic methods can be broadly subdivided as simple 'aeration devices', air
expansion devices (or 'air-blasters') and inflatable pads that act 'mechanically'
against the stored material.
Some examples of the first-mentioned type of pneumatic discharge aid are
illustrated in Figure 4.30, but it is important to note that there are two distinct
techniques of product aeration. One is to introduce air at the time that the
product is to be discharged, so as to 'fluidize' the material in the region of the
outlet opening and to reduce the friction effect between the solid particles and
the hopper wall. The second approach is to maintain a continuous 'trickle
flow' of air during the whole period that the product is stored, with a view to
preventing the gain in bulk strength that usually occurs with time in storage.
Aeration during discharge can be very effective in reducing the interparticle
THE DESIGN OF STORAGE BINS AND HOPPERS
Aeration pads
Figure 4.30
189
Porous bottom
Aeration methods.
forces and the particle-wall effects, thus rendering the product more freeflowing. However, this can itself cause problems as the product can become
excessively fluid, with the result that it 'floods' uncontrollably from the hopper
outlet. It has been suggested that if the air is introduced continuously at a very
low rate throughout the duration of storage, the problem of flooding should
not occur. The explanation is that the air that is lost by slow diffusion as the
product settles is continuously replaced so as to maintain the initial 'weak'
state of the product. Air flow rates of as little as 0.1 m 3 /m in per m 2 of hopper
cross-section (0.3 ft 3 /min perft 2 ) may be sufficient for this purpose, but it
should be noted that this is unlikely to be enough to restore the 'weak'
condition of the product and promote flow if the air has previously been shut
off for any length of time.
Whether the air is supplied continuously or just during discharge, the key to
success is to ensure uniform distribution throughout the product. Introducing
the air through some kind of high-resistance porous surface, such as sintered
metal, plastic or ceramic tile, or woven steel laminate, is commonly used
(Figure 4.30) but an alternative method is to use an internal distributor such as
the perforated ring device shown in Figure 4.31.
Continuous aeration is likely to be effective for fine dry powders of around
1-70 Jlm in size. For sub-micron powders the air flow would probably be
insufficient to reduce the high interparticle force. Materials coarser than about
70 Jlm settle quite rapidly, and the air flow necessary to maintain the 'weak'
condition approaches that required for 'fluidized' discharge. For these
materials (up to about 300 pm), aeration during discharge is likely to be
effective.
As an alternative to the introduction of air in a relatively gentle, uniform
flow, sudden bursts of air may be released into the hopper through one or more
jets (Figure 4.32). The pressure of air used may be up to 7 bar (100 lbf/in 2 ) and
190
BULK SOLIDS HANDLING
air
H
Figure 4.31
Ring distribution system.
by introducing this air into regions where arching or rat-holing are most likely
to occur, the kinetic energy of the expanding jet(s) serves to dislodge the
material and so initiate flow. These devices may be used in various ways,
depending upon the nature of the product being handled and the type of flow
problem to be overcome. Thus in some cases it might be appropriate to
operate the air jets at regular intervals (which could be anything from once or
twice a day to several times a minute) and in others it could be more effective to
install an automatic system which triggers the air blast only when the flow
from the hopper is sensed to be sluggish.
The fact that air expansion devices are widely available under a number of
commercial names, such as 'Air Cannon', 'Air Gun', 'Blast Aerator' and 'Big
Blaster' is perhaps an indication of the frequency at which flow problems are
encountered. Nevertheless, it should be appreciated that this technique
represents a 'brute force' approach and is therefore to be used only as a last
resort. Furthermore, the user should be aware that air expansion devices can
cause problems, for example, dust generation resulting from the quantity of
expanding air and excessive stresses on the hopper walls if the stored material
fails to move.
Another method of using compressed air to promote discharge from
hoppers is by supplying it to inflatable cushions or pads mounted on the inside
of the hopper wall in the region where arching is likely to occur (Figure 4.33).
Typically each of these cushions would have a surface area of around 8000 cm 2
(1240 in 2 ) and would be made of an elastic material some 12 mm (1/2 in) thick.
Inflation of the cushions to 'half-balloon' shape results in a physical push on
the stationary product in the hopper which should cause any arch to collapse.
THE DESIGN OF STORAGE BINS AND HOPPERS
191
Figure 4.32 Air expansion methods. (Top) Air blasters fitted to an underground coal bunker.
(Bottom) A configuration of four air blasters fitted as an integral part of a materials flow system.
(Courtesy Linemann- Halflo Ltd.)
192
BULK SOLIDS HANDLING
.
·o .
.
Figure 4.33
Inflatable pads or cushions.
In practice, however, it may be found that, although working well for so-called
'brittle arches' (in products for which flow /no flow is marginal), the air
cushions can compact products in which a strong arch has developed, so
making the situation worse. As with air expansion devices, inflatable cushions
may be either continuously cycled at suitable intervals or automatically
controlled by flow sensors positioned in the hopper outlet.
4.10.3 Vibrational methods
Vibration as a means of aiding the discharge of a bulk solid from a hopper is
widely used in industry, and many different forms of vibrating device are
available on the commercial market. Depending upon the design of the device,
vibrational frequency can range from 14Hz to around 1300Hz and amplitude
from about zero to more than 60 mm.
It is helpful to make a distinction between devices which cause the walls of
the hopper or bin to vibrate and those which operate directly upon the stored
material, although often both effects will be present to some extent. However,
before the various types of vibrational device are described it would be as well
to consider the effects that vibration can have on a bulk solid. If the product is
contained in a closed vessel, vibration at low frequency tends to cause it to
compact. High-frequency vibration could cause either compaction or dilatation, depending upon the amplitude and the nature of the product concerned.
The point to be made is that, where vibration is required as an aid to flow, it
should not be applied when the hopper outlet is closed, as this could result in a
strengthening of any arch formation.
Vibration of the wall of a hopper can be achieved in a number of ways which
are, in some cases, little more than a refinement of the straightforward 'big
193
THE DESIGN OF STORAGE BINS AND HOPPERS
hammer' technique. It is convenient to group the vibrators under three
headings: (i) air-powered piston; (ii) electromagnetic; and (iii) rotary eccentric
(electromechanical or air-operated).
The air-powered piston vibrator is perhaps the closest approach to simply
beating the outside surface of the hopper with a hammer. Electromagnetic
vibrators have a somewhat similar effect, and both produce vibrations
perpendicular to the wall of the hopper. Rotary eccentric vibrators are
generally more expensive than the electromagnetic types and are likely to have
a shorter working life. They impart a radial impulse so that the hopper is also
subjected to stresses parallel to the wall. Rotary eccentric vibrators are
generally operated at rather higher frequencies and lower amplitudes than
'
rectangular bins
with hopper bottom
Conical or
rectangular hoppers
''·underside,
near spout
Hoppers with
vertical side
Hoppers with sloping
discharge spouts
dead
rectangular or circular
bins with flat bottoms
Figure 4.34
Parabolic hoppers
Recommended positions for vibrators.
194
BULK SOLIDS HANDLING
other types and in spite of the disadvantages mentioned above, they have
achieved a reputation for successfully keeping difficult products on the move.
It is important that a device intended to vibrate the walls of a bin or hopper
should be correctly sited to achieve the optimum effect. The complexity of the
situation does not permit a mathematical analysis to predict the most suitable
point on the hopper wall to initiate a vibration which will be propagated
throughout the hopper. The best location(s) for vibrators are, in practice,
found by trial, but Figure 4.34 illustrates, for different shapes of hopper,
positions that are likely to prove suitable.
More recently there has been a trend towards devices which apply vibrations
directly to the bulk solid itself. The best known example in this category is the
well-established 'bin activator' (Figures 4.35, 4.38). This consists essentially of
a steel dish flexibly supported beneath the hopper opening. A baffie plate,
typically in the form of an inverted cone fitted above the opening of the
activated section, supports the head load of the stored material and transmits
vibrator
motor
outlet section/
Figure 4.35
Bin activator.
/ hopper bottom
~:~:b". ~;~:~~~~~~~~
_.,...
angled blades
(louvres)
.....
,:<~;' :'\
outlet/
section
Figure 4.36
......
•...
.·/:.(~
C 0::~ //;.; '
L-.,..---...,
...
'Siletta' discharge aid.
electromagnetic
vibrator
THE DESIGN OF STORAGE BINS AND HOPPERS
195
Vi bra tors off,
no flow
·_::·:/.:~:·::~/:~ ;: ~-~- -~ ~.: ~-~~/'< ~._: :. ·;:_::;.~ .~.;{ ·.
·.:~~K;-~iitj~~·~
,,....,_--1
..
.• ·•
VIbrators on
Figure 4.37
'Hogan' discharge aid.
the vibrations directly into it. Vibration at a frequency of around 25 Hz is
generated usually by an externally mounted rotary eccentric device and causes
the stored material to move steadily down the walls of the bin, through the
annular space between the baffie and the wall, and into the converging outlet
section. In this section the material is in a dilated, flowing state and having low
mechanical strength is able to pass through a relatively small final opening.
Some measure of control can be exercised over the discharge rate by altering
the size of the cone and by adjustment of the out-of-balance setting of the
vibrator. Table 4.1 [ 15] gives an indication of the size of activator to be used
with various types of stored material. Experience has shown that most dry and
semi-dry materials can be discharged, although flooding may be a problem
196
BULK SOLIDS HANDLING
Figure 4.38
Bin activators in a typical installation. (Courtesy Soli tee Ltd.)
with fine dry products. Materials in Group D (Table 4.1) which are likely to be
poor transmitters of vibration may also present problems.
Several varieties of bin activator are commercially available and offer
various features which are claimed to improve the discharge characteristics or
to offer some measure of flow control. These features include adjustment of the
vertical position of the cone and the width of the annular opening from outside
Table 4.1 Guidance for the selection of bin activators
Product
category
A
B
c
D
Descriptions
Granular, free-flowing
'Sluggish', e.g. starch,
flour.
'Fine adhesive' and 'light
flaky', e.g. bran, wheatings
'Sticky' or 'fibrous'
Activator/ bin
diameter ratio
!-+!
!-+1
t~i
1-+1
THE DESIGN OF STORAGE BINS AND HOPPERS
197
air-operated __
shaker
Figure 4.39
'Bridge breaker' discharge aid.
vibrating cage
Figure 4.40
'Vibro-Bi-Plan' discharge aid.
the hopper, simultaneous vibration and aeration (from porous membranes) of
products, and multiple outlet facilities.
The bin activator described above effectively provides a 'live' bottom to the
hopper on which it is fitted. Two other commercially available devices which
have the same objective of generating a live bottom to the hopper are the
'Siletta' and the 'Hogan' discharge aids (Figures 4.36, 4.37). These are somewhat similar in appearance, each consisting of a vibrating frame carrying a
number of angled blades or louvres and fitted across the bottom of the hopper
as shown. The discharge area is thus divided into a series of narrow slots across
which the product will tend to arch when in the stationary condition.
198
BULK SOLIDS HANDLING
However, vibration of the blades by an externally mounted motor breaks
down the arches and generates an active, flowing condition in the stored
material which can then be discharged through a relatively small opening.
In the case of the Siletta discharge aid the blade/slot dimensions and
inclination are pre-set by the manufacturers to suit the handling characteristics of the product concerned. Varying the amplitude of vibration is claimed
to give control over the product feed rate. A somewhat different approach to
solids flow control is adopted in the Hogan device. As shown in Figure 4.37,
the vibrating blades can be rotated to give a larger or smaller area of opening
so that the feed rate is controlled in much the same way as a butterfly valve
controls the flow of fluid in a pipe.
An alternative approach to the use of a live bottom device involves fitting a
vibrating cage or screen to the inside of the sloping wall of a hopper, with the
aim of breaking any arch of product that begins to develop across the
converging section. Two such devices currently available to industry are the
'Bridge Breaker' (Figure 4.39) and the 'Vibro-Bi-Plan' (Figure 4.40). The first
of these consists of one or more expanded metal screens, each with its own
externally-mounted air operated reciprocating shaker, which vibrates at low
frequency (around 20Hz) and high amplitude (2-4 mm) in a direction parallel
to the hopper walls. This results in a shearing of the material in the vicinity of
the screen(s) which assists its movement towards the hopper outlet. Experience
has shown the Bridge Breaker to be most effective when operated for thirty
seconds in every minute, and then only when the hopper outlet is open. The
Vibro-Bi-Plan (Figure 4.40) consists essentially of a shaking motor suspended
centrally in a hopper and transmitting vibrations to a fabricated cage mounted
parallel to the hopper walls. The position ofthe obliquely mounted motor can
be adjusted to give the most effective combination of horizontal and vertical
vibrational forces.
4.1 0.4 Mechanical methods
The traditional approach to mechanically dislodging a stored bulk material
which has become held up as a result of bridging or rat-holing is to provide the
bin or hopper with poke holes through which rods may be manipulated by
hand. This method is as bad as pounding the walls with hammers, to promote
flow, as the effect is negligible and damage can be caused.
A simple solution that has been found to work well with large-sized
materials such as crushed rock or ore is to suspend chains vertically within the
hopper so that, if a stable arch develops, an upward pull on the chains should
destroy it and restore the flow.
Many varieties of powered mechanical dislodger, such as vertical or
horizontal stirrers, have been used in industry with mixed success. One of the
most reliable of these is the 'circular bin discharger' (Figure 4.41 ). This
consists of an arch-breaker arm which is driven through a universal joint and
THE DESIGN OF STORAGE BINS AND HOPPERS
199
outlet section ----...
Figure 4.41
Circular bin discharger.
motor and
gearbox
\
planetary discharge screw
Figure 4.42
A typical sweep-auger discharge aid.
is free to work anywhere within the conical bin. Product is fed into the outlet
section by the rotation of the flights and the speed of the rotation does, in fact,
give some degree of control over the rate of discharge.
Various types of screw feeder may be used to mechanically extract difficult
products from storage containers. The essential features of screw feeders have
been described in section 4.9.5; the installation of these can be adapted for
handling awkward products by fitting multiple screws and extending them
right across the base of the bin or hopper so that the lower layers of product are
kept 'live'. Two examples are the 'Bowerhill-Parcey' and the 'Storall'.
The Bowerhill-Parcey system features a single rotating screw or sweep auger
which circles slowly around the base of the silo, cutting away the product and
discharging it through the central outlet (Figure 4.42). In the case of the Storall
(Figure 4.43), the screw operates in a fixed position but the base of the
200
BULK SOLIDS HANDLING
rotary table
Figure 4.43
Discharge using a fixed auger and rotating silo.
silo rotates in order to present the product to the screw. Although both of
these systems are expensive, it is claimed that they are capable of handling
products that are, for example, wet and sticky, and which could not be
satisfactorily discharged by other means. In order to match the operation of
the discharger to the flow characteristics of the stored bulk solid, devices such
as the sweep auger system may be fitted with separate motors for the rotation
of the auger screw and for the circular sweep, or at least have some means of
independently pre-setting these two movements.
4.11 Notation
D
Dl,D2
Da
DC
Dmin
DP
FF
FF 1
ff
G
g
H
Htotal
J
L
m
V
f3
Diameter of cylindrical bin
Upper and lower limits for diameter of cylindrical bin
Span of arch
Diameter of opening for circular-section hopper
Limiting value of hopper outlet dimension
Width of opening for plane-flow hopper
Bulk solid Flow Function
Time-consolidated Flow Function
Hopper flow factor
Empirical hopper outlet factor for core flow
Gravitational acceleration (specific gravitational force)
Height of cylindrical section of bin
Overall height of storage bin
Empirical hopper outlet factor for mass flow
Length of opening for plane-flow hopper
Mass of bulk solid stored in bin
Total volume of bulk solid stored in bin
Angle made by sloping hopper wall to vertical ( = half included
angle of hopper)
THE DESIGN OF STORAGE BINS AND HOPPERS
201
Wall angle for circular-section hopper
Wall angle for plane-flow hopper
Valley angle in plane-flow hopper
Surcharge angle of free-surface of bulk solid (=poured angle of
repose)
Bulk density of bulk solid stored in bin
Consolidating stress
Stress in stable arch
Unconfined yield stress
Critical value of unconfined yield stress
Angle of internal friction of bulk solid
Angle of wall friction
References and bibliography
References
!. Jenike, A.W. (1964) Storage and Flow of Solids. Bull. No. 123, Utah Engg. Exp. Station, Univ.
of Utah.
2. Draft Code of' Practice for the Design of Silos, Bins, Bunkers and Hoppers. 2nd edn., British
Materials Handling Board (1985).
3. Arnold, P.C., McLean, A.G. and Roberts, A.W. (1979) Bulk Solids: Storage, Flow and
Handling. TUNRA Ltd., Univ. of Newcastle, New South Wales, Australia.
4. Janssen, H.A. (1895) Versuchc iiber Getreidcdruck in Silozellen (Tests on Grain Pressure in
Silos), Verein Deutscher lngenieure, Zeitschr. 39 (35), 1045-1049 [in German].
5. Walker, D.M. (1966) An approximate theory for pressure and arching in hoppers, Chem. Eng.
Sci. 21, 975-997.
6. Proc. 1st Int. Con/. on Design of Silos for Strength and Flow, Univ. of Lancaster, 2nd-4th
September 1980, Powder Advisory Centre, London.
7. Lastnahmenfiir Bauen-Lasten in Siloze/len (Design Loads for Buildings-Loads on Silo Bins),
DIN 1055, Part 6, (Draft) February 1984. [In German].
8. Regles de Conception et de Calcul des Silos en Beton, Syndicat National du Beton et des
Techniques Industrialisi:es. No. 189, 1975. [In French].
9. Recommended Practice for Design of Concrete Bins, Silos and Bunkers for Storing Granular
Materials (and Commentary), ACI 313, American Concrete Institute 1984.
10. Jenike, A.W. Effect of Solids Flow Properties and the Hopper Feeder Unit on Silo Loads, in
Int. Con[. on Design of Silos for Strength and Flow, University of Lancaster, September 1980.
11. Guidelines for the Assessment of Loads on Bulk Solids Containers. Institution of Engineers,
Australia (1986).
12. Ibrahim, A. G. and Dickenson, R.P. Finite element analysis of the stresses in powdered coal
stored in silos, in Proc. Int. Symp. on Recent Advances in ?articulate Science and Technology,
liT, Madras, India (1982).
13. Reisner, W. and Rothe, M. (1971) Bins and Bunkers for Handling Bulk Materials. Trans Tech
Publications, Aedermannsdorf, Switzerland.
14. McLean, A.G. and Arnold, P.C. (1979) A simplified approach for the evaluation of feeder
loads for mass-flow bins. J. Powder Bulk Solids Techno/., 3 (3), 25-28.
15. Reed, A.R. and DufTell, C.H. Hopper discharge aids, in Proc. Solidex 80 Con[., Harrogate,
March/April 1980, Paper E3.
Recommended further reading
Draft Code of Practice for the Design of Silos, Bins, Bunkers and Hoppers. 2nd edn., British
Materials Handling Board (1985).
202
BULK SOLIDS HANDLING
Arnold, P.C., McLean, A.G. and Roberts, A.W. (1979) Bulk Solids: Storage, Flow and Handling.
TUNRA Ltd., Univ. of Newcastle, New South Wales, Australia.
Reisner, W. and Rothe, M. (1971) Bins and Bunkers for Handling Bulk Materials. Trans Tech,
Cleveland, OH.
Reimbert, M. and Reimbert, A. (1976) Silos-Theory and Practice. Trans Tech, Cleveland, OH.
Gay lord, E.H. and Gaylord, C. N. (1984) Design of Steel Bins for Storage of Bulk Solids. PrenticeHall International, Englewood Cliffs, NJ.
5
Dust control
5.1 Introduction
One of the main problems arising from almost any process involving the
handling of bulk particulate materials is the generation and release of dust.
Designers and operators of bulk handling systems have recently become
increasingly aware of the hazards associated with the release of airborne dust
in significant quantities. Thus, whereas the principal incentive for the control
of dust emissions used to be an economic one {i.e. the more valuable the
product, the more trouble would be taken to ensure its total recovery) there are
now the additional factors of environment, health and safety to be given the
most serious consideration. Since the Health and Safety at Work Act {1974)
became law, the avoidance of excessive environmental pollution has become of
prime importance, and where the product concerned is potentially dangerous
{e.g. toxic or explosive) extreme measures must be taken to prevent its escape
from the plant in which it is being handled.
The handling of a powder or granular product in bulk may involve many
individual operations which could result in the generation of dust. Some
examples of cases where dust concentrations can be very high are grinding,
drying and pneumatic conveying, but other forms of bulk transport, and also
operations such as crushing, mixing and screening, can give rise to considerable dust.
In general, there are three types of hazard associated with the emission of
dust: {i) respiratory effects, (ii) skin and eye effects, and {iii) fire and explosion.
It is almost always the very fine particles of dust that pose the problem as it is
these that tend to remain suspended in the air for a significant period of time.
For example, the terminal velocity of a I ,urn particle of silica is about I mm in
30 seconds, whereas that of a I 00 ,urn particle is about 300 mm per second.
(Figure 5.1 illustrates comparative size ranges of some familiar airborne
particles.) When suspended in air the smallest particle visible to the naked eye
is about 50-I 00 ,urn in diameter, but it is particles of 0.2-5 ,urn diameter that
are most dangerous for the lungs. Thus the existence of visible dust gives only
indirect evidence of danger, as finer invisible particles will almost certainly be
present too. The fact that no dust can be seen is no reliable indication that
dangerous invisible dust may not be present in the air.
There are many aspects to the problem of dust control, but this chapter
concentrates on the separation of the solid particles from the carrier gas in
some kind of'disengaging device' such as a filter or cyclone. Firstly, however, it
is worth examining a little more closely the nature of the problem of dust as a
204
BULK SOLIDS HANDLING
carbol black
viruses
I
oil smoke
I
tobacco smoke
paint pigments
I
insecticide dusts
Iface powder I
I
I
industrial airborne dusts
I
bacteria
milleJ flour
coal dust
fly ash
pollens
0.01
10
0.1
100
mean particle size [1'/Tl]
Figure 5.1
Size ranges of some familiar types of airborne particulate material.
hazard to health. In the next chapter attention will be turned to the other
dangerous feature of airborne dust --the risk of explosion.
5.2 Dust as a hazard to health
5.2.1 Dust particle size
Airborne dusts which may be encountered in industrial situations generally
consist of particles less than about I 0 !!ill in size and can be taken into the body
by ingestion, skin absorption or inhalation. The former is rarely a serious
problem, but diseases of the skin are not infrequent. Eyes may be affected by
irritant dusts or by allergic reaction, and allergic skin reactions are known to
be caused by powders containing, for example, metals such as chrome, nickel
or cobalt. However, it is inhalation that presents the greatest hazards for
DUST CONTROL
205
workers in a dusty environment. Inhalation of dust can lead to respiratory
disorders as a result of direct mechanical and/or chemical irritant action
on the respiratory passages, causing bronchospasm, cough, tightness of the
chest and, following prolonged exposure, chronic obstructive lung disease
[ 1].
The size of dust particles tends to determine the location and extent of dust
deposition in the lungs and influences the action of the dust, although the
pathological effects will depend also upon other factors such as the mass of the
particles and their surface area. Relatively large particles of dust that have
been inhaled and become deposited in the respiratory system will usually be
carried back to the mouth by ciliary action and subsequently swallowed or
expectorated. At the other extreme, ultra-fine particles (less than about
0.2 Jlm) are likely to pass relatively quickly and harmlessly into solution in the
extracellular fluids of the lung tissue [2]. Inhaled particles within the
approximate size range 0.2-5 Jlm can reach the lower regions of the lungs
where they will probably be retained. Prolonged exposure to such dusts can
cause various diseases, most of them potentially serious and often resulting in
permanent damage to the lung tissues. The best known are probably the
diseases collectively designated 'pneumoconiosis' and characterized by chronic
fibrosis of the lungs as a result of continual inhalation of mineral dusts such
as silica, asbestos and talc. Generally the symptoms are chronic shortage of
breath and increased susceptibility to respiratory infection. Other dustrelated diseases include pneumonitis (an acute inflammation of the lung tissue
or bronchioles), lung cancer and certain more specific manifestations and
symptoms [1 ], such as asbestosis, a form of progressive fibrosis of the lung
occurring in those occupationally exposed to significant levels of asbestos;
bagassosis, an acute or sub-acute respiratory condition which may occur in
workers handling bagasse (the fibre of sugar cane sticks remaining after juice
extraction); and suberosis, a relatively benign pulmonary fibrosis occurring in
workers exposed to high levels of cork dust.
It is convenient to classify dusts into four categories according to their
biological action [ 1]:
(i) Inert dusts: accumulate in the body but generally produce no reaction.
(ii) Toxic dusts: usually metal compounds, such as chromates or lead
compounds. Acute or chronic effects on specific organs such as the central
nervous system, the peripheral blood-forming system or the kidneys.
(iii) Allergenic dusts: may cause asthma or eczema, the actual effects varying
from person to person.
(iv) Fibrogenic dusts: the most important from an occupational health point
of view, as they cause the pulmonary fibrosis characteristic of
pneumocomos1s.
The relative dangers of some common dusts are compared in Table 5.1 in
which the materials are arranged in Groups I to IV, but more detailed and up-
Silica (silicon dioxide)
which has been heated.
In these circumstances
silica undergoes modification into biologically
active forms.
Calcined kieselguhr (diatomaceo us earth) is
dangerous on this account.
Beryllium,
particularly as the
oxide.
Very dangerous. Expert
advice should always be
obtained.
Group I
Mica
Ferrosilicon
Talc
Mixed dusts
containing 20~~ and more
of free silica; e.g.
pottery dust, granite
dust and steel foundry
dust.
Emery
Asbestine
Glass (including glass fibre)
Cement
Carborun dum
Barytes
Silica
e.g. as quartz, ganister,
gritstone. etc.
Alumina ('aloxite', corundum )
Minimal risk. Visible concentrations of these dusts,
although inexcusable on general grounds, probably
represent more danger to
welfare and comfort than to
health.
Mixed dusts
containing some free silica
but arbitrarily less
than 20~~. In this group
are included the dusts of
iron and non-ferrous
foundries
Moderate risk. Emission of
any of these dusts to form
a dense local cloud should
cause concern.
Dangerous. A visible haze
of any of these dusts is intolerable, and no possible
source of such dust should
be ignored, whether or not
there is a visible cloud.
Group IV
Asbestos, other than crocidolite.
The two important varieties in commerce are
amosite (brown asbestos)
and chrysotile (white
asbestos).
Group Ill
Group 11
Table 5.1 Relative dangers of some common dusts. Based on information from
[2]
N
0
r
z
Cl
0
z
p
:I:
C/J
5
r
~
~
r
c:::
1:0
0'1
Crocidolite (blue asbestos).
Evidence associates this
variety of asbestos with
the development of malignant tumours of pleura
and peritoneum.
Fireclay dust
with a total silicate (as
'silica') content in
excess of 60%
Perlite and dusts from other
basic rocks
Silicates other than those
already mentioned
Cotton dust and other dusts
of vegetable origin
Graphite
Synthetic silicas
Aluminous fireclay
Zinc oxide
Zirconium silicate and oxide
Titanium dioxide
Tin-ore and oxides
Mineral wool and slag wool
Carbides of some metals
Coal dust
Magnesium oxide
Limestone
Iron oxide
Non-crystalline silica
incl. unheated kieselguhr
Kaolin (china clay;
fuller's earth)
~
-..)
r
0
~
;l
n
~
c::
0
208
BULK SOLIDS HANDLING
to-date information is available in the publications concerned with dust
concentration limits, as described in the next section.
5.2.2 Dust concentration limits
One of the criteria used in monitoring the compliance of companies with the
1974 Health and Safety at Work Act and other relevant statutory provisions is
the concentration of airborne dust. The measured concentration is compared
with variously defined 'threshold limit values' (TL Vs) which are functions also
of the duration of the exposure of personnel to the dust.
Commonly used definitions of threshold limit value are [3]:
TLV-TWA
TLV-STEL
TLV-C
Time-weighed average concentration for a normal 8-hour
workday or 40-hour work week to which most workers can
be repeatedly exposed, day after day, without adverse
effect.
Short-term exposure limit: the maximum concentration to
which workers can be exposed for a period up to 15
minutes provided that no more than four excursions to this
value occur each day.
Threshold limit ceiling: the concentration that should not
be exceeded, even instantaneously.
For further information on actual threshold limit values [ 4] or [5] should
be consulted. Note, however, that more recent proposals [6] use the terms
'control limits' and 'recommended limits', these being generally expressed in
relation to long-term and short-term exposure limits (8-hour TWA and
STEL). The use of ceiling values has been abandoned in the UK because of the
practical difficulty of monitoring and applying these instantaneous levels. The
'control limit', which is applied for the more hazardous materials, is to be
regarded as absolute, with compliance being a legal requirement in the UK
under the Health and Safety at Work Act (1974) and the Factories Act (1961)
[1].
5.3 Dust suppression
5.3.1 Elimination of dust
Clearly the best solution to the problem of dust is to stop making it! However,
it is often difficult to eliminate completely the generation of dust in
manufacturing processes and during the handling of particulate bulk solids.
An assessment of the magnitude of a potential dust problem can be made by
examining the bulk material being handled, paying special attention to the
fines content of that material. A test has been described [7] to determine the
'dustability' of a bulk particulate material; that is, the propensity of particles
DUST CONTROL
209
from within the bulk to become airborne when the bulk is subjected to
external forces. Where such a test, or previous experience with a product,
indicates that the generation of dust is likely to present a real problem, serious
consideration should be given to methods of modifying or treating the product
in order to reduce its 'dustability'.
The first step towards control of dust generation is to examine carefully the
various operations which may be a source of dust. Some examples of these are
falling streams of product (especially where air displacement is involved),
crushing and grinding processes, pneumatic conveying at high velocity, open
stockpiles subjected to winds, and so on. It may well be possible at least to
reduce the amount of dust generation by modifying the process or the method
of handling; for example, by handling the product wet instead of dry, by
agglomerating the particles (pelletizing), or by minimizing air flows which
might disturb the dry product. For a more detailed discussion of this aspect of
dust suppression see, for example, [3] and [7].
5.3.2 Control o{ dust dispersion
If the total elimination of dust is not possible, or not feasible, some method of
'controlling' the dust must be used. Essentially this means keeping the dust
away from personnel and preventing its escape into the environment, but
attention must also be given to the question of dust clouds within enclosures
presenting an explosion hazard. (The latter is discussed in detail in the next
chapter.)
Total enclosure of the processing and handling plant is probably the most
desirable approach but, in addition to the high cost, there are obvious
problems over accessibility. A generally more satisfactory arrangement is to
use some kind of partial enclosure or hood in conjunction with an exhaust
system. In the case of partial or unsealed enclosure the exhaust system serves
not only to remove the dust particles but also to keep the enclosure below
atmospheric pressure so that any leakage occurring will be inward rather than
outward. In this way the egress of dust from the plant is kept to a minimum.
Extractor hoods are essentially of two types: captor hoods and receptor
hoods [8], [9]. The receptor hood is designed to capture dust that is forced
towards it by some external agency whereas the captor hood must be capable
of collecting dust which would otherwise not enter it.
The design of receptor hoods will thus be based essentially on observations
of the movement of dust-contaminated air in the region concerned. The size,
shape and position of the hood must be chosen to ensure that the dusty air is
collected, and the exhaust flow must be sufficient to ensure that at no point
over the entry plane of the hood is the velocity less than that of the
approaching air.
Some fundamental pointers to the successful design of captor hoods are
given in [8]. Figure 5.2 illustrates a range of hood types and shows how the
210
BULK SOLIDS HANDLING
Cal Slot CW • 0.2Ll
V=3.7Lux
(b) Flanged slot (W • 0.2Ll
V=2.8Lux
(cl Plain opening
(W · 0.2, or round)
V =u(10x 2 +Al
where A = WL for a
rectangular opening
(d) Flanged opening
CW • 0.2, or round)
V=0.75u(10x 2 +Al
where A=WL for a
rectangular opening
(e) Booth
V=uWH
(f) Canopy
V= 1.4PDu
where P is the perimeter of
the work space and D is the
height of the canopy above it
Figure 5.2 Forms of dust extraction hood, and formulae for calculating required air volume now
rates [8]. Note: V= extraction air volume now rate; u = centreline capture velocity.
required air flow rate may be estimated, once the capture velocity at a specified
distance from the hood has been selected. It should be noted that for a given air
flow rate the capture velocity, which may need to be anything from around
0.3 m/s for very fine dust in still air to I 0 m/s for coarse particles emitted at
high initial velocities, is inversely proportional to the square of the distance
from the entry plane of the hood. Thus the mean velocity at the entry plane
may need to be very high if the hood is to be effective over more than a short
distance and if the influence of draughts and convection currents is not to
cause an excessive reduction in its efficiency.
Dusty air collected from a booth, hood or other type of partial or total
enclosure must of course be cleaned before it can be released into the
DUST CONTROL
211
atmosphere, and the remainder of this chapter will examine some of the
commonly used types of air-cleaning system.
Methods of air cleaning fall broadly into three classes according to the
property of the solid particles on which the separation process depends. Thus
we have separation based upon (i) the mass of the particles, (ii) the size of the
particles, or (iii) the electrical properties of the particles. The selection of the air
cleaner to be used on any given application will be influenced by a number of
factors, notably the amount of bulk solid involved, the particle size range, the
collecting efficiency required and the capital/running costs. In general, the
finer the particles to be collected the higher will be the cost of a suitable
disengaging system.
Where the dust contains relatively large or heavy particles it would be usual
to select a cyclone separator in which a spin is imparted to the entering
gas/solid stream so that the solid particles are thrown outwards while the gas is
drawn off from the centre of the vortex. Where fine particles are involved,
especially if they are also of low density, separation in a cyclone may not be
fully effective and in this case the gas/solid stream may be vented through a
fabric filter. Many different types of fabric filter are in use and selection
depends mainly upon the nature of the solid particles being collected and the
proportion of solids in the gas stream. For materials containing extremely fine
particles or dust further refinements in the separation technique may be
necessary using, for example, wet washers or scrubbers, or electrostatic
precipitation.
Although a detailed consideration of dust collector selection procedures is
beyond the scope of this book, it must be emphasized that, in order to ensure
that the optimum choice is made, there are many factors to be taken into
account. Furthermore, it must not be overlooked that there is likely to be a
measure of interaction between the dust collecting device and other system
components, and therefore the dust collector should not be considered in
isolation. For a useful discussion of this topic the reader is referred to the
chapter on Plant Selection Procedure in [8], from which the information used
as the basis for Table 5.2 is taken.
5.4 Gravity and inertial separators
The simplest type of equipment for separating solid material from a gas stream
is the 'gravity chamber' in which the velocity of the gas/solid stream is reduced,
and the residence time increased, so that the particles fall out of suspension
under the influence of gravity (Figure 5.3a). Clearly the rate at which the solid
particles settle, and therefore the efficiency of separation, is very much
dependent upon the mass of the particles; that is, upon their size and density.
In general, settling chambers tend to be used as pre-cleaners for cyclones or
filters and would only be used on their own for disengaging bulk solids of
relatively large particle size (greater than about 150 J.lm, although naturally
212
BULK SOLIDS HANDLING
Table 5.2 Primary factors for the selection of dust collection devices [8]
Ga. temperature
mlct l!l
collccwr
ollcctor
lpe
c
c
c
eu
e e
oe
u u
.Do
<-
0
I
c
eu
e
.0
:s
VI
•
•
prec1p11ator
ggregatc liher
Fabn liher
ibrous liher
Key·
e
~u
_g
<
v
8.,.
.,.,
0
rl
8.
:s
uo
..er preference
(If pracucal)
c
8.
:s
..
-g
"'u
Ci
""'"' ...
_g<U f"'J
"'0
<~
/
.. 0
?;
0
u
:s
~
,,
+
•
•
••
•
•
u
8u
:s:~
0
-=
..J!:
:s:
0
;:;
u
-.
.c::
u
="
"" .....
=
-c.
;:;
R
..J 0
.~ E
:2:8
•
Generall} 'klll\factory
F r purely c nom1c rea. "'· ahernauvcs hould be con\1dcrcd
pcc.al aucnllon needed 1f operauonal problem\ arc tu be avmdcd
Pos 1ble evcrc operauonal d1fficuh•c' elect ahcrnall•c
this depends upon the density of the particles). For particles larger than about
300 ,urn a collecting efficiency in excess of 95% should be possible.
To improve the collecting efficiency of the basic gravity settling chamber,
when working with products oflow density or of a fibrous nature, for example,
one or more mesh separating screens may be fitted at an angle across the gas
flow (Figure 5.3b). This represents perhaps the simplest form of impingement
separator in which particles are separated from the gas stream by impingement
on collecting bodies arranged in some manner across the flow. The collecting
body may be a mesh or grid, a baffie plate, a set oflouvres, or a combination of
these. In general the more complex the device (i.e. the larger the number of
changes in flow direction) the greater will be the pressure-drop across it.
In both the gravity settling chamber and impingement separator, care
should be taken to ensure that its design allows, as far as possible, a uniform
distribution of velocity in the gas entering and leaving. Within the device itself,
particularly in the region of the gas exit, the velocity should be generally less
than about 3 m/s if excessive re-entrainment of collected particles is to be
avoided.
Various forms of inertial separator are available which rely on centrifugal
effects, the best known being the cyclone, dealt with in section 5.5. A
213
DUST CONTROL
gas out
______,,----,---'1
gas/solids
Trf"·- ~ ~;
(a) Basic gravity
settling chamber
t
(b) Simple form of impingement separator
~
mesh separating
',
~~'~' ;,\';~~' ~·
'
solids out
solids out
-~wear plate
(c) The principle of
the 'dust skimmer'
Figure 5.3
Gravity and inertial separators.
somewhat simpler device, that does not have the spiralling vortex characteristic of the cyclone, is the skimmer (Figure 5.3c) in which dust particles are
concentrated by centrifugal action on the outer wall of the scroll and then
skimmed off. Mechanically-assisted centrifugal separators are also available
commercially. These devices have the advantage of being compact and
collecting efficiencies are likely to be comparable with those of a highefficiency cyclone.
5.5 Air cleaners-cyclones
5.5.1 Principle of operation
The cyclone separator is dependent upon the mass of the particles for its
operation, the forces that disengage the solid particles from the conveying gas
being developed by imparting a spinning motion to the incoming stream so
that the particles migrate outwards and downwards under the influence of
centrifugal and gravitational effects.
The commonest form of cyclone is the so-called 'reverse flow' type,
illustrated in Figure 5.4, in which the rotation of the gas is effected by
introducing it tangentially to the cylindrical upper part of the device. The solid
particles are then collected from the outlet at the base of the conical lower part
H
214
BULK SOLIDS HANDLING
cleaned gas out
·~ (
...
gas/solids in
outer vortex carries
solid particles
to cyclone wall
Figure 5.4
Principle of dry cyclone separator.
fixed swirl vanes
deflector ring
Figure 5.5 'Straight-through' or 'uniflow' cyclone.
DUST CONTROL
215
whilst the cleaned gas flows in the opposite direction through the top outlet.
Alternative designs of cyclone separator that have been proposed include the
'straight-through' type in which the rotation of the gas/solids stream is
imparted by fixed vanes mounted in a circular duct (Figure 5.5). The cleaned
gas leaves through a concentric inner duct whilst the solid particles are
extracted through an annular space between the inner and outer ducts.
The size of particles that can be separated in a cyclone, and the collecting
efficiency, depend principally upon the difference in density of the solid
particles and the conveying gas, the solids concentration, the inlet gas velocity
and the dimensions (notably the diameter) of the cyclone itself. Increasing the
entry velocity or decreasing the cylinder diameter should normally result in an
increase in the collecting efficiency of finer particles, but the practical lower
limit on particle size is likely to be around 10 f.1m. It should be noted, however,
that decreasing the cylinder diameter will reduce the gas/solids throughput, in
addition to improving the collecting efficiency, and consequently more
cyclones will be needed for a given application, at greater cost. Operation at
higher solids concentrations may be advantageous as fine particles then tend
to be 'caught' and swept out by larger particles, resulting in an improved
collecting efficiency.
The dimensions of a cyclone designed for optimum performance will thus
depend on its actual application (i.e. on the nature of the solid material to be
separated and the separation efficiency required) but typically the proportions
would be as shown in Figure 5.6. For high collecting efficiency the shape of the
cyclone would be modified by decreasing the cross-sectional area of the
gas/solids inlet and the gas outlet and reducing the depth to which the gas
outlet duct extends into the cyclone cylinder. Also, for high efficiency a cyclone
of smaller diameter would be selected. These modifications to the shape of the
cyclone will have the significant effect of reducing the diameter of the
internal vortex and increasing its length, and so allowing smaller
particles to be collected. Note that it is important to maintain, as far as is
possible, the stability of the vortex and therefore it is usually recommended
that the gas exit duct should consist of at least three diameters of straight pipe
before any bend or other obstruction.
High efficiency cyclones do suffer, not surprisingly, from the disadvantage
that the gas throughput is comparatively low. Therefore, whilst it would be
usual to select a single cyclone of suitable capacity for a given application,
multiple parallel high efficiency units would give better collection of fine
particles. Two or more units in series might be preferable where the material to
be collected has a wide particle size range.
5.5.2 Prediction of collecting efficiency
When selecting a cyclone separator, the information that is usually of the
greatest importance is (i) its collecting efficiency over the particle size range of
216
BULK SOLIDS HANDLING
! I<J
?ij'l----=;f
0.350 (0.20)
\!:!2__ •
0.60 (0.50)
-o-
Figure 5.6 Proportions of a typical cyclone separator. (Dimensions in brackets indicate possible
modifications for high collecting efficiency.)
the material being handled: {ii) the pressure drop across it at the normal
operating gas/solids flow rate, and {iii) its cost {including repair/replacement
cost when handling abrasive materials). This information should normally be
supplied by the cyclone manufacturer.
Many attempts have been made to develop theoretical expressions for the
prediction of collecting efficiency based on the dimensions of the cyclone and
on the properties of the gas and solid material to be separated. None has
proved to be really satisfactory and reliance must be placed on experimental
data for cyclone performance. The data is normally presented in the form of
a plot of collecting efficiency against particle size for cyclones tested
with some 'standard' material {Figure 5.7). Over limited ranges, reasonably
reliable corrections can be made to a cyclone efficiency curve to
predict the performance of the device at different gas flow rates, for
different gas viscosities, and for particles of different densities. Table 5.3
217
DUST CONTROL
80
~
~
>c:
(.)
.!!l
.1.1
::::
Q)
low efficiency
(high throughput)
60
0>
.I;
u
~
0
(.)
40
20
80
40
60
particle size Ci<m)
20
100
Figure 5. 7 Performance curves for typical cyclone separators showing the variation that can
occur between designs for high efficiency and for high volumetric flow rate.
Table 5.3 Correction factors for collecting efficiency of a cyclone
Variable
Correction factor
Gas volumetric flow-rate
Gas viscosity
Particle density
,j(rated flow rate/actual flow rate)
,j(viscosity of actual gas/viscosity of tested gas)
,j(density of tested particles/density of actual particles)
summarizes these correction factors by which the particle sizes at the rated
conditions should be multiplied.
As an example of the way that these correction factors may be used, consider
a cyclone tested with a particulate solid of density 3000 kg/m 3 and a conveying
gas of viscosity 1.8 x 10- 5 N s/m 2 at a rate of 0.03 m 3 /min. An estimate of the
collecting efficiency curve for the cyclone operating with a material of density
pP kg/m 3 and gas of viscosity /lg Ns/m 2 and flow rate Vg m 3 /min could be
obtained by multiplying values of particle size on the tested collecting
efficiency curve by a factor K, where
K=
3000.
/lg
-~~~
t.8 x 10-s
0.03
vg
218
BULK SOLIDS HANDLING
A similar correction may be made for scale on cyclones that are geometrically similar by using the correction factor.
K' =)(diameter of actual cyclone/diameter of test cyclone)
provided that the difference in size is not great.
5.5.3 Prediction of pressure-drop
It is usually important to have some preliminary knowledge of the pressuredrop across a cyclone separator, especially where it is to be installed on a lowpressure pneumatic conveying system, since the volume flow rate produced by
the fan is very sensitive to the total system resistance. Variations in cyclone
design to increase the collecting efficiency also tend to increase the pressuredrop across it. Whilst at the present time there appears to be no simple
accurate method of predicting the pressure-drop across a cyclone, !lpc, a useful
approximate prediction can be made by using the following equation, based
on that proposed by Alexander and described in [1 0], to obtain the pressuredrop in terms of the inlet velocity head:
fl Pc= C x
area of gas inlet
f
x inlet velocity head
area o gas out 1et
where the factor C is a function of the cyclone body diameter, the gas outlet
diameter and the gas temperature, and can be estimated from Figure 5.8.
5.5.4 Cyclone selection
Summarizing, the selection of a single cyclone separator for a given application is matter of determining, from the dimensions of available models,
the velocity of the gas at the inlet section. The choice is then from cyclones for
which this inlet velocity is between about 19 mjs and 30 mjs. A rather higher
velocity could be beneficial when handling very fine particulate materials, but
it is more likely that such high velocities will result in a fall in efficiency because
of excessive turbulence within the cyclone and consequent re-entrainment and
carry-through of particles. Where the gas flow rate fluctuates to such an extent
that the inlet velocity may fall outside the acceptable range for a single cyclone,
it is possible to install a number of smaller cyclones in parallel with manual or
automatic shut-off of one or more as the flow rate falls.
A final choice of single cyclone, or a decision to use multiple cyclones in
parallel or in series, should be made on the basis of collecting efficiencies and
pressure-drops estimated as explained above.
5.6 Air cleaners-wet washers or scrubbers
5.6.1 Principle of' ope rat ion
A significant improvement in the performance of dry gas/solids separators
such as cyclones and fabric filters can be achieved by the addition of some form
8
§
~
0
....
100
~
v
200
500
~
1000
I
I
I
I
!
I
I
I
I
I
2000
cyclone body diameter (rrrn)
..-:::: ::::
...,
,...... /
.........
.........
~ .,.I-'
I-~
~I
5000
V
y. 1-r-· !- -·
f
h
-
'(
IJ
5
~{t ~~~v
!
t
I
I
I
I
I
I
coefficient C
10
~
15
20
Vv ~v/I/
V/ llll
1/ ~
I
~ ~V
r/ I~
I
-.I- 1j
~.3 lo.5,.7 I
I 'I!J
!- t--
1
J·5 /
Figure 5.8 Cyclone pressure-drop chart; lip = C x area of gas inlet/area of gas outlet x inlet velocity head.
,
...
loo"' ..... "' ...
50
1:
1250
u
~
!-- ...
Ja~
~
0.7
I I I
/
I
0.3
50
gas outlet diameter /cyclone body diameter
\0
N
-
r
~
~
()
0
§
220
BULK SOLIDS HANDLING
of water spray. Although there are many different types of wet washer, the
principle of operation is essentially the same. Solid particles entering the
device are 'wetted' by coming into contact with either an irrigated surface or
water droplets of a size much larger than that of the particles themselves. The
water is then drawn off into a suitable sump where it is left to stand for
sufficient time to allow the solid particles to settle out.
The main mechanisms by which dust particles are wetted and collected are
[11]:
(i) Impingement, in which the dust particles are made to impinge and adhere
to water droplets or a water film.
(ii) Diffusion, the mechanism by which the smaller particles are collected by
liquid droplets.
(iii) Condensation: if a liquid spray causes the gas to pass through its dew
point, condensation will take place, with the dust particles acting as
condensation nuclei. The increase in effective size of particles simplifies
their subsequent collection by mechanical means.
In addition to capturing the solid particles the water in the wet washer also
serves to keep the internal surfaces of the device clean and to carry the
collected dust to the disposal point.
The principal types of wet washers in use are [ 11 ], [ 12]:
(i) Low pressure-drop types
(a) Spray chambers
(b) Packed irrigated towers
(c) Irrigated porous beds
(d) Mechanically induced spray scrubbers
(e) Irrigated cyclones
(ii) High pressure-drop types
(a) Self-induced spray scrubbers
(b) Venturi scrubbers.
Probably the most important single advantage of wet washers is the
reduction in hazard level when handling potentially explosive materials.
However, their application is, in general, somewhat limited, and therefore
these devices will be described here only briefly. For further information the
reader is directed to [8], [11], [13] and [14].
5.6.2 Low pressure-drop wet washers
In the simplest type of spray chamber the dust-laden air is passed through a
series of water sprays (Figure 5.9). Baffle plates may be placed between the
sprays to assist the contacting of water and solid particles. In some designs the
air enters tangentially as in a cyclone and water is sprayed radially across the
air-stream (Figure 5.1 0). Pressure-drops are typically around 15-50 mm H 2 0
221
DUST CONTROL
clean air outlet
~
Figure 5.9
water
inlet
Typical simple spray tower.
for simple spray chambers, or up to 200 mm H 2 0 for the cyclone type.
Packed irrigated towers are really a development of the simple spray
chamber. Water is sprayed into the top of the tower and drips down through a
column of randomly packed elements (e.g. glass marbles or ceramic rings)
collecting dust from the upward-flowing contaminated air. Irrigated porous
beds are essentially similar but contain large numbers of small packing
elements (e.g. beads) in relatively shallow beds. Consequently the
collecting efficiency may be slightly better than for a packed bed, but the
pressure-drop is likely to be somewhat greater, perhaps up to 1.2 m H 2 0.
High maintenance costs and unreliable performance have resulted in the
decline of the mechanically-induced spray scrubber. One type which has
survived is based on a fan which atomizes and accelerates water sprayed into
the inlet so that inertial impaction takes place between the dust particles and
the high-velocity water droplets.
Irrigated cyclones are very similar in appearance to dry cyclones except that
water is introduced to provide a film over the internal surfaces of the device. In
this way the tendency for dust particles to be picked up by the inner upward-
222
BULK SOLIDS HANDLING
clean ai" outlet
core
breaker ---t-...,;?.--~o~
spray
manifold
ckJsty ai"
net
Figure 5.10 Cyclone spray scrubber.
flowing vortex is minimized, thus reducing one of the main sources of
inefficiency of dry cyclones. Irrigating a conventional dry cyclone can result in
a significant improvement in performance without increasing the pressuredrop.
5.6.3 High pressure-drop wet washers
The self-induced spray scrubber is probably the most widely used type of wet
washer. These devices operate by drawing the dust-laden air under or through
baffies partly submerged in water and so generating a dense spray
(Figure 5.11). This results in a compact design of collector and relatively high
collecting efficiency. Furthermore, the lack of moving parts means that
maintenance costs are low. However, pressure-drops can be quite high (up to
200 mm H 2 0). Good performance is obtained even with dusts as fine as
2.5 pm, and water usage is relatively low at about 7litres of water to 100m 3 of
air.
Another device capable of achieving high performance with very fine
223
DUST CONTROL
Figure 5.11
Self-induced spray scrubber.
clean air
outlet
' water inlet
I
water and
sludge outlet '
Figure 5.12
Arrangement of typical venturi scrubber.
224
BULK SOLIDS HANDLING
particles is the venturi scrubber (Figure 5.12). Water is injected into the dustladen air which has been accelerated in a throat section to a velocity of around
60-100 m/s. The resulting high relative velocity between water droplets and
solid particles ensures a high collecting efficiency. The dust-carrying droplets
are separated from the air in a cyclone separator. Energy requirements of
venturi scrubbers are high, pressure-drops being normally in excess of 500 mm
H 2 0.
Various developments have been proposed recently [8] with the aim of
reducing the high power usage of wet dust collectors. These include:
(i) Electrically augmented scrubbers providing an electrostatic charge to the
dust particles or to the water droplets, or both
(ii) Two- or three-stage venturi scrubbers
(iii) Bubble foam scrubbers
(iv) Flux force and condensation scrubbers in which a hot humid gas is
brought into contact with a cold liquid.
5.7 Air cleaners-filters
5.7.1 Mechanism offiltration
The second class of gas/solid separator to be considered is that which depends
for its action principally on the size of the solid particle to be collected. The
main representatives of this class are devices using screens or fabric filter bags.
In order to appreciate the principles on which filter units are designed or
selected it is helpful to understand the manner in which they operate. There are
two fundamental mechanisms by which particles can be removed from a
stream of gas passing through a porous fabric. The most obvious of these is a
'sieving' mechanism in which particles too large to pass through the mesh of
the fabric are caught and retained on the surface of the filter. The caught
particles gradually build up on the filter so that the labyrinthine nature of the
gas flow-path continually increases whilst the 'effective mesh size' decreases.
The collecting efficiency of the filter will therefore tend to be improved
by use, but of course the pressure-drop across it will also increase, and regular
cleaning is essential.
The less obvious but, especially for very fine particles, more important,
mechanism of filtration is that in which the particles are caught by
impingement on the fibres of the filter fabric (sometimes called 'depth
filtration' to distinguish it from 'sieving'). It is for this reason that filters usually
consist of a fibrous mat rather than a single woven fabric screen. The actual
flow-paths followed by the gas passing through a depth filter are thus
extremely tortuous and a particle, unable to follow these paths, is given a
trajectory which sooner or later brings it into contact with a fibre where it
adheres, largely as a result of van der Waals forces.
DUST CONTROL
225
The collecting efficiency of a fabric filter is mainly influenced by the gas
velocity through the fabric and the size of particle to be collected. Where the
particles are relatively large (greater than about 5,um) they are likely, because
of their greater inertia, to come frequently into contact with the filter fibres.
However, the tendency to 'bounce off' the fibres and escape from the filter is
also greater, especially where the gas velocity is high. Where the solids loading
is low, the performance of the filter may be improved by oiling the fabric to
enhance the adhesive properties of the fibres. For high solids loading, as would
be encountered in pneumatic conveying systems for example, a common
practice is to install a cyclone separator upstream of the filter in order to
remove most material over 5 ,urn in size. With extremely fine particles the
phenomenon of Brownian diffusion becomes significant. At low velocities
especially, the effect of this is to increase the collecting efficiency of the filter.
Increasing the gas velocity will reduce the influence of Brownian diffusion and
the particles, having low inertia, may be able to follow the flow-paths through
the filter. There is thus a minimum collecting efficiency between the peaks
corresponding respectively to Brownian diffusion (for fine particles at low gas
velocity) and inertial impingement (for larger particles at higher gas velocity).
This relationship between collecting efficiency and particle size/gas velocity is
illustrated in Figure 5.13. For a more complete discussion of this subject see
[14].
As with separation by sieving, the collecting efficiency and the resistance of a
depth filter generally increase with use. Once the pressure-drop across the filter
becomes unacceptably high the fabric must be cleaned or replaced.
decrease in
efficiency due
to 'bounce off
1
0
c
-~
0
~
Cl
.I;
i0
0
particle size
velocity
Figure 5.13
~
~
Variation of collecting efficiency as a net effect of particle size and gas velocity [14].
226
BULK SOLIDS HANDLING
Table 5.4 Summary of the characteristics of some typical fibres used in the manufacture of filter
fabrics
E ·;::"
ci.o=
<1)
-
x
<=:
0u
"U
~c_.
<=
0
<1)
u
<=:
·;n ro
"......
~
..0 V>
-<( ~
Fibre
---·-
Polyethylene
Cotton
Polypropylene
Wool (dry)
Nylon
(polyamide)
Orlon
(acrylic)
Dacron
(polyester)
Nomex
(polyaramid)
Teflon (PTFE)
Glass fibre
<=
<=
-~
-~
<=~ ~>-.
t::::=
~
~
(1):.0
8
V>
v'O
:-= ro
V> '"
<= "
..c:: ·-g
u
"'"'
f-;c:__.
.
-----""---~---··-
u
u
o;,
0
,;
,;
..c::
~
- -·---
-
~
--
81:
""
UOl
,.c::..>G
<=
0
v;·-
t:t::
0p....O
"
o..E
"
VJ
0
u
--~--------
65
70
90
95
Ex c.
Good
Ex c.
Av.
Ex c.
Fair
Ex c.
Poor
Ex c.
Poor
Good
Poor
Ex c.
Good
Good
Poor
Yes
Yes
Slow
No
95
Ex c.
Ex c.
Poor
Good
Yes
130
Good
Fair
Good
Av.
Yes
135
Ex c.
Ex c.
Good
Good
Yes
220
230
260
Good
Fair
Poor
Good
Fair
Ex c.
Fair
Ex c.
Av.
No
No
No
Av.
Ex c.
Poor
5.7.2 Filter media
A wide range of materials is available for the manufacture of filter fabrics.
Wool or cotton, the latter particularly having the advantage of low cost, may
be used, but for better resistance to abrasive wear or chemical attack and a
higher maximum operating temperature, either glass fibre or one of a number
of alternative man-made fibres should be selected. Table 5.4 indicates the
relative merits of several natural and man-made fibres commonly used for
filter fabrics.
Apart from the properties of the fibres themselves, specifications for filter
fabrics should include the 'weight per unit area', which gives an indication of
the thickness and therefore the strength and durability of a fabric, and the
permeability. The latter depends upon the construction of the fabric (that is,
whether it is woven or felted, its thickness, tightness of weave, and so on) and
allows the pressure-drop across a filter to be estimated. Various surface
treatments may be carried out on filter fabrics by the manufacturer, the
principal aims being to reduce the adhesion of caked solids to the fabrics and
thus render the cleaning process easier and more effective, and to increase the
resistance to combustion.
The current trend is towards the use of lightweight needlefelts which allow
filtration velocities some two or three times higher than those for woven
fabrics, and which generally give better collecting efficiencies.
227
DUST CONTROL
fabric bags
~
r;:_:.
solid material out
Figure 5.14
Typical bag filter unit (mechanically cleaned).
5.7.3 Bag filters~design and selection
Figure 5.14 illustrates diagrammatically a typical form of bag filter unit. The
gas/solid stream enters the device from beneath the fabric bags so that larger
particles are separated by gravity settling, often aided by a cyclonic action.
Fine particles are then caught on the insides of the cylindrical fabric bags as the
gas flows upwards through the unit. These filters are available in a very wide
range of sizes with bags varying in diameter from about 100 mm up to almost
one metre, and from 0.5~ 10 m long. The shaking mechanism represented in
Figure 5.14 is one several methods of bag cleaning that may be employed, but
these will be described in more detail in section 5.7.4.
A common alternative design of bag filter uses rectangular envelopes
instead of cylindrical tubes of fabric. Note also that filter units using cylindrical
bags may be designed so that air flows up the inside of the bag and through the
sidewalls (as shown in Figure 5.14) or from the outside of the bag through to
the inside (Figure 5.15). In the latter case the bags are supported on wire cages
to prevent them from collapsing inwards.
The selection of a fabric filter for a given application should be made after
228
BULK SOLIDS HANDLING
solenoid valves
r;=;e;;:F==;-;==;r===~
compressed
air inlet
air nozzles
cleaned
air outl:r-_ ____,
fabric bags
.\'
~ ~ ~ .~ ·..::.. :... .
:J;l:x,.f
solid material outlet
Figure 5.15
jets.
Fabric bag filter unit showing cleaning by use of high-pressure pulsed reverse air-
consideration of a number of criteria. The first of these should be the particle
size range and the nature of the solid material to be collected, and the
temperature of the conveying gas, which will dictate the type(s) of fabric that
would be acceptable. The size of unit required will depend principally upon the
maximum gas flow rate to be handled and the maximum allowable pressuredrop but will also be influenced by the proportion of solid material carried by
the gas, the method of cleaning to be used and the planned frequency of
replacement of the filter fabric. Obviously several of these criteria are affected
by cost factors and a careful balance must be struck between the capital cost of
the equipment, normal running costs and the cost of routine maintenance. A
Code of Practice has recently been published in the UK [15] which gives
detailed guidance on the selection of fabric filters for dust control.
The basic measure of filter size is the effective area of fabric through which
the gas has to pass. It should be noted that there may be a significant difference
between the total or 'gross' area of fabric and the effective or 'net' area that is
actually available for use (that is, not on a cleaning cycle). It is usual to specify
229
DUST CONTROL
the size of filter required on the basis of an assumed value of the so-called 'airto-fabric ratio', defined as the volume flow rate of approaching air divided by
the effective area of the filter fabric. It should be noted that this parameter is
not in fact a ratio but has the dimensions of velocity; it is perhaps better
regarded as a superficial velocity of air through the filter fabric and the term
'filtration velocity' is to be preferred.
The actual value of the filtration velocity to be used depends upon several
factors, as indicated previously, and, although there have been attempts to
develop theoretical expressions for the prediction of this parameter in various
situations, none is really satisfactory and reliance must be placed on
experience. The manufacturers of filter units should normally be able to advise
on suitable filtration velocities for the bulk particulate material being handled,
but typical values for felted fabrics would be about 2 m/min when handling fine
particulates and 'dusty' materials, up to 3.5 m/min with coarser or granular
products. For woven fabrics these figures should be halved since the free area
actually available for gas flow is much less. Table 5.5 gives some guide values
of filtration velocity for a range of familiar bulk solids and a more extensive list
can be found in [8] and [ 15].
In some situations, such as pneumatic conveying systems, the pressure-drop
across a fabric filter unit may represent a significant proportion of the overall
pressure-drop available, and consequently any increase in the resistance of the
Table 5.5 Guide values of filtration velocity for fabric filters [8]
··------
Woven fabric
Felted fabric
m/s
ft/min
m,s
ft/min
0.015
0,020
0.013
0.016
0.016
0.018
0.013
0.015
0.020
0.015
0.015
0.015
0.016
0.013
0.016
0.016
0.016
0.023
0.016
0.013
3,0
3.9
2.5
3.2
3.2
3.5
2.5
3.0
4.0
3.0
3.0
3.0
3.2
2.5
3.2
3.2
3.2
4.5
3.2
2.5
0.025
5.0
0,030
0.051
0.025
0.038
0.036
0.041
0.036
O.o38
0.041
0.030
0.033
0.025
0.033
0.025
0.041
0.036
0.036
().()46
0.036
0.038
0.018
0.051
6.0
10.0
5.0
7.5
7.0
8.0
7.0
7.5
8.0
6.0
6.5
5.0
6.5
5.0
8.0
7.0
7.0
9.0
7.0
7.5
3.5
10.0
Dust
Alumina
Animal feeds
Carbon black
Cement
Coal
Coffee
Corn starch
Fertilizer
Flour
Fly ash
Glass
Metal powders
Milk powder
Paint pigments
Pharmaceuticals
Plastics
Salt
Sand
Soda ash
Sugar
Titanium dioxide
Tobacco
230
BULK SOLIDS HANDLING
pressure-drop at which
/cleaning is triggered
t
cleaning
intervals
~~
~.m~
",I
I
c.
-
-"'
:
0
-oa,
\
5
(/)
(/)
Q)
0.
residual pressure-drop
virtually steady
.
gradual tncrease of
residual pressure-drop
during conditioning
initial pressure-drop
across clean fabric
time
Figure 5.16
•
Typical variation of pressure-drop across a fabric filter.
filter may have a serious effect on the performance of the system. Typically
the pressure-drop across a fabric filter should be around 100-150mm H 2 0
(or 4-6 in water gauge), and with a properly maintained cleaning routine this
value should not change appreciably during use. In normal use there will be, of
course, a small regular fluctuation in the resistance of the filter as a result of the
build-up of collected dust and its removal during cleaning. This is illustrated in
Figure 5.16, which also shows the gradual increase in the residual resistance of
the fabric that occurs during the initial conditioning period.
5.7.4 Filter cleaning
The design of present-day fabric filter units, with their multiple bags or
envelopes and their complex automatic cleaning mechanism, has gradually
evolved along with increasing awareness of the need to conserve energy and to
avoid atmospheric pollution. The use of multiple bags was simply a means of
getting a larger area of fabric into a small space, but a more important aspect of
filter design concerned the method of minimizing the proportion of fabric area
out of action at any one time for cleaning. This consideration led to the
introduction of filter units having two or more separate compartments, each
containing a number of bags. Then one compartment could be shut off for
cleaning while the other(s) remained in service handling the full gas/solids flow.
Modern filter units using pulsed air-jets for fabric cleaning do not require the
unit to be compartmented but are still designed to ensure that only a small
number of bags are out of service at the same time.
Basically there are three types of cleaning action-mechanical shaking,
reverse flow and air-jetting. Mechanical shaking (shown in Figure 5.14) tends
231
DUST CONTROL
to be cheaper, but its application is restricted to installations handling
materials which readily form a caked layer on the surface of the filter fabric.
Periodically shaking the framework on which the bags are mounted, typically
at a frequency of 6-8Hz and amplitude of around 50 mm, causes a flexing or
rippling movement of the fabric, with the result that the caked solids are
dislodged and fall clear of the bags into the collecting hopper. However, this
action is quite severe on the bags and the mechanical components of the
system, especially when abrasive materials are being handled.
An alternative method of causing the filter fabric to flex and so dislodge
caked material is to arrange for a periodic reversal of the direction of gas flow
through the fabric. This may be achieved either by diverting the total flow of
cleaned gas back through one section of the filter or by a system of lowpressure jets, operating in sequence, which inject cleaned air downwards
through the bag walls in the reverse direction to the normal airflow. Several
variations on these basic techniques are marketed by different manufacturers
and, as with mechanical shaking, continuous operation of the filter units may
be obtained by the use of dampers to shut off one compartment at a time for
cleaning.
Modern trends in high-efficiency filter cleaning mechanisms appear to be
towards high-pressure pulsed reverse air-jets which are claimed to produce a
pressure wave that travels down the bags dislodging the caked material from
the fabric surface and forcing the fine particles out of the body of the fabric.
Pulse pressures are typically around 7 bar gauge for cylindrical filter elements
and about half this value for rectangular envelopes. Each cleaning cycle
lasts for a very short period of time (50-150 ms) at intervals of I 0-30 s, so that
minimum interruption is caused to the normal flow through any one bag, thus
allowing maximum utilization of the fabric area (Figure 5.15).
More detailed information on the design and selection of fabric filter units,
earthed plate electrodes
at positive polarity
uncharged
particles
/
+
electrical
field
\--r-r1'1""1i~"l'l'l~~~'l':"'''"l"!:l'~~:'l'!'!"l"??"!'l"'''"'""'""l':':'?::---::>-/
, 'o 6 o W10CJI2)6q:p3~M1W&/&Atw7
\'1:/
0
dusty~
o
\\
0
J I
1/
:W-
1 I
1
discharge
electrode wires at
negative polarity
Figure 5.17
11:1
;1J \ / \
O\ 1
. o
~-
o
I
~
1 I I I
I I~>-\
b~ o eR>
+ j_
~
'11/
~\ 1
flll"b \I
:JI \ I I IJ>
fill"" \ \ I /
1 1
~//
lltlr'ttfJo
Ill'(-~
~~ 1
I 1
\1 ,' /
fill'"
\\
~)"~' o
'*~
0
0
I I
~-
__..
cleaned
gas out
\\
1
I 1
I I I 1f
I 1~
I I i' d
i'g ~/ Wl£difflfbg
charged particles
attracted to
collector plates
The principle of electrostatic precipitation as a means of dust collection.
232
BULK SOLIDS HANDLING
rapping
mechanism~
~
cleaned
gas
outlet
/
dusty
gas
inlet
/
collect1ng
electrodes
~
~ rapp1ng
mechan1sm
discharge electrodes
Figure 5.18 Electrostatic precipitator (plate-type).
and on the types of fabric and cleaning techniques available, may be obtained
from literature published by the manufacturers of such equipment or from
textbooks and guides such as [8], [11], [13] and [15].
5.8 Air cleaners-electrostatic precipitators
Basically, electrostatic collection involves passing the dusty gas through a
high-voltage field set up between two electrodes, one of which is live and the
other earthed (Figure 5.17). When the fine solid particles have acquired a
sufficient charge they migrate towards one of the electrodes (mostly to the
earthed one) from which they are periodically removed by rapping or, more
rarely, by spray washing.
Industrial electrostatic precipitators can take various forms. These include
the tubular or pipe-type in which round wire discharge electrodes are
suspended axially in vertical-hung tubes, and the plate-type (illustrated
DUST CONTROL
233
diagrammatically in Figure 5.18) where the collecting electrodes are vertical
plates hung in rows to form passages through which the dirty gas passes
horizontally.
The collecting efficiency, which can be quite high, comparing favourably
with wet washers and bag filters, varies exponentially with the area of the
collecting electrodes for a fixed gas flow rate. The capital cost of an
electrostatic precipitator could therefore be considerable, since it is likely to be
proportional to the size and consequently would vary exponentially with the
collecting efficiency. However, the running costs tend to be comparatively
small, and on very large installations, to which this type of gas/solid separator
is best suited, the combined capital and running cost would usually be less than
that of alternative systems.
5.9 Notation
c
D
K,K'
vg
/",.pc
Pp
Jlg
Cyclone pressure-drop coefficient (Figure 5.8)
Diameter of cylindrical body of cyclone
Correction factors for cyclone collecting efficiency
Gas volume flow rate
Pressure-drop across a cyclone
Particle density
Gas viscosity
References and bibliography
References
I. Croner's Health and Safety at Work. Croner Publications, UK. [Amendment July 1984.]
2. Health: Dust in Industry. Dept. of Employment and Productivity, HM Factory Inspectorate
Technical Data Note 14. HMSO, London (1970).
3. Schofield, C. Dust: the problems and approaches to solutions, in Proc. Solidex 82 Conf,
Harrogate, UK, March/ April 1982, Paper B l.
4. Threshold Limit V a lues 1980. Guidance Note EH 15/80, Health and Safety Executive. HMSO,
London (1980)
5. Threshold Limit Values. Ann. pub!., American Conf. of Governmental Industrial Hygienists,
USA.
6. Occupational Exposure Limits 1985. Guidance Note EH40/85, Health and Safety Executive.
HMSO, London (1985) (Annual.)
7. Schofield, C., Sutton, H.M and Waters, K.A.N. (1979) The generation of dust by materials
handling operations; J. Powder and Bulk Solids Technol., 3 (1), 40-44.
8. Muir, D.M. (ed.) (1985) A User Guide to Dust and Fume Control. (2nd edn.), Instn. Chem.
Engrs., London.
9. Principles of Local Exhaust Ventilation and Factory Dust Control. Health and Safety
Executive, HMSO, London (1975).
10. Caplan, K.J. (1977) Source control by centrifugal force and gravity. In Air Pollution, Vol. IV,
97-148.
11. Separation of Dust from Gases. EEUA Handbook No. 19, Constable London (1967).
12. Swift, P. (1976) Industrial dust collectors up-to-date. Filtration and Separation, May/June,
257-270.
13. Perry, R.H. and Green, D.W. (eds.) (1984) Perry's Chemical Engineers' Handbook, 6th edn.,
McGraw-Hill, New York, 20.89-20.97.
234
BULK SOLIDS HANDLING
14. Stenhouse, J.I.T. ( 1969) Mechanisms of gas filtration, in Process Engineering Technique
Evaluation-Filtration, Morgan-Grampian, London, 70-76.
15. Code of Practice for the Purchase and Operation of Fabric Filters for Dust Control, British
Materials Handling Board (1985).
Recommended further reading
Muir, D.M. (ed.) (1985) A User Guide to Dust and Fume Control, (2nd edn.), lnstn. Chem. Engrs.,
London.
Code of Practice for the Purchase and Operation of Fabric Filters for Dust Control, British
Materials Handling Board (1985).
Perry, R.H. and Green, D.W. (eds.) (1984) Perry's Chemical Engineers' Handbook, 6th edn.,
McGraw-Hill, New York, 20.75-20.121.
6
Explosion hazards
6.1 Introduction
Many bulk solids, when dispersed in air to form a cloud or suspension and
ignited, rapidly propagate a flame through the suspension, with a subsequent
sudden increase of pressure as a result of the release of heat and gaseous
products from the burning dust. This is commonly called a 'dust explosion', in
contrast to a 'fire' which would be said to occur if the burning dust were in a
pile or layer. In fact, dust will generally smoulder or burn with a flame: some,
especially plastics, tend to melt or flame or give off noxious vapours which are
readily detected, but others may glow and smoulder, remaining an undetected
hazard which could persist for days. Although only a minority of dust fires
actually result in an explosion, the potential danger is a very real one. Typical
examples would be the explosions of airborne dust following the sudden
disturbance of a smouldering layer during cleaning or the collapse of a burning
pile of material.
When an explosible product is dispersed in the open air, the result of ignition
is likely to be a flash of flame developing little hazardous pressure. However, if
the suspension is confined, for example in an enclosed hopper or in a
pneumatic conveying system, large pressure effects would be expected,
depending upon the volume of the suspension, the nature of the product and
the ease of escape to atmosphere.
A wide range of particulate solids may be regarded as posing an explosion
hazard, including common foodstuffs such as sugar, flour and cocoa; synthetic
materials such as plastics, chemicals and pharmaceuticals; metals such as
aluminium and magnesium, in addition to traditional fuels such as coal and
wood. However, research has shown that, although a material may be known
to burn in air when it is in solid form, it is in fact only when existing as particles
having diameters less than about 200 ,urn that the material may become
dangerously explosive. Oxidation of such fine particles occurs rapidly, in
association with a rapid rise of temperature, since the surface area of the
particles in contact with the air is large and their volume relatively small.
It is important to appreciate that the main danger to equipment and
personnel is not necessarily from an explosion occurring within the bulk
handling plant itself. Such an explosion may rupture a weak component (for
example, a cyclone receiver) and the resulting sudden release of burning dust
and gases may then throw up external settled dust into a very large cloud. A
secondary explosion of this airborne material can be devastating and the
importance of good 'house-keeping' cannot be over-emphasized.
236
BULK SOLIDS HANDLING
A number of serious dust explosions are known recently to have occurred,
particularly in the USA, involving many fatalities and the destruction of
industrial plant of a substantial value. In the United Kingdom, the most
serious dust explosion in recent years occurred in 1981 in a plant manufacturing custard powder [1]. An accumulation of corn starch powder caused a
malfunction of a valve and consequent leakage of powder from a feed bin into
a workroom. The dust cloud was ignited by electrical arcing, and in the
resulting explosion nine men were burned and serious structural damage was
caused to the building. During the seventeen years from 1962 to 1979 there
were 474 recorded dust explosions in the UK, resulting in 25 deaths [2], and in
just two years, 1976 and 1977, dust explosions in grain handling plant in the
United States claimed the lives of 87 workers and caused injuries to over 150
more [3].
Of identified causes of explosions in such plant, the commonest are welding
and cutting operations, and there is evidence that the most frequent location is
in bucket elevators. These comments apply specifically to grain handling
facilities, and in a more general analysis of lOO recent explosions [4] it was
Figure 6.1 Example of results of a violent industrial dust explosion, in this case, aluminium dust.
Reproduced by permission of the Health and Safety Executive. © Crown Copyright.
EXPLOSION HAZARDS
237
Figure 6.2 Explosion damage to a bag filter and cyclones. Reproduced by permission of the
Health and Safety Executive. © Crown Copyright.
shown that (excluding explosions in mines and furnaces) 38% occurred in
grinding, pulverizing and crushing equipment, 15% in dust collecting or
storage systems, 10% in dryers and the rest in blending, conveying and
moulding operations. Figures 6.1 and 6.2 illustrate typical results of industrial
dust explosions.
Three conditions must exist before an explosion can occur: (i) a suspension
of combustible dust of explosive concentration, (ii) an ignition source, and
(iii) oxygen in sufficient quantity to support combustion. If any one of these
conditions does not exist it will be impossible for an explosion to occur, and
the approach to minimizing the hazard is therefore to eliminate, as far as
possible, dust clouds and sources of ignition. Where the risk is still considered
to be significant, steps may be taken to remove the third condition, for example
by the use of an inert gas such as nitrogen. An alternative approach is to ensure
that if an explosion occurs within the plant, it does so in a controlled manner
with combustion products being directed safely through explosion vents.
In this chapter, discussion is concerned initially with the general characteristics of dust explosions. A brief description of tests for product explosibility is
238
BULK SOLIDS HANDLING
then given, followed by some consideration of the influence of possible
explosion hazards on system design. Finally there is a short introduction to the
phenomenon of electrostatic charging, as this appears to be a common, if
somewhat unpredictable, source of ignition in bulk solids handling systems.
6.2 Characteristics of dust explosions
6.2.1 Ignition
Two sources of ignition frequently met in industrial plant are a hot surface and
a spark. Consequently, the minimum ignition temperature and minimum
ignition energy are the ignition characteristics commonly measured in routine
testing for explosibility. Ignition temperature is not a fundamental characteristic of a dust cloud: it depends upon the size and shape of the apparatus used
to measure it, as well as on the rate of temperature rise of the cloud. Therefore,
minimum ignition temperatures are determined in a standardized form of
apparatus. This enables meaningful comparisons between products to be
made. Typical values have been determined to be 370, 500 and 575 oc for
sugar, cocoa and coal respectively. It is worth noting that a hot surface can be a
hazard even at a somewhat lower temperature if a layer of dust is allowed to
build up on it, since the insulating properties of the dust can result in localized
'hot spots' which could ignite the layer.
The minimum ignition energy is particularly relevant to ignition by sparks.
There are a number of ways a spark can be produced; for example, by
electricity, friction and hot cutting. However, a characteristic of all these forms
of spark is that a small particle or small volume of gas at high temperature is
produced for a small period of time. Since it is much easier for experimental
purposes to measure the energy delivered by an electric spark than by friction
or other thermal processes, the routine tests for determining this characteristic
use an electric spark ignition source. Typical values of minimum ignition
energy have been shown to be 30, 120, 50 mJ for sugar, cocoa and coal
respectively, using the standard spark source circuit of the US Bureau of Mines
and the UK Fire Research Station. Lower values of minimum ignition energy
may be determined in tests involving different methods of spark generation. It
may be debated, for example, whether it is more appropriate to have a spark of
short or long duration, and whether the test would be more relevant to an
industrial situation if the spark circuit is designed to ignite a dust with greatest
efficiency [ 5].
It is quite possible with some products for an ignition source to occur
spontaneously as a result of self-heating. This phenomenon is the result of
exothermic oxidation or decomposition of the product, and in the case of
organic materials can be initiated by bacteriological action. The nature of selfheating reactions is quite complex, but the critical factor is the rate at which
heat is generated, since a runaway situation occurs once the rate of self-heating
EXPLOSION HAZARDS
239
flame quenched
J
UPPER
LIMIT
typically
2-10 (kg productlm3 air)
EXPLOSION RISK
'
' '
LOWER
LIMIT
----!•---t
flame cannot
be sustained
Figure 6.3
e.g. polyethylene 3
0.02 kg/m air
coffee
0.085 kg/m3 air
Explosibility limits (dust concentration).
exceeds the rate of heat dissipation and, in general, bulk solids have a very low
thermal conductivity.
6.2.2 Explosibility limits
As already mentioned, for a flame to propagate through a dust cloud, the
concentration of product to air must fall within a favourable range so that the
solid particles are sufficiently close together for heat from one particle to affect
the next, yet far enough apart for the oxygen in the air to have free access to the
surface of each particle (Figure 6.3). Combustion may then be propagated so
rapidly from a small ignition source that an explosion occurs. The range of
explosible concentrations is defined by lower and upper limits, although only
the lower explosion limit can be determined reliably from small-scale tests.
Values of these limits are usually expressed in terms of mass of product per unit
volume of gas. Typical values of minimum explosible concentration are 0.02
and 0.085 kg of product per m 3 of air for polyethylene and coffee respectively.
For a given concentration, the nature of a dust explosion is strongly
influenced by the particle size of the material in the cloud. As the particle size is
reduced a given material generally becomes more hazardous and the
consequences of an explosion more severe. Experience suggests that particulate material larger than about 200 Jl.m is unlikely to be responsible for
initiating an explosion. However, even a small concentration of fines can
render a cloud of coarse particles explosive and, since in industrial situations it
is possible for such concentrations of fines to occur, laboratory tests are
usually undertaken on samples that have been sieved (typically< 75 Jl.m) in
order to reproduce a 'worst case'.
When the concentration of product is raised above the lower explosibility
limit and past the stoichiometric value (i.e. when the quantities of product and
air present for its combustion are exactly in balance), the flame spreads and
vigour of explosions increases. As the dust concentration is further increased,
the quenching effect of the surplus product becomes more marked and
240
BULK SOLIDS HANDLING
eventually a concentration is reached at which flame propagation no longer
occurs. This concentration is the upper explosion limit. In practice, this
concept is of questionable usefulness since any kind oflocalized disturbance or
primary explosion can disperse a dense dust cloud into one of explosible
concentration. In any case, the upper explosion limit is not easily measured,
mainly because of the difficulty of ensuring that the particles are uniformly
dispersed in the cloud. Those values that have been determined suggest that
for most common products this upper limit is probably in the range 2-10 kg of
product per m 3 of air. Finally, it should be noted that the presence of even a
small quantity of flammable gas or vapour could render explosive a dust cloud
that was apparently 'safe' by virtue of large particle size or dense
concentration.
More specifically, although the particle size has little effect on the maximum
explosion pressure, it has been shown that with a decrease in particle size the
rate of pressure rise increases significantly, and the minimum energy required
to ignite dust clouds is lowered [6].
6.2.3 Expansion effects and explosion pressures
A dust explosion may be envisaged as combustion of a dust cloud which
results in either a rapid build-up of pressure or in an uncontrolled expansion.
The gas in which the dust is suspended takes part in the combustion, and hence
in considering the properties of dust explosions the nature of both the dust and
the gas are important. It is the expansion effect, or the pressure rise if the
expansion is restricted, which presents one of the main hazards in dust
explosions. The expansion effects arise principally as a result of the heat
developed in the combustion and, in some cases, gases being evolved from the
dust because of the high temperature to which it has been exposed. The heat
generated in a dust explosion is eventually lost to the surroundings and so the
expansion and pressure effects are transient quantities.
When a dust explosion occurs in industrial plant spectacular destruction
may result if it is initially confined in a system which is ultimately too weak to
stand the full force of the explosion. Two of the factors governing the violence
of an explosion, and therefore having an influence on the design of vessels in
which the explosion could occur, are the maximum explosion pressure and the
maximum rate of pressure rise. The potential maximum pressure clearly needs
to be known if the explosion is to be contained, while the rate of pressure rise
indicates the speed at which any suppression or automatic venting system
must operate.
Maximum pressures obtained with some products may be as high as 10 bar
(150 lbf/in 2 ) and could be reached in as little as one hundredth of a second, as
rates of pressure rise of the order of lOOObar/s (15000lbf/in 2 s) are not
impossible.
EXPLOSION HAZARDS
241
6.3 Measurement of explosion parameters
All tests in the United Kingdom concerned with assessing the explosibility or
measurement of explosion characteristics of bulk solids in suspension are
methods agreed with HM Factory Inspectorate and are carried out in the
sequence shown in Figure 6.4. As a result of this established procedure,
data regarding the explosion characteristics of many products already exist
[2, 4, 7-9].
With a product which has not been previously tested, the first step is to
determine whether it is potentially explosive. This should in fact form part of
the product characterization procedure. The outcome of such a test indicates
the necessity of incorporating any of the precautionary measures outlined in
the following section into the handling system at the design stage.
In the UK, explosibility tests are conducted on an official basis by the Fire
Research Station, with apparatus of the type summarized in Table 6.1. Several
types of test apparatus are required because bulk solids have a wide range of
dispersability, and different means to form the cloud are necessary, as well as
scope for varying the quantity of product and the pressure for dispersing the
air or gas.
In the vertical tube apparatus the dust is placed in the dispersion cup and
dispersed upwards over the ignition source (an electric spark or a heated coil)
by a controlled air blast. Observation of the flame propagation can then be
made. Modifications to the electrodes allow this device to be used for the
determination of minimum ignition energy. The Hartmann bomb (Figure 6.5)
is a strong version of the vertical tube apparatus which can be used for
investigation of minimum ignition energies and also for the measurement of
maximum explosion pressure and maximum rate of pressure rise.
The horizontal tube apparatus (Figure 6.6) also involves the dispersion by
air of a dust sample over an ignition source (a heated platinum coil). Since the
residence time of dusts near the coil is short, any that are observed to
propagate a flame must be regarded as presenting a serious explosion hazard.
The inflammator (Figure 6.7) is again essentially a vertically mounted glass
tube fitted with a heated coil or electric spark ignition source. In this
instrument, however, the dust, which may be introduced at different positions
relative to the ignition source, is dispersed downwards.
Although convenient for the testing of explosion characteristics, the
Hartmann bomb has been criticized on the grounds that test results do not
reliably scale up to correspond to industrial storage vessels of realistic size.
Investigations into the minimum size of test vessel to give results which could
be scaled up with confidence led to the development of the so-called 20-litre
sphere apparatus (Figure 6.8). This consists of a stainless steel spherical vessel
fitted with a water jacket. A dust cloud is formed in the vessel as the dust enters
from a pressurized chamber through the perforated dispersion ring. Sixty
milliseconds after the dust is released into the 20-litre sphere the detonator is
hot surfaces
I
I
I
I
I
I
I
I
I
minimum
ignition
temperature
I
use of
inert gas
I
I
I
I
maximum
permissible
oxygen
concentration
to prevent
ignition
i___ i
Group A
explosible
containment
and explosion
relief venting
I
I
I
I
I
I
maximum
explosion
pressure
and rate of
pressure rise
1
Group B
non-explosible
Basic scheme of explosion tests in the UK.
static
electricity
I
I
I
I
I
I
I
I
I
r-
minimum
ignition
energy
Figure 6.4
type of system
I
I
I
I
I
I
I
I
I
minimum
explosible
concentration
r
classification tests
product sample
RELEVANT HAZARD
OR METHOD
OF PREVENTION
EXPLOSION
CHARACTERISTICS
CLASSIFICATION
PRODUCT
t"'
z
Cl
0
z
~
"'
0
t:
~
;>:;
o::l
ct"'
~
243
EXPLOSION HAZARDS
Table 6.1. Classification test apparatus [10].
Direction of dispersion
of product
Apparatus
Vertical
tube
Vertically upwards
Horizontal
Horizontal
Inllammator
Vertically downwards
pressure - - - -- ..r::::.l.
transducer
Igniting source
Application
Electric spark or
electrically heated
wire coil
Electrically heated
coil at 1300 oc
All types of dust
Electrically heated
wire coil or electric
spark
Carbonaceous materials; especially
of small particle
size
Carbonaceous and
metal dusts; especially large or
fluffy/flocculent
particles
perspex or stamless steel
combustion tube 305 mm long.
64 mm onsode doameter
mushroom-shaped
deflector
brass. tube 10 mm
msode doameter
pressure
gauge
Figure 6.5 The Hartmann bomb.
244
BULK SOLIDS HANDLING
/
temperature
controller
platinum
ignition coil
/
/
combustion tube
76 mm inside
diameter
tube 6.4 mm
inside diameter
I
I
1
'power supply
I
,...,._460 mm-• .... - - - - 9 2 0 m m - - - - - • 1
Figure 6.6
Horizontal tube apparatus.
combustion tube
/
/1020 mm total length
76 mm inside diameter
deflector
plate
ignition coil
power supply
side arm f o r /
electrode for
spark igniting source
10V 20A ac
Figure 6.7
lnflammator apparatus.
fired, and the resulting pressure rise is monitored using the pressure transducer
fitted to one side of the vessel.
Gradually, test data from the 20-litre sphere apparatus is replacing that
previously obtained from the Hartmann bomb which generally tends to give
somewhat high values of maximum explosion pressure [11]. Also, the
Hartmann bomb is of questionable value for the measurement of maximum
rates of pressure rise. Nevertheless, it is relatively inexpensive and convenient,
EXPLOSION HAZARDS
245
exhaust port
igniter (detonator)
Figure 6.8 Twenty-litre sphere tester.
and a detailed discussion and comparison of results from these two pieces of
equipment can be found in [11].
Depending upon the outcome of the explosibility tests, a bulk solid is simply
classified as follows:
Group A
Group B
Products which ignited and propagated flame in the test
apparatus.
Products which did not propagate a flame in the test apparatus.
Obviously, Group A products represent a direct explosion risk and
therefore it would be a wise precaution, or even a legal requirement, to
incorporate protection measures of the type indicated in the following section.
The range of products which falls into this group is widespread and, as
indicated in the Introduction, includes common foodstuffs like sugar, flour
and cocoa; synthetic materials such as plastics, chemicals and pharmaceuticals; metals such as aluminium and magnesium as well as traditional fuels
such as coal and wood. Group B products, although not explosible, may
present a fire risk and the presence of a flammable gas or vapour may render a
Group B product explosive. Sand, alumina and certain paint pigments are
examples of Group B products. Further details of products which have been
categorized according to this A and B classification may be obtained from [9].
If a product is shown to be of Group A type, further information on the
extent of the explosion hazard may be required when considering suitable
precautions for its safe handling. The following parameters can be determined
by use of the test methods described in for example, [2], [8] and [10].
246
(i)
(ii)
(iii)
(iv)
(v)
BULK SOLIDS HANDLING
Minimum ignition temperature
Maximum permissible oxygen concentration in an inerted system
Minimum explosible concentration
Minimum ignition energy
Maximum explosion pressure and rate of pressure rise.
Since the explosion characteristics, in terms of these parameters, of many
products are well documented elsewhere [ 4, 7, 8], it is not appropriate to
include detailed information here. However, in order to illustrate the
magnitude of the quantities involved, details are shown in Table 6.2 for a few
well-known powdered products. A summary of the application of the results of
these various tests to practical conditions is included in Figure 6.4. Their
application will also be discussed in greater detail in the following section.
Various other test procedures are used to investigate specific characteristics
of combustible dusts. For example, the ignition of a dust layer may be
investigated by placing a layer of dust, say 0.5 mm thick, on a hot plate and
observing the temperature(s) at which the dust chars, smoulders, melts or
ignites [3]. Techniques known as differential thermal analysis (DT A) and
differential scanning calorimetry (DSC) have been used to determine the
temperature at which an exothermic reaction begins and the heat generated in
such a reaction, thus giving a valuable insight to the self-heating behaviour of
the bulk solid concerned [3].
6.4 Explosion risks and system design
Since the dispersion of bulk solids in air or gas occurs inevitably in many bulk
handling installations, it is evident that, if a product is known or shown to be
potentially explosive, consideration should be given to the hazard this
presents at the time the system is designed. Whilst it is equally obvious that the
generation of sources of ignition should be minimized, unforeseen mechanical,
electrical or human failures mean that the complete elimination of ignition
sources cannot be relied upon, particularly where powered machinery is
involved. To avoid the catastrophic effects of an explosion, reliance is normally
placed on the adequate functioning of an alternative means of protection for
the system. Such protection is normally based on one or more of the following
approaches:
(i) Minimizing sources of ignition and prevention of ignition
(ii) Allowing the explosion to take its full course but ensuring, by either
containment or explosion relief venting, that it does so safely
(iii) Detection and suppression.
The method of protection selected will depend upon a number of factors,
including the design of any associated plant or process, the running costs, the
economics of alternative protection methods, the explosibility of the product,
Aluminium
(atomized)
Magnesium
Wheat flour
Cocoa
Coffee
Sugar
Wood flour
Coal
(43% volatiles)
Polyethylene
Nylon
Acetylsalicylic
acid (aspirin)
Product
0.045
0.03
0.05
0.065
0.085
0.045
0.05
0.05
0.02
0.03
0.015
560
380
500
360
370
430
575
390
500
550
Minimum explosible
concentration
kg/m 3
650
Minimum ignition
temperature
'C
Table 6.2 Explosion characteristics of some well-known products [4]
16
10
20
40
50
120
160
30
20
50
50
Minimum ignition
energy
mJ
6.6
5.4
6.5
7.9
7.4
4.7
2.6
7.4
6.4
6.3
5.7
bar
97
80
95
116
109
69
38
109
94
92
84
lbf/in 2
Max. explosion
pressure
524
510
272
1020
252
80
10
340
573
136
1360
bar/s
7700
7500
4000
15000
3700
1200
150
5000
8500
2000
20000
lbf/in 2 s
Max. rate of
pressure rise
6
7
7
10
cone.
%vol.
Limiting
oxygen
0
-...J
""'"
N
"'
ti
>
N
>
:>:l
:I:
z
"'0
.,r:><m
248
BULK SOLIDS HANDLING
the extent to which an explosion and its consequences can be foreseen,
together with the requirements of any authorities concerned. The next three
sections are intended to promote an awareness of the various techniques that
fall within these categories.
6.4.1 Minimizing sources of ignition and prevention of ignition
Even if all the conditions required for an explosion are appropriate, a dust
cloud will only explode if an ignition source of sufficient energy is present. The
first step in any explosion protection programme (after ensuring that
standards of 'housekeeping' are adequate) is therefore to eliminate or
minimize, as far as possible, all potential sources of ignition. Some dust clouds
can be ignited by temperatures as low as 200 oc and clearly the 'minimum
ignition temperature' is the parameter most relevant to ignition by hot
surfaces. Although it is unlikely that temperatures of this order would be
reached in the average simple bulk handling installation, it is certainly possible
for high temperatures and even open flames to be encountered in processing
operations or during maintenance (e.g. gas cutting, welding, grinding, etc.).lt is
obvious that any maintenance work of this kind must be undertaken only
when the plant is shut down, but perhaps less obvious that there may still be a
considerable danger from residual layers of dust in apparently empty
containers. Any electrical equipment used during normal plant operation
should be sited well away from any possible dust source, or else made
completely dust- and spark-proof. Static electricity is also a likely source of
sparks, and care should be taken to avoid the build-up of excessive
electrostatic charge. This problem is discussed in more detail in section 6.5.
Another possible source of ignition is excessive friction, for example, in the
bearings of rotary valves, belt conveyor systems, and so on, which can result in
the generation of sufficient heat to cause local temperatures above the
minimum ignition temperature. This problem can be aggravated by the
presence of dust layers acting as thermal insulators. Thus it is clear that 'good
housekeeping' and regular preventive maintenance of the system and its
associated components are essential.
The 'minimum ignition energy' of a product is relevant when assessing the
possibility of an explosion being initiated by a briefly occurring spark. A rule of
thumb value of 25 mJ (US Bureau of MinesjUK Fire Research Station
method) is often taken for the minimum ignition energy, and products with
ignition energies less than this value may be regarded as particularly prone to
ignition by sparks.
Should a source of ignition be present, the likelihood of an explosion can be
reduced by ensuring that the solids-to-air concentration is kept well above the
maximum explosibility limit of the product being handled. However, complete
reliance should not be placed on this approach since it is possible for a
concentration favourable to an explosion to exist at some point in the plant;
EXPLOSION HAZARDS
249
for example, the collection hopper/receiver. The risk of ignition can of course
be eliminated altogether by introducing into the system an inert gas such as
nitrogen or carbon dioxide which replaces, or at least dilutes, the air so that the
oxygen level is below that at which flames can be supported. This concentration level depends on the product in question and, as discussed in the
previous section, is a parameter that can be readily measured (see Figure 6.4
and Table 6.2). However, inert gases such as nitrogen are not cheap and, unless
an inert gas happens to be available as a waste product, economics dictate that
this approach is generally applicable only to recirculating systems or other
cases where the gas can be recovered. Alternative inerting gases such as argon,
helium and various halogenated hydrocarbons are occasionally used, but
these are even more expensive than nitrogen or carbon dioxide.
Even with an inerting system there are disadvantages and possible risks
which necessitate a certain amount of caution. For example, it has been said
that the use of carbon dioxide can introduce an ignition hazard as a result of
static electricity generated by the C0 2 issuing at high speed from the gas
cylinder [5]. Care must be taken to ensure that gradual dilution of the inerting
gas over a period of time does not lead to a dangerous situation. For example,
in pneumatic conveying installations a considerable amount of air (around
50% by volume) can enter with the product at the feed point unless some kind
of inerted filling system is employed, and in any part of the plant below
atmospheric pressure the inward leakage of air must be avoided. Another
serious hazard which requires stringent controls on access of personnel to an
inerted plant [11] is the risk of asphyxiation if the plant is entered or opened
without care.
6.4.2 Containment
The philosophy behind this approach is that, once an explosion has begun, it
should be allowed to take its full course whilst suitable precautions are
employed to ensure that it does so in a safe manner. Two separate protection
methods fall within the category: containment and explosion relief venting. If
either of these approaches is adopted it follows that the plant should be
divided into small separate volumes, as far as possible, between which the
explosion is unable to propagate, and that part of the plant within which the
explosion occurs must be either strong enough (i.e. containment) or sufficiently
well protected to withstand the explosion (relief venting).
In practice, containment is only likely to be attractive on plant of small
dimensions, because the cost of building large hoppers, cyclones and the like to
withstand explosion pressures is usually not competitive with alternative
methods of protection. The maximum explosion pressure which can occur
within the system can be determined by tests (see Figure 6.4 and Table 6.2).
For the general case a safety factor is normally added to the measured
maximum explosion pressure, and a value of 50% is often taken. If the
250
BULK SOLIDS HANDLING
containment approach is adopted, the resulting figure is the static pressure
which the system must be designed to withstand.
It is beyond the scope of this book to describe in detail the methods for the
design of pressure-resistant components for bulk handling installations. For
further information on this subject the reader is referred to [2], [4] and [10].
However, a few general points will be made.
It is not easy to specify precisely the speed of combustion through a dust
cloud because so much depends upon the movement of the air that is
maintaining the material in suspension. Also, the pressure effects will depend
upon the conditions prevailing in the plant at the time of the explosion,
particularly the dust concentration. However, in general it is recommended
that equipment should be designed for pressures up to 7-8 bar (100120 lbf/in 2 ) developing at a rate from virtually nil up to 700 bar/s
(1 0 000 lbf/in 2 per s) [1 0]. The usual design technology for pressure vessels,
following codes such as BS 5500 or, in the USA, ASME 8, is generally
appropriate.
When designing equipment to contain a dust explosion there are two basic
approaches; one is to design for the full maximum explosion pressure to be
withstood without rupture or deformation ('pressure-resistant'); the other is to
accept that, although the full explosion pressure will be resisted, permanent
damage to the containing vessel may occur ('pressure-shock resistant').
Equipment designed to the latter standard is likely to be considerably less
costly initially, but in the event of an internal explosion, expensive repairs or
replacement could well be necessary. The decision on which standard to adopt
is essentially a commercial and economic one, and should be considered in
conjunction with alternative methods of explosion protection such as venting
and suppression.
The influence of internal structures on the rate of propagation of an
explosion should be carefully considered. In general, fittings such as filter bags
and trays can inhibit flame spread and therefore reduce pressure effects, but in
a system protected by explosion vents it is important that such fittings do not
impede the progress of the pressure wave towards the vents.
Care should be taken to recognize, and if possible avoid, the possibility of
'pressure piling'. This phenomenon can occur when two vessels are directly
connected so that an explosion in one of them pressurizes the other before the
arrival of the flame front. In these circumstances the pressure reached in the
second vessel will be significantly greater than that in the first.
6.4.3 Explosion relief venting
Because of difficulties in preventing ignition, or the unsuitability of the system
for containment of the explosion, recourse is often made to the subdivision of
the plant or system as far as is economic, coupled with explosion relief venting
to atmosphere to prevent dangerous pressures damaging the structure of the
251
EXPLOSION HAZARDS
system and so creating a hazard to personnel. This venting is customarily sited
in the roof of a silo or on the separation unit(s) and may take the form of burst
panels, displacement panels or hinged doors which operate once a predetermined pressure has been reached. In venting explosions to atmosphere, strict
attention must be paid to the safe dissipation of the explosion products. The
volume of flame discharged from vents can be very large, and obviously must
be directed to a safe place away from operatives and neighbouring plant. If
such diversion is necessary it is normally achieved by attaching a length of
ducting to the vent, or by installing deflector baffles. If the cyclone or filter is
inside a building, the vented flames should be directed to the exterior; in all
cases the duct attached to the vent should be short, free from bends and other
restrictions to flow, and be kept clear from dust at all times. Much has been
written on venting silos, cyclones and filter units [4,6, 7, 12-14] and this will
not be discussed in detail here. However, a few words are necessary about the
calculation of vent size and how this is related to the maximum rate of pressure
rise as determined by tests of the type mentioned in section 6.3. Experience has
shown, as would be expected, that the more vigorously explosive products
require larger areas of venting. Approximate vent areas can be determined
from the information in Table 6.3. This table relates the maximum rate of
pressure rise, as measured using the Hartmann apparatus, to the area required
for explosion relief, which is expressed in terms of the 'vent ratio'; that is, the
area ofthe vent per unit volume of plant. (It should be noted that this is not a
ratio of similar quantities and has dimensions of C 1 .) For systems which have
large-volume receiving silos, the required amount of venting may be
impracticable. For tall cylindrical vessels the area of the vent may, in fact,
exceed the cross-sectional area and so a reduced criterion is necessary. For
these large volumes the vent ratio can be reduced from 1/7 m - 1 (i.e. 1m 2 of
vent per 7m 3 system volume) to as little as 1/28 m - 1 .
A recent investigation has resulted in some useful information on the
venting of bucket elevators [15].
Unfortunately, the provision of relief venting is still regarded to some extent
as a 'rule of thumb' operation, although recent work in Europe and the USA
has led to a rather more reliable quantitative design method. Tests on a large
number of vessels with volumes from 1 to 100m 3 have shown that the
maximum rate of pressure rise is approximately proportional to the reciprocal
Table 6.3 Approximate values of 'vent ratio'
Maximum rate of pressure rise
Vent ratio
bar/s
lbf/in 2 per s
m-1
ft - I
< 350
350-700
>700
<5000
5000-10000
>10000
1/7
1/5
1/3
1/20
1/15
1/10
252
BULK SOLIDS HANDLING
Table 6.4 The West German system of dust classification, on which is based the NFPA method of
determining explosion vent area [5, 14].
Dust
class
KsT (bar/ms)
weak source
KsT (bar/ms)
strong source
Characteristics
StO
St 1
St2
St3
0
< 100
100-200
> 200
0
<200
200-300
> 300
No explosion
Weak explosion
Moderate/strong explosion
Very strong explosion
St 1
Pred
bar g)
St 2
St 3
0.4
r'\"\ '\..
1"\.
...... 0 .6
"
V'.....- ~ ;;.::178.5
'\..
oz;
'"I'1"\..'\..'\..
~/ ~
~ -:..~ V'
V
"\
.'\ '\..
r--..1'\..
r-..."......
10
~/. ;..-::
~ ?'
V
0.1 1
1
vent area (m2)
"'
"'
V
,/'....-.:
~
~~ 2.0
~
vessel
~olume
(m3)
100
(a) Strong ignition source: vent release pressure=0.2 bar gauge
St 1
St 2
St 3
I' ....... '\..
......
'\..
'\..
/
['\
1''\ "\..
'\..
'""' "\..
"
.......
. / .......
' '"
"'
/ ./
/..
/
//
~
~
./
1...0-
,.,
l\..."'o
......
0.1 1
10
vent area (~2)
vesse1 °volume (m3)
(b) Strong 1gnition source: vent release pressure= 0.5 bar gauge
Figure 6.9
"'"' "1"'1
V/ /
........
.......-:: V
V ~
//
100
Charts for the determination of explosion vent area.
Pred
bar g)
0 .6
0 .8
.0
.5
2.0
EXPLOSION HAZARDS
253
of the cube root of the volume of the vessel. This allows a constant (KsT ),
indicative of the violence of the explosion, to be defined as
KsT=(dp)
Vl/3
dt max
where (dp/dt)max is the maximum rate of pressure rise and Vis the volume ofthe
vessel.
This constant (called the 'explosion rate constant') provides the basis of the
West German method of classification of powders. It can be regarded as the
rate of pressure rise that would occur in a vessel of one cubic metre, but it
should be noted that its value will be affected by the shape of the vessel, the
strength of the ignition source and the degree of turbulence. Values of KsT can
be determined experimentally (a vessel of at least 20-litre volume being
recommended) and products placed in a 'Dust Class' as indicated in Table 6.4.
Based on the original work ofBartknecht, a series ofnomographs has recently
been prepared by the USA National Fire Protection Association [6] which
allows vent areas to be calculated for products according to their Dust Class
(or KsT value), the vent release pressure (p5131 ) and the maximum allowable
overpressure during venting (Pred). Typical nomographs, for a strong ignition
source and vent release pressure of0.2 bar (2.9lbf/in 2 ) and 0.5 bar (7.2lbf/in 2 ),
are shown in Figure 6.9.
For more complete details of the vent ratio method, nomograph method
and other design techniques for the sizing of explosion relief vents, the reader is
directed particularly to [13] and [14].
Protection of ducts and pipelines tends to be more difficult since vents, for
example, would need to be positioned every few metres. It is likely to be more
practicable to design the pipe system for containment of an explosion, in spite
of the fact that the pressure on the pipe walls can almost instantaneously reach
values of 25-30 bars if detonation occurs; that is, when the velocity of the
advancing flame front exceeds the velocity of sound [5].
A wide variety of types of explosion relief vent is available to the industry,
and includes bursting diaphragms, hinged flaps or doors, blow-out panels and
automatic triggered vents. Once the required vent area has been determined,
the type of vent must be selected on the basis of cost, operating conditions and
the type of vessel or component to be protected. For a detailed discussion of
vent closure design, see [14].
6.4.4 Detection and suppression
If a system is awkwardly sited, if the product is toxic so that it cannot be freely
discharged to atmosphere, or where normal working under inert gas
conditions would be impracticable, protection may be achieved by a detection
and suppression approach. Although there may be only milliseconds between
the ignition of the product to the build-up of pressure to destructive
254
BULK SOLIDS HANDLING
~~----------/
--- ,
....
'
1/
Pmax
r
~
::J
I
(/)
(/)
a.
Q)
1
I
I
I
I
I
I
I
I
~
I
slope = (dp/dt) max
time_,.
Figure 6.10
Pressure record for a suppressed explosion.
proportions (Figure 6.10), this is sufficient for an automatic suppression
system to operate effectively. Commercially available equipment for detecting
an explosion [16, 17] operates on the basic principle shown in Figure 6.11 and
is capable of triggering some or all of the following actions:
(i) Suppression of the explosion within the system
(ii) Venting the system automatically
(iii) Automatic shut-down of the system.
Detectors which pick up heat or light from the flame front can be used, but
suffer from the disadvantage that they are liable to lose sensitivity if coated
with dust. Simple mechanical devices which trigger the suppression or
automatic venting system at the first indication of an unexpected pressure rise
are usually considered to be more reliable.
Suppression involves the discharge of a suitable agent into the system within
which the explosion is developing. The composition of the agent depends on
the product involved, and is typically a halogenated hydrocarbon, an inert gas
or a powder such as limestone or ammonium phosphate. The suppressant is
contained in a sealed receptacle attached to the plant and is rapidly discharged
into the system by an electrically fired detonator. Thus, as soon as the existence
of an explosion is detected, the control mechanism fires the suppressant into
the plant and the flame is extinguished wherever the ignition may have been
developed.
EXPLOSION HAZARDS
action signal
shutdown
control
255
action signals
detection signal
vent to
/atmosphere
suppressant
blower/
ignition source
\mpressor
/feeder
Figure 6.11
A basic scheme for the detection and suppression of an explosion in a receiving silo.
pressurized
suppressant
container
contr\1
~
detection signal
Figure 6.12
duct.
A 'barrier' of suppressant used to prevent the propagation of a flame front along a
Alternatively, the explosion can be automatically vented to atmosphere.
When the explosion is detected a vent closure is ruptured automatically, thus
providing a rapid opening of a vent. The vented explosion then proceeds as for
cases in which the vents are opened by the pressure of the explosion. The
automatic method has the advantage that vents are opened extremely rapidly,
and for very explosible products this helps to reduce the maximum explosion
pressure. Since it is obvious that once an explosion has been initiated no more
product should be fed into the system, plant shut-down can also be rapidly
achieved with the detector approach.
256
BULK SOLIDS HANDLING
In the case of a large industrial plant the whole installation would be
effectively divided up into a number of discrete zones, each of which would be
protected by its own suppression system, comprising explosion sensor and
suppressant container. It is usually good practice to isolate the explosion event
to as small a part of the plant as possible, and various forms of barrier are used
to ensure that the combustion effects do not proceed from one zone to another.
These barriers may be physical, for example, explosion-proof rotary valves
and fast-acting isolation valves ('slam valves') or they may take the form of
'advance inerting' in which suppressant is automatically injected at an
appropriate point in a duct, for example, ahead of an advancing flame front
(Figure 6.12).
6.5 Static electricity
Wherever particulate materials are handled in bulk, and especially where
movement of streams of such material in a dry condition is involved, static
electricity may be a problem. Often this problem is merely a nuisance, but in
some circumstances the consequences of electrostatic charging can be
extremely serious. Charge potentials in excess of 250 kV can be achieved in
pneumatic conveyors. The risks of an incentive discharge or of physiological
shock are considerable and it is important therefore that designers and users of
bulk handling plant have an awareness of the problem and of the preventive
measures that can be taken.
The electrostatic charge acquired by a powder during industrial processes is
as much a function of the process as of the powder itself, and, although some
tests have been described [5] it is not easy to assess realistically the changing
characteristics of different products. The charge that a single particle can hold
is very small, and in order for a dangerous spark to occur there must exist some
mechanism of charge accumulation from the insulating powder particles. The
most common sources of electrostatic sparks are isolated conductors on which
static charges have accumulated. Many examples can be seen in industry of
such isolated conductors, ranging from trolleys on nylon wheels to metal joints
on insulating conveyor belts and unearthed conducting wires in filter cloths.
Powder being conveyed along an isolated section of metal pipe or poured into
an isolated bin are other situations where hazardous static charges can occur.
The main practical step to be taken in the avoidance of electrostatic sparks is
to ensure that all conductors are earthed. The bulk solid itself can, in certain
circumstances, act as an isolated conductor, although the mechanism by
which the powder becomes charged is not well understood.
Certain operations in the processing or handling of bulk solids are especially
liable to generate electrostatic charges. These include fluid bed drying, filling
or emptying of plastic containers, and pneumatic conveying. In fluid-bed
driers, for example, conditions as the product approaches dryness are ideal for
static electrification to occur [18], and the situation may be particularly
EXPLOSION HAZARDS
257
Does dust present explosion hazard?
Control dust suspensions
and accumulations. Avoid
ignition sources.
Reduce oxygen level.
Figure 6.13
Overall assessment of dust explosibility.
dangerous if the process involves drying off flammable solvents. Recent work
[19] draws attention to the hazards resulting from increasing use of plastic
containers, especially in the chemical industry. Almost anyone who has
poured granular material from a plastic sack will have heard the crackle of
electrostatic charges, and it is generally considered that if a spark is audible it
could be incendive and therefore dangerous. Various solutions to the problem
include the use of plastic sacks and bags with woven-in conducting wires which
must be earthed, the reduction of charge on the incoming powder, for instance
by neutralization of the charge using ionized air [19], and the provision of
antistatic clothing and conducting footwear for personnel.
This has been a necessarily brief discussion on the subject of electrostatic
charging in bulk solids handling. There is now a fairly extensive literature on
258
BULK SOLIDS HANDLING
the subject, but for practical advice the reader is referred to Refs. [5] and [6],
and to the recently published British Standard Code of Practice [20].
6.6 Conclusion
Careful study of the literature will soon make it clear that there is still much to
be learned about the fundamental mechanism of dust explosions, especially
with regard to ignition characteristics and ignition sources. The motivation for
such learning is too often the need to find out what went wrong rather than to
ensure that no dangerous situation occurs. Nevertheless, a systematic
assessment of the situation following, for example, the flow chart (Figure 6.13)
suggested by Field [21], with rigorous attention to a few essential details, such
as elimination of ignition sources (especially electrostatic sparks), provision of
adequate explosion vents or detection/suppression systems and general 'good
housekeeping' should go a long way towards the reduction of the explosion
hazard.
References and recommended further reading
References
1. Corn starch dust explosion at General Foods Ltd., Ban bury, 18 November 1981. Health and
Safety Executive Report, HMSO, London (1983).
2. Field, P. (1982) Dust explosions, in Handbook of Powder Technology, Vol.4, Elsevier,
(Amsterdam).
3. Cross, J. and Farrer, D. (1982) Dust Explosions. Plenum Press, New York.
4. Palmer, K.N. (1973) Dust Explosions and Fires. Chapman and Hall, London.
5. Cross, Jean (1981) Fire and explosion hazards. In Plastic Pneumatic Conveying and Bulk
Storage, ed. G. Butters, Applied Science, Barking.
6. Committee on Explosion Protection Systems ( 1978) Guide for Explosion Venting. NFPA No.
68, National Fire Protection Association, Boston.
7. Dust Explosions in Factories. HM Factory Inspectorate Health and Safety at Work Booklet
No. 22, HMSO, London (1976).
8. Raftery, M.N. Explosibility Tests for Industrial Dusts. Fire Research Technical Paper No. 21,
Ministry of Technology and Fire Offices' Committee, HMSO, London (1962).
9. Dust Explosions in Factories. Classified list of dusts that have been tested for explosibility in
the form of a dust cloud. Department of Employment, HM Factory Inspectorate SHW 830,
HMSO, London (1974).
10. Field, P. (ed.) (1979) The hazards of industrial explosion from dusts. Oyez Intelligence
Reports, Oyez Publishing Ltd.
11. Watkins, G.K.P. and Moore, P.E. Dust explosion protection, in Proc. Solidex 86 Con[.,
Harrogate, UK, June 1986, Paper B5.
12. Abrahamsen, A.R. and Field, P. Application of dust explosion pressure data to the sizing of
explosion relief vents, in Proc. Solidex 84 Con[., Harrogate, UK, April 1984, Paper C6.
13. Lunn, G.A. ( 1984) Venting Gas and Dust Explosions- A Review. Instn. Chem. Engrs., London.
14. Schofield, C. Guide to Dust Explosion Prevention and Protection: Part 1- Venting. Inst. Chem.
Engrs., London.
15. Gillis, J.P. and Fishlock, F.H. (1982) Explosion venting and suppression of bucket elevators.
(Report ESV -81-066 of the Nat. Grain and Feed Assoc.). J. Powder and Bulk Solids Technol., 6
(2), 5-16.
16. Moore, P.E. (1984) Explosion suppression trials. The Chemical Engineer, December, 23-26.
EXPLOSION HAZARDS
259
17. F orsyth, V.G. Dust explosion protection in pneumatic conveying processes. Fire Prevention
135, 25~30.
18. Pay, F.J. (1978) Electrostatic: potential hazard when handling powders in bulk. Bulk: Storage
Movement Control, January/February, 51~55.
19. Gibson, N. and Lloyd, F.C. Dust explosion risk in intermediate bulk containers. Proc. Solidex
82 Conf., Harrogate, UK, March/April 1982, Paper B4.
20. British Standard 5958: 1980 Control of undesirable static electricity (Code of practice). British
Standards Institution, London.
21. Field, P. Industrial dust explosion hazards: assessment, prevention and protection. Proc.
Solidex 82 Conf., Harrogate, UK, March/April 1982, Paper B2.
Recommended further reading
Palmer, K.N. (1973) Dust Explosions and Fires. Chapman and Hall, London.
Field, P. (1982) Dust explosions, Handbook of Powder Technology, Vol. 4, Elsevier, Amsterdam.
Cross, 1. and Farrer, D. (1982) Dust Explosions. Plenum, New York.
Lunn, G.A. (I 984) Venting Gas and Dust Explosions- A Review. Instn. Chem. Engrs., London.
Schofield, C. ( 1984) Guide to Dust Explosion Prevention and Protection: Part 1- Venting. Instn.
Chem. Engrs., London.
Bartknecht, W. ( 1981) Explosions: Course, Prevention, Protection (2nd edn.), Springer-Verlag,
Berlin.
7
Belt conveyors
7.1 Introduction
The belt conveyor is one of the commonest means of transportation for bulk
solids and is capable of carrying a greater diversity of products at higher rates
and over longer distances than any other kind of continuously-operating
mechanical conveyor.
In essence, a belt conveyor is simply an endless strap of flexible material
stretched between two drums and supported at intervals on idler rollers
(Figure 7.1 ). Developments of the basic configuration include troughing the
belt or fitting sidewalls to increase the carrying capacity, and fitting transverse
slats or texturing the surface of the belt so that operation on a steep incline is
possible (Figure 7.2). These and other aspects of practical belt conveyor design
will be discussed in this chapter.
The earliest reported use of belt conveying, almost two hundred years ago,
was for handling grain, and this was virtually the only application of the
technique during the next hundred years. Attempts to carry heavier materials
seem to have caused problems as a result of wearing of the idler bearings and
splitting of the conveyor belt itself. More recently, especially during the last
thirty years or so, development of the belt conveyor has been rapid. The
greatest use of belt conveyors at present is in the mining and quarrying
industry. However, there is now effectively no restriction on the type of bulk
materials that can be carried, and efforts are being concentrated on increasing
the carrying capacity without sacrificing reliability.
Many examples exist of actual belt conveyors that are remarkable in respect
of the distances over which they operate or the quantity of bulk material that
they have transported. One of the earliest of the really large-scale installations,
constructed in Pennsylvania, USA, in 1924, carried a daily average of 10 000
tonnes of coal [1]. A much more recent example of a very long conveying
system is the phosphate conveyor in Spanish Sahara [2] which consists often
individual sections making up an overall length of 100km (62 miles).
Another recent example is the 15-km installation in the Selby coalfield, UK,
which is capable of conveying 3200 tonnes of coal per hour at speeds of up to
8.4 m/s [3]. Claimed to be the highest-capacity belt conveyor in the world,
however, is the remarkable 3 m wide Japanese example, installed in a test
plant, which, running at 5.3 m/s, has successfully conveyed sand and rock at a
rate of 30 000 tonnes/hour [ 4].
This chapter will be a necessarily brief study of belt conveying. It is written
with the aim of giving an awareness of the capabilities of various types of belt
261
BELT CONVEYORS
~solids feed
(+
-
carrying Idlers
head end
··~~~
return Idlers
solids
discharge
Figure 7.1
The basic principle of belt conveying.
conveyor and an introduction to their design and selection. For a more
detailed and complete treatment of belt conveyor design the reader is advised
to consult the appropriate British Standards [5]-[7] or one of the published
design guides [8]-[11].
7.2 Features of belt conveyors
7.2.1 Belt construction
Although special forms of conveyor belt are available for particular applications, such as belts with sidewalls, or with transverse slats, cleats or other
surface projections for use on steep inclines, the great majority of conveyors
installed use a conventional flat belt. However, there are many different forms
of construction, even of flat belts, and, since the belt is the most vulnerable
and expensive part of a conveyor, representing a substantial proportion
of the overall capital cost, it is essential that great care is taken over its
selection.
A conveyor belt consists basically of a carcass or core which carries the
tensile force necessary to move the loaded belt and to absorb the impact
energy of the bulk solid as it is loaded on to the belt, and a cover which protects
the carcass against damage by the conveyed material. The carcass is usually
composed of from two to ten plies or layers of woven fabric bonded together
with rubber. The fabric comprises longitudinal (warp) cords which provide the
tensile strength to transmit power, and transverse (weft) cord11 which are
lighter, but which still have to provide sufficient rigidity to support the
conveyed product on the belt. An alternative to the multiple construction
consists of a single solid interwoven ply of suitable thickness (Figure 7.3a).
The textile yarns used are typically natural cotton or a man-made fibre
such as nylon or polyester. For special applications, other materials such as
asbestos and glass fibre may have the necessary qualities, and for long-haul
262
BULK SOLIDS HANDLING
Figure 7.2 A belt conveyor carried on three-roll idler sets up a steep incline. The cleated
pattern on the surface of the belt can just be seen. (Photo courtesy of Fyson Conveyors).
installations, where high strength and low stretch are important requirements,
steel-reinforced belting is available.
When selecting the belt construction, the choice of carcass is dictated by the
following principal considerations:
(i). Maximum tension in belt when in operation
(ii) Impact forces occurring during loading
(iii) Flexibility required in transverse direction (for troughing) and longitudinally (to wrap around drums and pulleys).
Natural or synthetic rubber, or a blend of the two, would normally be
BELT CONVEYORS
Filler yarn
0
Nylon binder yarn
AA!N'"§S·N•
Cotton warp yarn
Nylon warp yarn
(a) Typical structure of solid woven belt carcass
(b) Modern patterns of cleated belt
(c) Typical design of conveyor belt with sidewalls
Figure 7.3
Construction of conveyor belts.
263
264
BULK SOLIDS HANDLING
chosen for the cover of the belt. The quality or grade of the cover, and its
thickness, are selected after careful consideration of the intended service
conditions. The main features influencing the choice of cover are:
(i) Nature of conveyed material (i.e. size, abrasiveness, temperature, oil or
water content, corrosiveness, etc.) and quantity to be conveyed
(ii) Method by which material is fed to belt (i.e. sympathetically, or from a
height, etc.)
(iii) Speed of belt
(iv) Environment (i.e. exposure to rain, sunlight, freezing conditions, fire
hazard, etc.).
Since the primary purpose of the belt cover is to protect the carcass against
damage it is normal for the top cover (i.e. the carrying side) to be of greater
thickness than the back cover. Typically the back cover is 1-1.5 mm thick,
whilst the top cover may be from the same thickness for conveying light
materials and up to around 10 mm thick for heavy and sharp materials.
In order to increase the adhesion between the belt cover and the carcass, one
or two additional layers of open-weave fabric (called tie- cloths or 'breakers')
may be fitted next to the carcass. A further benefit of these breakers is that they
increase the impact and puncture resistance of the belt and cushion the carcass
as heavy Jumps of conveyed material pass over the idlers.
Frequently it is required to operate a belt conveyor on an upward incline.
The normally accepted maximum angle of inclination for smooth-surfaced
troughed belts is around 16°-20°. The actual value depends mainly upon the
characteristics of the conveyed material (especially its angle of repose) and to a
lesser extent on the speed, length and tension of the belt and on the disposition
ofthe supporting idlers. In order to work on a somewhat steeper incline (up to
around 30°) a belt may be selected having a pattern of cleats or flights moulded
into its surface to reduce the tendency for the conveyed material to slip. The
height of these cleats is likely to be between 15 and 25 mm and, in addition to
allowing operation at steeper angles, may result in a significant increase in
carrying capacity in comparison to a smooth troughed belt. Typical patterns
of modern cleated belt are illustrated in Figure 7.3b [12].
A relatively recent development in conveyor belts has been the introduction
of'vertical' sidewalls, which may be supported by transverse slats as illustrated
in Figure 7.3c. The principal advantage of this type of belt is that it will
operate successfully on a much steeper incline than the normally accepted
maximum for troughed belts. Indeed, conveyors are now available having
pockets moulded into the surface of the belt, so that they can operate
vertically, and these will be discussed under the heading of Bucket Elevators in
Chapter 8.
Since by its nature a conveyor belt has to be endless, jointing of the ends is
obviously an important consideration. The two methods in common use are
BELT CONVEYORS
265
the vulcanized splice and mechanical fasteners. The vulcanized splice gives a
much stronger and longer-lasting joint but is difficult and costly to make on
site. Mechanical fasteners are much cheaper but do tend to restrict the working
conditions of the belt. Also, leakage of fine particles of conveyed material can
occur through the 'fingers' of a mechanical joint.
7.2.2 Idlers
For conveying bulk solids it is usual practice to increase the carrying capacity
of the flat belt by modifying its cross-sectional profile so that it forms a trough.
This is achieved by using 'troughing idlers' which consist of sets of two to five
rollers (usually three), generally from 100 mm to 175 mm diameter, arranged to
support the belt and at the same time to bend it into a trough shape. The
standard three-roller troughing set (Figure 7.4c), which has largely replaced
the idler with concentrator rolls (Figure 7.4b), is generally used with an outer
roll angle of 30° to 35°. However, the optimum troughing angle will depend to
a large extent upon the angle of repose of the product being conveyed. With
very free-flowing products, for example, the deepest acceptable trough is likely
to be preferred. The greater flexibility of man-made fibres has, in recent years,
(a) 'Flat' idler
(b) Idler with concentrator rolls
(c) Standard 3-roll idler set
(d) Two-roll idler set
(e) 5-roll catenary idler
Figure 7.4
Various configurations of carrying idlers.
266
BULK SOLIDS HANDLING
allowed belts to be run with the outer (or 'wing') rollers inclined at as much as
70° to the horizontal, resulting in very deep troughing. The two-roll set
(Figure 7.4d) is becoming increasingly common for handling bulky lightweight
materials on narrow belts, while on very wide conveyors there may be some
advantage in using five rollers to give a smoother transverse curve of the belt
and consequently longer belt life. A method that has been used to ensure a
smooth curving belt cross-section is to suspend the idlers, in a set of three or
five, or even more, on a catenary (Figure 7.4e).
In order to assist the alignment of the belt, idler sets may be made with a
slight forward tilt in the direction of belt travel. Modern practice is to have an
angle of 1o (as seen in the plane of the belt) between the axis of the wing rollers
and the axis of the centre roller. The current British Standard [6] and ISO
Standard measure the angle of forward tilt of the wing idlers in elevation, and
stipulate that this must not exceed 3°.
Other types of idler are available for special applications, for example,
rubber-covered 'impact rollers' to reduce wear on the belt at the loading point,
and 'self-adjusting troughing idlers' which are suspended on springs in such a
way that the troughing angle automatically increases with the load on the belt,
thus increasing its capacity. Although the rollers are usually of steel, for use in
severe working conditions (e.g. when handling corrosive materials), solid
plastic or plastic-coated rollers are available.
Return idlers are usually flat and of the same diameter as the carrying idlers.
However, since they are in contact with the top cover of the belt, care must be
taken to guard against build-up of fine materials on these idlers. For this
reason various forms of rubber disc or spiral wire rollers have been developed
(Figure 7.5) and these may also be designed to assist belt alignment. For wide
belts, and particularly for high-speed belts which may tend to develop a
vertical vibration on the return side, V-idlers set at a lOo angle are
recommended.
It has been pointed out previously that the belt itself represents a large
proportion of the capital cost of the conveyor and therefore careful attention
must be given to all factors that have an influence on its useful life. In order to
avoid spillage of conveyed material and to minimize wear of the belt, it is
essential that it is not allowed to sag unduly, and therefore the spacing of the
idlers is of prime importance. The required spacing is a function of belt width
and of belt tension, and therefore the bulk density of the conveyed material
must be taken into account when determining the idler pitch on the carrying
side of the belt.
On long belts there is a significant variation in tension along the length, and
thus there may be some advantage in graduating the idler spacing to equalize
the belt sag [2].
Two other important features of idler rollers are that the frictional resistance
to rotation is minimal and that the inclination of the wing rollers is matched to
267
BELT CONVEYORS
-
~
(a) Impact resistant roller
-
~
(b) Rubber disc return roller
(c) Return roller with rubber spiral
(d) Return roller with open steel spiral
Figure 7.5
Typical non-standard idler rollers.
the transverse flexibility (sometimes called the 'troughability') of the belt.
Clearly the design of the idler bearings and seals is important, not only to
minimize wear of the belt, but also because the frictional resistance will affect
the belt tension and therefore the driving power requirements. Figure 7.6
illustrates the importance of using belts of the correct transverse flexibility for
the desired troughing angle.
/
excessive wear of
belt and rollers \
angle of belt too sharp
causing longitudinal
splitting
~~
(a) Belt too stiff and/or wing
rollers too steeply inclined
Figure 7.6
(b) Belt too flexible
Consequences of incorrect matching of belt to idlers.
268
BULK SOLIDS HANDLING
Finally, an important consideration in the selection and positioning of idler
rollers is the transition from troughed belt to flat belt that must occur
immediately prior to the terminal pulley at the discharge point. If this
transition is made too rapidly, the edges of the belt will be stretched
excessively, even to the point where the elastic limit is exceeded. The result is
permanent damage to the belt with consequent problems of wear and spillage.
On the other hand, if the last troughing idler set is positioned too far before the
discharge point, the premature flattening of the belt is likely to result in an
unacceptable level of spillage of the conveyed product over the edges. Detailed
information on the calculation of transition distance is given in [11], but
typically it would be in the range of one belt width for a lOo troughing angle, up
to twice the belt width for 45o troughing. Transition idlers, set at angles smaller
than the troughing idlers, are advisable in heavy duty applications and the
stresses in the belt can also be reduced by raising the terminal pulley above the
level of the centre roller of the troughing idlers (Figure 7.7).
7.2.3 Drive arrangements
As illustrated in Figure 7.1, on a basic belt conveyor the belt runs between two
terminal cylindrical drums, one of which is powered. Standard terminology
refers to the end of the conveyor where the transported material is loaded as
'tail end' or 'feed end', and the other end, from which the load is discharged, as
the 'head end'. The drive may be at either end of the conveyor, although it is
generally better to drive the head end drum as this will involve the smallest
amount of belt being subjected to the maximum tension. An alternative
arrangement is to have the drive at an intermediate point on the return strand
(a) Normal transition
(b) Terminal pulley raised by half depth of trough
Figure 7.7 Transition from troughed belt at the discharge point showing raised position of
terminal pulley to reduce edge stresses in the belt.
BELT CONVEYORS
(a} Plain drive
(c) Tandem drive on
return strand
()
269
(b) Snubbed drive
(d) Dual drive with
horizontal tensioner
~---o=B
----B~)--~-..:::---+)
(e) Dual drive arrangement having both drums
in contact with clean side of belt
Figure 7.8 Some common belt drive arrangements.
of the belt close to the head end. Where the conveyor is operating downhill and
involving regenerative effects, the tail end drum should be driven, or a
separate driven pulley on the return strand fitted as close as possible to the tail
end.
The effectiveness of the conveyor drive is dependent upon a number of
factors, principally the difference in tension between the 'tight side' and the
'slack side' ofthe belt, the friction between the belt and the drive drum and the
angle of wrap, or arc of contact, of the belt to the drum. The power that can be
transmitted from the driving drum to the belt is limited by the point at which
the belt begins to slip. In order to increase the power it is necessary either to
increase the coefficient offriction, for example by applying a rubber lagging to
the surface of the drum, or to increase the angle of wrap by 'snubbing' the drum
or providing a multiple drive. Figure 7.8 shows some common types of drive
arrangement and the corresponding angles of wrap are listed in Table 7.1. For
a much fuller discussion of drive arrangements see [11].
With the plain drive (Figure 7.8a) the angle of wrap is limited to 180°. The
snubbed drive (Figure 7.8b) is more popular, since in addition to the larger
270
BULK SOLIDS HANDLING
Table 7.1 Angles of wrap for basic types of drive
[1].
Type of drive
Angle of wrap
Single drum
Snubbed drum
Tandem or dual drive
180°
180°~240°
360°~480°
angle of wrap it has the advantage that it brings the carrying and return
strands of the belt closer together and thus reduces the depth of supporting
structure required.
With a tandem drive, two drums are geared together and driven by a single
motor (Figure 7.8c) and this arrangement gives an angle of wrap almost
double that of a single drum. The same advantage is obtained with a dual drive
(Figure 7.8d) but in this case the two drums are separately motorized. Note,
however, that a drawback to both of these arrangements is that one of the
driving drums will be in contact with the carrying (i.e. 'dirty') side of the belt.
Using bend and snubbing pulleys as shown in Figure 7.8e, it is generally not
difficult to reverse the belt so that only the clean side is in contact with the two
driving drums. A further disadvantage of the geared tandem drive is that,
because of slight differences in the tension of the belt as it passes over the
drums, there will inevitably be some slip between the belt and the second drum.
It is perhaps appropriate at this point to remark that even on a single drum
there will inevitably be a certain amount of belt 'creep' resulting from the
varying tension in the belt as it passes around the drum. The term 'creep'
actually refers to the relative movement between the belt and the surface of the
drum that happens as the stretch in the belt decreases with the reduction in
tension. The arc of the drum surface over which creep occurs will tend to
increase as the tight-side tension increases, for example as a result of increasing
the load on the belt, and if the 'angle of creep' approaches the 'angle of wrap'
the belt will clearly be on the point of slipping. It is for this reason that a certain
inherent tension should be maintained, even in the slack side of the belt.
The inherent tension in the conveyor belt, needed to ensure that the drive is
maintained, can be provided in a number of ways. The simplest method, used
for small or light-duty conveyors of the type shown in Figure 7.1, is to adjust
the distance between the head and tail drums, for example by pulling back the
tail drum on a screw tensioner (Figure 7.9a). A similar type of tensioner
operating on an idler pulley is illustrated in Figure 7.8d. A common alternative
method is to use a 'drop-weight' or 'gravity take-up' device (Figure 7.9b) which
can be easily adjusted to give the tension required. The gravity take-up has the
great advantage that it can readily accommodate small changes in the length
of the belt, such as the stretching that occurs on starting from rest.
Hydraulically or electrically powered automatic take-ups are also available,
271
BELT CONVEYORS
(a) Screw tensioner
/weights
(b) Gravity take-up
Figure 7.9
Belt-tensioning devices.
relying on a load-sensitive device to move the tensioning pulley in response to
changing operating conditions of the belt.
7.2.4 The power unit
When selecting the driving motor and power transmission for a belt conveyor
there are a number of factors to be considered, such as single- or multi-speed
requirements, type of electrical power supply and environmental conditions,
but the most important consideration is the starting characteristic. A long
conveyor may require a considerable time to accelerate to its normal running
speed, especially if it is fully loaded, and the power unit should normally be
capable of providing a constant torque during the whole of this period.
The electric motor most commonly used for driving belt conveyors is the
squirrel cage induction type, although compound (series/shunt wound) de
motors may be used where starting conditions are severe. The squirrel cage
motor is a high-speed machine which will not start under a heavy load, and
therefore some kind of speed reduction mechanism is essential, usually in
conjunction with an automatic clutch. For speed reduction it is usual to use
either worm gears or a gear train involving two or three stages of reduction
through straight-cut or helical gears.
The method of power transmission from the motor/gearbox unit to the
conveyor is also a prime consideration when designing a belt conveyor
installation. Torque control devices, such as fluid couplings and eddy-current
couplings, are widely used as they offer a means of changing the torque/speed
characteristics of the motive unit to suit the conveyor and thus allow some
flexibility in the selection of the electric motor. The eddy-current coupling is
an electromagnetic device which, placed between the squirrel cage motor
shaft and the speed reducer input shaft, allows a measure of control over the
acceleration of the conveyor belt. However, this type of coupling tends to be
bulky and expensive and fluid couplings are normally preferred.
Various kinds of fluid coupling are available commercially, including
272
BULK SOLIDS HANDLING
variable-speed types and so-called 'dry-fluid' types charged with steel shot
instead of the more usual oil. Any fluid coupling is, in essence, a form of slip
clutch which allows a controlled difference in the speeds of rotation of the
input and output shaft. In its basic form the fluid coupling can be regarded as a
pump and a turbine, fitted in the same casing, with the output fluid from the
pump being used to drive the turbine. Thus, the 'impeller' is fitted to the input
shaft and the 'runner' is fitted to the output shaft. Flow control devices, such as
guide vanes, located within the casing between the impeller and the runner,
will then enable the operating characteristics of the coupling to be varied. In
this way the fluid coupling can produce a smooth acceleration of a fully-loaded
belt conveyor from start-up to normal operating speed. For variable-speed
operation, special types of fluid coupling are available, such as the scoopcontrolled hydraulic coupling which is normally capable of operating steadily
at speeds down to 25% of maximum.
7.2.5 Loading and discharge arrangements
Loading of a bulk material on to a belt conveyor is usually from a hopper or
bunker by direct gravity discharge, or from a preceding conveyor or feeder
which may be of belt, apron, screw or vibratory type. Whatever loading
method is used, it should provide a steady flow of product to the belt and
distribute it uniformly about the centreline of the belt to ensure that the
optimum loading level is achieved without problems of spillage or dust
generation. Ideally the product should 'flow' on to the belt in the direction of
travel and with the same forward velocity in order to minimize acceleration
losses and abrasion of the belt surface.
Usually the use of some kind of transfer chute would be involved in order to
avoid the product falling vertically on to a moving belt. The design of such a
chute must be undertaken with some care in order to avoid build-up of product
on the sides and bottom of the chute (and possible complete blockage). Skirt
plates are generally fitted at the outlet from the chute to confine the product
towards the centre of the belt and minimize spillage. These would typically
extend along the belt to some two or three times the belt width beyond the feed
point, the distance between them being normally about two-thirds of the width
of the belt.
The most straightforward approach to discharging product from a belt
conveyor is simply to 'throw' it over the head-end drum. In this case the
trajectory of the material is an important consideration in the design of a
discharge chute so that erosive wear of the front plate of the chute and
degradation of the product are not excessive. Methods of plotting the material
trajectory from a knowledge of its density and velocity over the head pulley are
beyond the scope of this book and the reader requiring guidance on this
subject is directed to [2] and [ 11].
Where conveyed product is to be discharged at one or more points before
BELT CONVEYORS
Figure 7.10
273
A typical travelling tripper.
the head-end drum there are basically two methods that can be employed. The
simplest of these is to use a plough at each desired discharge point. A timber or
steel platform is positioned beneath the belt to flatten it so that the plough
blade, which may also be constructed of timber or steel, can be lowered on to
the belt to direct the conveyed product into a chute at one side of the belt. Use
of a V-shaped plough allows the product to be discharged simultaneously to
chutes on each side of the belt.
A more satisfactory method in most cases, especially where a single variabledischarge point is specified, involves the use of a 'tripper' comprising a pair of
bend pulleys which raise the belt towards a discharge chute directing the
product to one side of the conveyor or the other. In the travelling tripper
(Figure 7.1 0), the pulleys are mounted on a wheeled carriage which may be
propelled either by hand (over short distances), by power obtained from the
conveyor belt and transmitted to the carriage wheels through a suitable
gearbox, by a winch-hauled endless rope system, or by a separate driving
motor mounted on the carriage itself.
7.2.6 Belt cleaners
Of the many different accessories used with belt conveyors, belt-cleaning
devices are possibly the most important. When transporting bulk materials
that have any tendency to stick to the surface of the belt, it is essential to
employ some kind of cleaning technique at the head end to minimize the buildup of material on snub pulleys and return idlers. Any such build-up can cause
sharp particles to be pressed into the belt cover or cause the belt to run offcentre, both of which can drastically shorten the life of the belt. It is also
necessary to ensure that any product spilt on to the 'clean' side of the belt is
removed before it enters an in-running nip (such as the tail pulley) and
becomes trapped between the belt and the pulley.
Various types of cleaner are available, such as rotary brushes or scraper
blades of steel or rubber, which may be spring-loaded or counterweighted to
bear against the surface of the belt (Figure 7.11). Care must be taken to ensure
274
BULK SOLIDS HANDLING
Figure 7.11
Typical belt-cleaning devices.
that the cleaner is effective without causing damage to the belt and also that
excessive build-up of cleared particles does not occur on the brush or scraper
and so reduce its efficiency. An effective cleaning method is by a water spray to
soften and loosen the material sticking to the belt, followed by one or more
rubber wiper blades to plough the material off. However, this technique
presents the considerable problem of subsequently disposing of the waste
water and it is therefore rarely used except on high-speed conveyors. For a
comprehensive coverage of belt cleaning methods the reader is directed to
[13].
7.3 Belt conveyor design
7.3.1 The bulk solid to be transported
The design of a belt conveyor begins with a careful study of the bulk solid to be
transported. It is evident that the rate at which a bulk solid can be moved on a
belt of specified speed and width depends principally upon its bulk density and
the height to which it can be piled on the belt.
The bulk density of a particulate material has been defined (in Chapter I) as
the mass of the material divided by its total volume (particles and voids).
Clearly a knowledge of this property allows the conveying rate (in
tonnes/hour) to be calculated from the belt speed and the average cross-
BELT CONVEYORS
275
carrying
side of belt
Figure 7.12 Cross-section of a typical troughed belt conveyor showing angle of surcharge of
material on the belt.
sectional area of the conveyed material as stacked on the moving belt.
Also in Chapter 1 the property 'angle of repose' was defined as the angle to
the horizontal made by the sloping surface of a freely-formed heap of the
material. This property strongly influences the height of material piled on a
conveyor belt, but, recognizing that the movement ofthe belt inevitably causes
the heap to slip and 'flow out' slightly, an 'angle of surcharge' is defined as the
angle to the horizontal which the surface of the material assumes while at rest
on a moving conveyor belt (Figure 7.12). The angle of surcharge is, for most
materials, some 5° to 15° less than the angle of repose.
Table 7.2 details bulk densities, angles of repose and angles of surcharge for
a selection offamiliar bulk solids. More extensive lists are published in design
guides such as [1], [2], [9] and [11].
Note that there are other properties of the conveyed product that should be
given due consideration. These include its moisture content, dustiness,
cohesiveness (and adhesiveness), abrasiveness and chemical corrosiveness.
Perhaps the most important, however, since it has a direct bearing on the
speed ofthe belt and the belt width to be used, is the 'lump size' of the material.
Most manufacturers of belt conveyors use an empirical relationship between
the width of the belt and the size of lumps to be handled. The usual practice is
to allow a maximum lump size of one-fifth of the belt width for surcharge
angles of 20° or one-tenth of the belt width for surcharge angles up to 30°,
although larger lumps can be handled if the conveyed material contains a high
percentage (around 90%) of fines.
7.3.2 Belt speed
The choice of belt speed is to some extent arbitrary, and there has been
considerable debate on whether it is better to run a narrow belt at high speed
or a wider belt at lower speed. A number of factors have to be taken into
account: principally the nature of the material to be conveyed, the carrying
capacity required and the belt tensions.
276
BULK SOLIDS HANDLING
Table 7.2 Relevant properties of a selection of familiar bulk solids.
Material
Alumina
Ammonium chloride
Ammonium nitrate
Ashes (coal)-dry
-wet
-fly
Barley
Barytes (fine)
Bauxite (granular)
Cement
Chalk (fine)
Chalk (lumpy)
Clay (dry fines)
Coal (bituminous)
Coke
Copper ore
Iron ore
Kaolin clay
Limestone
Phosphate rock
(broken dry)
Pyrites (lumpy)
Sand-dry
-foundry
Soda ash (light)
Sugar-raw
Wheat
Wood chips
Bulk density
(tonnes/m 3 )
Angle of
repose
Recommended
max. angle of
inclination
0.8-1.08
0.72-0.83
0.72
0.56-0.64
0.72-0.80
0.5-0.8
0.61
1.8-2.0
1.20-1.36
1.20-1.36
1.0-1.2
1.2-1.4
1.6-1.9
0.72-0.88
0.4-0.5
1.92-2.56
2.08-2.88
1.0
1.44-1.52
22°
12"
1.2-1.3
2.1-2.3
1.4~-1.60
1.3-1.4
0.35-0.55
0.88-1.04
0.77
0.16-0.48
45°
45'
42°
230
35"
30°
30°
42"
42°
35°
35°
38°
38"
35°
35°
38°
28°
35°
35°
37°
45°
28°
Surcharge
angle
too
100
100
23°
20°
20°
2SO
30°
30°
30°
5-10°
lOo
20°
10-20°*
25°
lOo
220
12"
ISO
20°
15-18°
25°
!5°
20"
18°
18"
20°
18°
19°
18°
14°
16°
16°
24°
220
18°
25'
25°
20°
20°
25°
100
18°
20°
20°
30°
25°
30°
27"
30"
220
120
too
(*Surcharge can be oo if cement is aerated and max. inclination could then be 5-l 0°).
Relevant material characteristics include the abrasiveness of the bulk
solid, its lump size and its tendency to 'dusting'. Abrasive wear is greater
at high speeds, as is the impact effect of large lumps passing over the
idlers. Also, there is more risk of lumps rolling off the belt if it is running fast.
Very light or dusty products should normally be conveyed at low speeds in
order to minimize the loss of material from the belt. This is especially
important at the head end where dust nuisance may be quite unacceptable if
the velocity of discharge of the product is too high.
At high belt speeds, general wear on the moving parts of the conveyor is
greater, and, especially with narrow belts, satisfactory belt tracking becomes
increasingly difficult to maintain.
Typical practical belt speeds are around 1.5 m/s for very abrasive material
or large lumps, up to 3 or 4m/s for free-flowing, non-abrasive products.
Figure 7.13 gives an indication of the maximum speeds currently recommended for normal applications involving the conveying of various types
of bulk material. Modern trends seem to be towards higher belt speeds because
277
BELT CONVEYORS
~-
1--I - -
r-
4
--
u;
§
"0
Q)
Q)
3 -
--
1--·
-
0.
"'
a; 2 -
--···
-
---
D
--
. J
V
.I
-··
I
I. //
V
/
~ I; ~.,..,.
~'4
/
Conveyed material
-
5
Fine: free-flowing
non-abrasive
./
Fine: mildly abrasive
or lumpy
~
Granular: abrasive or
lumpy, mildly abrasive
~
Granular: very abrasive
or lumpy, moderately
abrasive
~
Lumpy and very abrasive
Belts used with
belt-propelled trippers
7
Belts used with ploughs
~
500
picking and
w ~ ~ 8:'0w w ~ 1 For
feeding belts
1000
1500
2000
belt width (mm)
Figure 7.13 Guide to maximum recommended belt speeds in normal applications. Note:
(i) Considerably higher speeds may be possible in some situations. (ii) When operating on upward
inclines close to the maximum for the product the speed may need to be significantly lower.
of the significant cost advantages that can be gained; 6 m/s is fairly common,
and up to 10 mjs is possible in some situations. It has been suggested recently
[14] that if care is taken over the dynamic design of the system, belt speeds
above 15 mjs are technically feasible.
7.3.3 Belt width
The carrying capacity rits of a belt conveyor can be expressed as
rits = PbksAv
(7.1)
where Pb is the bulk density of the conveyed material, A is the average crosssectional area of this material stacked on the horizontal moving belt, v is the
belt speed, and ks is a 'slope factor' to take account of the decrease of the loadstream cross-section when the belt operates on a gradient.
Clearly the difficulty in using equation (7.1) to determine the maximum
transport rate (or the minimum belt width for a specified transport rate) lies in
the calculation ofthe cross-sectional area of the load stream, A. The maximum
value of A will depend upon the nature of the conveyed material, the width of
the belt and the configuration of the idlers. It is possible to use simple geometry
K
278
BULK SOLIDS HANDLING
SU"charge angle 6
Figure 7.14 Cross-section of load stream on a flat belt.
to derive a mathematical expression for the nominal cross-section of the load
stream, and the method for a troughed belt running on conventional three-roll
idlers is given in [6].
In the case of a flat belt the cross-sectional area A of the load stream can be
easily calculated if it is assumed that the surface of the conveyed material is
parabolic (Figure 7.14).
Thus
(7.2)
and
(7.3)
where b is the width ofthe load stream on the belt and b is the surcharge angle.
Tabulated values of A for flat belts of various widths are given in [7], and for
various configurations of troughed belt in [7] and [11].
op1imum troughing angle
(to give maximum Ul
0.24 r--r--r--r''-'-li'"--r---r---r--'-r--;---,
:::>
0 0.16
;:;
~
g_ 0.12
"'"'
.r:::
0.08
0.04
o·~~-,Lo~--2~0-J--~~~~~~so
!roughing angle, {3
Figure 7.15 Shape factors for V-troughing on two-roll idler systems.
279
BELT CONVEYORS
angle of wing idlers to horizontal
(!roughing angle) - degrees
(J
Figure 7.16 Shape factors for standard three-roll idler set having all rollers of the same size.
A useful alternative approach for the somewhat more difficult cases of tworoll and three-roll idler configurations is to express the cross-section of the
load-stream in terms of the 'contact perimeter' b of the material on the belt
using a shape factor V which is a function of the transverse profile of the belt
and the surcharge angle of the conveyed materials:
(7.4)
so that
(7.5)
For the flat belt V clearly has the value (tan o)/6, but for other belt profiles it
is more convenient to present charts from which the relevant shape factor can
be determined.
Typical charts are given here for two-roll idler systems (Figure 7.15) and
standard three-roll systems having rollers of identical length (Figure 7.16). A
full analysis and discussion of optimum idler configurations can be found in
[2].
-
280
BULK SOLIDS HANDLING
t-. !'---
0.9
........
!'-..
' ['-..
0.8
0.7 0
Figure 7.17
I"'\
4
8
12
16
angle of inclination (degees)
20
Slope factor k, for smooth (unpatterned) belts operating on a gradient.
Values of the slope factor k., which allows for the reduction in the crosssectional area of the load stream when conveying on a gradient, can be
determined from Figure 7.17 (from [7] ).
Naturally some allowance must be made for 'edge clearance'; that is, the
distance between the conveyed material piled on the belt and the edge of the
belt. One formula relating the minimum width Bmin of the belt to the contact
perimeter b (recommended in BS 5934/ISO 5048) is:
Bmin = 1.11 b + 0.056
(7.6)
where Bmin and b are in metres.
Thus, for a given idler configuration (and hence, shape factor V) and given
belt speed v, the minimum belt width required to transport material of bulk
density Pb at a rate m, can be estimated from
m
Bmin = 1.11 ( __s _
PbksUv
)o.s + 0.056
Table 7.3 Preferred widths of conveyor belt as
recommended by the UK Mechanical handling
Engineers Association [ 11].
Belt width (mm)
400
500
600
650
800
1000
1200
1400
1600
1800
2000
(7.7)
BELT CONVEYORS
281
The belt selected would then normally be the nearest standard size above
available from the manufacturer. Preferred widths of conveyor belt, as
specified by the UK Mechanical Handling Engineers Association [11], are
listed in Table 7.3. Note, however, that the minimum belt width may be
dictated by the lump size of the conveyed material as explained in section 7.3.1.
(In this case equation (7.7) can be used to give an indication of the belt speed
required.)
Bmin
7.3.4 Belt tension
The power required to drive a belt conveyor has to be transmitted from the
driving drum or drums to the belt through friction between the two surfaces.
(By a similar mechanism, a belt conveyor operating downhill can have a
regenerative effect, transmitting power from the belt to one or more drums.) As
in all belt drives, the power is transmitted by means of a difference in the
tension in the belt as it approaches (T1 ) and leaves (T2 ) the driving drum
(Figure 7.18). In the usual case of power transmitted from the drum to the belt
T1 will be greater than T 2 , so that the ratio TJIT2 is greater than unity.
The magnitude of the ratio TJIT2 depends upon the coefficient of friction
between the drum and the belt, and the extent of the arc of contact between
them. In order that the belt conveyor installation operates correctly it is
essential for the :ensile forces in the belt to be such that two basic conditions
are fulfilled. These are that the necessary power is transmitted from the driving
drum or drums to the belt without slippage occurring and that excessive sag
does not occur between any pair of idler sets. Two useful parameters in belt
conveyor design are the 'effective tension' Te, defined as the difference between
the tensions in the belt as it approaches and leaves the driving drum, and the
'drive factor' or 'wrap factor' Kd which is the ratio of the 'slack-side' tension T2
to the effective tension Te i.e.
K d_- T2
(7.8)
Te T1 - T2
Now from an analysis of the forces in the belt it can be shown that
T!
-
T2
=
exp(J18)
T1
(tight side)
T2
(slack side)
Figure 7.18
Tensile forces in a conveyor belt.
(7.9)
282
BULK SOLIDS HANDLING
Table 7.4 Typical values of friction coefficient 11 between
drive drum and belt.
Operating conditions
Bare drum
Lagged drum
Dry
Clean wet
Wet and dirty
0.3
0.2
0.1
0.35
0.2-0.3
0.2
where J1 is the coefficient of friction between the belt and the drum and (J is the
angle of wrap. It should be noted that the value of J1 is very much dependent
upon operating conditions and may range from 0.35 or more for a clean lagged
drum to as little as 0.05 for an unlagged drum in a wet and dirty situation
(Table 7.4).
Rearranging and combining equations (7.8) and (7.9) we have
(7.1 0)
where
I
Kd=--·--exp (Jl(J) - I
(7.11)
Clearly the value of the drive factor Kd will depend principally upon the
coefficient of friction between the belt and the driving drum and the angle of
contact. Figure 7.19 is a chart based on equation (7.11) from which Kd can be
estimated for various operating situations. Note that when a screw tensioner is
in use instead of an automatic take-up device, it will be necessary to put an
initial stress on the belt and therefore a higher value of wrap factor should be
used. Generally for a single drum Kd should be 20% greater if the drum is bare
and 30% greater if it is lagged, and for a tandem or dual drive Kd should be
about 25% greater for both bare and lagged drums.
The tensile forces in a working conveyor belt will vary along the whole
length of the belt, and will change when the belt is stopped or started and when
the product feed rate is altered.
When selecting a conveyor belt it is necessary to know the maximum
tension to which it will be subjected, and for simple belt configurations this is
equal to the 'tight-side' tension T 1 • The corresponding minimum tension
(equal to the 'slack-side' tension T 2 ) is also an important design parameter, as
it must not be so low that slipping occurs between the driving drum and the
belt. Furthermore, a certain minimum tension in the belt is necessary to ensure
that the sag between the idlers does not exceed the usually recommended
figure of around 3% of the idler pitch. This is particularly important on the
carrying side where excessive spillage of material from the belt can occur if the
sag is too great.
Various methods are available for determining the maximum and minimum
belt tensions and where they occur, the complexity of the analysis depending
283
BELT CONVEYORS
3"0
r--r--r--,-------.-.1-,--,
11_,..1--,-~
= r p l a i n drive (1800)
1
snubbed
I
rdrive
1
2.5
r-
~~
I
tandem a
dual drive
- r- -
+++-'r---'---.. . . -
r- - -+-+--+--+--+--+--+--+--+--+--+---t--t
1--
I
l
'Ul
r-
.j! 2.0
\
:
bare dn.ms
t--t--;--t--f-'lr\.-+--twet and dirty
1
\ r clean wet
.........,~~-+--+-+---1'<-~_,V-L. dry
J'
!
!5 1.5
-g
+-+\-\+-+--+--+--+--+--+-+-+--+-+-+-+--+--!
t---1r-flrt-\--+-+---t-"'JK -+--t---tI
'i
>
~
l/
I
\..
1
CD
lagged dr~
wet and drty -
/
clean wet
dry
I
..!
-
V
p.
1\. I'·
i.. f'
I
0 ..
,
/ / ........_
'//
'-1,.(
.... ,
0.10
'
-
, __ -
.......
I
300
200
angle of
0.15
o:2o
--- 0.25
-- -F400
500
8:1
oontact (degees)
Figure 7.19 Approximate values of the drive factor (Kd) for conveyor belts fitted with gravity or
automatic tensioning devices. (For belts tensioned manually, values from this chart should be
increased by 25% if drum is bare or 15% if lagged.)
upon the configuration of the conveyor. Full details may be found in the
literature, for example [1], [2], [8-11].
For a simple belt system, the procedure involves estimating the
driving force needed to move the loaded belt (as explained in the next section)
and equating this to the effective tension Te. The maximum and minimum
tensions in the belt can then be estimated from equations (7.10).
An important requirement at this stage is to check that the value of the
minimum tension is sufficient to prevent the belt sagging excessively between
the idlers. The tension throughout the length of the belt must always exceed
the so-called 'sag tension', which can be estimated as follows:
For the carrying side,
(7.12)
and for the return side
(7.13)
284
BULK SOLIDS HANDLING
where mb and mL are respectively the mass per unit length of the belt and of the
conveyed material on the belt, Lie is the idler pitch on the carrying side, Lir is
the idler pitch on the return side and K, is a 'sag factor' which has values 4.2 for
3% sag, 6.25 for 2% sag and 8.4 for 1.5% sag [2].
7.3.5 Idler spacing
The spacing of the idler sets along the length of a belt conveyor installation will
be influenced by various factors such as the load being carried, the width and
stiffness of the belt (longitudinal and transverse) and the tension within the
belt. It has now become almost universal practice to arrange the return idler
sets on a 3 m pitch, but on the carrying side the idler spacing would typically be
anything from 0.93 m to 1.6 m. Table 7.5 gives recommended pitch of carrying
idler sets for various densities of conveyed material and various belt widths
[6].
Although it appears to be customary to have the carrying and return idlers
arranged on a uniform pitch, there are definite advantages in terms of lower
initial cost and reduced frictional resistance to having graduated spacing to
correspond to the varying tension along the length of the belt. However, these
advantages may be largely outweighed by the practical difficulties of installing
such an arrangement. Equations (7.12) and (7.13) can be adapted to show the
optimum idler spacing once the actual tension throughout the belt has been
determined [2].
7.3.6 Power requirements
The power required to transport a material on a belt conveyor is absorbed in
overcoming frictional effects and (if upward movement is involved) in
increasing the potential energy of the material. Accelerating the material fed
on to the belt may also account for some of the power requirement.
The currently favoured approach [7] to assessing the overall resistance to
motion of a belt conveyor, (and therefore the belt tension and power
requirement), is to consider separately the various component resistances
which are classified into five groups as shown in Figure 7.20.
Table 7.5 Recommended pitch of idler sets [6]
Pitch of carrying idler sets (mm)
Bulk density of conveyed material
Belt width
(mm)
400-1200kgjm 3
1200-2000 kg/m 3
2000-2800kgjm 3
400-650
650-900
900-1050
1050-2000
1650
1500
1350
1200
1500
1350
1200
1000
1425
1275
1125
925
Note: Recommended pitch of return idlers is 3000 mm for all the above applications.
285
BELT CONVEYORS
Occur on all
belt conveyors
"'•""' ""'
{
(1)
.{
(2)
SECONDARY
RESIST ANCES
(3) SPECIAL MAl
certain instalations
(4)
(5)
Figure 7.20
Occur continuously
MAIN
RESIST ANCES- over the length of
the belt
RESIST ANCES
SPECIAL
SECOOOARY
RESISTANCES
SLOPE
RESISTANCE
Occur locally
May have positive,
zero or
negative values
Classification of resistance to motion of belt conveyors (British/ISO standard).
A detailed list of these various resistances may be found in [2] and [7], but
in order that the explanation of the design process may be continued a
summary of the most important resistances is given below:
(i) Belt friction resistance, Frb· This is the resistance to movement of the empty
belt and results chiefly from the rolling resistance of the idlers together with a
contribution from the belt itself due to flexing and sliding contact with various
components. Clearly the actual magnitude of Frb is not easily predicted, and
the conventional approach used by conveyor manufacturers is to calculate the
total mass of all the moving parts of the conveyor (belt, idlers, drums, etc.) and
then multiply this by an empirical 'friction coefficient', J.1., 1 . Figure 7.21 can be
used to give an approximate indication of the mass of moving parts of simple
conveyors (from [15]) but where possible the mass should be determined more
accurately.
Thus, the total effective mass of all moving parts may be calculated as
(7.14)
where mic and mir are the mass of the rotating parts of the idlers per unit length
of belt on the carry side and the return side respectively, mb is the mass of the
belt per unit length overall, a is the angle of elevation and Lis the overall length
ofthe conveyor ('centre-to-centre'). Note that the term 2mb cos a represents the
contribution of the belt itself to the force carried by the idlers. Thus,
(7.15)
where M c is the total mass of moving parts.
The value of the 'belt friction coefficient' f.1., 1 depends to some extent upon
the conditions (especially the temperature) in which the belt is used, but for
most applications a value of 0.025 should be reliable.
(ii) Load friction resistance, FrL· This is defined as the resistance to horizontal
movement of the conveyed material; it is usually expressed in terms of the total
mass of material on the belt, multiplied by an empirical friction coefficient, f.1, 2 .
286
BULK SOLIDS HANDLING
80
I
m~ss of belt 1
(including both carryilg
strand and return strand)
I--
60
'E
I
/
I
heavy d u t y /
Cl> 40
.:5
I--
--
Q)
g
/
!'!! 20
.!!I
__
~
,!;
g60
~ 0
1--
-
I
---
I
I
mass of trouahi'la idlers
(1 metre pitch) ,
--:::
Q)
.i!:
Q)
j
-
l
I
I
mass of return idler§
20 -~
0
I
___.. ~
-
152/1~m~ -127mm .---
-----~L..--~ 400
I--
200
(3 jtre plitch) f - - -
400
600
.---r>
I
/
----
~
I.
I
___.......... ~
/
__..........
j:;3Y.r-av~
V
__..........
"0
Cl
/
/
102mm
1--
------ -
l--
I
152/1681T1Tl
-127~{·\·
102m
I
800 1000 1200 1400 1600 1800 2000
belt wldth Crm\1
Figure 7.21 Charts for estimating the total mass of moving parts per unit length of conveyor.
Example: for IOOOmm wide belt, 127 mm idlers, on average duty, total mass= 6.5 + 24.5 + 25.5
= 56.5kg/m.
The value ofthe 'load-friction coefficient' is likely to be slightly higher than the
belt friction coefficient J1, 1 , but for design purposes is generally taken to be the
same. Thus,
(7.16)
where mL is the mass of conveyed material per unit length of the belt and L is
the conveying distance.
Note that mL can conveniently be written in terms of the carrying capacity of
the belt and the belt speed as
(7.17)
so that
m.gL
FrL = Jl,z--
v
(7.18)
BELT CONVEYORS
287
The belt friction resistance and the load friction resistance together make up
the so-called 'main resistance' FH to the movement of the belt. Thus
FH =
and setting
Jlrl
=
llrl (mic+
mir +2mb cos rx)gL + Jlr2mLgL
(7.19)
Jlrz = 0.025 and simplifying,
FH = 0.025g( MC+
:s )L
(7.20)
(iii) Load slope resistance, F 51 • Where a belt conveyor operates on an upward
incline, the largest contribution to the total driving force required is likely to
result from the gravity force on the load. However, it should be noted that F 51
may be positive or negative, depending upon whether the movement of the
conveyed material is upwards or downwards.
Thus the load slope resistance can be expressed relatively simply as
(7.21)
or
rhsgH
Fst=-V-
(7.22)
where His the net change in vertical elevation and can be positive or negative.
(iv) Load acceleration resistance, FaL· If the load being fed on to the belt has
an initial component of velocity v0 in the direction of the belt, the resistive force
on the belt can be expressed as
(7.23)
or
(7.24)
The load acceleration resistance is probably the most significant of the
'secondary resistances'. Others are the resistance due to friction between the
conveyed product and the side walls or skirt plates in the loading region,
bearing resistance of snub pulleys and bend pulleys (but not driving drums),
and resistance due to wrapping of the belt on the various pulleys and drums.
References [2] and [7] give guidance on the calculation of these resistances,
but BS 5934/ISO 5048 [7] also recommends, for belt conveyors longer than
80m, an abbreviated approach in which the secondary resistances are given
by
(7.25)
where the coefficient KsR varies from 0.025 for conveyors longer than 3000 m
up to more than 1 for conveyors less than 80 m in length (Figure 7.22).
Although the so-called 'special resistances' occur only on certain installations, they may be significant in comparison with the other resistances to
288
BULK SOLIDS HANDLING
c
Cl>
I
11
"13
1
.i
I--
- -
f.----
[\
Cl>
--
f...-- I--
t-----1\
0.5
~
~-·
>-
~5l 0.1
'
I-I--
+----
+----
0
10 20
1---~-
I
I
i
--
!"'
-
50 100 200
I
"""'
500 10002000 5000
centre-to-centre length L of conveyor (m)
Figure 7.22
[7].
Variation of secondary resistance coefficient Ks• with length of belt conveyor from
movement of the conveyor belt. The special resistances include such effects as
drag resulting from the forward tilt of the idler wing rollers and drag due to
belt cleaners, ploughs, trippers and skirt plates (other than in the loading
region). As with the secondary resistances, [2] and [7] give methods of
estimating the special resistances.
The load acceleration resistance is probably the most significant of the
above constituents. Thus
(7.26)
or
(7.27)
The required driving force at the motor drum will be effectively equal to this
total resistance, and consequently the 'effective tension' Te can be substituted
for F R• so that
(7.28)
Maximum and minimum tensions in the belt can now be estimated as
explained in the previous section
The operating power required at the driving drum can be expressed as the
product of the effective tension and the belt speed:
P= Tev
(7.29)
so that the motor power can be determined from
Tev
P
=I]m
(7.30)
where '1 is the efficiency of the motor/drum transmission (usually around 8595%).
BELT CONVEYORS
289
7.4 Belt conveyor variants
7.4.1 The cable belt conveyor
The cable belt system was originally conceived as a means of separating the
driving and carrying functions of a conventional belt conveyor. The system
was developed in Scotland in the late 1940s and early 1950s and is now well
established as a reliable means of transport offering several advantages over
more traditional conveyors.
The basic concept of the cable belt system is a laterally rigid but
longitudinally flexible belt, supported at or near its edges on two parallel
endless steel cables, these in turn being supported by idler pulleys spaced at
regular intervals over the length of the conveyor (Figure 7.23a). The construction of the belt itself involves a central composite core, sandwiched between
two layers of wire and textile mesh, the whole matrix being enveloped and
(a) A typical linestard showing the concept of separate driving
and carrying functions
'1-·
(b) Belt construction
(c) Natural !roughing under load
(d) A recently developed pre-formed belt, the sides of which
flatten to pass round the end puleys (Ref. 16)
Figure 7.23
The cable belt conveyor.
290
BULK SOLIDS HANDLING
vulcanized in suitable outer covers (Figure 7.23b). The belt sits on, but is not
attached to, the drive cables and thus does not transmit tension. When empty
the belt is flat and is positively located on the drive cables by longitudinal Vgrooves. Its lateral rigidity is sufficient to allow it naturally to form a trough
when carrying a load (Figure 7.23c), but longitudinally the flexibility of the belt
permits it to wrap around the head and tail drums of the conveyor. A very
recent development [16] has the belt pre-formed into a trough profile
(Figure 7.23d). Built-in reinforcement gives the belt sufficient lateral stiffness to
maintain its profile between idlers whilst allowing the inclined sides to flatten
naturally as the belt passes around the head and tail drums.
There are many examples of cable belt conveyors having a proven record of
successful operation, including a number working over long distances, in the
range 5-15 km, and conveying at rates of up to 1000 tonnes/hour. More
recently a cable belt system has been designed to transport bauxite at a rate of
2040 tonnes/hour over a distance of 50 km on a 950 mm-wide belt travelling at
more than 6 m/s [ 17], the longest single flight being over 30 km.
7.4.2 Belt conveyors without idlers
A number of manufacturers have developed modified forms of belt conveyor
with the objective of eliminating some or all of the idler rollers.
In one type, the angled wing-idlers are dispensed with and replaced with a
continuous strip of low-friction material, whilst the centre rollers are retained
for belt support and load carrying (Figure 7.24). The low-friction sealing strips
are, for normal applications, a basic reconstituted UHMW polyethylene, but
alternatives are glass-impregnated UHMW polyethylene for abrasion resistance and stainless steel for use at high temperature. It is claimed that a seal is
created between the low-friction material and the underside of the conveyor
belt, and that spillage from the conveyor is completely eliminated by
continuous vertical walls fitted to the main support channel frame. In order to
belt - canying strand
top cover
return
idle~
Figure 7.24 Non-spill design oft roughed belt conveyor in which wing idlers are replaced by lowfriction strips.
291
BELT CONVEYORS
belt - carryin~->--11~
strand
air holes
plenum
charrtler
-lli~~~3i~
belt - return
strand
Figure 7.25
Idlerless !roughed belt supported on an air-cushion.
make the conveyor weatherproof and dust-tight, a top cover may be fitted to
the vertical sidewalls, so that the carrying side of the belt is effectively running
inside an enclosed duct.
An extension of the concept of a low-friction surface replacing rollers has the
carrying side of the belt supported on a thin cushion of air trapped between the
underside of the curved belt and the continuous steel or plastic trough in which
it runs (Figure 7.25). Conveyors of this type are marketed under various
names, such as 'Aerobelt', 'Hovertube', 'Simveyor' and 'Jetbelt', available in
trough widths up to 0.6 m, and lengths of 2 to 100 m. Air is supplied to the
plenum chamber beneath the curved trough by a suitable blower at a rate of
some 20-40 m 3 /h per linear metre, and passes through small holes in the
trough to form a thin, lubricating film on which the belt effectively 'floats'. This
film is maintained at pressure by the weight of the conveyed product on the
belt and the flow rate of air to the plenum chamber needs to be sufficient only
to replace the air that bleeds continuously from the gap between the edges of
the belt and the surface of the trough. Thus the air supply rate should be
adjusted to suit the belt speed, which is normally up to about 7 mjs, and
loading so that a suitable edge clearance is maintained. Thus are ensured the
advantages of the system in terms of reduced frictional resistance, minimal
wear of the belt and the trough, and minimal spillage over the sides of the belt.
7.4.3 Closed-belt or pipe conveyors
The pipe conveyor can be regarded as a variant form of a conventional belt
conveyor in which the troughing effect is continued to the limit so that the
edges of the belt roll over and butt together to form an enclosed tube of more of
less circular cross-section. This type of conveyor is particularly suitable for the
transport of fragile products, since they are wrapped in the belt and carried
gently with little, if any internal movement except at filling and discharge
points. This feature also permits highly abrasive materials to be conveyed with
negligible wear of the belt and other plant components. Another important
advantage of the pipe conveyor is its flexibility: curves in both the horizontal
292
BULK SOLIDS HANDLING
(a) The zipper' conveyor (Ref. 18)
spring clip
outriding drive belt
conveyor
(cross-section)
(c) The Japan pipe conveyor
Figure 7.26
Forms of closed-belt or pipe conveyor.
and vertical planes are possible within a short space, so that twists and turns
can be accommodated to suit almost any requirement of the plant layout.
Probably the earliest form of pipe conveyor was the 'zipper' conveyor in
which the edges of the belt have moulded teeth that are meshed and unmeshed
by rollers in much the same manner as the familiar clothing fastener
(Figure 7.26a). A more recent design, registered under the name-'Solitube', has
the belt assembled with spring clips which, in the natural state, hold it closed in
the form of a tube having a 'tear-drop' cross-section (Figure 7.26b). This tube is
BELT CONVEYORS
293
supported by a system of outriggers connected to twin independent driving
belts. This independent drive arrangement enables the tube to be moulded in
rubber compounds suitable for negotiating filling and emptying stations and
bends rather than for power transmission. Also, the drive belts guide and
support the conveying tube and, by geometric displacement of the idler rollers
and movement of actuating arms, provide a means to open the tube against the
resistance of the spring clips. The tube is filled with product via an inlet spout
which is inserted into the aperture at the feed station and emptied under
gravity by rotating the whole assembly through 180° before opening it. With
the standard 80 mm diameter tube running at 2 mjs, the Soli tube has a
potential volumetric capacity of about 30m 3 /hour.
The Japan pipe conveyor has more in common with a conventional belt
conveyor since it has a head and tail pulley over which the belt passes flat.
Beyond the loading point the belt is rolled into tubular form by a series of
idlers (Figure 7.26c). Curves in any direction can be negotiated under the
control of further circumferential idler sets, and as the belt approaches
the discharge point at the heat pulley, it undergoes the transition from
tubular back to flat belt. Conveyors built to date include belt diameters
ranging from 100mm to 500mm, and capacities ranging from 36 to
1800m 3 /hour. Operating speeds are from 1 m/s to 4m/s and conveying
distances of several hundred metres are being achieved [19].
Operating in a very similar way to the Japan pipe conveyor is a recently
proposed system based on a pre-formed rubber belt having a rectangular
trough section [ 16]. The sides of the trough, which may be notched along their
upper edges in the same manner as the previously mentioned zipper conveyor,
can be turned in by rollers to form a closed tube.
7.4.4 Sandwich belts
The principle of the 'sandwich' belt is relatively simple-the carrying belt, flat
or slightly troughed, has a second belt running at the same speed in a close
parallel plane, the conveyed product being the 'filling' in the 'sandwich'. The
second (retainer or 'hugger') belt presses against the first with the edges
effectively sealed by air pressure or by rollers. The bulk solid being carried is
thus 'hugged' and prevented from sliding or rolling back when the conveyor
operates on an incline, and the system can therefore work at any angle, even
vertically upwards.
An early application of the sandwich belt arrangement was for selfunloading vessels [20]. In a typical example (Figure 7.27) a conventional belt
conveyor runs horizontally the length of the ship or barge and then curves
upwards towards the deck. A second belt loop runs with the first to form the
sandwich for the vertical rise, and in this way the bulk product is discharged
from the vessel by a compact system without the complication of transfer to a
separate elevator and without the need for substantial dockside equipment.
294
Figure 7.27
system).
BULK SOLIDS HANDLING
A sandwich belt conveyor installation used on a self-unloading vessel ('loop-belf
\
......
_
---
Figure 7.28
The 'Simporter' ship unloader [22].
Commercial variations of the sandwich belt conveyor have been developed
under names such as 'Beltavator', 'Speed-Up' and 'HAC' (High-AngleConveyor), and the last-named particularly is finding useful applications in the
sphere of open-cast mining and quarrying [21]. High-angle conveyors are
operating at angles of up to 60° (with a claimed potential of90°). One example,
in Yugoslavia, is designed to convey copper ore at 4000 tonnes/hour on a 2-m
wide belt running at 2.7 m/s. The elevating height in this case is 93.5 m and the
relatively modest inclination of 35.SO represents the limit of stability of the
mine slope. Potential capacities in excess of 9000 tonnes/hour are claimed for
this type of high-angle conveyor.
An important industrial application of the sandwich belt concept is in the
dock-mounted ship unloading system known as the Simporter, which can be
BELT CONVEYORS
295
built for capacities from 300 to 2000 tonnes per hour. In the usual
arrangement, a type of paddle feeder delivers the bulk material to the main
belts which run up the vertical elevator leg and along the boom assembly
(Figure 7.28). These belts run on slider plates, but air is introduced between the
belt and the slider plates to reduce frictional resistance. The pressure of the air
within the closed elevator leg and boom also helps to maintain the seal
between the two belts.
7.5 Notation
A
Bmin
b
FaL
Frb
FrL
FH
FN
FR
F••
g
H
Kd
K.
KsR
k.
L
Lie
Lir
mb
MC
mic
mir
mL
m.
p
pm
r.
Tsag
Tl
T2
V
V
Cross-sectional area of bulk solids stream on conveyor belt
Minimum overall belt width
Width ofload stream on belt (i.e. cross-sectional contact length)
Load acceleration resistance
Belt friction resistance
Load friction resistance
Total main resistance
Total secondary resistance
Total resistance (main and secondary)
Load slope resistance
Gravitational acceleration (specific gravitational force)
Net change in vertical elevation
'Drive factor' or 'wrap factor' defined by equation (7.11)
Sag factor in equations (7.12) and (7.13)
Secondary resistance coefficient
Slope factor
Length of conveyor (centre to centre)
Idler pitch on carrying side of belt
Idler pitch on return side of belt
Mass of belt per unit length
Total effective mass of moving parts of belt conveyor
Mass of carrying idlers per unit length
Mass of return idlers per unit length
Mass of conveyed material per unit length of belt
Carrying capacity (mass of solids per unit time) of a belt
conveyor
Operating power required at driving drum
Motor power, in equation (7.30)
Effective belt tension
Conveyor belt 'sag tension'
Tension in the tight side of the belt
Tension in the slack side of the belt
Shape factor for load cross-section
Linear velocity of belt
296
BULK SOLIDS HANDLING
Component in direction of belt travel of initial product velocity
Angle of inclination of belt conveyor (to horizontal)
Surcharge angle of material on belt
Efficiency of motor/drum transmission
Angle of wrap (or arc of contact)
Coefficient of friction
Belt-friction coefficient
Load-friction coefficient
Bulk density
References and bibliography
References
1. Belt Conveyors for Bulk Handling, Conveyor Equipment Manufacturers Association
(CEMA), Cahners Books (1966).
2. Roberts, A.W. and Hayes, J.W. (1979) Economic Analysis in the Optimal Design of Conveyors,
TUNRA Ltd., Univ. of Newcastle, Australia.
3. Comley, P.D.H. High speed belt conveying in modern industry. Proc. Solidex 82 Conf,
March/April 1982, Harrogate, UK; Paper Al.
4. Sahara, K. and Kuroda, Y. ( 1985) Test run of a 3 m wide, 30,000 t/h capacity belt conveyor.
Bulk Solids Handling 5 (3) 599-601.
5. BS 490: Part 1. Conveyor belting for general use. British Standards Institution, London.
6. BS 2890: 1973. Troughed belt conveyors. British Standards Institution, London.
7. BS 5934: 1980. Calculation of operating power and tensile forces in belt conveyors with
carrying idlers on continuous mechanical handling equipment. British Standards Institution,
London. (Also ISO 5048-1979).
8. BTR Conveyor Belt Manual, BTR Belting Ltd., Preston, Lancashire (1979).
9. Dunlop Starjlex Conveyor Belt Manual., December 1976.
10. Dunlop Solid Woven Conveyor Belt Manual, June 1983.
11. Recommended Practice for Troughed Belt Conveyors. Mechanical Handling Engineers
Association, London ( 1986).
12. Fyson, R.O. (1977) Two angles on conveying bulk materials up steep inclines. Chartered
Mech. Engr., April, 50-53.
13. Conveyor Belt Cleaning Devices. Mechanical Handling Engineers Association, London.
14. Harrison, A. and Roberts, A.W. Technical requirements for operating conveyor belts at high
speed. Proc. Inc. Con[. on Bulk Materials Storage. Handling and Transportation, Newcastle,
Australia, August 1983, 84-89.
15. Lancaster, J.L. Application and design of belt conveyors. Proc. Solidex 80 Con(, Harrogate.
UK, March 1980, Paper A4.
16. Melander, S. and Wehtje, A. ( 1986) Theoretical and practical background of a new type of
conveyor belt. Bulk Solids Handling 6 (5) 941-946.
17. Farry, K.P. and Burleigh, A.C. 50 km conveyor for the aluminium industry. Proc.lnt. Con( on
Bulk Materials Storage, Handling and Transportation, Newcastle, Australia, August 1983,9094.
18. Perry; R.H. and Green, D. (1984) Perry's Chemical Engineers' Handbook. McGraw-Hill, 6th
edn., McGraw-Hill, New York, 7-16,7-17.
19. Buchanan, C. (1986) Japan pipe belt conveyor system. South Aji-ican Mechanical Engr 37 (2)
31, 33-35.
20. Walker, K. Self-unloading vessels. Proc. Solidex 84 Con(. Harrogate, UK, 1984, Paper D3.
21. Dos Santos, J.A. (1986) Sandwich belt high angle conveyors-HAC evolution to date. Bulk
Solids Handling 6 (2) 299-314.
22. Napier, L.M. and Marsden, A.M.L. ( 1985) The Simon-Carves Simporter system. Bulk
Solids Handling 5 (I) 53-55.
BELT CONVEYORS
297
Recommended further reading
Troughed Belt Conveyors. Mechanical
Association, London ( 1986).
Roberts, A.W. and Hayes, J.W. (1979) Economic Analysis in the Optimal
Chapter 4, Belt Conveyor Design and Performance, TUNRA Ltd.,
Australia.
Colijn, H. (1985) Mechanical Conveyors for Bulk Solids, Chapter 2, Belt
Amsterdam.
Recommended Practice for
Handling Engineers
Design of Conveyors.
Univ. of Newcastle,
Conveyors. Elsevier,
8
8 ucket elevators
8.1 Introduction
In the preceding chapter on belt conveyors, brief mention was made of
adaptations to the basic flat- or troughed-belt to enable it to operate on steep
inclines. For example, whereas a conventional belt conveyor would generally
be limited to a slope of about 20o, texturing the surface of the rubber belt to
incorporate moulded ribs or nubs will allow conveying up an incline of some
60-70°, or even more, depending upon the nature of the bulk solid being
carried. Taking this idea further, the rubber belt could be fitted with sidewalls
and curved or sloping transverse slats so that it is capable of lifting the
particulate or granular material vertically. The conveyor then approaches the
design concept of the well-known bucket elevator.
In many situations where the lifting of bulk solids is involved, the bucket
elevator is the most simple, efficient and reliable machine that could be used
(Figure 8.1). It can be obtained in a wide range of capacities and the current
trend is towards standardized units, although for 'difficult' materials and high
conveying rates it is advisable to use specially engineered equipment. The
detailed construction of the bucket elevator obviously varies from one
manufacturer to another and certain design features such as the pitch of the
buckets, the operating speed and the feed and discharge arrangements may be
chosen to suit the product being handled. However, the essential components
of the device are:
(i) An endless belt or chain(s) as a traction element to which are attached a
series of carrying vessels or buckets
(ii) A single or double casing which serves to enclose or partially enclose the
moving buckets
(iii) A 'head' at the upper end of the elevator which includes a belt pulley or
chain wheel to turn the traction element and a suitable discharge chute
(iv) A 'boot' at the lower end which again includes a belt pulley or chain wheel,
a tensioning device (usually), and a means of feeding the material to be
conveyed so as to ensure optimum filling.
It is convenient to classify bucket elevators according to their bucket
spacing and mode of discharge, and the two principal typescentrifugal discharge (spaced bucket) and continuous discharge-will be
described in the next section.
Another important group of bucket conveyor/elevators discussed in this
BUCKET ELEVATORS
Figure 8.1
299
A typical bucket elevator.
chapter includes all those having various types of pivoted or hinged buckets.
These allow combinations of horizontal and vertical conveying without the
need for transfer points and, as a further advantage, allow unloading at any
desired point in horizontal section.
The final type of elevator to be described here is the profiled rubber belt, but
it should be noted that this by no means exhausts the list of potential methods
for raising bulk solids through a vertical distance. Some methods, such as
screw conveyors, spiral vibratory elevators, en-masse conveyor/elevators,
sandwich belts and tubular drag conveyor/elevators are discussed elsewhere in
this book; others are omitted, principally because of their limited or specialized
application. Neither is it possible here to discuss the enormous variety of
applications that are found for bucket elevators, ranging from small light-duty
300
BULK SOLIDS HANDLING
Figure 8.2
A ship-unloader using a form of bucket elevator.
units in the food and pharmaceutical industries, to the very large dockside
installations capable of unloading ships at rates greater than 5000 tonnes/hour
(Figure 8.2).
The second half of the chapter is concerned with the design and selection of
bucket elevators, and guidance is given on the calculation of capacity and
power requirements for the more conventional types.
8.2 Principal types of bucket elevator
8.2.1 Centrifugal discharge elevators
Spaced-bucket centrifugal discharge elevators are very commonly used for
handling free-flowing fine or granular products. Small lump materials can also
be handled without difficulty. The buckets tend to be quite widely spaced
(Figure 8.3a) and are typically of the shape shown in Figure 8.3c. Low-front
buckets (Figure 8.3d) are used for handling wet, stringy or sticky products
which are difficult to discharge. Material feed to the buckets is likely to be a
combination of direct flow and a scooping action as the buckets turn under the
bottom pulley or chain wheel.
Discharge takes place by centrifugal action as the buckets pass around the
head pulley. This is sufficient to empty the buckets of relatively free-flowing
materials, but for those which are sticky or tend to pack, a modified
arrangement (known as 'positive discharge') may be used, with the buckets
mounted on two strands of chain and snubbed back under the head sprocket
(Figure 8.3b). The slight jolting of the chain passing over the snub sprocket is
generally sufficient to dislodge the material from the inverted buckets, but in
extreme cases some kind of rapping mechanism may be employed.
The speed of travel of the buckets must be sufficiently high to permit
centrifugal discharge of the product and around 1.3 to 2 m/s would be usual.
For very free-flowing granular materials (such as grain) belt speeds greater
than 3.5 m/s can be used without difficulty. The positive-discharge type of
BUCKET ELEVATORS
(a) Centrifugal -discharge
(c) Standard bucket profle
Figure 8.3
301
(b) Positive discharge
(d) Low-front style of ~et
Bucket elevator types (spaced buckets).
elevator is considerably slower, typically around 0. 7 mjs, and the buckets must
be larger or more closely spaced to give a comparable capacity to the
centrifugal discharge pattern.
8.2.2 Continuous bucket elevators
Materials that contain large lumps or that are, for other reasons, too difficult
to handle with centrifugal discharge machines, can often be carried in elevators
in which the buckets are closely spaced with virtually no gap between
(Figure 8.4a). These tend to be operated at lower speed than the centrifugal
discharge type-typically around 1 to 1.3 mjs. The low operating speed and
generally more gentle handling behaviour of the continuous bucket elevator
also makes it suitable for friable products and for those that are very fine, light
302
BULK SOLIDS HANDLING
(a) Slardard
(b) Higl capacity
(c) Starrlard and low-front buckets
Figure 8.4
(d) Higl capacity bucket
Bucket elevator types (continuous buckets).
or fluffy. Feeding of material to the closely-spaced buckets is predominantly by
direct flow rather than the scooping action of the centrifugal discharge
elevator, and discharge is largely by gravity, the back of the preceding bucket
serving as a discharge chute for the bucket which is dumping as it rounds the
head pulley.
Continuous type buckets are generally back-mounted to the chain or belt at
close intervals, the standard design of bucket being as illustrated in
Figure 8.4c. For high throughputs, especially of large-lump materials, highcapacity designs of elevator are available. These have extra large buckets and
are usually operated at an incline to improve feeding and discharge conditions
(Figure 8.4b).
303
BUCKET ELEVATORS
8.2.3 Pivoted buckets
In order to enable a bucket-type transporter to operate horizontally as well as
vertically, a system has been developed in which the buckets are suspended
between parallel roller chains in such a way that they can freely swing or tip.
The buckets are closely spaced and each is fitted with a lip which overhangs the
adjacent bucket so that filling can be carried out with minimal spillage whilst
the buckets are moving horizontally (Figure 8.5a).
The usual arrangement for a pivoted-bucket system would involve the
buckets travelling around a closed circuit in a vertical plane. Typically the
buckets would be filled at some point in the lower horizontal section and then
would be lifted vertically. Since the centre of mass of each bucket, whether full
or empty, is below the pivot, the buckets naturally remain in the carrying
position during the vertical rise (Figure 8.5b) but guide rails may be used to
ensure stability. The special mounting of the buckets on extended chain links
ensure that transition from horizontal to vertical, and back to horizontal
again, takes place without jamming and with the lips properly overlapping.
-
(a) Buckets horizontal for filling/carrying
e
,,I
j
(b) Buckets travelling
vertically
•o
I;
(c) Transition - vertical to horizontal
(d) Buckets tipped for discharging
Figure 8.5
Pivoted-bucket conveyor/elevator.
304
BULK SOLIDS HANDLING
Discharging generally occurs on the upper horizontal section and may be at a
single fixed location, at one of a number of selectable locations, or even at a
continuously variable location. The buckets are automatically tipped by a
relatively simple arrangement of rollers which bear against fixed or movable
cams (Figure 8.5d). A movable cam may permit a given discharge station to be
selected or de-selected, and if the cam is mounted on a travelling carriage or
tripper it is possible for the buckets to be discharged anywhere along a
horizontal section.
Pivoted-bucket conveyors are available to suit a wide range of carrying
capacities, generally within the range 5 to 500 tonnes/hour, bucket widths
being between 300 to 1000 mm. Conveying speeds are usually within the range
0.2 to 0.4 mjs, but with large and heavy buckets lower speeds, down to 0.1 mjs,
are used to reduce dynamic loading on the chains. Attempts to convey at
higher speeds may also result in excessive swinging of the buckets unless some
kind of damper or stabilized bearing system is used.
8.2.4 Profiled-belt elevators
Various designs of moulded rubber belt are produced that enable a beltconveyor to be constructed which can operate at steep angles, even up to 90°.
One form has 'cups' moulded into the carrying side of the belt, but much more
common is the flexible sidewall pattern having transverse cleats or slats
(Figure 8.6). The purpose of the corrugated sidewalls is to permit the belt to
curve in the vertical plane, even when loaded. Thus, like the pivoted-bucket
conveyor, the belt can be filled on a horizontal section and then turned round
guide wheels into a direct vertical lift. Discharge can be from the end of another
horizontal run in the same manner as a conventional troughed belt conveyor.
In order to increase the carrying capacity of flexible sidewall belts when
operating on steep inclines, they can be used in conjunction with a cover belt
which helps to prevent backsliding of the conveyed material over the cleats.
Figure 8.6
A flexible sidewall belt suitable for vertical operation.
BUCKET ELEVATORS
305
8.3 Design and selection of bucket elevators
8.3.1 Design features
The bucket elevator is, in essence, a very simple device and the earliest form,
dating back perhaps to pre-Roman times, could be regarded as the system of
crude buckets tied to an endless loop of rope and used for lifting water. In spite
of its basic simplicity, however, if the bucket elevator is to provide optimum
performance in terms of running costs and reliability, careful attention must be
paid to its design in relation to the nature of the product being handled.
A very wide range of bulk solids can be transported by bucket elevators and,
not infrequently, materials are encountered for which this system proves to be
the only really satisfactory method of conveyance. An average material would
be dry, free-flowing, of lump size less than 100 mm, at ambient to moderate
temperature, slightly to moderately abrasive and not especially friable.
However, bulk solids having unusual or difficult characteristics can often be
handled satisfactorily by bucket elevator if appropriate modifications are
incorporated at the design stage. For example, if a material is cohesive or wet
and sticky, it may be necessary to use specially shaped buckets or some kind of
rapping mechanism to ensure that the material discharges properly; very highdensity products may require strong buckets fitted to heavy-duty belting or
chains with strengthening of the supporting framework, and high-temperature
products may necessitate similar modifications to the elevator.
The design feature that is most strongly influenced by the nature of the
carried material is the shape and construction of the buckets themselves.
Bucket selection can be summarized as follows:
(i) Abrasive products
(ii) Very 'watery' products
and light free-flowing
products
(iii) Products susceptible to
aeration
(iv) Cohesive or sticky
products
Front lip of bucket strengthened to reduce
wear damage when digging into material
High front lip to bucket to provide maximum
capacity
Bucket drilled with air holes to help product
to 'settle'
Shallow rounded buckets to reduce tendency
for material to lodge in corners.
The properties of the bulk solid being handled will also have a strong
influence on the choice between centrifugal-discharge and gravity-discharge
elevators. As explained previously, the principal factors to be considered are
the lump size, the abrasiveness and the cohesiveness of the product. Table 8.1
[1] serves as a guide to the choice of discharge pattern and bucket type for a
few different bulk solids covering a range of particle sizes.
Various materials are used for the construction of elevator buckets. For
example they may be stamped and welded from sheet steel, typically 2 mm to
High-speed centrifugal
discharge
Slow-speed gravity
discharge
wrt ~·d.
powdered
chalkw"
Moist chemicals,
fluffed peat
r·rth,
Crushed stone, ore,
slags
Charcoal, coke
Slow-speed directed
gravity discharge
High-speed centrifugal
discharge
Slow-speed directed
gravity discharge
Slow-speed gravity
High-speed centrifugal
discharge
Ditto
Elevator type
High-speed centrifugal
discharge
Slow-speed directed
gravity discharge
Ditto
Peat in lumps
t"''
Sand, ashes, earth
rock
{"""'· "''· ''''"
{Coal dust
Cement, chalk,
phosphate fertilizer
Sawdust, dry clay in
lumps, coal, peat
Typical loads
*Bucket types: D, deep; S, shallow; V, V-pattern.
Ditto, highly
abrasive
Lumped, fragile, down
graded by crushing
Sluggish, powdered
and granular, moist
Medium and large
lumped (>60mm)
mildly abrasive
Granular and small
lumped ( < 60mm),
mildly abrasive
Ditto, highly abrasive
Powdered (ground)
Bulk load
characteristics
Table 8.1 Guide to the selection of bucket elevators [ 1]
1.25-1.4
0.5-0.8
1.6-1.8
0.7-0.8
0.6-0.8
0.5-0.7
0.6-0.8
0.6
0.4-0.6
0.4-0.6
D
V
D
V
V
s
s
1.25-1.8
0.6-0.8
0.6-0.8
0.8-1.0
0.7-0.85
V
0.6-0.8
1.25-1.6
0.6-0.8
0.8-1.0
1.25-1.6
1.25-2.0
D
0.7-0.8
0.85
1.25-1.8
D
D
For chain
0.6-0.8
Speed m/s
For belt
*Type
of
bucket IJb
Average
loading
efficiency
of buckets
w
0
z
z
c
r
0
>
:r
[J)
a
cr
[J)
~
l:tl
er
0'\
BUCKET ELEVATORS
(a) Spaced buckets
307
(b) Continuous buckets
(c) Section of bucket fastening
Figure 8.7
Buckets fitted to rubberized textile belt.
6 mm in thickness, moulded from nylon or polypropylene or cast from
malleable iron. The buckets are carried either on a rubberized textile belt
(Figure 8.7) very similar to those used for conventional belt conveyors, or on a
chain assembly (Figure 8.8). In the former case the buckets are normally fitted
to the belt with small-diameter bolts having large flat heads (Figure 8.7c) in
order to resist the tendency for the bolts to pull through the belt when a load is
applied to the bucket, particularly during loading. Chains, either single- or
double-strand, are less commonly used as the carrying member for elevator
buckets because of the problems of erosive wear when handling abrasive
materials and the limitation on bucket speed. Chain elevators are generally
limited to a speed of about 1.3 m/s, whereas belt elevators can often be
operated satisfactorily at speeds up to 2.5 mjs. Nevertheless, there are
applications, such as the handling of hot or corrosive products, where chainmounted buckets are the only option.
Figure 8.8
Buckets fitted to a single chain.
308
BULK SOLIDS HANDLING
8.3.2 Loading
With a conventional bucket elevator the bulk solid is either scooped up from
the boot by the buckets as they round the lower pulley, or it is fed directly into
the buckets as they begin their upward travel from the boot. In practice, bucket
filling is likely to be by a combination of these two methods.
The centrifugal discharge elevator, because of its spaced-bucket configuration, relies on the scooping action for loading the buckets and is therefore
restricted to the handling of relatively fine free-flowing bulk solids, or to
materials having such a high water content as to render them free-flowing. In
either case the resistance to the movement of the buckets through the product
in the boot of the elevator is not excessive, and operation at the somewhat
higher speeds necessary to ensure satisfactory emptying of the buckets under
centrifugal action is possible without tearing the buckets from the belt.
Extremes of size of the product being handled should generally be avoided.
Loading problems can occur with materials so fine that they become readily
aerated and, at the other end of the size spectrum, severe damage can be caused
to the elevator if large lumps (greater than about 50 mm) are encountered in
the boot.
Bulk solids that are highly abrasive or that include large lumps must be fed
directly into the buckets. This method of loading requires the buckets to be
closely spaced so that there is little opportunity for the bulk material to fall
between them. Transport of these more difficult types of product is the main
application of the continuous bucket elevator since, although it is well able to
handle the finer free-flowing materials, it tends to be somewhat less
economical to operate than the spaced-bucket machine. Loading directly into
the buckets, especially where lumpy materials are concerned, necessitates a
lower working speed to minimize the tendency for the product to bounce or
splash from the buckets.
Loading of pivoted-bucket conveyors is, in some senses, rather easier than
for fixed-bucket types since it can be carried out on a horizontal section. The
main requirement is to ensure that the bulk solid does not fall between the
buckets. This means either that the feed must be intermittent, and controlled to
shut off for a short period after each bucket becomes full, or (the method used
almost exclusively at the present time) the buckets must be very closely spaced,
preferably with an overlap to close any gap into which particles might fall.
Solids feed
~
~
~
~~-tJ~
Figure 8.9 Concertina-elfect to close up the buckets during loading of a pivoted-bucket
conveyor.
BUCKET ELEVATORS
309
Current practice is generally to have the buckets closely spaced on the carrier
chains, as illustrated in Figure 8.5, but an alternative scheme is to have a
special arrangement of track which causes a concertina effect of the chain links
as the buckets pass through the loading station (Figure 8.9).
8.3.3 Discharge
The manner in which the transported bulk solid is ejected from the buckets as
they pass over the head-wheel (i.e. centrifugal, gravity or a combination of the
two) depends upon the speed of the buckets and their spacing. A simple model
of the situation existing at the head of the elevator is illustrated in Figure 8.1 0.
As the loaded buckets travel vertically towards the head-wheel the only
force acting upon the load is the gravity force Fa· However, as the belt or
chain turns and begins to carry the bucket round the head-wheel, an
additional accelerative force FA also acts on the load. These two forces
combine to give a resultant F R• which changes in both magnitude and
direction as the bucket moves along its curved path. However, the line of
action ofF R always passes through a fixed point P, called the pole point, which
lies vertically above the centre of the head-wheel. Noting the similarity of the
force triangle and triangle OCP (Figure 8.10), the distance of the pole point P
above the head-wheel centre 0 can be written
L=rFa
FA
(8.1)
where r is the radial distance of the centre of mass C of the load in the bucket
from the head-wheel centre.
Now, if m is the mass of bulk solid in the bucket and vis the linear velocity of
force
triangle
F
A
FG
Figure 8.10 Discharge characteristics of a bucket elevator [I].
L
310
BULK SOLIDS HANDLING
the point C, the gravity and accelerative forces can be written
F 0 =mg
(8.2)
and
(8.3)
Further, writing v = 2nrN, we have
FA= 4n 2 N 2 mr
(8.4)
where N is the rotational speed of the head-wheel in revolutions per second, so
that
L-g
-
(r)2 - 4ng
~
-
2
.
1
N2
(8.5)
It is thus evident that the distance of the pole point above the head wheel
centre depends upon the rotational speed of the head-wheel (or the linear
velocity of the buckets and the radius of the head-wheel). As the rotational
speed N increases, the pole point P moves downwards and the ratio of the
accelerative (or centrifugal) force FA to the gravity force F 0 increases.
It has been suggested [1] that the discharge characteristic of a bucket
elevator can be conveniently classified according to the position of the pole
point (Figure 8.11). Thus, if the pole point lies outside the circle passing
through the outer edge of the bucket (i.e. L > r.) the centrifugal force will be
relatively small and the elevator can be classified as a gravity-discharge type.
However, if the pole point lies within the circumference of the head wheel (i.e.
L < rb) the centrifugal force predominates and the elevator is classed as
centrifugal-discharge. Where r. > L > rb the discharge will involve a combination of gravity and centrifugal effects.
In the case of centrifugal discharge, after the bulk material leaves the bucket
it tends to follow a parabolic path until deflected by impact with the casing (or
(a) Gravi1y discharge
(L > ral
Figure 8.11
(b) Cen1nfuga1 d1S"charge
CL< rbl
Classification of bucket elevators according to the location of the pole point.
BUCKET ELEVATORS
311
discharge chute) or a preceding bucket. It is important that the casing of the
elevator is correctly designed so that the material leaving the buckets is thrown
cleanly into the discharge chute, and therefore there is a need to predict the
trajectory of the discharged particles. For a detailed analysis the reader is
directed to references [2- 4], but the following, greatly simplified, approach
should provide an understanding of the problem.
Using a model in which the bulk solid leaves the bucket as one 'lump',
without first sliding and without being affected by air resistance, the point of
discharge can be identified as when the radial component of the gravity force
becomes equal to the centrifugal force, i.e. when
mv2
mgcos8= r
(8.6)
where angle8is measured from the vertical (Figure 8.12a). Thus the position of
the bucket at the point of discharge is given by
e= eL = cos - 1
G:)
(8.7)
Now, provided that the 'lump' of material leaves the bucket smoothly
without, for example, hitting the top edge of the bucket, it will follow a free
(a)
Point ot diSCharge
(b) Parabolic trajectory
Figure 8.12
Trajectory of pa rticles discharged from an elevator bucket.
312
BULK SOLIDS HANDLING
trajectory With initial velocity at angle eL (downward) tO the horizontal
(Figure 8.12b). Its position after time t is then given by
x = vtcoseL
(8.8)
Y = - Vt sin 8L- igt 2
(8.9)
Combining equations (8.8) and (8.9) to eliminate t, and then substituting for
8L from equation (8.7), leads tO an expression defining the parabolic path
taken by the 'lump' of material ejected from the bucket:
(8.1 0)
Using this equation to plot the trajectory of the particles allows the position
of the mouth of the discharge chute to be determined to ensure that material
enters cleanly without spilling down the inside of the elevator casing.
Gravity discharge tends to occur in low-speed bucket elevators, typically
running at 0.4 to 0.8 mjs and handling wet, flaky or cohesive materials. If the
elevator is inclined, the contents of each bucket can fall directly, under gravity
alone, into a suitable discharge chute, but with vertical elevators care must be
taken to ensure that the falling material is suitably directed. Continuous
discharge elevators are designed with the back of each bucket shaped to form a
short discharge chute for the contents of the following bucket. This arrangement does not work for spaced-bucket elevators and, if these are to operate at
low speed so that centrifugal effects in the discharging buckets are small, the
only satisfactory approach is to mount the buckets on twin parallel chains
which are snubbed back under the head-wheel (Figure 8.3b).
8.3.4 Capacity
Although the bucket elevator is essentially simple in concept, in order to
obtain optimum performance in terms of running costs and reliability,
attention must be paid to its design in relation to the nature of the product
being handled.
In addition to the nature of the material itself, the main parameters that
would be fixed in the design specification are the required solids throughput
and the height of the vertical lift. Additional constraints may be placed on the
design by the space actually available below the feed point and above the
delivery point.
The principal variables in the elevator design are:
(i) The bucket size and pitch
(ii) The belt (or chain) speed
(iii) The diameter of the head and tail pulleys (or sprockets).
The selection of a centrifugal discharge or continuous discharge type of
313
BUCKET ELEVATORS
Table 8.2 Preliminary selection data for centrifugal-discharge bucket elevators (belt type). From
data in [5]
·----
Size of bucket
Width Projection
(mm) (mm)
150
200
250
300
350
400
100
125
150
175
175
200
Pulley diameter Head
Capacity (for
Bucket
pulley
Belt Pb = 1600 kg/m 3 )
speed
Depth Spacing Head
Tail
speed
(mm) (mm)
(revjmin) (m/s) (kg/s)
(mm)
(mm)
(tonne/h)
105
135
155
180
180
210
300
350
400
450
450
450
500
600
600
750
750
750
350
350
400
450
450
500
43
41
41
38
38
38
1.1
1.3
1.3
1.5
1.5
1.5
3.9
8.3
14.0
23.3
27.8
41.7
13
27
47
76
90
136
Table 8.3 Preliminary selection data for continuous bucket elevators (chain type). From data in
[5]
Sprocket
diameter
Size of bucket
Width Projection Depth
(mm)
(mm) (mm)
200
250
300
350
350
400
450
135
175
175
175
200
200
200
195
295
295
295
295
295
295
Bucket
spacing
(mm)
Head
(mm)
Tail
(mm)
Capacity
Head
sprocket Chain (for Pb = 1600kg/m 3 )
speed
speed
(tonne/h)
(rev/min) (m/s) (kg/s)
200
300
300
300
300
300
300
520
635
635
730
730
730
730
350
445
445
445
445
445
445
28
23
23
20
20
20
20
0.76
0.76
0.76
0.76
0.76
0.76
0.76
9.7
16.7
19.4
22.2
27.8
31.9
36.1
32
55
63
73
91
104
118
elevator is obviously related to (i) above, and is largely governed by the nature
of the product to be handled. Guidance on the selection of elevator type has
been given previously (see Table 8.1) and preliminary design details for a given
application can then be developed from tabulated performance data such as
that given in Tables 8.2 and 8.3, derived from data in [5]. It should be noted
that the figures in these tables are for a granular material of bulk density
1600mg/m 3 (such as sand or crushed stone). For other products the capacity
at the stated belt speeds will vary in direct proportion to the bulk density, but
the optimum belt speed is a function of the product being handled. The
recommendations given here for the calculation of capacity and driving power
strictly apply only to bucket elevators operating vertically and not to inclined
elevators or pivoted-bucket types having both vertical and horizontal
sections. However, in the words of a recent European document [6], 'the
design of these can be calculated in implementing artfully the aforesaid
recommendation by extension or deduction'!
314
BULK SOLIDS HANDLING
The actual volumetric capacity (or flow rate) may be expressed as
•
V
v. = '1b Vb"J:
(8.11)
where Vb is the volume of each bucket, '1b is the bucket filling efficiency, vis the
belt velocity and A is the bucket pitch.
Mass throughput is then given by
•
V
m. = Pb v. = Pb'1b vb;:
(8.12)
where Pb is the bulk density of the material in the buckets. Note that the actual
quantity of material in each bucket is expressed as I'Jb Vb, where Vb is the
nominal capacity of the bucket when filled with a horizontal surface (water
capacity), and the filling efficiency '1b normally has a value of 0.65 to 0.75.
However, the quantity of material that gets into a bucket depends principally
upon the feeding arrangement, the shape and speed of the buckets and their
pitch on the belt or chain, and so the value of I'Jb could in fact vary over a wide
range (from around 0.4 to slightly greater than unity). Typical values of bucket
filling efficiency are to be found in Table 8.1, and volumes of buckets of various
types may be estimated from Figure 8.13. Note that the size of bucket selected
should be consistent with the maximum lump-size of the material being
handled, the bucket projection required being some four or five times the size
of the largest lump.
200.-r-.--.-.-.--.-.-.--,-,
100~+-~~--~~------~~_,
;;; 20
.>t.
0
::>
D
0
5 1--+--+-- KI
Width of bucket (mm)
Figure 8.13
Chart for the estimation of the volume of elevator buckets.
315
BUCKET ELEVATORS
8.3.5 Driving power
The conventional approach to an assessment of the power requirement of a
bucket elevator is similar to that used for belt conveyors and involves an
estimation of the various resistances to the movement of the elevator.
The main resistance is of course that resulting from the vertical lifting of the
load in the buckets.
Now the total mass of material on the upward side of the elevator can easily
be determined as the product of the mass in one bucket and the number of
buckets. Thus the gravity force opposing motion of the elevator is given by
H
F H = pbg1Jb vb T
(8.13)
where H is the difference in height between the feed and discharge points.
The next most significant resistance is likely to be that caused by the feeding
of product to the buckets. This comprises a drag force on the buckets and on
the belt or chain(s) as they pass through the material in the boot. The scooping
action occurs principally in the centrifugal-discharge type of elevator, but in all
bucket elevators there will be significant work done as the product is
accelerated from the feed point.
Rigorous mathematical analysis of the resistances associated with the filling
of the buckets is very difficult, and the approach usually adopted is to express
the losses in this region as an 'equivalent height' Hr which is then included in
equation (8.13) for the determination of the main resistance. This equivalent
height, or loading factor, is likely to be in the range 3-12 m. The actual value to
be used depends upon the nature of the product and the method of filling;
Table 8.4 gives recommended loading factors taken from [7].
The combined resistive force, F u• is thus given by
F
u=Pbg1Jb
H+Hr
(8.14)
Vb-~.~A
or
Fu=FH(l+~)
(8.15)
Minor or secondary resistances include frictional resistances and inertial
effects as the. loaded buckets swing over the head pulley. These are often
negligible but may increase the total resistance force by 10% or more. It is
Table 8.4 Values of loading factor, Hr [7].
Type of elevator
Material type
Continuous bucket
Pb < 1600 kg/m 3
Pb > 1600 kg/m 3
Spaced bucket
Free-flowing grains
Other materials
Loading factor Hr (m)
3.1
4.6
9.2
12.3
316
BULK SOLIDS HANDLING
convenient to include these secondary resistances in an 'overall drive
efficiency' 1] 0 , the value of which is typically 0.8 to 0.85.
Thus the motor power can be estimated from
Fuv
p mol = -'lo
(8.16)
It should be noted that considerable additional power may be drawn from
the motor on initial start-up.
8.4 Notation
FA
FG
FH
Fu
g
H
Hr
L
m
m.
N
pmot
r
r.
rb
t
vb
V,
V
X
y
'1b
'lo
Jc
()
()L
Pb
Accelerative (centrifugal) force on contents of bucket
Gravity force on contents of bucket
Net gravity force on upward side of elevator, equation (8.13)
Combined resistive force on elevator
Gravitational acceleration (specific gravitational) force
Height of discharge point above feed point
Equivalent height or loading factor, accounting for resistances
associated with bucket filling
Distance of pole point above centre of head wheel (Figure 8.1 0)
Mass of contents of bucket
Capacity (mass flow rate)
Rotational speed of head-wheel (revolutions per second)
Motor power
Radial distance of centre of mass of load in bucket from centre
of head-wheel (Figure 8.1 0)
Radius of circle passing through outer edge of bucket
(Figure 8.11)
Radius of head-wheel
Time
Volume of bucket
Volumetric capacity (flow rate)
Linear velocity of centre of mass of load in bucket
Horizontal coordinate of centre of mass of bucket contents after
ejection
Vertical coordinate (measured downwards) of centre of mass of
bucket contents
Bucket filling efficiency
Overall drive efficiency
Linear pitch of buckets
Angular position of bucket, measured from vertical
Angular position of bucket at instant of discharge of its contents
Bulk density
BUCKET ELEVATORS
317
References and bibliography
References
I. Spivakovsky, A. and Dyachkov, V. Conveyors and Related Equipment. Peace Publishers,
Moscow.
2. Beverly, G.J., Robcrts, A. W. and Ha yes, J. W. ( 1983) Mechanics of high speed elevator
discharge. Bulk Solids Handling 3 (4) 853-859.
3. Fort, J.C. (1973) Berechnung und Auslegung von Becherwerken (Calculations and design of
bucket conveyors). Fordern und 1/ehen 23 (8) 432-436.
4. Koster, K.H. ( 1985) Centrifugal discharge of bucket elevators. Bulk Solids Handling 5 (2) 449464.
5. Perry. R.H. and Green, D. ( 1984) Perry's Chemical Engineers' Handbook. 6th edn., McGrawHill, New York, 7.11 to 7.13.
6. Anon. Recommendation for the calculation of throughput, power requirement and tensile
forces in belts and chains of vertical bucket elevators. FEM (Federation Europeenne de la
Manutention). Section 11, Continuous Handling, Paper 2.122, January 1981.
7. Anon. Handbook fiir Conveyor and Elet•ator Belting. Apex Belting Pty. Ltd., Australia.
Recommended further reading
Spivakovsky. A. and Dyachkov, V. Conreyors and Related Equipment, Chapter VII, V-bucket,
pivoted-bucket and swing-tray conveyors, and Chapter XI, Bucket, arm- and swing-tray
elevators, Peace Publishers, Moscow.
Roberts, A.W. and Hayes, J.W. (1979) Economic Analysis in the Optimal Design of Conveyors,
Chapter 5, Bucket elevators, Tunra Ltd. University of Newcastle, Australia.
Handbook fiJr Com•eyor and Eln•ator Belting. Apex Belting Pty. Ltd., Australia.
Colijn, H. ( 1985) Mechanical Conreyors fiir Bulk Solids. Chapter VI, Elevating conveyors,
Elesevier, Amsterdam.
9
Chain and flight conveyors
9.1 Introduction
In addition to the very familiar belt conveyor and the scarcely less familiar
bucket elevator, there are a number of alternative mechanical techniques that are commonly used to carry, drag or scrape bulk solids from
one location to another. It is not particularly easy to place these various
techniques into distinct categories, and the division of this part of the book
into separate chapters and sections, while not being entirely arbitrary, should
be regarded as a matter of convenience rather than as a serious attempt at
classification of bulk handling systems. In some cases there is an almost
continuous gradation of design from one type of conveyor to another, so that
the placing of an artificial 'boundary' between the two types becomes
somewhat subjective. For example, if an apron conveyor is fitted with deep
pans and operated on a steep incline it becomes a bucket elevator, and if a
bucket elevator is fitted with shallow bottomless buckets and enclosed in
a casing it becomes an en-masse conveyor.
In Chapters 7 and 8 the conventional belt conveyors and bucket elevators
were discussed in some detail along with a number of important variants of
these systems. In this chapter other types of mechanical conveyor that rely on
continuous ropes or chains for their operation will be described. The number
of such conveyors that are, or have been (sometimes briefly!) available to
industry is quite large, and the decision has been taken to limit the scope of this
chapter to the following groups: drag conveyors, en-masse conveyors, tubular
drag conveyors, apron conveyors and aerial ropeways. It is believed that the
reader will thus be able to acquire an awareness of all the major types of
continuous mechanical conveying system although, as explained, the coverage
is not intended to be exhaustive.
The first groups that will be considered are those which drag or scrape the
bulk solid along some kind of trough or duct with the aid of a continuous rope
or chain which may or may not be fitted with 'flights'. Attention will then be
turned to the class of conveyor which has slats or pans fitted to the chains in
order to carry the bulk material, and finally a system is briefly described where
the endless rope is used to support large widely-spaced buckets carrying the
conveyed product-that is, the aerial ropeway.
9.2 Drag conveyors
A simple means of encouraging a bulk solid to move along a horizontal trough
is to draw through the trough, in the required direction of'flow', some form of
CHAIN AND FLIGHT CONVEYORS
319
endless chain. The amount of movement caused in the bulk solid will then
depend upon a number of factors, principally the effective cross-section of the
chain and the shape of the links, the speed of the chain and the nature of the
bulk solid itself. To consider the two extremes, a small-diameter chain
travelling at high speed will simply pull through the bulk solid with virtually
no transporting effect, whereas a chain fitted with large flights extending over
most of the cross-section of the trough will have the potential to move the bulk
solid at a high rate, but probably at a prohibitive power consumption.
Between these extremes exist a range of practical conveyors variously
classified as drag-, scraper-, and en-masse conveyors. The latter term applies
specifically to chain conveyors fitted with submerged flights and operating in
an enclosed trough so that the conveyed material moves as a continuous mass
filling almost the whole cross-section of the trough. En-masse conveyors are
discussed in the next section and attention is here restricted to the group of
conveyors known simply as drag- or scraper-conveyors.
There is little point in attempting to distinguish between drag conveyors,
scraper conveyors and flight conveyors as the difference is quite arbitrary,
usually being related to whether or not the chain links have identifiable flights
fitted to them. Figure 9.1 illustrates some examples of chain patterns used in
drag conveyors. The chain is normally arranged between end sprockets so that
the lower strand runs in the trough and serves as the carrying element
(a) Drag chain
(b) Single-strand scraper chains
(c) Double-strand scraper chain
Figure 9.1
Examples of chain patterns used on drag conveyors.
320
BULK SOLIDS HANDLING
Figure 9.2
Standard drag conveyor with single-strand working.
(Figure 9.2). However, it is quite possible to have two separate troughs, or one
trough divided longitudinally into upper and lower sections, so that both
strands of the chain are actively conveying material in opposite directions.
Drag conveyors tend to have fairly limited application, although they are
the generally accepted means of handling certain materials such as hot cement
clinker and ash. They are also widely used in the mining and chemical
industries for conveying a variety of bulk solids. Operating speeds are quite
low, typically around 0.1 to 0.6 m/s, and conveying capacities tend to be rather
small.
The estimation of conveying capacities of drag- and scraper-conveyors is
essentially a matter of determining the average velocity of the bulk solid along
the trough and the effective depth of the bulk solid stream, and for further
guidance the reader is directed to [ 1].
Figure 9.3
A basic en-masse conveyor.
CHAIN AND FLIGHT CONVEYORS
321
9.3 En-masse conveyors
The en-masse conveyor, sometimes called 'continuous flow conveyor', was
developed in England during the 1920s (Figure 9.3). It relies for its operation
on the frictional effects between the chain or flight and the surrounding bulk
solid, and also on 'internal friction' amongst the particles of the bulk
solid. Successful transport is dependent upon the frictional resistance between
the material and the casing being less than the internal shear strength of the
bulk material itself.
In a properly designed installation the bulk solid is induced to move along
the trough as a continuous mass at a speed close to that of the chain. There is
very little relative movement of the particles and, since the whole column or
mass of material moves slowly with the chain, the possibility of degradation of
the conveyed bulk solid is reduced to a minimum.
Initially the system was conceived for the gentle horizontal transport of bulk
material by the action of a skeletal framework, formed by the chain and flights,
moving steadily along the base of a trough. Soon the design was adapted for
vertical transport with the flights modified effectively to follow the internal
profile of the trough and so wrap around the conveyed material. Provided that
a continuous supply of bulk solid was maintained to the bottom of any vertical
section it was found that, even though the flights did not 'fill' the cross-section,
the material would still be carried steadily upwards within the closed duct. In
fact, a major feature that the en-masse conveyor has in common with the
pivoted-bucket elevator is the ability to incorporate changes of orientation
from horizontal to inclined, or even to vertical, in one unit without any transfer
points.
9.3.1 Design features
Various flight profiles are used to suit the type of material being conveyed.
Some examples of chain and flight arrangement for specific applications are
shown in Figure 9.4. Most commonly used for horizontal conveying is the flat
flight (Figure 9.4a), which may have the front face chamfered to counteract any
tendency for the flight to climb out of the material. Suspended flights
(Figure 9.4e) are also used on horizontal circuits. The skeleton flights shown in
Figures 9.4b, c and d are normally used on elevator applications. Various
other flight patterns, such as the solid peaked flight (Figure 9.4f), have been
produced for special purposes. The usual arrangement of flights is one at each
link of the supporting chain. However, improved discharge characteristics
with materials which tend to bridge (such as wood chips) may be obtained by
fitting flights to alternate links. Other variations to the standard flight
arrangement include neoprene wipers to improve 'clean-out', and oversize
'scavenger' flights, having ground edges fitted at five- to ten-link intervals for
better handling of sticky materials.
322
BULK SOLIDS HANDLIN G
(a) Flat flights
l~~Skel.eton flight~ for
(du vertiCal conveying
(e) Suspended flights
(f) Solid peaked flights
Figure 9.4 Variations on the pattern of flights for en-masse conveyors.
CHAIN AND FLIGHT CONVEYORS
Figure 9.5
323
Box-section casings for en-masse conveyors.
In addition to the shape of the flights, important design considerations are
the material from which the flights are made, and the type and size of the chain
to which they are fitted.
The trough or casing in which the chain and flights run is basically a simple
box section fabricated from mild steel (Figure 9.5). An installation would
usually be made up from a number of, say, 3 m long sections, which may
incorporate features such as feed and discharge points, inspection ports,
bursting panels (when handling potentially explosive products), etc. Curved
sections (horizontal to horizontal, or horizontal to vertical) can also be built
into an installation to give considerable flexibility in the route taken. Inclined
sections are also possible. There are, of course, precautions to be taken in
certain situations; for example, when handling very abrasive or hot
products and conveying over long distances where trough alignment becomes
critical. High wear regions need to be identified, and it may be necessary to fit
wear-resistant lining plates to the sides and (especially) the base of the trough
on horizontal runs, also around the inside curve of horizontal bends.
Transporting products at high temperature over long distances can cause
difficulties as a result of expansion of the casing and the chain. Allowing a
controlled sag on the chain and mounting the casing on rollers should
overcome this problem.
9.3.2 Performance calculations
The volumetric throughput of an en-masse conveyor is principally a function
of the cross-sectional area Ab of the bed of conveyed product, the velocity of
the chain v and a 'velocity factor' rv which is defined as the ratio of the average
velocity of the product to that of the chain.
324
BULK SOLIDS HANDLING
0.1
Figure 9.6
0.3
0.2
conveyor chain velocity (m/s)
0.4
0.5
Typical capacities of horizontal en-masse conveyors.
Thus
(9.1)
and the mass throughput is given by
(9.2)
For horizontal conveyors r. can generally be taken as unity, but on vertical
and inclined sections its value is likely to be around 0.6 to 0.85, depending
upon the nature of the material and the way that the section is fed.
The optimum velocity of the chain and flights is very much dependent upon
the nature of the conveyed product. For free-flowing particulate and granular
materials, velocities in excess of 0.5 m/s are usually possible, whereas abrasive
materials and products which tend to become aerated (such as cement) should
not be conveyed at more than about 0.25 m/s. For fibrous and flaky products
the optimum velocity is likely to be around 0.4 m/s. Attempting to operate at
too great a speed results in excessive abrasion, degradation ofthe product and
reduced efficiency as the flights pull through the product, leaving the top layer
stationary or moving at reduced speed.
The capacity chart (Figure 9.6, from [2]) gives an indication of the
volumetric throughputs that could be obtained in a typical range of widths of
en-masse conveyors operating horizontally. For vertical operation the
capacity values are likely to be reduced by anything from 10% for coarse
granular materials, to 35% for fine granular materials, to 50% for free-flowing
powders.
Estimation of the power requirement is not easy, as so much depends upon
the nature of the product being conveyed and the configuration of the
325
CHAIN AND FLIGHT CONVEYORS
Figure 9.7
Basic en-massc conveyor. Controlled or flood feed, with multiple inlets and outlets.
(a) Basic vertical elevator with
controlled or flood feed
.
~~~~~~~~~,,~,,,~
--...:~J
(b) Combined vertical and horizontal conveying
with controlled or flood feed and multiple
inlets/outlets
Figure 9.8
Vertical cn-massc conveying.
conveyor installation. In the absence of previous experience of the particular
product it is almost essential to undertake pilot tests in order to determine the
power requirement with a reasonable degree of confidence.
9.3.3 Applications of en-rnasse conveying
The most common application of these conveyors is for the movement of
product from one location to another on approximately the same horizontal
plane {Figure 9. 7). Distances may range from a few metres to more than I 00 m,
and conveying rates from I tonnc/h to 1000 tonne/h.
326
BULK SOLIDS HANDLING
(a) Chain type
(b) Rope type
Figure 9.9
The tubular drag conveyor.
Figure 9.10 Tubular drag conveyor installation showing a typical arrangement of feed and
discharge points.
Combinations of horizontal and vertical runs are also common and the enmasse principle works well in integrated conveyor/elevator installations of 'L'
or 'Z' arrangement (Figure 9.8a, b).
The versatility of the en-masse conveyor makes it suitable also for combined
processing/transport applications such as cooling, heating or drying of the
conveyed product. Movement of a blended mixture of products without
segregation can be readily achieved in an en-masse conveyor. Sources such as
327
CHAIN AND FLIGHT CONVEYORS
[2] and manufacturers' literature give more details on many examples of
successful and unusual application of this method of conveying.
9.4 Tubular drag conveyors
Very similar in principle to the continuous-flow flight conveyor is the tubular
drag conveyor which has, in its commonest form, a series of discs mounted on
an endless chain or steel cable and drawn through tubes of circular crosssection (Figure 9.9).
Normally the system is totally enclosed, and the chain-type is able to
smoothly negotiate bends of any orientation so that quite complicated
installations can be constructed involving both horizontal and vertical
transport, and multiple feed and discharge points (Figure 9.10). Drive is
2000
1000
'2 500
.E
.....
(/)
.~
:::
"(3
0
C1l
c.
C1l
0
100
50
~
~
~
--·
--
-r-------
------·----
~
-----
250 ~
v....- 200 ~
E
-~1 50 .!!!
- -- - ":?': ~
100 ~
-----~_....... V
......
_..--V
f= --f:::c:--'~ -79 ~r;
-/
~/
10 _.,... "'"V./'
V
,..v
r---
. . . ~z ,......::_-
/
2
0.3 0.5
V
V
V
75
.c
.3
_..--V:....---
/
/
'---
2
--f
5
10
20
30
chain speed Cmetres/minl
Figure 9.11
Typical capacities of chain-type tubular drag conveyors.
solids feed
Figure 9.12
Rope-driven tubular conveyor ('aero-mechanical' conveyor).
328
BULK SOLIDS HANDLING
through a sprocket placed at a convenient location (Figure 9.10a) These chaintype conveyors are available in sizes ranging from 50 mm to about 250 mm in
diameter, and a typical circuit might include three or four changes in direction
and cover a total distance of some 30 to 40 m. Discharge points can be fitted
with gates made by hinging a section from the lower half of the conveying tube
and, when handling cohesive materials, small vibrator units can be mounted
close to these gates to ensure satisfactory emptying of the conveyor. From
Figure 9.11 the approximate capacity of chain-type tubular drag conveyors
can be determined.
The rope-type tubular conveyor, sometimes described as an 'aeromechanical' conveyor, is similar to the system described above but has the
endless steel rope running in a simple loop through two straight parallel tubes
between end sprockets (Figure 9.12). Combinations of these units can be
constructed to provide horizontal, vertical or inclined sections, and again
multiple feed and discharge points can be quite easily incorporated in such an
installation. Available tube sizes are 50-100 mm diameter, offering capacities
of up to about 40 tonnes/h with free-flowing granular materials. Conveying
distances in a single unit of up to 50 m are possible.
9.5 Apron conveyors
Apron conveyors consist of a close-fitting series of metal pans supported
between two strands of roller chain. The pans are designed to interlock or
/
/
Figure 9.13 An apron conveyor ('leak proof type).
/
/
CHAIN AND FLIGHT CONVEYORS
329
overlap and thus form a continuous moving surface on which bulk solids can
be carried (Figure 9.13). In this respect alone apron conveyors are similar to
belt conveyors, but they have the advantage of being able to handle heavy,
large-lumped, abrasive and hot materials. Very high capacities-greater than
2000 tonnes/h-are possible, and running costs relatively low. However,
because of the nature of their construction, apron conveyors are very heavy
and very expensive in terms of investment cost.
Various types of pan are available to suit different applications, but all are
designed to fit together, either interlocking or overlapping, to minimize the
risk of solid particles falling through the conveyor or becoming lodged in the
gaps.
For conveyors operating horizontally or on a slight incline (up to about 20°)
there are advantages in using pans that are almost flat (Figure 9.14a), but for
operation on steeper slopes apron conveyors should be fitted with deeper pans
(Figure 9.l4b, c). These deeper pans are also better when handling bulk solids
containing large lumps.
Apron conveyors are normally available in widths from 200 mm to 2 m,
and fitted with side flanges of up to 300 mm in height. Operating speeds are
quite low, being generally less than 0.2 m/s and rarely exceeding 0.5 m/s.
Calculation of the carrying capacity of an apron conveyor is very similar to
that for belt conveyors and is thus largely a matter of estimating the crosssectional area of the load stream, which can be represented by one of the
shapes shown in Figure 9.15.
Thus, for a flat pan,
(9.3)
and for a flanged pan
(9.4)
(b) Flanged pan
(a) 'Flat' pan
(c, d) Deep pans
Figure 9.14
Some different shapes of apron conveyor pan.
330
BULK SOLIDS HANDLING
(a) Flat pan
Figure 9.15
(b) Flanged pan
Cross-sections of the load stream on an apron conveyor.
where k. is a 'slope factor' to correct the cross-sectional area when the
conveyor is working on an incline.
Now the surcharge angle b (that is, the angle that the sloping surface of the
moving load-stream makes with the horizontal) can conveniently be approximated as
b = 0.48
(9.5)
where () is the static angle of repose of the material. This is somewhat higher
than the surcharge angle of the same material on a conventional belt conveyor,
principally because of the much lower speeds involved and the consequently
'smoother' ride.
The height h 1 of the triangular cross-section of the load stream can now be
written in terms of the surcharge angle b as
h 1 =thtanb
(9.6)
The transport rate can then be expressed as
m. = pbvk.±b2 tan b
(9.7)
for a conveyor with flat pans, and as
m.= pbvth(tk.b + 1) tan b
(9.8)
for flanged pan conveyors, where Pb is the bulk density of the conveyed
material and vis the velocity of the carrying pans. Values of the slope factor k.
can be determined from Figure 9.16.
For deep pan conveyors the transport rate must be determined by
estimating the carrying capacity of each pan and multiplying this figure by the
apron speed v and by the linear pitch A. of the pans.
Thus
(9.9)
where Vb is the volumetric capacity of each pan, taking account of any
surcharge of material.
Calculation of the power requirement involves estimation of the various
frictional losses in the chains, rollers, guideways, etc. and from these estimating
the tension in the chains. For further guidance the reader should see [1].
331
CHAIN AND FLIGHT CONVEYORS
1.0
"""":::: 1::::--
"'
!'----
-"'
-- r-
.........___
..........,
0
ti 0.9
~
Cl>
0.
----
.._
............
- r--
.........
--
............
0
(jj
0.8
0
Figure 9.16
10
angle of inclination
20
Slope factor k, for apron conveyors.
9.6 Aerial ropeways
The aerial ropeway or cableway, comprising essentially a succession of largecapacity buckets suspended at intervals from an overhead cable, is very similar
to the familiar personnel-carrying cable-car system. One of the oldest forms of
long-distance bulk solids transport, the aerial ropeway has, during the last
hundred years or so since the development of the steel cable, become capable
of achieving very high tonnage rates with good reliability and efficiency over
difficult terrains (Figure 9.17). It has thus earned its place amongst belt
conveyors, hydraulic pipelines and road or rail systems as a means of carrying
bulk materials overland. Although, like the belt conveyor, an aerial ropeway
system would involve a high capital cost, the running costs would be small
compared with transport by road or rail vehicles.
Probably the major disadvantage of the aerial ropeway is its visual impact
on the environment, but to offset this is the fact that, because the system is high
above the ground, it causes minimal interference to wild life and does not
involve the splitting up of properties or the acquisition of extensive rights-ofway. Furthermore, it can be contructed over very difficult terrain, taking the
most direct route, with relatively little disturbance, and manufacturers today
are prepared to go to considerable lengths to minimize the effect of such
systems on the landscape [ 4].
There are two fundamental types of aerial ropeway; bicable and monocable.
In the bicable system (Figure 9.18a) the weight of the buckets is carried on the
main cable suspended between the supporting towers whilst the drive is taken
Figure 9.17 Longitudinal profile of a typical aerial ropeway designed to transport ore at a rate of
145 tonnes/hour over a distance of 15 km [3].
332
BULK SOLIDS HANDLING
Figure 9.18 Bicable and monocable ropeway systems. (Top) Bicable ropeway carrying iron ore at
a rate of 250 tonnes/h over a distance of 10 km. (Bottom) A monocable system. (Courtesy of
BRECO)
CHAIN AND FLIGHT CONVEYORS
333
by a secondary cable linking the wheeled carriages from which the buckets are
hung. The monocable system, however, has a single cable which serves as both
the carrying and the hauling element (Figure 9.186).
On modern aerial ropeways, in order to achieve the required high capacities,
bucket speeds of up to about 5 m/s are becoming common and, as a
consequence, special handling techniques are needed at the filling and
emptying stations. This usually involves disconnecting the buckets from the
rope driving system, for example by automatically lifting the buckets from the
main carrying cable on to rails where they are retarded and passed at a
controlled rate past the loading or unloading point. One method of reattaching the buckets to the transport cable is to release them on to a
downward sloping rail which causes them to accelerate to the speed of the
cable so that coupling can take place without damage.
The dimensions and carrying capacity of aerial ropeways are dependent
upon many factors, not least the nature of the territory that the system has to
cross. Typical conveying distances would be up to about 20 km with spans
between towers of around 500 m or more. Transport rates of up to 500
tonnes/h are usual, although a rate of 2500 tonnes/h has been reported [3].
Bucket capacities are typically around 2 tonnes, with buckets spaced at
intervals of 50-100 m and travelling at up to 5 m/s.
9.7 Notation
Ab
b
hl
hz
k_.
m.
rv
v.
V
(J
e
;_
Pb
Cross-sectional area of bulk solid bed
Contact width of bulk solid on conveyor
Height of triangular part of load-stream cross-section
Height of rectangular part of load-stream cross-section
Slope factor (Figure 9.16)
Capacity (mass flow rate)
Ratio of average velocity of bulk solid to the velocity of the
chain
Volumetric flow rate of bulk solid
Velocity of chain
Surcharge angle
Static angle of repose of bulk solid
Linear pitch of apron conveyor pans
Bulk density
References and bibliography
References
1. Spivakovsky, A. and Dyachkov, V. Conveyors and Related Equipment. Peace Publishers,
Moscow.
2. King, B.C. The application and design of en-masse conveyors. Proc. Solidex 80 Conf,
Harrogate, UK, March/ April 1980, Paper A3.
334
BULK SOLIDS HANDLING
3. Spyer, V. ( 1984) Aerial cableways as a transport mode in Brazil with special reference to
Minera<;ao Morro Yelho. Bulk Solids Handling 4 (2) 413-415.
4. Bullivant, D. (1983) Modern aerial ropeways and the environment. Bulk Solids Handling 3 (I)
185-187.
Recommended further reading
King, B. C. The application and design of en-masse conveyors. Proc. Solidex 80 Con[., Harrogate,
UK, March/ April 1980, Paper A3.
Colijn, H. (1985) Mechanical Conveyors for Bulk Solids. Chapter 4, Chain conveyors, E1sevier,
Amsterdam.
Spivakovsky, A. and Dyachkov, V. Conveyors and Related Equipment. Chapter VI, Flight
conveyors; Chapter V, Apron conveyors, Peace Publishers, Moscow.
10
Screw conveying
10.1 Introduction
The modern screw conveyor is essentially a development of the well-known
Archimedean screw which was conceived some 2000 years ago as a means of
raising water for irrigation. Applications of this device were naturally very
limited until relatively recent times, and its evolution has consequently been
slow. A fundamental feature of the original pattern of Archimedean screw
which distinguishes it from other types of screw conveyor is that the helical
screw (or 'flight') is attached to the inner surface of the cylindrical casing and
rotates with it (Figure 10.1 ). It will be noted from the diagram that the
Archimedean screw operates effectively as a positive displacement elevator,
the angle at which it will work successfully depending upon the diameter of the
casing and the pitch of the screw.
In the late 18th century the need for efficient mechanical handling of grain to
feed the expanding world population provided the impetus for the improvement of screw conveyors for the transport of grain and other dry bulk
materials. For such materials it was found that there was no need for a perfect
seal between the helical flight and the casing. Consequently an easier
construction was adopted, comprising essentially a central shaft to which was
fitted the flight, the whole assembly rotating within a fixed casing (Figure 10.2).
In the earliest recorded examples of screw conveyors the flights consisted
simply of a series of wooden ploughs set in a helical arrangement around a
wooden shaft. Later versions used steel flights cut from flat sheet as circular
rings, split on one side and with the two edges then pulled apart to form one
helical section of the screw. Any number of these sections could be riveted
together to make a continuous helix of the required length which would then
be fitted to a steel or iron core. Around 1900 the smooth 'helicoid' flight was
introduced, formed by rolling a continuous strip of steel into a helix.
The design of the screw conveyor was thus basically simple and could be
produced, at least in a crude form, at relatively low cost. As a result its use
became widespread, at first in agriculture and then throughout the developing
industrial world, for handling a great variety of bulk solids.
The advantages and disadvantages of screw conveyors can be conveniently
summarized as follows [I]:
Advantages
(i) Low investment cost compared to other conveying devices of comparable
capacity
336
BULK SOLIDS HANDLING
screw flight auached
IO casing so lhal bolh
rorare together
Figure 10.1
The Archimedean screw.
Figure 10.2 Standard pallern of industrial screw conveyor with helical screw rotating inside a
fixed casing.
(ii) Compact design, comparatively easy to seal against water or dust passing
in or out; the solids being handled can be blanketed with a dry or inert gas
where necessary
(iii) Fairly simple fabricating with unsophisticated equipment; a high degree
of part standardization exists within the industry
(iv) Generally lower maintenance than with most types of mechanical
conveyor; there are less moving parts to wear or get out of order
(v) Ability to handle a wide range of solids.
Disadvantages
(i) Lumpy, fibrous or sticky materials may cause problems
(ii) Lengths are limited by the allowable torque capability of the drive and
coupling shafts
(iii) Power requirements can be high with solids that tend to pack
(iv) Conveying efficiency is considerably reduced when screws are inclined or
mounted vertically.
337
SCREW CONVEYING
It is fairly evident that the screw conveyor has evolved into two basic types:
(i) The high-speed enclosed screw or 'auger' conveyor, originally developed
for grain handling and now extensively used for elevating products that are
light and free-flowing
(ii) The low-speed industrial-type screw conveyor ('U-trough' conveyor),
generally larger and of heavier construction and ideally suited to the
movement of more dense or cohesive products over short distances
horizontally or on a slight incline.
A very common application of the helical screw device for moving bulk
solids is as a feeder to assist and/or control the flow of material from storage
hoppers. The screw feeder has already been introduced in this context, and
some of its special features described, in Chapter 4.
A brief explanation will be given here of the principles of operation of screw
conveyors and then the general construction of the two types will be described
and their application discussed. Procedures will also be outlined for the design
or selection of screw conveyors for particular duties.
10.2 Principle of operation of screw conveyors
In order to appreciate the significant design features of screw conveyors it is
necessary to understand clearly their principle of operation. If the intake end of
the conveyor is fed with a continuous supply of particulate material it will be
evident that rotation of the screw must tend to lift the material by a 'wedge'
action. This action can be conveniently illustrated if the helical flight is
imagined to be 'straightened out' so that it advances horizontally into a heap
of the bulk solid (Figure 10.3). If the surface of the wedge is very smooth and
the bulk solid itself is free-flowing it could be expected that the particles would
be lifted with relatively little horizontal movement. Any tendency for the
particles to move horizontally in the direction of the wedge might be reduced
by allowing the wedge to slide against a roughened vertical plate as shown,
the frictional resistance between the particles and the vertical plate being
significantly greater than that between the particles and the advancing wedge.
This illustration not only explains the wedge action of the screw conveyor but
particles lifted
vertically by
action of wedge
/
Figure 10.3
Wedge action to lift bulk solid.
338
BULK SOLIDS HANDLING
also serves to demonstrate an important function of the cylindrical casing in
resisting the rotation of the particulate material in the conveyor.
Clearly the most effective performance of the screw conveyor would occur if
the only component of velocity were axial (i.e. no rotation), whilst the other
extreme could be regarded as the case where the bulk material adheres to the
screw and rotates as a solid cylindrical plug with no axial movement at all.
This explains why an Archimedean screw, in which there is nothing to prevent
the rotational movement of the particulate material, will only lift free-flowing
products successfully at angles of up to about 20°; above this there is no
discharge.
In a practical screw conveyor the performance would be somewhere
between the two extreme modes of action described above, being a combination of shearing and tumbling of the product as it advances along the screw.
Predicting the actual rate of transport for a given bulk solid, and the power
required to rotate the screw, are the main problems that an engineer has to face
when designing or selecting such a conveyor.
If there were no rotational motion of the particulate material in the
conveyor the rate of advance of this material would be directly proportional to
the pitch of the screw. However, some rotational motion will occur, the
amount depending upon the helix angle of the screw, and therefore upon the
pitch. Normal manufacturing practice is to adopt a screw having a pitch equal
to its outside diameter as this seems to provide a satisfactory compromise
between the required axial motion and the undesirable rotation of the
conveyed product. Nevertheless, different designs of screw are often used for
special conveying duties, as described elsewhere in this chapter.
10.3 The enclosed screw or 'auger' conveyor
10.3.1 Constructional features
The original form of enclosed screw, as developed for grain handling, is still
very popular, especially where a lightweight or portable conveyor is required
which is capable of operating at a steep upward incline, or even vertically.
Auger conveyors are generally designed to run at relatively high speed (from
200 rev/min up to as much as 2000 rev/min) and to handle materials which
have free-flowing, non-abrasive characteristics. They can work successfully at
any angle from horizontal to vertical, picking the material up at the lower end
and discharging it through a chute at the opposite end of the casing.
Figure 10.4 illustrates the features of a typical auger-conveyor [2]. The
screw is mounted in bearings at each end, the lower one generally being
'outboard' on a suitable framework to give a clear entry of material. The
driving motor is, of course, situated at the upper (discharge) end of the auger.
SCREW CONVEYING
339
radial
, clearance
minimum immersion
-:J;'~~.~~~~~~ ~--- level
.... - .
~
Figure 10.4 Constructional features of an auger conveyor [2].
Dimensions for portable and mobile screw conveyors (augers) of the tubular
type constructed of mild steel for agricultural and light industrial use are
specified in BS 4409 [3].
In recent years a number of variants of the auger conveyor have become
available. Generally these have involved differences in the form of the screw
itself; for example, several manufacturers offer this type of conveyor with an
'open pitch' screw. However, perhaps the most interesting development has
been the flexible screw conveyor in which an open pitch spiral spring, rotating
within a flexible nylon tube of around 40-80 mm diameter, forms the basis of
an economical and versatile unit capable of competing with pneumatic
conveyors on a wide variety of light-duty, short-distance applications
(Figure 10.5).
340
BULK SOLIDS HANDLING
Figure 10.5
Shaftless flexible auger conveyor.
10.3.2 Prediction of the performance of an auger conveyor
The theoretical maximum throughput of an auger conveyor would be
obtained if the conveyor were running full with the particulate material
moving purely in the axial direction. An expression for this maximum output
could then be written in terms of the dimensions of the screw and casing, and
the rotational speed as
(1 0.1)
where De and D,h are respectively the internal diameter of the casing and the
diameter of the shaft on which the flights are fitted, A. is the pitch of the screw, t,
is the thickness of the screw flight and N is the speed of rotation.
In practice the capacity of the conveyor is likely to be well below this
theoretical maximum. The shortfall is greatest for augers operating at high
speeds and steep angles with short choke lengths [ 4]. In absolute terms,
however, the volumetric throughput of the auger tends to increase with
increasing speed up to around 2000 rev /min for small-diameter machines
(approximately 40 mm): at higher speeds there is little change in the
throughput. For augers of larger diameter the maximum capacity is likely to
be reached at lower speeds.
Variation in throughput with angle of elevation is mainly attributable to the
increased tendency for the conveyed product to rotate with the screw as the
inclination of the conveyor becomes steeper. For a given auger speed the
341
SCREW CONVEYING
500
1-
200
150
-;:,.
100
......
.&:
1
8
~
20
15
"'
10
~l5.
5
Cll
:::1
~
~ -~
fbb
0
50
~
~
1-
2
1.5
lj
!?'11/ 'I
.,Q~
>?ifs;;, 1
~ ~V
~
~
Wl
v;
V
~'
uger speed _
~(rev/min)
~~8
80~
VJ """"
~
~1~~
/V
fl
51~
wIJ1/ /
~ ~ ~ 1 10,
~
'\.
_\,
'\.
.:J 5o.
.\.
..\.
J.
.\
70
100
c:
Al
~
\.
\.
. \.--..4L.....).
~\d·\
50
-
.\
.\
,_\
.:\.
.\ .
.\
150 200
auger diameters for various
angles of elevation (ITYTl)
90
75
60
45
30
\ ~5
3
~
-~ ......
>.,
"* i1'1.
o!
G>~
t
"'
Figure 10.6 Predicted capacity of different size augers at various rotational speeds and angles of
elevation [2). This chart relates to augers having the following proportions:- pitch=
screw diameter; choke length = twice pitch; shaft diameter= one third screw diameter; screw
clearance = 0.0833 x screw diameter; average particle size= 0.05 x screw diameter.
volumetric flow rate of product may fall by 50% as the conveying slope
increases from horizontal to vertical.
The 'choke length' (Figure 10.4) also has a significant influence on the
performance of an auger conveyor. A minimum choke length equal to one
screw pitch is essential even at low speeds, but a choke length of up to three
screw pitches may be required at high speeds.
Roberts and Hayes [2] have published charts for the prediction of
volumetric capacity and power absorbed for auger conveyors having screw
diameters in the range 40-300mm. These charts, reproduced in SI units as
Figures 10.6 and 10.7, are based on a set of empirical equations relating to the
transport of a free-flowing granular material similar to grain, and illustrate the
influence of the speed of the auger and its inclination to the horizontal.
M
342
BULK SOLIDS HANDLING
1000
500
300
200
100
50
10
c
5
.Q
o;~
>"'
~$
a> ...
_o
oa>
"0
Q)....,
c.
c
auger diameters for various angles
of elevation (mm)
"'
Figure 10.7 Predicted power per metre length of different size augers at various rotational
speeds and angles of elevation [2). This chart relates to the conveying of wheat (bulk density
768 kg/m 3 ) in augers of the proportions given in Figure 10.6.
10.4 The industrial screw conveyor or 'U-trough' conveyor
10.4.1 Constructional features
The widely used industrial screw conveyor consists essentially of a substantial
helical screw which rotates in a horizontal U-shaped trough in order to move a
bulk solid continuously from one end of the trough to the other (Figures 10.2
and 10.8). For the 'standard' construction of screw, helical flighting is welded
to sections of steel pipe which can then be coupled together to make up a
conveyor ofthe required overall length. Bearings for the screw would normally
be located at the ends of the trough, often outboard, and for long conveyors
one or more hanger bearings would be provided to prevent undue deflection of
the screw under load (Figure 10.9). Also illustrated in Figure 10.9 is the way
SCREW CONVEYING
343
Figure 10.8 A ribbon-type screw conveyor, showing a typical arrangement of the screw in the
trough.
Figure 10.9 Diagram to show a typical arrangement of bearings for a screw/shaft assembly. Leftand right-hand screws are used in this example to provide two feeds to a single discharge point.
that screws of opposite 'handedness' can be used to feed material from two
directions to a single discharge point. Needless to say, when designing a screw
conveyor installation it is essential to ensure that the correct direction of
rotation is specified.
The 'regular' pattern of flighting has a pitch approximately equal to the
diameter of the screw and is generally made by one of two methods:
(i) A set of identical rings is made from sheet metal and each is cut radially and
formed into a single helix. These are then assembled on the shaft and
welded to form a continuous helix, the thickness of which will be constant
from the inner edge to the outer.
(ii) A continuous metal strip is rolled into a helix by reducing the thickness of
one edge of the strip to approximately half that of the other edge. The
resulting helicoid flight is then welded on to the shaft to give a screw in
which the flight thickness tapers from its inner to its outer edge.
A wide range of'special' types of screw is available from manufacturers to be
used in applications for which the regular pattern of screw is, for some reason,
not the most appropriate. Some examples of these are illustrated in
Figure 10.1 0.
344
BULK SOLIDS HANDLING
(a) Regular helicoid !lighting
(d) Ribbon !lighting. Used for conveying
substances that are sticky , gummy'
or viscous
(b) Cut screw !lighting. Used for
conveying, cooling and moderately
mixing materials, simultaneously
(e) Regular screw !lighting with mixing paddles.
Used to mix materials where the conveyor
length provides time for proper mixing
(c) Cut and folded screw flight. Continual
lifting and tumbling of the material
by the folded flights improves
aeration and promotes mixing
(f) Double flight conveyor screw. Used to
promote a smooth and gentle flow of
material
Figure 10.10 Some examples of different patterns of screw conveyor flighting for special
applications.
A few of the major aspects of the design or selection of industrial screw
conveyors are discussed in the following pages, but for a more detailed
description and specification of their constructional features the reader is
directed to [ 4]-[6].
10.4.2 The conveyed product
As with other forms of conveyor, it is essential to have a thorough knowledge
of the nature of the bulk solid to be handled before a attempting to design or
select a machine for the application concerned. For example, because of the
mode of action of the screw conveyor, the product being conveyed tends to
become aerated with a resulting decrease in bulk density. The design or
selection of the conveyor in terms of mass throughput of product must
therefore be based upon the aerated bulk density rather than the packed value
if the device is not to be seriously under-sized.
In general, the kind of product that is best suited to transport in a screw
conveyor is one that will shear and 'tumble' easily, since this is the mode of
action upon which the device relies. Experience suggests that the more freeflowing a product is, the less power will be required to transport it in a screw
conveyor. However, care must be taken when assessing the 'flowability' of a
product to relate it to the 'as-conveyed' condition and not to some other static
condition.
345
SCREW CONVEYING
cover
..,-------'1~;. trough
or
casing
screw
screw
diameter
(conveyor
shaft or pipe
diameter
d]t~J
radial
clearance
screy/t
clearance
Figure 10.11
Screw conveyor terminology.
Materials that are very sticky, and especially those consisting of 'particles'
that are long and stringy, are mostly unsuitable for screw conveying since they
tend to clog the screw, either rotating with it as one mass or becoming jammed
between the screw and the casing. At best, such products may require screws of
special heavy construction.
For more detailed guidance on the influence of product characteristics on
the design or selection of screw conveyors see, for example, [ 4].
10.4.3 Conveyor selection
The two essential parameters to be established in the design or selection of a
screw conveyor for a given application are the screw size, and its rotational
speed.
Note, however, that the choice of a suitable screw size (Figure 10.11)
involves consideration ofthe overall diameter of the screw, the diameter of the
shaft, the radial clearance between the shaft and the containing trough
(typically 12-15 mm) and the type and pitch of the helical flight.
The first :1nd overriding consideration in the determination of a suitable
screw diameter is the amount and size oflumps (greater than 15 mm across the
largest dimension) present in the product to be conveyed. The presence oflarge
hard lumps may necessitate the use of a screw of significantly greater diameter
than would be indicated by the mass throughput required. As a guide, the
radial clearance between the shaft and the casing should be 1.75 to 3 times the
size of the largest lump in the conveyed product, and up to 4.5 times this
dimension if the proportion of lumps is very high (greater than about 90%).
Figure 10.12 allows the selection of screw conveyor size for products of various
lump sizes. It should be noted, however, that the nature of the lumps may be
relevant; so that, for example, if the lumps are soft and readily degradable they
should impose no limitation on the size of the screw.
An expression for the capacity (i.e. volume or mass throughput) of a screw
conveyor can be derived using the simple model illustrated in Figure 10.13.
346
BULK SOLIDS HANDLING
maximum lump size (mm)
Figure 10.12 Screw conveyor maximum lump size. Drawn from recommended data in [ 4]. Note:
(i) The 'percentage lumps' in a mixture of fines and lumps is defined as the proportion of lumps
ranging from the maximum size to one-half of the maximum. (ii) The recommended dimensions
are approximate and may be further influenced by the choice of shaft size.
A ~ k x nominal area
of trough
b
Figure 10.13
Capacity of a screw conveyor.
As the screw rotates within the trough the conveyed material is 'picked up'
against the side of the trough and then tumbles back, only to be picked up
again, and so on. This action, although in fact intermittent, results in an
effectively continuous movement of the material along the trough at
approximately the same speed as the advancing screw. Thus the distance that
the conveyed material moves forward during one revolution of the screw is
approximately equal to the pitch of the screw, and the average velocity V of
this material can be written
(1 0.2)
where A. is the pitch of the screw and N is the rotational speed in rev /s.
The volumetric throughput of the screw conveyor is then given by
(10.3)
347
SCREW CONVEYING
0.50
\;(;_. k ~ 0.45
Screws without hangers:
materials which flow easily,
slightly abrasive (e.g. flour.
cereals)
~- k m0.30
0.30 k::=---+---~---1-=--..:::---l AVerage
materials.
moderately abrasive, graded
---J~-=---.:--i from grains to smalllurrc;>s
0.20
(e.g. salts. sand. coal)
0.40
~
0
0
~
0
c
'6
"'
..Q
'
0.10
0
Heavy btik
k · O.lS
1-----t-- --+- --=P=--.= materials, very abrasive,
aggressive (e.g. ash. gravel,
minerals)
5
10
15
trough Inclination
(degrees to horizontal - upward)
20
Figure 10.14 Typical loading factors for screw conveyors having pitch }., where 0.6D" <
}. < l.OD". Note: these loading factors should be reduced for conveyors having screws of large
pitch or having small-diameter screws supported on cumbersome intermediate bearings [7, 8].
and the mass flow rate by
(10.4)
where Ab is the cross-sectional area of the moving bed of particulate material
and Pb is its bulk density as conveyed.
It is usual practice to express the area Ab in terms of the trough diameter,
shaft diameter, and a 'loading factor' (or 'trough filling factor') k which should
generally be between 0.15 and 0.45 (Figure 10.14).
Thus, we have
(10.5)
The degree ofloading depends largely upon the nature of the material to be
conveyed. Bulk solids that are fine, free-flowing and non-abrasive can be
handled in a screw conveyor at loading factors of up to about 0.45. If the
material tends to be cohesive, the loading factor should be restricted to about
0.3, and if it is also moderately abrasive, the speed of rotation of the screw
should be reduced. For very abrasive materials the loading factor should be
further restricted, perhaps to about 0.15.
An important consideration when using equation (10.5) for the design or
selection of a screw conveyor is the maximum rotational speed at which the
device can safely be run. Maximum operating speeds are principally a function
of the diameter of the conveyor screw, but are also dependent upon the loading
factor and the nature of the material being handled. The manufacturer would
normally specify the limits on operating speed but, as a guide, recommended
speeds taken from [4] are shown graphically in Figure 10.15.
348
BULK SOLIDS HANDLING
1
.~ 100 f -- -
;;;
§
E 50
~
·~
diamerer of screw (ITYT1)
Figure 10.15 Maximum recommended operating speeds for screw conveyors at different trough
loadings, from [4].
4
t)
l5
0 3
.l!1
·I
u
2
:c
~
conveyor loading factor, k
Figure 10.16 Capacity factors for screw conveyors with special types of flight. (For standard
flight CFr = 1).
It should be understood that equation (10.5) can only give an approximate
indication of the capacity of a screw conveyor because of the uncertainty in the
value of the loading factor k. Within this factor, corrections for the thickness of
the flight and for movement of material in the clearance space should be
included and, inevitably, there is some uncertainty in the degree of trough
loading.
The particular type of screw used will also have an effect on the conveying
capacity so that where the screw is of special design (such as those illustrated in
Figure 10.10) it is necessary to further modify the result of equation (10.4). One
approach [4] is to multiply the required capacity by various 'capacity factors'
in order to determine the equivalent capacity for which the conveyor must be
sized. Examples of capacity factors to account for special types of flight (CFr)
and for the effect of mixing paddles fitted within the flights (CF m) are given in
Figures 10.16 and 10.17.
SCREW CONVEYING
349
E 1.4r-----.------.-----.-----.
~
:5
t> 1.3 1------+------+----+-
~
~
-~1 .2
t
1.1
.S',.
"E
nurrber ot mixing paddles per pitch
Figure 10.17 Capacity factors for screw conveyors with 45o reverse pitch mixing paddles fitted
within the flights.
The capacity of a screw conveyor may then be expressed, in general as
kAN
2
2
1
•
m. = Pb4n(D.c - D.h) CF r' CF m
(10.6)
Alternatively, this equation may be rearranged to give the required
operating speed for a given throughput as
N=
m.CFrCFm
2
2
Pb(n/4'J(Psc- Dsh)kA
(10.7)
The conveyor selection procedure can now be summarized as follows:
(i) Examine the product to be conveyed and assess its suitability for
transport by screw conveyor. The type of flighting to be used and the
loading factor should also be considered.
(ii) If the product is 'lumpy', determine its size distribution and select
minimum screw size from Figure 10.12.
(iii) Determine maximum operating speed from Figure 10.15.
(iv) Determine capacity factors from Figures 10.16 and 10.17for chosen screw
type and loading factor.
(v) Calculate mass throughput (at maximum speed) from equation (10.6). If
this is greater than the required capacity use equation (10.7) to determine
the necessary operating speed; if higher capacity is desired choose a larger
diameter screw and repeat from step (iii).
10.4.4 Conveyor power
The power absorbed by a screw conveyor, even one that is operating
horizontally, is not easy to estimate with confidence since it depends, in a
somewhat unpredictable manner, on the nature of the bulk solid to be
350
BULK SOLIDS HANDLING
conveyed. The approach outlined here is based on that currently being
recommended in the relevant British Standard [7] and in similar authoritative
publications, for example, [ 4] and [8].
It is generally convenient to regard the total power as the sum of the power
required to transport the bulk material at the specified rate and the power
required to overcome frictional resistance between the moving parts of the
conveyor. Thus
ptot =
p mat+
Prrict
(1 0.8)
The friction power will depend principally upon the length and diameter of
the conveyor and its rotational speed. An empirical expression that should
give a fairly reliable indication of this quantity is
Prrict =
75.7 LN D;~ 7
(10.9)
where D,c is the screw diameter (m), Lis its length (m), and N is the rotational
speed (rev /sec) giving the frictional power (W). It should be noted however that
other factors, such as the type, number and condition of the bearings in use, the
mass of the screw, and so on, may have a significant influence on the power
required to overcome friction. These considerations are discussed in [ 4].
The somewhat simpler expression
(10.10)
which does not take into account the speed of rotation of the screw, is given by
[7] and [8] with the justification that Prrict is very low compared to the power
required for the progress of the material. Note that D,c and L are both in
metres in equations (10.9) and (10.10), giving Prrict in watts.
Even more difficult to predict with confidence is the power required to move
the bulk material forward through the conveyor, since this depends to a large
extent upon the nature of the material concerned. It is reasonable to suggest
that this power should be proportional to the volume throughput or capacity,
the bulk density of the conveyed material, and the length of the conveyor (or,
more precisely, the conveying distance). Thus, introducing coefficients F, to
account for differences in the types of screw that could be used and F m to
account for the nature of the conveyed material, we have
p mat= F ,F mPbY V,L
(10.11)
where g is the gravitational acceleration.
The value of the coefficient F, can be taken as unity for a standard helical
screw (at all conveyor loadings) but should be increased to 1.2 for cut flights or
ribbon flights at 45% loading, or to 1.7 for cut and folded flights at 45%
loading. The use of mixing paddles on the screw will naturally require
considerable additional driving power, and F, should be increased by 30% for
each 'paddle-per-pitch'. (For example, for a standard screw with two mixing
paddles per pitch, take F, = 1.6.)
351
SCREW CONVEYING
3
~
u.O
(5
0
~
"0
"'
0
-;:::
Cl)
>
0
2
'--..
:::::--..,1-
1":: -....,
1--
-I-
-- - 1-- - - --1- -
1-
0.2
·-
t-
1- 1-
~
-
-
~
C.5
-
1- 1-
"""' """'
pow8f CPrret • Ptrictl kW
Figure 10.18 Values of the 'overload factor' F 0 .
The 'material factor' F m• also called 'progress resistance coefficient', depends
upon the characteristics of the bulk material, but apparently not in any
kind of consistent manner that would allow it to be determined from a simple
bench test. Values ofF m for a large number of bulk solids can be determined
from data in [ 4]. Table 10.1 lists a few of the more common bulk solids with
corresponding values of F m which, in general, range from 0.8 to 4.0.
Once an assessment has been made of the total power required to transport
the material and to overcome the inherent conveyor friction, it is necessary to
take into account the drive efficiency and so determine the normal input
power. The value of the drive efficiency would naturally depend upon the
arrangement in use, but typically should be around 85-95%.
In addition, it is usual practice to make allowance for possible overload
conditions which may occur, for example, when starting up a fully-loaded
conveyor. The problem is likely to be particularly acute for small conveyors
using low power driving motors, as in this situation the torque range required
may be more than a small motor can provide. In [ 4] the use of an 'overload
factor' F 0 is recommended; this is a function of the total power required, up to
about 4kW (see Figure 10.18).
Thus the size of driving motor required is indicated by
p
mot
= (P mat+ Prrict)F 0
'1
(10.12)
where '1 is the drive efficiency.
10.4.5 Inclined screw conveyors
The operation of an industrial-type screw conveyor on an incline may be
convenient in terms of plant layout, but is likely to result in a significant loss of
efficiency because of two effects: firstly, the maximum potential capacity of the
conveyor decreases and secondly, the power per unit mass throughput
increases, both effects resulting principally from the greater amount of
352
BULK SOLIDS HANDLING
Table 10.1 Bulk densities and material factors for a selection of common bulk
solids [ 4]
Material
Bulk density
Pb(kg/m3)
Fm
Alumina
Ammonium nitrate
Barytes (powder)
Bentonite (fine)
Bonemeal
880-1040
720-990
1920-2880
800-960
800-960
3.6
2.6
4.0
1.4
3.4
Cement (Portland)
China clay (kaolin)
Coal ( -15mm)
Coffee (ground)
Cullet (fine)
1510
1010
780-980
400
1280-1920
2.8
4.0
2.0
1.2
4.0
530-640
480-720
960-1280
560-720
640-720
1.2
4.0
3.2
1.2
1.2
Mica flakes
Milk (powdered)
Mill scale (steel)
Oats (crushed or rolled)
Peas (dried)
270-350
320-720
1920-2000
300-380
720-800
2.0
1.0
6.0
1.2
1.0
PVC (powders)
PVC (pellets)
Polyethylene, resin pellets
Rice
Sand
320-480
320-480
480-560
700-800
1440-1920
2.0
1.2
0.8
0.8
3.4-5.6
Sawdust (dry)
Soap powder, detergent
Sugar (dry granulated)
Talcum powder
Vermiculite (expanded)
160-208
240-800
800-880
800-960
260
1.4
1.8
2.0-2.4
1.6
1.0
Wheat
Wood (flour)
Wood (shavings)
720-770
260-580
130-260
0.8
0.8
3.0
Flour (wheat)
Fly ash
Gypsum (fine)
Ice (crushed or cubes)
Ice (flake)
tumbling and turbulence within the rotating screw. Although attempts have
been made to develop analytical models of the 'flow' in inclined screw
conveyors, for example, [9], most of the published information is of a
qualitative nature.
Special designs of screw conveyor are available for vertical operation, as
described in section 10.5, and modifications can be made to the standard
form of conveyor which will improve, to a limited extent, its performance when
operating on an incline. Nevertheless, there tends to be a slope, typically
around 45°, for which its throughput falls to a minimum (Figure 10.19).
353
SCREW CONVEYING
100~--------------------~
~
:::
·~
50
0.
"'
0
65
90
inclination of conveyor (degrees)
Figure 10.19 Variation in performance of screw conveyors when operating on an incline [4].
Provided that the incline is not too steep (generally, less than 20°) the
efficiency of a standard design of screw conveyor may still be acceptable,
especially if the rotational speed is increased somewhat to compensate for the
loss in the average forward velocity. Figure 10.14 gives an indication of the
extent to which loading factors should be reduced when operating on shallow
upward inclines, the general recommendation being a 2% reduction in k per
degree of inclination.
Alternatively, modifications may be made to the conveyor itself, for
example:
(i) Reduce the clearance between the trough and the screw to a minimum.
(ii) Use a tubular trough, again with minimum radial clearance. The loss in
efficiency of conventional V -trough conveyors when working on an incline
is partly caused by the tendency of the bulk solid to fall backwards over
the top of the rotating screw. A close-fitting tubular trough helps to
contain the material and prevent this fall-back, especially if the screw is
rotating at a somewhat higher speed than usual.
(iii) Reduce the number of intermediate hangers supporting the screw, and if
possible eliminate their use altogether. Obviously this will mean that the
screw sections are longer, and it may be necessary to make these of heavier
construction to reduce the risk of the screw shaft flexing to an unacceptable extent when under load.
(iv) Use screw of shorter pitch, for example, two-thirds or even one-half of the
standard pitch. This will result in an improvement in the angle of the screw
flight relative to the bulk solid through which it passes. An increase in
rotational speed may be necessary, however, to compensate for the fact
that the forward movement of the bulk solid per revolution of the screw
will be less as a result of the reduction in pitch.
Once the capacity of an inclined screw conveyor is determined, estimation of
the additional power consumption, over that for horizontal operation, is
relatively straightforward.
354
BULK SOLIDS HANDLING
Thus
(10.13)
where H is the vertical elevation of the top end of the screw above the feed
point, and the power of the driving motor will then be given by
p
mot
= (P mat+
pfrict + pst)F 0
1J
(10.14)
10.5 Vertical screw conveyors
At angles of inclination greater than about 20° the elevating capacity of a
conventional industrial-type screw conveyor decreases sharply, and in order
to achieve a satisfactory throughput some modifications to the basic design
are essential. Examples of such modifications for screw conveyors to operate
on an incline have been given in the preceding section and attention is now
turned to the special case where the axis of the conveyor is vertical, i.e. the
screw elevator.
The screw itself is, for vertical conveyors, generally the same as for the
horizontal type, with helicoid flighting of standard pitch welded to a central
shaft. However, a casing of tubular pattern replaces the U-trough and the
feeding arrangement is different. An important feature of vertical screw
elevators is that they will work satisfactorily only if a continuous feed of bulk
solid is maintained to the lower end of the screw. Interruption of the feed will
almost immediately result in stoppage of the discharge from the top end ofthe
screw as the elevator will not empty itself. Thus, unless it is deliberately cleaned
out, there will always be material within the screw, whether it is rotating or
stationary.
A common method of providing a positive feed to the vertical screw elevator
at a controlled and uniform rate is by means of a horizontal screw feeder which
may be arranged in line with, or particularly for fragile materials, offset from,
the axis of the vertical screw. Since the screw elevator runs full, the actual
discharge rate is generally independent of the speed of rotation and thus any
required turn-down in the solids flow rate can be simply obtained by reducing
the speed of the screw feeder rather than that of the main elevator.
Approximate capacities and recommended maximum rotational speeds of
vertical screw elevators are given in Figure 10.20. The power required can be
estimated using equation (10.14), but it must be understood that there are
many variables which can have an unpredictable effect on the performance of
the elevator. The only reliable estimate of power will be from the results of
laboratory tests on a similar material or from a manufacturer's previous
experience.
Various attempts have been made to improve the efficiency of helical screws
operating vertically to lift bulk materials. One method is to vary the pitch of
the helicoid flighting in the intake region so as to provide a firm continuous
355
SCREW CONVEYING
'0
q,
'0
c:
~
E
0
0
~
0
diameter of screw (mm)
Figure 10.20 Approximate capacity of vertical screw conveyors [6].
Figure 10.21
The contra-rotating screw feeder device used on the Siwertell bulk discharger.
'plug' of material which is pushed upward by the rotation of the screw.
Another method that has been used to ensure efficient filling of the vertical
screw is a concentric contra-rotating screw fitted over the inlet end of the
elevator (Figure 10.21). This arrangement is used on the Siwertell shipunloader [11]:
A somewhat different approach to vertical screw conveying uses a
combination of rotating and fixed helicoid flights (Figure 10.22). The stationary right-hand flight, which is attached to the tubular casing, is split at 180° at
every half-pitch. The rotating flight (left-hand) is fixed to the central shaft and
is split in the same manner. In order that the shaft can turn, with the rotating
flights passing through the splits in the fixed flights, an axial reciprocation of
the shaft is necessary and this is achieved by means of a cam arrangement
housed in the pedestal base of the unit. It is claimed that this type of elevator
356
BULK SOLIDS HANDLING
shaft reciprocates
----
flights fixed
to shaft
flights fixed
to casing
Figure 10.22 Special flight configuration used on the 'Verti-lift' [12].
works by lifting a batch of material from each stationary flight to the next until
the discharge point is reached and, in doing so, achieves volumetric efficiencies
much greater than more conventional vertical screw elevators.
10.6 Conclusion
Although various important aspects of the design and construction of screw
conveyors have been covered in this chapter, there is clearly a great deal more
to be studied in order to acquire a thorough working knowledge of these
devices. In particular, the materials of construction, torsional ratings and
drive configurations, considered to be outside the scope of this brief
introduction, need to be appreciated before taking major decisions concerning
the design or selection of screw conveyors. Probably the most useful source of
guidance is the CEMA handbook on Screw Conveyors [4], but a number of
other publications should also prove useful, for example, [1 ], [2], [6] and [ 10],
the last-named having over sixty further references.
10.7 Notation
Ab
CFc
CFm
DC
DSC
Dsh
Fm
F.
g
H
k
L
m.
N
Cross-sectional area of moving bed of bulk solid in a screw
conveyor
Flight capacity factor (Figure I0.16)
Mixing paddle capacity factor (Figure 10.17)
Internal diameter of conveyor casing
Diameter of screw
Diameter of conveyor shaft
Material factor, equation (10.11) (Table 10.1)
Screw factor, equation (10.11)
Gravitational acceleration (specific gravitational force)
Vertical elevation of conveyor discharge above feed point
Trough loading factor (Figure I 0.14)
Length of screw conveyor
Mass flow rate (capacity or throughput)
Speed of rotation of screw (revolutions/second)
SCREW CONVEYING
pmat
357
Power required by screw conveyor to overcome friction
between moving parts
Power required by screw conveyor to move bulk solid at a
specified rate
Power required by screw conveyor to raise bulk solid through
height H
Total power absorbed by screw conveyor
Thickness of screw flight
Average velocity of bulk solid in the axial direction within a
screw conveyor
Volumetric flow rate (capacity or throughput)
Pitch of screw
Bulk density of conveyed material
References and bibliography
References
I. Thomson, F.M. {1973) Applications of screw conveyors. In Bulk Materials Handling, Vol. II,
ed. M.C. Hawk, School of Engineering, Univ. of Pittsburgh, 84-98.
2. Roberts, A.W. and Hayes, J.W. {1979) Economic Analysis in the Optimal Design of Conveyors,
Chapter 3, Performance of enclosed screw or auger conveyors, Tunra Ltd., Univ. of
Newcastle, Australia.
3. British Standard BS4409: Part 2: 1970. Screw conveyors-Portable and mobile tubular type
{augers) for agricultural and light industrial use. British Standards Institution, London.
4. Screw Conveyors. CEMA Book No. 350, Conveyor Equipment Manufacturers Association
{USA), 1971.
5. British Standard BS 4409: Part I: 1969. Screw conveyors~ Trough type for industrial use.
British Standards Institution, London.
6. Colijn, H. {1985) Mechanical Conveyorsfor Bulk Solids. Chapter 3, Screw conveyors, Elsevier,
Amsterdam.
7. British Standard BS 4409: Part 3: 1982. {Also ISO 7119-1981). Screw conveyors~ Method
for calculating drive power. British Standards Institution, London.
8. Screw conveyors for bulk materials~recommendations for the design. federation Europeenne de la Manutention, Section II, Continuous Handling, FEM 2.121, September 1985.
9. Kuznetsov, V.!. {1983) Calculation of the capacity of screw conveyors with an arbitrary angle
of inclination. Soviet Engg. Research 3 {8) 15-18.
I 0. Bates, L. Application and design of helical screw equipment. Proc. Solidex 80, Solids Handling
Conference, Harrogate, UK, March-April 1980, Paper B2.
11. Robinson, G. {1981) The Siwertell bulk discharger. Bulk Solids Handling I (3) 405-408.
12. Korach, D. A new look at vertical screw conveyors. Proc. 11th Powder and Bulk Solids Conf,
Chicago, USA, May 1986, 101-107.
Recommended further reading
Screw Conveyors. CEMA Book No. 350, Conveyor Equipment Manufacturers Association
(USA), 1971.
Colijn, H. (1985) Mechanical Conveyors for Bulk Solids. Chapter 3, Screw conveyors, Elsevier,
Amsterdam.
11
Vibratory conveyors
11.1 Introduction
Vibratory conveyors are commonly used in industry to carry a wide variety of
particulate and granular materials. Although the majority of engineers
involved in bulk materials handling will be aware of vibratory conveying as a
useful technique, few have the necessary understanding of this method to be
able to design or select a system with confidence. However, there is little doubt
that vibratory conveyors have some useful advantages, and an insight into
their mode of operation and into the parameters governing their performance
should enable the system designer to ensure that his choice of conveyor is the
most efficient and the most reliable.
The basic vibratory (or oscillatory) conveyor consists of a trough (generally,
but not necessarily, horizontal) which is supported on or suspended by springs
or hinged links and caused to oscillate at high frequency and with small
amplitude by an appropriate drive mechanism (Figure 11.1). The actual
configuration of the mountings and the type of drive unit used depends upon
the application and will be discussed in more detail in sections 11.3 and 11.4.
The fundamental action of the vibrating trough on the bulk material carried in
it is to throw the particles upward and forward so that they advance along the
trough in a series of short hops.
There is a need to differentiate here between 'feeders' and 'conveyors',
although the distinction is in fact mainly one of application. An important
aspect of vibratory handling is the ease with which the flow rate of the
conveyed product along the trough can be adjusted by altering the amplitude
and/or the frequency of the vibration. This has led to the widespread use of
vibrating troughs as feeders, for example, mounted directly beneath a hopper
to control the rate of discharge.
Thus a feeder must be capable of operating under varying head-loads,
whereas a conveyor requires a regulated feed rate and should not be subjected
to changes in head-load. A further difference between vibratory feeders and
conveyors is that the former are normally operated at higher frequencies and
smaller amplitudes. Table 11.1 gives an indication of the approximate ranges
of operation of vibratory equipment.
The size of vibratory feeders can vary over a very wide range from tiny units
delivering just a few grams per second (for example, in pharmaceutical
tabletting machinery) to heavy duty vibrating troughs handling hundreds of
tonnes per hour. Possibly the largest of these machines currently in use is a
VIBRATORY CONVEYORS
359
(a) Multi-drive trough with electromagnetic units mounted
on springs
(b) Trough mounted on leaf springs and driven by a single
vibrator unit
Figure 11.1
Typical vibratory conveyors showing two different mounting/drive arrangements.
Table 11.1 Normal operating ranges for vibratory
equipment
Type of machine
Frequency
(Hz)
Vibratory feeder
13-60
Vibratory conveyor
3-17
Reciprocating conveyor 1-3
Amplitude
(mm)
12-1.0
50-5.0
300-50
combination feeder and screening unit, having a trough 4 m wide and over
11 m long, designed to handle discarded motor vehicle batteries [1].
In general, the trough in a vibratory feeder is quite short (less than about 2 or
3 m), but flow rate control by amplitude or frequency variation works well
also on longer troughs, and the distinction between feeder and conveyor
becomes blurred.
At this point it would perhaps be appropriate also to distinguish between
360
BULK SOLIDS HANDLING
vibrating and reciprocating conveyors. Reciprocating or shaker conveyors
operate by moving the whole carrying trough, and the material in it, forwards
and then leaving the material in the forward position by a rapid return stroke
of the trough. There is no significant throwing action: the conveyed material is
carried forward by a frictional effect between itself and the floor of the trough
(which effect may be enhanced by small saw-tooth ramps in the floor) and
depends upon inertia to be left in the forward position as the trough returns for
the next stroke. Thus, an important feature of reciprocating conveyors is that
the vertical force exerted on the trough by the carried bulk solid remains
constant, whereas there is a cyclic variation in this vertical force in the normal
type of vibratory conveyor or feeder. The magnitude of the constant vertical
force on a reciprocating trough can be expressed simply as
Fv=mg
(11.1)
where m is the mass of bulk solid in the trough and g is the gravitational
acceleration. Then if Jlr is the coefficient of static friction between the bulk solid
and the surface of the trough, the limiting value of the horizontal force on the
bulk solid is given by
F Hm., = Jlrmg
( 11.2)
The maximum acceleration of the trough before sliding of the bulk solid occurs
is thus
(11.3)
and it follows that on the forward movement of the trough the acceleration
should always be less that Jlrg, while on the return stroke the acceleration
should be, for the major part of the travel, greater than Jlrg.
Operating frequencies of 1 or 2Hz are typical, with strokes of up to about
250 mm (compared with 3 to 20Hz frequency and stroke usually less than
25 mm for vibratory conveyors). Smooth granular or lumpy products of
relatively high density are generally the most appropriate products for this
method of conveying. However, reciprocating conveyors have a somewhat
limited application because of the severe abrasive effect of the continual sliding
of the conveyed material on the surface of the trough, and therefore they will
not be considered further in this book.
When selecting or designing a vibratory conveyor for a given application
the most important requirement is to be able to predict with a reasonable
degree of confidence the mass flow rate of the bulk material being conveyed
along the trough. This is equal to the product of the bulk density of the
conveyed material, the cross-sectional area of the bulk flow and the average
conveying velocity. The problem thus becomes effectively to predict the
average conveying velocity, and this depends principally upon the amplitude
and frequency of the trough displacements, its slope (if not horizontal), the
VIBRATORY CONVEYORS
361
angle of oscillation and the nature of the bulk solid itself. These aspects will be
considered in some detail in this chapter, following which the main features of
practical vibratory conveying equipment will be briefly discussed. On a first
reading, it may be preferred to turn directly to section 11.3 for a description of
the principal design features.
11.2 Movement of a bulk solid in a vibrating trough
The following analysis, leading to an expression for the average conveying
velocity, and thus for the mass flow rate, of particulate material in a vibratory
conveyor, is based on the approach presented by Oehman [2]. More detailed
and rigorous analyses can be found, for example, in [3]-[5]. However, it is
essential that predictions of the performance of vibratory conveyors and
feeders based on mathematical analysis are treated with caution. The extreme
complexity of the situation actually existing in a vibrating trough and the
vagaries of the bulk solids in their response to vibration stimuli means that
only limited confidence can be placed in such analysis. At the present time
there is little option open to the design engineer other than laboratory testing
to determine conveyor performance and the inclusion of adequate control of
transport rate in the installed system.
11.2.1 The motion of the trough
The typical arrangement of the trough in a vibratory feeder or conveyor is
illustrated in Figure 11.2. In this case the trough is 'directionally constrained',
that is, it can move only in a direction perpendicular to the fixed guide springs.
The line of motion of the trough is represented by sT which makes an angle f3
with the horizontal. This angle, termed the 'angle of oscillation' or 'drive angle'
is generally around 20-300.
The simple harmonic motion of the trough is represented by Figure 11.3,
from which it can be seen that, if the trough is oscillating at frequency f and
with amplitude ), its position at any time t is given by
ST
product feed
Figure I 1.2
=),(I -COS 2nft)
trough
Fundamental model of a vibratory conveyor.
(11.4)
362
BULK SOLIDS HANDLING
highest
----position
-
-
-
lowest
position
Figure 11.3 Simple harmoninc motion of the trough, along line inclined at angle
horizontal.
P to
the
The acceleration of the trough in the direction of oscillation is then
sT
=
d 2s
dt 2T
= .l..(2nf) 2 cos 2nft
(11.5)
Now the horizontal and vertical displacements of the trough at timet can be
written
XT
= A(1 -COS 2nft) COS {3
(11.6)
YT
= .l..(1 -cos 2nft) sin f3
(11. 7)
and
Also the horizontal and vertical components of the acceleration of the
trough can be written
and
.X\ = .l..(2nf) 2 cos 2nft cos f3
(11.8)
.Yr = .l..(2nf) 2 cos 2nft sin f3
(11.9)
Now the bulk material being conveyed will lift ofT the surface of the trough at
the moment when the acceleration of the trough, in the downward vertical
direction, becomes equal to the gravitational acceleration g; that is, when
YT = - g
(11.10)
The time at which this occurs is then given by
tl =
2~! cos
-1 [
.l..(2nf/sin f3
J
(11.11)
While in flight, the particles will tend to follow a parabolic trajectory to the
next impact point, after which they will be carried forward and upward for a
VIBRATORY CONVEYORS
363
short interval before being thrown again as the trough decelerates. Thus, as the
conveyed bulk solid is transported forward along the trough, the total time of
contact will be very small and the amount of abrasive wear occurring should
be minimal. For the most efficient operation of the conveyor there should be
no backward movement of the particles at any part of the cycle and therefore
the impact point should coincide with the start of the flight phase.
An important parameter in the modelling of vibratory conveyors is
therefore the ratio of the vertical acceleration of the trough to the gravitational
acceleration g, as this will determine the point at which the flight phase begins.
The maximum value of this parameter, which would normally be determined
at the design stage by chosen values of frequency, amplitude and angle of
oscillation, is sometimes called the 'dynamic material coefficient' or 'throw
factor' and given the symbol r.
Thus
r
=
YTm.,
g
=
A(2nf) 2 sin f3
g
(11.12)
At the start of the flight phase YT/g = - 1, and it follows that, if the positive
value of r is less than unity, the bulk solid will not leave the surface of the
trough and forward movement will be little, if any.
Combining equations (11.11) and (11.12) it is seen that the flight phase
begins at a time t 1 given by
(11.13)
The determination of the time at which the particles re-impact on the surface
of the trough is a little more difficult. Clearly this is where the 'tuning' of the
conveyor becomes important, since for efficient transport the particle
trajectories should be matched to the vibrations of the trough.
Figure 11.4 shows the vertical displacement of the conveying trough with
time and also the variation of the vertical component of the trough
acceleration. Typical flight phases and contact phases are shown, with impact
occurring within the same cycle as the lift-off.
Another essential consideration when selecting the operating condition for
a vibratory conveyor is the relationship between the frequency and the
amplitude of oscillation. In general the higher the frequency, the smaller must
be the amplitude. It is convenient to express this relationship in terms of a ratio
of the maximum trough acceleration to the gravitational acceleration g.
Thus
), _
.~T max
·- (2nf) 2
_
Kg
-
(2nf) 2
(11.14)
364
BULK SOLIDS HANDLING
contact
fh!f\t phase phase
.1
...
ft
number of
cycles
ft • 2
1
impact of material
on trough
matenal hft· off
•
-o
cir
g
Figure 11.4 Variation of trough displacement and acceleration with time.
Figure 11.5 The relationship between amplitude, frequency and dynamic machine coefficient K .
where
K
=
sTmu = - r g
sin f3
(11.15)
and is termed the 'dynamic machine coefficient' or 'machine number'.
The relationship between amplitude and frequency expressed by
equation ( 11.14) can be represented graphically by curves of the type shown in
Figure 11.5. Each of these curves corresponds to a different value of the
VIBRATORY CONVEYORS
365
parameter K: in practice vibratory conveyors are usually designed to have K
between 1 and 4, but for vibratory feeders K may be as high as 12, since inertial
effects are less of a problem in the smaller units.
11.2.2 The motion of bulk material in the trough
It has been explained that bulk material contained within the trough will lift off
the bottom surface at the instant that the downward vertical acceleration of
the trough exceeds the gravitational acceleration. From this instant the
movement of a single particle of the material may be modelled as a parabolic
trajectory and during the time of flight the trough continues its downward and
backward motion before meeting the particle at the next impact point
(Figure 11.6). The actual position of the impact point within the cycle of
movement of the trough is dependent upon the characteristics of the system
and, to some extent, can be adjusted by 'tuning' the conveyor (that is, by
varying the frequency and/or the amplitude of oscillation). When the conveyor
is operating at its optimum condition the impact point will occur just before
the lift-off point, allowing only a brief contact time, as illustrated in
Figure 11. 7.
The bulk material thus advances along the trough by a continuous series of
'micro-bounces'. Particles are carried forward by the movement of the trough
in the contact phase of duration Tc. The initial upward acceleration of the
trough results in an increase in the frictional effect between the particles and
the floor of the trough and thus minimizes sliding. In the flight phase of
duration Tr the particles fly forward while the trough is on the return stroke.
The net result is a forward progression of the particles at an almost steady
horizontal velocity (Figure 11.7).
It is helpful now to define a dimensionless parameter n as the ratio of the
time of flight to the period of the vibration applied to the trough, that is
tl-
tz
Tr
n=--=-
TT
TT
Yp
Figure 11.6 Trajectory of a 'single particle'.
(11.16)
366
BULK SOLIDS HANDLING
partK;Ie Ooadl movement
Xp
contact phase
(ctration TcJ
4
nuni:Jer of cycles
Figure 11.7
Horizontal motion of material in a vibrating trough.
I'-<
12
..
f - - - f-
--
---
-
/
··~
~
)<__/
0
Figure 11.8
(11.17).
1
fli{tll ratio n
Relationship between dynamic material coefficient rand flight ratio n, equation
Thus n may be regarded as a 'flight ratio' which characterizes the condition of
vibratory conveyance.
An analysis of the particle trajectory will lead to an expression for the flight
time Tr in terms of the amplitude of the vibration, the frequency and the drive
angle [3. It is then possible to show that the relationship between the dynamic
material coefficient r and the flight ratio n is of the form
r = [(2n 2 n 2 + co_s 2nn- 1 ) 2 + 1] 1 12
2nn - sm 2nn
and this relationship is illustrated, for n up to 3, in Figure 11.8.
( 11.17)
367
VIBRATORY CONVEYORS
Clearly, larger values of n require large values of r, which in turn means
high accelerations of the trough. Structural considerations obviously place a
practical limit on the inertia effects that can be tolerated and therefore it is
currently the usual practice to operate vibratory feeders and conveyors with a
value of n less than unity, which means that the flight phase takes place within
one period of the trough movement. Inspection of Figure 11.8 then shows that
the practical upper limit of r is 3.3.
11.2.3 Average conveying velocity
Perhaps the most significant problem facing engineers concerned with the
design and application of vibratory conveyors is the determination of a
suitable combination of parameters (notably r, f1 and n) to give the maximum
transport rate of a specified bulk solid along the trough. Since the actual
velocity of the particles in the trough will vary throughout each cycle, it is the
average conveying velocity that is of significance.
Now the horizontal displacement of the trough is given by
xT = A.( 1 - cos 2nft) cos f1
( 11.6)
and thus the horizontal component of velocity is
.XT = A.2nf sin 2nft cos f1
(11.18)
and the maximum velocity of the trough in the horizontal direction is
XT max = A2n J COS /1
(11.19)
The average velocity of the bulk solid along the trough can be conveniently
expressed in terms of this maximum as
(11.20)
where IJu is an 'efficiency of transport' which is found to be a function of the
dynamic material coefficient r, the vibration angle f1 and the coefficient of
friction fJ.r between the bulk solid and the surface ofthe trough. The form of the
functional relationship involving IJu, r, f1 and JJ.r is very complex and is the
subject of considerable research effort. In fact, the efficiency of transport will
also depend upon a number of other variables, such as the depth of the bulk
solid layer on the trough, the inclination of the trough (if not horizontal) and
the flow properties of the conveyed bulk solid. These effects are customarily
taken into account by introducing a number of empirical factors to modify the
value of average transport velocity predicted by equation (11.20).
Figure 11.9 [6] allows a value of the transport efficiency IJu to be determined
so that equation (11.20) can be used. Note, however, that it will be necessary to
specify the coefficient of friction (for example, for sand on steel fJ.r ~ 0.5), the
dynamic material factor r and the drive angle fl.
As previously mentioned, the practical maximum value of r is 3.3 but, in
368
BULK SOLIDS HANDLING
1.6
1.4
1.2
!Lf la1 11
Figure 11.9
drive angle
Values of transport efficiency "'u as a function of dynamic material coefficient
f3 and coefficient of friction /lr [6].
80
-
r-~\
L
I
\
~
i
I"-V
V
~ 20
r----
0
K
1/
-
1-
.,t.-
I
~ .......
-
-
==
_.....V
1.0
10
,1- r-- -
I',_ I
Q)
r,
-
2.0
3.0
dynanic material coefficient r
Figure 11.10
Optimum values of drive angle
f3 to give greatest transport velocity [2].
order to keep the inertia forces within acceptable limits, vibratory conveyors
are generally operated with r in the range 1.5-2.0. Optimum values of the
drive angle [3, for greatest transport rate, are plotted against the dynamic
material coefficient r in Figure 11.1 0, from data in [2], and from this chart it is
seen that f3 is likely to be in the range 30° to 50°. The dynamic machine
coefficient K is also plotted on Figure 11.10.
Three empirical multiplying factors which are recommended to modify the
value of transport velocity predicted by equation (11.20) are:
Fm A factor to allow for different material characteristics. Its value needs to be
determined experimentally, but would normally be less than unity for low
load densities and small grain size; 0.8 to 0.9 for heavy, granular, dry
material; 0.1 to 0.8 for material with more than 20% minus 300 ,urn; 0 for
particle size less than about 60 .urn (no transport).
Fh Factor to allow for depth of bulk material on trough. Value varies from
unity for small depths to about 0. 75 for depths of 300 mm.
VIBRATORY CONVEYORS
369
Fi Factor to allow for slope of trough. Value is around unity for horizontal
conveying and upward conveying to about 15°, but decreases rapidly for
steeper slopes. For downward slopes Fi is greater than unity, up to about
1.8 for a 15° downward slope. Note, however, that this factor may be much
affected by the friction between the bulk solid and the surface of the
trough.
The transport velocity of the bulk solid along the trough is thus predicted
using the expression
u,=YJuFmFhF). 2nfcos{J
(11.21)
Finally, the solids mass flow rate, or capacity, of a vibrating conveyor can
then be predicted by introducing the cross-sectional area of the bulk material
in the trough and its bulk density.
Thus
(11.22)
11.2.4 The influence of the design parameters
A number of conclusions can be drawn from the preceding relationships and
from published experimental data.
It has been established, for instance, that the conveying velocity u, is
inversely proportional to the operating frequency f [7]. Thus, in general, for
high conveying rates the frequency should be as low as possible. Note,
however, that in order to maintain a constant acceleration of the trough this
would require high amplitudes of vibration.
Equation (11.15) shows that an increase in trough acceleration means an
increase in the dynamic machine coefficient K, and from Figure 11.10 it can be
seen that this would result in a decrease in the optimum angle of oscillation
and an increase in the proportion of the cycle for which the bulk material is in
flight. It might therefore appear that increasing the trough acceleration would
result in an increase in the conveying velocity, and certainly this is true up to a
point. (The bulk material will not lift off the floor of the trough until h >g.)
However, excessive trough acceleration causes the operation to become
unstable owing to displacement of the particle/trough impact point and
consequent irregular 'bouncing' of the material.
It is clear that the angle of oscillation {3 will have some influence on the
conveying velocity. In general a small value of {3 means that there is little
variation in particle/trough friction since the vertical component of acceleration is small. On the contrary, a large value of {3 would indicate only a small
component of forward motion.
The actual value of the optimum angle of oscillation will depend upon the
trough acceleration and the coefficient of friction between the bulk material
and the surface of the trough. This is because the greater adherence of the
370
BULK SOLIDS HANDLING
material to the trough floor that results from an increase in either of these
effects allows the use of a smaller oscillation angle whilst still achieving
satisfactory forward motion. Naturally, fitting the trough with a high-friction
lining (e.g. rubber) will give an improvement in performance for the same
reason. Furthermore, it may be noted that increasing the depth of the
conveyed material should also result in an increase in friction at the trough
floor and therefore improve the conveying velocity. However, this effect has
not been observed consistently in practice.
11.2.5 Two-phase trough motion
It has been suggested [7] that the performance of the conventional arrange-
ment of vibratory conveyor is limited because the relative magnitudes of the
vertical and horizontal motions of the trough are governed by the fixed angle
of oscillation. This limitation could be overcome if the trough is excited
independently in the vertical and horizontal directions (at the same frequency
but with amplitudes and phase difference adjusted to cause the path of a point
on the trough to be elliptical). It is claimed that the two-phase system will
inevitably result in greater conveying rates than in the conventional system,
the maximum conveying rate occurring at some optimum phase angle which
depends upon the nature of the conveyed product and the vibration
conditions. Conveying velocities from 50% to 300% higher than those in
conventional systems have been obtained by using two-phase trough motion.
11.3 Design features
11.3.1 Drive mechanism
It is convenient to classify vibratory conveyors into a number of groups
according to the method that is used to transmit vibrations to the trough. The
four principal types of drive mechanism are:
(i) Direct or positive mechanical, using a crank and connecting rod
(ii) Eccentric-mass mechanical, using out-of-balance weights driven by an
electric motor-typical designs use single or double (contra-rotating)
eccentric masses, or twin self-contained vibrator motors
(iii) Electromagnetic drive using pulsed single-phase ac supply
(iv) Hydraulically-powered pulsating pistons.
The main features of each of these drives will now be described briefly.
(i) Positive mechanical drive. The usual application for this type of drive is on
the longer heavy-duty conveyors where low-frequency high-amplitude oscillation is appropriate. Figure 11.11a illustrates the general arrangement of a
positive-drive vibratory conveyor supported on guide springs. In this case the
VIBRATORY CONVEYORS
371
s
(a) Si'r(:lle erect ctive with trough sLPPOrted on g.Jde sprilgs
(b) Resonance-type conveyor with counterweight
Cc) Balanced conveyor using a split trough
Figure 11.11
Vibratory conveyors with positive mechanical drive.
displacement of the trough is predetermined as twice the crank radius. An
alternative arrangement (Figure 11.11 b) designed to oscillate near resonance,
has a spring positioned between the trough and the supporting frame and a
coupling spring linking the connecting rod to the trough. This ensures that the
trough has free movement, rather than being restricted to a fixed vibration
path.
Positive-drive vibrating conveyors can be a serious source of trouble as a
result of vibration transmitted to their surroundings. Heavy supporting
structures are required, especially if the conveyor is not counterbalanced. Care
should be taken to ensure that the frequency of vibration ofthe conveyor is not
close to that of the supporting structure. There are several ways in which the
problem of transmitted vibration can be reduced, such as the use of a
counterweight (Figure 11.11b) or contra-vibrating double troughs
(Figure 11.11 c).
Operating frequencies are relatively low (5-15Hz) and conveying distances
372
BULK SOLIDS HANDLING
generally about 5-30 m. Amplitudes are typically 3-15 mm, resulting m
conveying speeds of 0.2-0.8 mjs.
(ii) Eccentric-mass mechanical drive. Whilst a conveying trough can be caused
to vibrate using a single rotating eccentric mass, the much more common
approach is to use two contra-rotating masses of equal size. Twin selfcontained vibrator motors, for example, contra-rotating with their axes in the
same plane, will synchronize to produce an oscillating linear motion
perpendicular to the axes of the motors (Figure 11.12). The chief advantage of
a twin rotor arrangement is that the resulting linear oscillating force can be
relatively easily adjusted for direction. This means that, within the constraints
of the trough mounting, the vibration angle can be altered to suit the
characteristics of the product being conveyed.
As with positive drive mechanisms, the conveying trough may be mounted
on leaf springs which restrict the direction of the trough movement
(Figure 11.12a) or on compression or tension springs which allow the motion
of the trough to be governed by the direction of oscillation of the drive unit
(Figure 11.12b).
Operating frequencies are moderately high, being typically around 15Hz
(a) Twin vibrator motor drive with
trOUitl SlqiOI1ed
on leaf spri1gs
\
(b) Free-oscillati'lg conveyor
Figure 11.12
Vibratory conveyors with rotating eccentric mass mechanical drive.
VIBRATORY CONVEYORS
373
for conveyors and 15-30Hz for feeders. Unlike the positive-drive types,
eccentric-mass vibrating conveyors do not have a fixed amplitude. Generally
the amplitude would be in the range 1-10 mm but this is very much dependent
upon the load on the trough. Conveying velocities are likely to be somewhat
less than would occur in positive-drive conveyors, while conveying distances
would be much the same for each type.
The growing importance and use of variable-frequency controls which have
proliferated on the commercial market in recent years has had a significant
effect on the application of eccentric mass vibrators. Conveyors and feeders
driven by three-phase ac vibrator motors can now be offered with a variable
speed control which provides an element of adjustment on feed rate whilst the
equipment is operating. Eccentric-mass vibrators are now able to compete on
cost effectiveness with electro-magnetic units for driving large feeders, although
for handling low volumes of bulk materials the electro-magnetic drives are
probably still superior.
(iii) Electro-magnetic drive. This drive mechanism relies on the cyclic energization of one or more electromagnets to generate the vibratory motion of the
trough. In most designs there is no contact between the parts of the
electromagnet, one part being mounted on the supporting framework and the
other on the oscillating trough (Figure 11.13).
Electromagnetic drives are generally designed to work from the 50Hz (or
60Hz in the USA) alternating current mains supply. Since each cycle has two
impulses the effective operating frequency is 100Hz (or 120Hz). Reduction of
the frequency to a minimum of 50% of these values is possible if a half-wave
rectifier or thyristor control is used. Amplitudes tend to be very small (typically
0.1-3 mm) and consequently the conveying velocity is quite slow, rarely being
more than about 0.3 mjs. Whilst electromagnetic excitation oflong conveyors
is possible, particularly when tuned to operate close to the resonant frequency,
the most common application of this type of drive is on short vibratory feeders
(Figure 11.14).
(iv) Hydraulic drive. In order to eliminate any possible risk of an explosion
being initiated by the electrical equipment, pneumatic or hydraulic receiver
pistons fitted to the conveying trough can be driven by a remotely situated
pump unit. Speed control of the motor, by thyristor drives for example, or the
Figure 11.13 Typical arrangement of electromagnetic drive.
N
374
BULK SOLIDS HANDLING
Figure 11.14 Vibratory feeder with electromagnetic drive.
use of cone pulleys between the motor and the pump unit, allows variation of
the frequency of oscillation of the trough. Also, capacity control of the
conveyor can be readily achieved using manual or automatic pressure control
valves on the pneumatic or hydraulic supply. The applications of this type of
drive are similar to those of electromagnetic drives but it is capable in general
of heavier-duty work.
11.3.2 Mounting systems
It will have become evident from the foregoing discussion that there are
different methods of mounting the trough(s) in a vibratory conveying
installation. The type of mounting to be used may depend upon the kind of
drive mechanism, the loading on the trough and the susceptibility of the
supporting structure to transmitted vibration. Mounting systems can be
usefully classified into three groups: directionally-constrained, nondirectional, and natural frequency systems.
(i) Directionally-constrained systems. In this class of conveyor the trough unit
is supported at intervals by leaf springs or by hinged links and the direction of
oscillation is restricted to a line perpendicular to these supports. The vibration
angle is thus fixed. Generally the system would be tuned so that the operating
frequency is well away from the resonant frequency. The performance of the
conveyor is then relatively insensitive to variations in the trough loading.
Directionally-constrained vibrating troughs are used principally for conveying and do not usually perform well as feeders.
(ii) Non-directional systems. Mounting the trough freely on isolator springs
results in a system which is more easily tuned to suit different conveyed
products, but which is in other respects very similar to the directionallyconstrained type.
(iii) Natural frequency systems. In order to achieve a significant reduction in
the power requirement of a vibratory conveyor it should be set up to oscillate
375
VIBRATORY CONVEYORS
at a frequency close to resonance. Such a system tends to be highly loadsensitive and it is therefore only really suitable for situations in which the
combined mass of load plus trough remains virtually constant; i.e. the solids
feed rate must be carefully controlled, or the mass of the trough must be large
compared with the mass of the load in it.
11.4 Applications of vibratory conveying
Vibratory conveyors are suitable for handling a very wide range of material
types although, in general, granular materials handle better than pulverized,
and flat or irregular shapes better than spherical. Also, materials that aerate
can be difficult to convey satisfactorily and low-density products can be
troublesome because of the effect of air resistance on the trajectory of particles.
On the positive side, friable products such as granules of milk powder or
instant coffee can be conveyed gently and without excessive degradation. Even
very abrasive materials should not cause too much difficulty since the time in
contact with the bottom surface of the trough is relatively short and, in any
case, wear-resistant trough liners can readily be fitted. As a guide to the
conveying characteristics of various bulk solids, Table 11.2, based on data
Table 11.2 Typical characteristics of bulk solids on vibratory conveyors
Material
Alumina
Bagasse
Carbon black
Cement clinker
Cereal
Coal
Crumb rubber
Detergent powder
Glass cullet
Gravel
Limestone
Milk powder
Plastic pellets
Sand-damp
Sand-dry
Salt (table)
Steel shot
Steel turnings
Sugar (granulated)
Tobacco
Wood chips
Approximate
size
(mm)
Average
bed depth
(mm)
Average
transport
velocity
(m/s)
0.15
0.25-5
1.5 (pelletized)
6-10
6-10
18-26
6
0.15
3-12
6-10
10-30
0.075
3-6
0.8
0.8
0.4-0.8
1.5-3
6 -12
0.5-0.8
75
150
75
125
150
125
100
75
100
125
100
35
100
100
75
50
50
100
60
250
250
0.15
0.4
0.18
0.36
0.36
0.3
0.3
0.25
0.3
0.33
0.36
0.13
0.36
0.4-0.45
0.25-0.3
0.3
0.36
0.28
0.25
0.36
0.4
Cut
10
376
BULK SOLIDS HANDLING
from [6], lists typical operating bed depths and transport velocities for some
familiar materials.
Although the 'fundamental' application of vibratory conveying is for the
horizontal (or near-horizontal) movement of particulate or granular bulk
solids, there are many opportunities for variation. Conveying on a downward
slope presents no real problems and conveying on upward slopes of up to
about 15° should also be possible in most cases. Systems with multiple inlets or
outlets can be constructed, in the latter case perhaps having the exit points
controlled by suitable shut-off gates. The outlets may be arranged 'in series'
along the length of the conveyor or alternatively the conveyor may be designed
to split the flow from one inlet point into two or more streams.
Vibratory conveyors are especially amenable to adaptations which allow
some kind of processing operation (such as screening, de-watering, cooling or
drying) to be undertaken while the product is being transported. Where the
product is such that its escape or contamination must be avoided, the trough can
be fitted with a sealed cover. Plastic or stainless-steel troughs are useful where
cleanliness or hygiene is a prime requirement.
Segregation or mixing of the conveyed material can occur in the vibrating
trough, and it is not always immediately predictable which of the effects will
prevail in a given case. Sometimes 'de-mixing' of a previously blended product
in a vibrating conveyor can be a great nuisance, but in other situations this
phenomenon can provide the means of a simple and effective way of removing
contaminants: for example, by skimming off a segregated top layer of
unwanted material. On the other hand, it has been found [8] that instant coffee
and chicory can be blended in a vibrating trough after feeding them separately
to the conveyor. With larger-sized materials manual 'picking' of contaminants
may be convenient because of the continual tumbling movement and relatively
slow forward progress of the product. For the removal of ferrous contaminants, some kind of magnetic separation system could easily be devised.
It is a relatively simple matter to combine various screening operations with
vibratory conveying in order, for example, to remove large lumps or to remove
very fine particles. Quite sophisticated classifying devices have been developed
using vibration as the mechanism of forward transport.
Contacting the conveyed product with gas or liquid is also rendered much
simpler by vibrating it in a suitably-designed trough which may have, for
instance, perforated sides or floor. Heating and cooling operations are easily
carried out using hot or cold air, and washing of products is also very straightforward in principle.
11.5 Spiral elevators
A common, if somewhat novel, application of the vibratory method of
transporting particulate materials along an almost horizontal surface is the
spiral elevator. In this device the conveying trough is wound helically, at a
VIBRATORY CONVEYORS
377
(a) A typical elevator
(b) A c<:lfT¥)act vibratory elevator installation
Figure 11.15
The vibratory spiral elevator.
shallow angle, on a central supporting core to which the vibratory motion is
applied (Figure 11.15a). Although, as the name suggests, spiral elevators have
as a main function the lifting of the conveyed material through vertical
distances of up to 10 m, or possibly more (Figure ll.l5b), a further important
advantage is their ease of use in processing applications. Processes involving
heat transfer, for example, are especially appropriate because a long contact
surface can be obtained that takes up very little floor space. The requirement of
a long transit time for the product on the trough can also be easily satisfied.
378
BULK SOLIDS HANDLING
Where the conveyed material is to be processed in this manner the central
supporting core can be conveniently used to carry electrical heating cables,
heating (or cooling) air, etc., and in one design the air is actually distributed
from the central core into a plenum chamber beneath the perforated floor of
the trough and thence into the product. Where the process demands it is a
relatively simple matter to enclose the complete spiral elevator in a gas-tight
container so that a gaseous atmosphere or vacuum can be maintained.
An interesting example developed for the manufacture of a chemical
product in powder form has the helical trough mounted on the inside of a large
tube in order to ensure gas-tightness [9]. The height of the elevator was 1.5 m
and the track length 26 m, the whole unit being driven by out-of-balance
electric motors.
11.6 Notation
A
a
FH
Fv
Fh
FJ
Fm
f
g
K
m
m.
n
ST
ST
Tc
Tr
TT
t
tl
t2
u.
XT
XT
YT
.h
{3
r
1/u
Cross-sectional area
Acceleration
Horizontal component of force
Vertical component of force
Material depth factor, equation (11.21)
Slope factor, equation (11.21)
Material flow factor, equation (11.21)
Frequency of vibration
Gravitational acceleration (specific gravitational force)
Dynamic machine coefficient, defined by equation (11.15)
Mass
Mass flow rate of bulk solid
Flight ratio, defined by equation (11.16)
Linear displacement of trough
Acceleration of trough ( = d 2 sT/dt 2 )
Duration of contact phase
Duration of flight phase
Period of vibration of trough
Time
Start time of particle flight ('lift-off')
End time of particle flight ('impact')
Average conveying velocity
Horizontal displacement of trough
Horizontal component of trough velocity
Vertical displacement of trough
Vertical component of trough acceleration ( = d 2 YT/dt 2 )
Angle of oscillation of trough to horizontal
Dynamic material coefficient, defined by equation (11.12)
Efficiency of transport, equation (11.20)
VIBRATORY CONVEYORS
379
Amplitude of vibration
Coefficient of friction between surface of trough and conveyed
bulk solid
Bulk density
Angular acceleration
References and bibliography
References
1. Dumbaugh, G.D. An analysis of drive methods for vibrating equipment used in bulk solids
systems. Proc. lOth Powder and Bulk Solids Conf, Chicago, May 1985, 452-470.
2. Oehmen, H.H. (1981) Theory of vibrating conveyors. Bulk Solids Handling 1 (2) 245-254.
3. Ganapathy, S. and Parameswaran, M.A. On the design of the unbalanced mass excited
vibratory conveyor: power requirements and motor selection. Bulk Solids Handling 6(1) 59-63.
4. Ng, K.L., Ang, L.A. and Chng, S.C. (1982) A computer model for vibrating conveyors. Proc.
Instn Mech. Engrs 200 (B2) 123-130.
5. Gaberson, H.A. (1972) Particle motion on oscillating conveyors. Trans. ASME, J. Engg.for
Industry, February, 50-63.
6. Colijn, H. (1985) Mechanical Conveyors for Bulk Solids. Elsevier, Amsterdam, 265-271.
7. Schofield, R.E. Vibratory conveying of bulk materials. Int. Conf on Bulk Solids Storage,
Handling and Flow, November 1976, Stratford-upon-Avon, UK.
8. Hill, T.J.E. The application and design of vibratory conveyors. Solidex 80 Conf., Harrogate,
March/April 1980, Paper Bl.
9. Haneman, S. and Mocha, H.K. (1978) Vibration has wide range of practical uses. Bulk Storage
Movement Control, May/June 1978, 101-103.
Recommended further reading
Dumbaugh, G.D. (1984) A comparative review of vibratory drives for bulk solids handling
systems. J. Powder and Bulk Solids Technol. 8 (2) 1-17.
Spivakovsky, A. and Dyachkov, V. Conveyors and Related Equipment, Chapter XIV, Oscillating
and vibratory conveyors, Peace Publishers, Moscow.
Colijn, H. (1985) Mechanical Conveyors for Bulk Solids, Chapter V, Vibratory conveyors, Elsevier,
Amsterdam.
12
Basic pneumatic conveying
systems
12.1 Introduction
The entrainment of solid particles in a high-velocity flow of air is a well known
phenomenon, with examples ranging from sandstorms to domestic vacuum
cleaners, and it is therefore not surprising that it should be the basis of an
essentially simple and reliable method for the controlled conveying of bulk
solids. Pneumatic conveying, as the method is called, may be formally defined
as the transportation of dry bulk particulate or granular materials through a
pipeline by a stream of gas. Whilst the gas concerned would normally be air,
other gases are occasionally used, such as nitrogen in situations where there is a
fire or explosion risk.
The main purpose of a pneumatic conveyor is to move solid particles from
one location to another; for example, from a bulk transport vehicle to a storage
hopper, or from a storage hopper to a bagging machine. These conveying
systems require only a source of compressed air (or other gas, as previously
mentioned), a means of feeding the product into the pipeline, and a receiving
hopper fitted with a means of separating the conveyed product from the
conveying air (Figure 12.1 ). Appropriate selection and arrangement of these
components provides flexibility in both plant layout and operation. Thus, for
example, material can be transported from several sources into a common line,
or a single conveying line can distribute material into a number of receiving
hoppers. The material flow rate can be monitored and controlled, and systems
can usually be designed for fully automatic operation.
The earliest commercial applications of pneumatic conveying were probably the capsule transport lines developed during the first half of the 19th
century (see Chapter 17), and it was not until 1886 that B.F. Sturtevant
demonstrated that solid particles could be conveyed, in a controlled manner,
directly in a stream of air [1]. These first practical pneumatic conveyors were
gas in
(usually airJ
I
solids in
I
gas/solids
disengaging device
solids· out
Figure 12.1
The elements of a pneumatic conveying system.
BASIC PNEUMA TIC CONVEYING SYSTEMS
381
fan-driven vacuum systems, mostly used for handling sawdust and grain, and
it was the beginning of the 20th century before positive pressure systems were
much used. Conveying velocities were relatively high, with the particles carried
in suspension at low concentration--the so-called 'dilute phase' mode of
transport. Gradually the technology of pneumatic conveying was developed,
starting perhaps from the need to separate the conveyed product from the air
stream, in cyclones and filters, and then extending to the problem of
introducing the bulk solid into the conveying line against an adverse pressure
gradient (hence, the rotary feeder and, later, the screw pump). In the 1920s it
began to be recognized that by introducing a small amount of air into fine
particulate materials they could be made to exhibit some of the characteristics
ofliquids, including the ability to 'flow' freely. Interest in this phenomenon of
'fluidization' no doubt helped the designers of pneumatic conveying systems to
realize that they were not restricted to the mode of transport in which the
individual particles are carried in suspension at high velocity, and so 'densephase' conveying became established as an alternative, with a high proportion
of the particles effectively sliding on the lower surface of the pipe.
Although the movement of solid particles by air through pipelines has thus
been established practice for over half a century, this method of transportation
is being 'rediscovered' because of its suitability for modern industrial processes
and the economics of handling in bulk. Pneumatic conveying of particulate
and granular materials is now commonplace in many industries, such as the
pharmaceutical, food, chemical, glass, cement, plastics, mining and metal, and
normally provides for storage, transport, recovery and metering of the
products. Indeed it would be difficult to envisage how the everyday handling of
products such as plastics, flour and sugar during in-plant distribution could be
cost-effective without pneumatic conveyors.
The difficulties encountered when designing or selecting a pneumatic
conveyor to meet a particular need are normally due to:
(i) The wide range of pneumatic conveying systems which are available
(ii) Variation in the product, caused by conveying or by a change in the
process or original source of the product
(iii) The inability of manufacturers to specify a system based upon product
characteristics, frequently resulting in a dependence on dubious empirical
correlations
(iv) The need to know whether or not the product is explosive, toxic, abrasive,
friable, hygroscopic, fine or granular, since a small change in a product's
characteristics can affect considerably the conveyability of the product
(v) The gas -solid flow in a pipeline being extremely complex and each
product having its own unique flow characteristics.
Nevertheless, across the world, the number of manufacturers of pneumatic
conveying systems has, in recent years, risen substantially, and installations
are becoming increasingly complex (Fig. 12.2).
382
BULK SOLIDS HANDLING
Figure 12.2 A pneumatic conveying system for handling PVC resins, showing the complexity
and flexibility of modern installations. (Photo Courtesy Neu Engineering Ltd.)
Most manufacturers' literature on pneumatic conveying includes a very
impressive list of materials- from asbestos powder to coffee beans, moulding
sand to grass seeds, gold ore to talcum powder-which their systems can
handle dust-free, without segregation, with complete flexibility and very little
maintenance. Even whole fish and live chickens are reported to have been
BASIC PNEUMA TIC CONVEYING SYSTEMS
383
conveyed successfully in this way [1]. Some users and most manufacturers
realize that system design is rarely straightforward, especially with a new
product, and it is often the inventiveness and innovatory skill of the pneumatic
conveying engineer which ensures a satisfactory, reliable working system. In
spite of this, the literature abounds with claims such as 'optimum design', 'all
parts manufactured of the most suitable material'; 'versatility and ease of
future changes in use'; 'our systems use the minimum air giving the minimum
product degradation and plant erosion with minimum power consumption';
and so on. The design of pneumatic conveying systems is however largely
based upon practical experience and empirical design curves and/or equations. The more enlightened manufacturer will carry out conveying tests in a
pilot plant before designing a handling system for a new product. Unfortunately, the manufacturer's pilot plant may not be the most suitable system for
handling the user's product on account of the manufacturer being unable to
supply the many different types of system. The user has the problem of
interpreting the results of manufacturers' tests and assessing the suitability of
the conveying system that is proposed -the cheapest system initially could
be the most costly in the medium term on account of unscheduled plant shutdown or, perhaps, the inability of the transport system to meet the
specification of conveying rate and so on. It is highly desirable for a user of
pneumatic conveying plant to be able to evaluate a proposed system, and it is
always wise to employ a reputable manufacturer who has considerable
expertise in ensuring compatibility of the transport system with the material to
be conveyed and the duty required.
Although it is desirable to be able to express a real flowing gas-solid
suspension as an analytical model which can be described in mathematical
terms, the sheer complexity of pneumatic conveying means that work in this
field must rely heavily on empirical correlations. The correlations must be
confirmed by experimental data; however. experiments with real gas-solid
flows are difficult and require skill in experimentation and instrumentation
and the utmost care in the interpretation of data. Despite the vast number of
publications dealing with pneumatic conveying, there is little agreement on the
correct method of predicting system pressure losses, especially in the case of
dense-phase conveying. In fact, even the most reputable manufacturer cannot
guarantee with absolute confidence that an installation will unquestionably
meet the design specification. However, pneumatic conveying systems do
work and the industry has a right to be proud of many successful plants.
Pneumatic conveyor design is not yet a science, but it is no longer a 'black art',
since experience and industrially-orientated research have provided some
answers in the quest to fully understand the behaviour of gas-solids
suspensions flowing in pipelines. The position today is that the component
designer can adopt a strategy which will enable him to optimize the design of a
system for handling a particular product. Perhaps the theme of this
384
BULK SOLIDS HANDLING
introduction can be summarized by the following two equations:
"black art"
(the past)
+
experience
technical art
(mainly last 30 years)
->
(the present)
technical art
experience
industrially(the present)+ (next decade)+ oriented research
( 1970-2000)
the technology
of pneumatic
conveying
the near future ...
(2000!)
One of the principal constraints on the use of pneumatic conveyors is the
nature of the material to be conveyed, although conveying distance or
conveying rate may be the deciding factor. Thus, although the list of materials
which have been successfully conveyed in pneumatic systems is very long,
there is still, and always will be, a need in the bulk solids handling field for
mechanical conveyors using, for example, belts, buckets, drag-chains, screws
and vibrating troughs. Total costs are important considerations in the
selection of a conveying system, but other features such as versatility,
compactness and manpower requirements often influence the final decision.
Table 12.1 represents a method of analysis used by at least one manufacturer
to provide a simple comparison for the selection of pneumatic conveying and
other forms of transport.
Table 12.1 Comparative analysis of pneumatic conveying and other forms of bulk solids
transport.
Performance/suitability rating scale
Poor
Satisfactory
Capital costs of installation
1---.-Operating costs
I- Space requirements of system
I- Ease of installation in existing buildings I- - Versatility and ease of future changes
I- Suitability for automation
r--Maintenance
1--Safety
f--Cleanliness, minimal contamination
1--Handling toxic materials
Range of materials handled
Distance conveyed
Capacity
Reliability
-
-
- -
-
Good
- - -- - -- - - - - - - -
Excellent
-- -
----
--- - - - - - - - -- - - - - - - - -- - - - - - - - - - - - - -- - - - - -
BASIC PNEUMA TIC CONVEYING SYSTEMS
385
Once it has been decided to install a pneumatic conveying system there are
three major problem areas to be considered, each one relating to the product
to be handled. The first of these is the erosion of the plant by the conveyed
product, the second is the effect of the plant on the product in terms of particle
degradation, and third is the explosion risk with certain products. These
problems should be taken into account when choosing the particular system;
for example, the product must be conveyed at low velocity to minimize plant
erosion by abrasive products and to avoid excessive degradation of friable
products. If a particular product is potentially explosive when suspended in air
as a dust cloud, then ignition can occur due to the electrical energy generated
by static electricity or by friction sparking. The risk of explosion can be
minimized or eliminated in a number of ways and it is generally accepted that
pneumatic conveyors reduce fire and explosion hazards. Starch, flour,
cellulose acetate, wood flour and gunpowder pellets are just some of the
common combustible materials which are pneumatically conveyed. It has
been reported that one insurance company gives discount rates to flour mills
which use pneumatic handling for the milling process, on account of the
reduced fire and explosion hazard compared with mechanical handling
systems.
In addition to the benefits offered by pneumatic conveying systems for
handling bulk materials in new plant, there are also distinct advantages if the
system has to be fitted into an existing building. The flexibility of the
installation means that the pipelines can easily be routed along walls and
ceilings to avoid obstructions without radical structural modifications.
Furthermore, spillage and wastage can be virtually eliminated, working
conditions are safer as a result of the minimal dust pollution, and the small
number of moving parts means lower maintenance costs and less danger to
operators.
These are some of the advantages, and they have been sufficient to sell many
pneumatic conveying systems to a large number of industries and for a wide
range of products. But just how do pneumatic conveying systems actually work
and what are the problems that have to be overcome in operating and
maintaining such systems? And what types of pneumatic conveying system are
available and which ones are likely to be the best for a given situation? The
answer to these questions will be provided in this and the following chapters
and a start will be made by introducing the basic forms of the pneumatic
conveying system. An explanation of how these work will be given first, along
with brief comments on some of the constituent plant items (which will be
enlarged upon in Chapter 13). Interwoven with this at appropriate points will
be an explanation of some of the problems encountered and how they can be
overcome. The main parameters which influence the choice of system and
dictate design decisions will be considered and, in Chapter 14, some approaches to the design of pneumatic conveying systems will be outlined.
386
BULK SOLIDS HANDLING
12.2 Modes of conveying-dilute-phase and dense-phase
It is often useful to classify pneumatic conveying systems according to the
mode of flow of the bulk solid as it travels along the pipeline. Although it is
possible to identify several possible flow regimes, as described in Chapter 3,
only two or three of these could really be regarded as stable and it is current
practice to base the classification on just two broad categories-dilute-phase
and dense-phase.
In the case of dilute-phase flow the bulk solid is conveyed essentially in
suspension with the particles more or less uniformly distributed over the crosssection of the pipeline. The solids loading ratio (that is, the ratio of the mass
flow rate of the bulk solid to the mass flow rate of the conveying fluid) for dilute
phase flows is likely to be less than ten, with the particles relatively widely
spaced, typically with a centre-to-centre distance of more than about eight
diameters. In order to keep the particles in suspension in the pipeline it is
necessary to ensure that the conveying velocity does not fall below a certain
minimum value which, for the majority of bulk solids, is about 13-15 m/s.
Where the conveying velocity is less than that required to keep the bulk
solid in suspension and particles begin to settle to the bottom of the pipe, the
flow is said to be in a dense-phase mode. As explained in Chapter 3 (and
illustrated in Figure 3.16), there is a wide range of flow behaviour that could
occur at these lower velocities. In fully-developed dense-phase flow, which
tends to occur at solids loading ratios greater than about 40, the product is
conveyed through the pipeline in discrete masses, or 'plugs', which may form
quite naturally, in horizontal flow, as a result of layers of particles sliding over
the deposited layer and building up dunes of increasing thickness.
The maximum value of solids loading ratio that can be achieved depends
upon the nature of the bulk solid concerned and the conveying air velocity.
With some materials, solids loading ratios of several hundreds are possible.
The range of bulk solids that can be successfully conveyed in dense phase, by
conventional means, is limited, but for those that can be conveyed in this mode
the minimum conveying velocity can usually be reduced to about half that
required for dilute-phase flow. However, for products that will not convey in
fully-developed dense-phase flow, very little reduction in minimum conveying
velocity is generally possible, especially in horizontal flow, since the consequent increase in product concentration will result in some particles dropping
out of suspension. Blockage of the pipeline then usually occurs as the
deposited material is swept up to fill the full bore of the pipeline, generally at a
bend or some other pipeline discontinuity.
12.3 Low-pressure pneumatic conveying systems
12.3.1 Positit•e-pressure systems
Probably the most fundamental form of pneumatic conveyor is the simple
positive-pressure system in which air (or other gas) is blown along a pipeline
BASIC PNEUMA TIC CONVEYING SYSTEMS
387
storage silo
or hopper
fan or
blower
-
\
receiving hopper
Figure 12.3 Simple positive-pressure pneumatic conveying system.
~~"~ ~
air
(a) Rotary valve
(b) Screw feeder
air
(c) Venturi feeder
Figure 12.4 Examples of devices for feeding a bulk solid into a pipeline continuously against an
adverse pressure gradient.
picking up, at a feed point, the bulk solid to be conveyed and discharging it
finally into a receiving hopper (Figure 12.3). These systems generally use fans
or blowers which normally have a maximum pressure of under one bar
(14.5lbf/in 2 ). Basically, the air is delivered from the fan or blower into the
pipeline; the material is fed into this pipeline from the bottom of a storage
hopper or silo and is then conveyed in suspension with the air along the
pipeline to the discharge point; this is usually another hopper or silo, and from
here the material can be gravity-discharged for use. This introduces two
fundamental problems: how to get the material into the conveying air stream,
and how to separate the material from the air at the end. The necessary two
plant items will be introduced here briefly to help provide a basic understanding of the complete conveying system.
The first of these problems, that is, introducing the material into the
pipeline, arises because the conveying gas is under pressure, and so the feeding
device has to cater for this. A number of pipeline feeding systems which will
satisfactorily transfer material from a hopper into a pipeline under these
conditions are shown in Figure 12.4. All three devices shown are capable of
feeding at a controlled rate, and they are all capable of continuous operation,
since the top of the supply hopper can be open to the atmosphere in each case.
For feeding against pressures in excess of one bar the rotary feeder is generally
unsuitable, and alternatives are the screw pump which is capable of working at
pressures up to about 2.5 bar (36lbf/in 2 ) and, for higher pressures, the various
types of blow tank. Blow tank systems are discussed in section 12.4 and all of
the feeders mentioned above are described in more detail in Chapter 13.
Separation of the conveyed bulk solid from the conveying air stream at the
388
BULK SOLIDS HANDLING
I air
airlsOif<t?A·'·''···
· •·
,,
·d
sdids
(a) Cyclone separator
Figure 12.5
(b) Bag !iter lrit
Gas/solids separation units.
diverter valves
conveying line
storage
silo or
hopper
\\
fan or
blower
/#
·/
receiving hoppers
feeder
Figure 12.6 A typical positive-pressure system showing delivery of bulk solid from one point to
several receiving hoppers.
discharge end of the pipeline is usually achieved with the aid of a cyclone
separator or bag filter unit (Figure 12.5) and these devices are also mentioned
in Chapter 13, but described fully in Chapter 5.
Low-pressure pneumatic conveying systems can handle a wide range of
pulverized, granular and fibrous materials. They can be readily adapted and
extended to provide an economical and flexible installation in which a bulk
solid, picked up at one point, can be directed to any one of a number of
receiving hoppers using pipe switches or diverter valves. A typical plant layout
is illustrated in Figure 12.6. In general, a positive-pressure system is not
suitable for multiple pick-up points because the air leakage through several
rotary valves can be quite high in relation to the total air requirement for
conveymg.
There are a number of precautions to be taken in the design and operation of
any pneumatic conveying system and it is convenient to classify these under
the following key areas:
389
BASIC PNEUMA TIC CONVEYING SYSTEMS
storage
hopper
convey~
ine
--cyclone
separator
solids
outlet
Figure 12.7
(i)
(ii)
(iii)
(iv)
A closed-loop pneumatic conveying system.
Supplying the product to the conveyor
The pneumatic conveyor itself (i.e. the pipeline)
Discharging the pneumatic conveyor
The control of the complete system.
Of particular concern in the case of positive-pressure systems are the feeding
of product into the conveying line, the filter unit and/or vent lines on the
receiving hopper(s) and the elimination of leakage from the system to the
surroundings, the last-named being especially important where toxic materials
are being conveyed. Problems with irregular feeding of product into the
pipeline, which can cause undesirable pressure surges and even complete
blockage of the line, may be the result of poor feeder design but can also occur
as a result of hold-up in the supply hopper. Obstruction of air flow by a
clogged filter or blocked vent line can also be the cause of localized high
pressures leading to air leakage or unreliable solids flow through the system.
The versatility of the pneumatic conveying system has already been well
illustrated, but an important variation of the basic positive-pressure system is
shown in Figure 12. 7. This diagram shows a closed-loop arrangement of the
type that might be used where the conveying medium is some gas other than
air, in order to minimize the wastage of the gas, or where it is essential to avoid
pollution of the surrounding atmosphere, where the conveyed material is toxic
for instance. A special precaution to be observed with closed-loop systems
concerns filtration, in order to ensure that unacceptable levels of dust are not
returned to the suction of the air mover. Also, when conveying under an inert
gas such as nitrogen, it is important to monitor the oxygen level so that
additional gas can be injected when necessary to make up losses through the
rotary valve and at the solids discharge point.
390
BULK SOLIDS HANDLING
12.3.2 Negative-pressure (vacuum) systems
It is, of course, po~sible to convey on the suction side of the fan or blower. The
humble domestic vacuum cleaner is a long-established and very familiar
example of this. There is, however, a limit on the available conveying line
pressure-drop (about 0.7 bar, in practice) and they are therefore not capable of
achieving such high tonnages or of conveying over such long distances as are
positive-pressure systems.
A vacuum conveying system is fundamentally similar to a positive-pressure
system in so far as the bulk solid is picked up at the inlet end of the conveying
line and transported by the flowing gas to the discharge end. There are,
however, three main differences, the most obvious of which is that the air
mover is at the discharge end of the pipeline (Figure 12.8). The other significant
differences concern the components required to feed the bulk solid into the
conveying line and to separate it from the gas at the discharge point. Clearly,
since the conveying gas finally has to pass through the fan or blower, it is
especially important to ensure that the solid material is adequately separated
from the gas. Thus a high-efficiency gas/solids disengaging device is an
essential requirement except in certain circumstances where the air mover is
specifically designed to handle solids-laden gas. At the inlet end of the
conveying line the situation is somewhat easier since the solid material does
not have to be fed against an adverse pressure. The feeding mechanism can
therefore be very simple, often involving little more than a basic suction nozzle
of the kind used on domestic vacuum cleaners. Where a rotary valve is used as
the feeder it can be somewhat lighter (and cheaper) construction as it does not
also have to serve as a pressure seal. However, the filtration plant would tend
to be larger because of the larger volume of air that has to be cleaned under
vacuum conditions.
The main application of vacuum conveying is in installations involving the
transport of bulk solids from several different locations to a single collection
point (Figure 12.8). Thus it is well suited to unloading systems and in
processing plant for handling ingredients fed from several hoppers into a single
process line.
Vacuum systems have the particular advantage that all air leakage is
Figure 12.8
A typical negative-pressure (vacuum) system.
vacuum
··!
M·
\
\
blower
\
.. ,
n
rner~age
~~1
!iter l.rits
hoppers
,g/
receivi'lg /
~
clverter valves
Figure 12.9 A combined negative- and positive-pressure pneumatic conveying installation
('suck-blow' system).
hopper
feed
'''''""''''''"
suction nozzle
convey~~
cyclone separator
>
-l
>0
w
[/)
~
m
[/)
<
[/)
Cl
z
~
<
m
z
0
(')
n
>
-l
~
zm
c
-c
[/)
n
1:1:1
392
BULK SOLIDS HANDLING
inward, so that injection of dust into the surrounding atmosphere is virtually
feature that is especially important when handling bulk solids
that are toxic or potentially explosive. It is still necessary, of course, to keep air
leakages to a minimum, since inflowing air could result in unwanted
contamination of the conveyed product and would tend to reduce the air
available for conveying at the upstream (inlet) end of the pipeline.
eliminated~a
12.3.3 Combined negative/positive pressure systems
A fairly frequent requirement in industry is for a bulk solid to be collected from
a number of different locations and then redistributed to several delivery
points. This typifies the application of a combination system comprising
vacuum pick-up and delivery to an intermediate storage hopper and positivepressure conveying from the intermediate hopper to the discharge points~the
so-called 'pull-push' or 'suck-blow' system (Figure 12.9). Routing of the
conveyed material would be by remotely-operated diverter valves. Because of
the difficulties of passing solids-laden gas through the air mover it is usual to
separate the solids from the gas stream and then re-feed it after the pressure of
the gas has been raised (hence the need for an intermediate storage hopper).
As with the simple vacuum system, and with the closed-loop system, it is
essential that the air mover is adequately protected against ingress of solid
particles. It should also be noted that the available power for the complete
installation has to be shared between the vacuum side and the positivepressure side. The pipelines for the two parts of the system must therefore be
carefully sized to take account of the different operating pressures and possible
losses through rotary feeders.
It may be noted that the same form of 'central processing installation',
comprising gas/solids separator, air mover, hopper and feeder, could also be
used as a booster station on long-distance positive-pressure conveying
systems.
12.4 High-pressure systems
12.4.1 General features
The systems considered so far have been essentially of the low-pressure type,
operating with fans or blowers, and have been capable of continuous
conveying. The available pressure of about one atmosphere, however, with
rotary valve and Roots-type blower systems, imposes limitations on the product transport rate and, more particularly, on the conveying distance. Furthermore, the air velocity of 15-30 mjs necessary to maintain the product in
suspension sets a lower limit to the air requirement for the successful operation
of such systems. A direct consequence of this is that dilute-phase pneumatic
conveying systems tend to have much higher running costs than mechanical
BASIC PNEUMA TIC CONVEYING SYSTEMS
393
conveyors. Another disadvantage of this mode of conveying is that it gives rise
to numerous particle~particle and particle~wall collisions which, with friable
materials, result in significant degradation of the material with various
consequent problems of excessive dust generation, such as coated system
components and clogged filters. With abrasive materials the high particle
velocities tend also to lead to erosive wear of feeders, piping and other fittings.
In attempting to overcome these criticisms of pneumatic conveying,
designers and manufacturers have moved increasingly towards the use of
'dense-phase' systems. The lower air consumption of these systems means that
running costs are substantially reduced and also that filters will be smaller,
again representing a useful cost saving. An important disadvantage, however,
is the significantly higher pressure required which means an increase in the
capital cost of the system when compared with dilute-phase conveyors of
similar duty. Compressors of the reciprocating or screw type are invariably
required to generate these pressures, which may be as high as 7~8 bar, even for
systems of quite modest length, and the blow tanks needed to feed the bulk
solid into the conveying line against these high pressures are coded pressure
vessels and therefore expensive.
The facility of operating at higher pressure levels means that bulk solid can
be conveyed at much greater concentrations, and consequently lower values of
specific energy consumption. Alternatively the higher pressures available can
be used to convey over much greater distances, as discussed in section 12.4.4.
12.4.2 Single blow tank systems
The most vital component of a simple high-pressure pneumatic conveying
system is the blow tank itself, which provides the means for feeding into the
pipeline the bulk solid to be transported. Blow tanks, also known by an
assortment of other names, such as blow pots, blow eggs, pressure eggs and
powder pumps, are described in more depth in the next chapter, and attention
here is directed more to the types of system in which they would be used.
Figure 12.10 illustrates the fundamental pattern of pneumatic conveying
systems using a single blow tank. It is important to understand that in this type
of system the solids flow through the conveying line is not continuous: product
is delivered to the pipeline in batches as the blow tank is filled and emptied.
The blow tank itself is essentially a pressure vessel which is gravity-fed with
product from the top and then, after closing the feed valve, and with the valve
on the conveying line closed, is pressurized. With the compressor still
operating, the outlet valve is opened and conveying starts.
Since the product flow is batchwise it is necessary, in order to achieve a
required equivalent mass flow rate, to ensure that instantaneous values of flow
rate during conveying are somewhat higher. This point is illustrated in
Figure 12.11 which shows a number of successive blow-tank cycles. Air
requirements and pipeline sizes have to be based on the maximum, or steady-
394
BULK SOLIDS HANDLING
erlrit
storage
hc:JR)er
conveyilg tne
'111111
rr===c:f-=l
Figure 12.10 High-pressure pneumatic conveying system using a blow tank feeder.
tine-
Figure 12.11
Single blow tank cycling.
state, conveying rate and so the system designer will endeavour to ensure that
the ratio of the time-averaged mean flow rate to the steady-state value is as
high as possible.
The system illustrated in Figure 12.10 incorporates a valve at the start of the
conveying line, and this arrangement permits rapid pressurizing of the blow
tank with a consequent increase in the time-average flow rate relative to the
steady-state value. However, this valve inevitably is subjected to harsh service
and it is common practice to omit it, so allowing the blow tank to begin
discharging automatically, as soon as the necessary pressure has been reached.
Figure 12.12 shows a typical operating cycle from which it is seen that after the
product begins to enter the conveying line there will be a short time interval
before steady-state conveying is achieved. Then, towards the end of the
conveying cycle, when the batch of product has almost been discharged, the
blow tank has to be de-pressurized and the entire conveying line has to be
cleared of product and vented. This process also takes a significant interval of
time and, when the time required to fill the blow tank and set the valves is taken
395
BASIC PNEUMA TIC CONVEYING SYSTEMS
Iota cycle ti'ne
blowng cycle
20
G>
16
j~
12
iO
~s
~.:::;
8
A
4
0
'
~
I
.S'
>
·a
>
Qj
~
"'
0
2
3
tine CnrutesJ
~
A
5
4
Figure 12.12 A typical operating cycle for a single blow tank without a discharge valve.
vent lne
_
blow tank
ar SI.WIY
convey·
()"18
~ I~
~ ~ >
i ~ i
r.e
cycle
:~i
~~
~
'ia a.~l
g
!»>
!!!~
i~'
ttme Figure 12.13 Single-plug blow tank system and its operating cycle.
into account, it is apparent that there is a considerable period during which the
system is not actively conveying.
Another approach to pneumatic conveying with a single blow tank is
illustrated in Figure 12.13. In this system the whole charge of material in the
blow tank is pushed into the conveying line as a single plug under the influence
of air introduced to the top of the vessel at high pressure. This pressure has to
overcome the frictional resistance ofthe plug of material in the pipeline, which
places a limit on the length of the plug and therefore on the quantity of material
in each batch fed into the blow tank. For example, a typical plug in a 150 mmdiameter pipe would be about 15 m long. This gives a plug volume of about
396
BULK SOLIDS HANDLING
0.27 m 3 , and for a bulk solid having a density of 1600 kg/m 3 would represent
about 430 kg of product.
It should be noted that conventional blow tank and conveying line
characteristics do not apply to the 'single plug' type of system, the operating
sequence of which is shown in Figure 12.13, and the bulk solids flow rate is
very much dependent upon the velocity of the plug and, particularly, the
length of the conveying line. The velocity of the plug is usually quite low,
typically around 3 mjs, but problems can arise on discharge as the highpressure air released behind the plug can cause severe erosion on venting.
12.4.3 Twin blow tanks and continuously operating systems
If two blow tanks are used, rather than one, a significant improvement in
performance can be achieved and a high-pressure pneumatic conveying
system can be developed that goes a long way to meeting the objections to the
Typical operatilg
S9(J.IElrCe:
Blow tar1< A
Blow tali< B
fl
dscharge
preSSllize
change (:
over
chcn;J'l
over
~
change (:
over
VEri!
fil
one cycle
dsc:la"ge
pressuize
dscharge
Figure 12.14
vent
fiU
preSSiiize
cischarge
~
vent
fl
Parallel arrangement of blow tanks and typical operating sequence.
BASIC PNEUMA TIC CONVEYING SYSTEMS
397
___ vent ine
pressl.fe balance
and vent li'le
transfer presstre
vessel
Figure 12.15
Series arrangement of blow tanks capable of continuous operation.
batch operation of single blow tanks. There are two basic configurations of
twin blow tank-arranged in parallel and in series.
With the parallel configuration (Figure 12.14) one blow tank can be depressurized, filled and brought up to working pressure again while the other is
being discharged. By this means almost continuous conveying can be achieved
through a common pipeline, so that the ratio of the time-average flow rate to
the steady-state value approaches unity.
The alternative arrangement with the two blow tanks in series, vertically in
line beneath a supply hopper, is shown in Figure 12.15. It is possible with this
system to use a high-pressure air supply for the continuous conveying of a
product. The transfer pressure vessel, rather than the main blow tank, cycles
between the conveying pressure and atmosphere and thus allows the main
blow tank to be kept topped up in order to maintain a continuous flow of
product to the conveying line. Automatic sequencing of the valves is controlled
so that when the bulk solid in the main blow tank falls to a predetermined low
level the transfer pressure vessel is vented and then filled from the supply
hopper. The vent line is then closed and the transfer pressure vessel is
pressurized, either by means of a pressure balance line from the blow tank, or
with a direct line from the main air supply. Once the pressure in these two
vessels is balanced, the connecting valve is opened so that the product level in
the blow tank is restored.
It is an important feature of the system illustrated in Figure 12.15 that there
is virtually no pressure difference between the lower pressure vessel and the
conveying line. Thus, the feeding device can be a rotary valve or a screw feeder,
as shown in Figure 12.16.
A particular application of these systems is for the direct injection of
pulverized coal (DI PC) into boilers and furnaces since the product often has to
398
BULK SOLIDS HANDLING
c..---- va11 line
---- trcnsfer pr8SSU"e
vessel
__ product feed
vessel
air Sl.4)Piy
conveyi1g line
Figure 12.16
A twin blow tank system with screw feeding.
be delivered against a pressure. Further general requirements ofDIPC systems
are that the product must be conveyed at a very steady rate and that a high
turn-down ratio, perhaps of the order of 10 to 1, should be possible. Blow tank
systems are capable of operating quite successfully over this range and so they
are ideally suited to such an application.
12.4.4 Long-distance conveying
One of the oft-quoted drawbacks of pneumatic conveying, in comparison with
other forms of bulk solids transport, is the limitation on distance. However, in
certain industries, especially those associated with mining and quarrying,
there is considerable interest in the potential for long-distance pneumatic
conveying. Already there are examples of systems operating successfully over
distances greater than 2500 m [2].
The high pressure required to maintain solids transport over long distances
dictates the use of a blow tank system, either as a single unit or in a twinned
arrangement as described previously. However, a further characteristic of
long-distance conveying relates to the influence of the pipeline length on the
solids mass flow rate. This effect itself is related to the variation in the velocity
of the air along the pipeline and the influence that this has on the pressuredrop.
The expansion of the air in the conveying line means that excessively high
velocities are soon reached and it has become accepted practice to step up the
diameter of the pipe at one or more locations in order to keep the air velocity
within reasonable limits. Figure 12.17 shows a plot of conveying air velocity
against pressure for flow in pipes of various diameters. In this example it is seen
399
BASIC PNEUMA TIC CONVEYING SYSTEMS
~r------.-------.------~----~------~
0
2
3
4
5
Figure 12.17 The variation of air velocity with pressure in a stepped pipeline (for a flow rate of
60m 3 /min).
that, if the air expands from 4 bar gauge to atmospheric pressure, it will be
necessary to increase the pipe diameter in two steps from an initial size of
125 mm in order to keep the velocity within a range appropriate for dilutephase conveying (that is, 15-30 m/s).
The decision on where to step the conveying line is an interesting one that
has exercised both manufacturers and research workers. Whilst the first
criterion is to keep the transport velocity within acceptable limits, there might
also be some latitude which allows the overall system pressure-drop to be kept
to a minimum. However, as yet there appears to be no recognized procedure
for optimally designing a stepped-pipeline conveying system.
12.5 Low-velocity conveying and the use of supplementary air feeds
12.5.1 General features
For the reasons explained previously (that is, to minimize product degradation
and erosive wear of the conveying line and system components) there has long
been interest in transporting bulk solids pneumatically at low velocity.
Conventional dense-phase systems have enabled conveying velocities to be
reduced from the 15- 30m/s normal in dilute phase to somewhere around half
these values, and recent research has shown that some materials can be
reliably conveyed at velocities down to I m/s and less in such systems [3].
In order to extend the range of bulk solids, especially those of a friable or
abrasive nature, that can be conveyed in dense phase at low velocity there have
been developed a number of interesting systems designed generally with a view
to keeping the product 'live' and moving along the conveying line, and to
enabling flow to be re-started in a line full of stationary material. The systems
400
BULK SOLIDS HANDLING
described here may not all be still commercially available, but are included for
interest. Certainly some of these systems, although quite complicated and
consequently expensive, have proved to be remarkably successful in transporting 'difficult' products that would be impossible to handle in more conventional pneumatic conveying systems.
Before describing the various low-velocity conveying systems it is worthwhile to attempt to explain the manner in which plugs of particulate or granular
material move along a pipe. Figure 12.18 illustrates the relationship, confirmed by experiment, between the length of a plug of material and the force
required to push it 'mechanically' through a pipe. This shows the reason why
bulk solids cannot be 'pumped' through a pipeline in a single-phase mode in
the manner of a liquid: the pressures involved would be prohibitively high. In
order to transport bulk solids in a similar mode the wall friction effects must be
drastically reduced, and it is in this respect that using compressed air as the
motive force plays a vital role. The effect of the air expanding through the
interestices aerates the product so as to reduce the friction between the
particles and the pipe wall, so that the relationship between the length of a plug
of material and the force required to move it perhaps corresponds to the lower
curve on Figure 12.18. There will still be a practical limit on the length of plug
that can be 'pushed', as mentioned when discussing the so-called 'single-plug'
blow tank systems, and with some materials there may be a critical length of
plug, above which the plug becomes immovable as a result of the frictional
resistance at the pipe wall increasing at a greater rate than the propulsive force.
a.
I
j
·~
plJg length, L ----.
Figure 12.18
Pressure required to maintain movement of a plug of bulk solid in a pipe.
BASIC PNEUMATIC CONVEYING SYSTEMS
401
'ar eu:tions'
Figure 12.19 Relationships between pressure and plug length for continuous and intermittent
dense phase conveying.
Therefore, in order to ensure reliable continuous conveying at very high solids
loading ratios, it is necessary to ensure that plugs of excessive length do not
build up in the pipeline.
One way oflimiting the length of plugs of material in a pneumatic conveying
line is by the injection of air, either at the start of the pipeline or at intervals
along it. Figure 12.19 shows how, by dividing the bulk solid into a series of
short plugs separated from each other by 'air cushions', the pressure required
to convey them is very much less than that needed to move a single plug of
equivalent length. By increasing the length of the air cushions, thereby
decreasing the number of plugs in the pipeline, it should be possible to convey
over longer distances for the same system pressure, albeit at a lower solids flow
rate. Thus it is apparent that achieving a given throughput over a given
distance is largely a matter of optimizing the operating pressure, pipe diameter
and plug/cushion length.
12.5.2 Plug-forming systems
The 'Pulse-Phase' system, originally developed during the late 1960s by the
Warren Spring Laboratory in the United Kingdom, operates on the shortplugs principle discussed previously. The system incorporates two key
elements:
402
BULK SOLIDS HANDLING
(i) A steep-sided mass-flow blow tank which introduces a uniform plug of
material into the pipeline
(ii) An 'air-knife' which intermittently pulses air into the pipeline, thereby
dividing the discharging bulk solid into discrete plugs.
The basic arrangement of the hardware is as shown in Figure 12.20 and
the operating sequence begins as follows. The bulk solid to be conveyed is
introduced into the blow tank which is fitted with one or more aeration rings
in the conical section (air injection into this part of the blow tank is said to be
vital to the successful operation of the system since it keeps the product 'live' so
that it flows more readily into the pipeline in an aerated state. Aeration enables
the material to be more easily split into plugs and assists the movement of the
plugs in the pipeline by reducing friction at the walls.)
When the blow tank is full the inlet valve is closed and the vessel is
pressurized. The product then flows into the pipeline through the 'air-knife', an
annular device incorporating a series of small holes equally spaced around the
conveying pipe. Intermittent switching on and off of the supply to the air-knife
causes cushions of air to form between plugs of the bulk solid, and this
continues until the blow tank is empty, after which it is vented to atmosphere
and refilled so that the cycle can be repeated.
soleroid valve
ar knife
prod.lcl
Figure 12.20
The Warren Spring Laboratory 'Pulse Phase' system.
BASIC PNEUMA TIC CONVEYING SYSTEMS
403
c:xn.1eYi1Q line
air cushons
Figure 12.21
The Buhler Takt-Schub' system.
The original concept of the 'Pulse-Phase' system was proposed as a solution
to the problem of conveying cohesive bulk solids, although the range of
materials successfully handled in this type of system has now been increased to
include coarser, granular materials. Many systems are operating successfully
at high solids loading ratios (values greater than 300 have been achieved) and
low conveying velocities (typically 1.5-3 m/s). The low air requirements also
make the use of dried air for hygroscopic products and inert gas for explosive
powders economically viable.
A very similar system, which also aims to divide the bulk solid in the
conveying line into discrete plugs, is the Buhler 'Takt-Schub' (Figure 12.21). In
this case the air cushions are created by the injection of air intermittently
through a simple swept tee, the air supply to this swept tee alternating with
that to the blow tank. This system was developed for the handling of granular
bulk solids, which are found to travel steadily along the conveying line, at
velocities around 2-6 mjs, in plugs up to a few metres in length.
12.5.3 Plug-limiting systems
Despite the use of air injection devices in systems such as the Pulse-Phase and
Takt-schub, there is much evidence to suggest that, provided the conveying
parameters are carefully chosen, most free-flowing bulk solids will tend to
form plugs spontaneously in the pipeline [4]. However, as previously
explained, it may be necessary, if reliable conveying is to be assured, to limit the
length of plug that can develop. The Waeschle 'Pneumosplit' system and the
Buhler 'Fluid-Schub' system both aim to do this by sensing the formation of a
plug and automatically injecting air directly into the plug at one or more
points in order to split it and so facilitate its movement.
The essential features of the Pneumosplit system are shown in Figure 12.22.
Reference [5] gives a detailed explanation of the operating principle of this
system, but a general understanding can be obtained from the pressure plot
404
BULK SOLIDS HANDLING
one-way vaNe
/
• Pf'OSSIIe i1 <D1Yeyf1g li1e
wtilsl bbd<age IS fonrr.g
location ot blockage
/
1
/press..-e n by-pass me
bbd<age n <Xnleyng
IS fonrr.g
Figure 12.22 The Waeschle 'Pneumosplit' system.
shown in Figure 12.22. During normal conveying the pressure in the main
conveying line will be almost equal to that in the external by-pass line that runs
parallel to it from the blow tank. This results in a small steady flow of air
(some 5- l 0%) through the by-pass line, but if a plug forms in the conveying
line the situation changes, the pressure on the upstream side of the plug being
greater in the conveying line than in the by-pass line, whilst on the downstream
side of the plug the pressures are reversed. This makes it possible for air to flow
from the by-pass line into the conveying line through a series of one-way
valves, but additional valves, connected to special pressure sensors, ensure
that the air is injected only in the vicinity of the plug itself. After the plug has
dispersed, pressures return to their normal levels and steady flow is reestablished in the main conveying line and the by-pass line.
Although the Pneumosplit system is expensive, with between two and ten
one-way valves, typically five to ten pipe diameters apart, fitted between any
two pressure sensors, it has been shown to be capable of successfully conveying
BASIC PNEUMA TIC CONVEYING SYSTEMS
---blow
405
tati<
conveyi1g li1e
by-pass ine
d1eck valves
Figure 12.23 The Biihler 'Fiuid-Schub' system.
bulk solids that have proved impossible to handle in more conventional
systems.
The Buhler 'Fluid-Schub' system is very similar in concept [6], having a bypass line connected to the main conveying line via equally spaced check valves
(Figure 12.23). The total conveying air is metered into the system at a constant
rate and distributed to the blow tank, the discharge elbow and the by-pass
pipe. If an excessively long plug forms in the conveying line, part of the air is
automatically diverted into the by-pass line and from there it is injected into
the plug, causing it to break up into smaller plugs. This is a dynamic process
which is self-stabilizing and requires no external control or monitoring
devices.
12.5.4 Air-injection and booster systems
A number of systems available commercially are based on the concept of a
continuous supply of supplementary air fed into the conveying line at intervals
in a largely uncontrolled fashion. The purpose of the supplementary air is to
ensure that the conveyed material is kept aerated and 'live' along the whole
conveying line. One of the first of these systems was the Gattys, in which air at
relatively low pressure is supplied continuously to the bulk solid in the
conveying line through an internal perforated pipe which runs its whole
length. The Buhler 'Fluid-Stat' and the Moller 'Turbuflow' are currentlyavailable commercial systems operating in a similar manner.
The Fluid-Stat system features a small pipe running inside the conveying
line and having fluted exhaust ports at regular intervals (Figure 12.24). If the
conveyed bulk solid shows any tendency to block the pipeline there will be a
flow from the higher-pressure region behind the plug through the by-pass line
p
406
BULK SOLIDS HANDLING
7
inner 1lbe
e'-'L------\,---'"')
H
fllted nozzles
L
1\t;{~:·~Jf,~:·:~-f~~&~--­
~
~ preSSU"e reQied 10 generate
t
i
'
''
rrovement of ptJg of 1eng1t1 L
''
,
preSSU"e i1 by-pass line
.>:::
'
preSSU"e ~tream
of pUg
"
preSSU"e avaiable to
generate movement of
"'plug of length L1
pl.Jgleng1h(b) The '!Ud-s1af b'anspOrt mecharism
Figure 12.24 The Buhler 'Fiuid-Stat' conveying system.
secondary air line
conveying line
Figure 12.25 The Miiller 'Turbuflow' system.
into the forward end of the plug, thus causing it to be gradually cleared. The
'Turbuflow' system (Figure 12.25) is very similar, but is claimed to work by
constantly restoring the turbulence of the conveyed bulk material as it moves
along the pipeline [7].
The Semco Trace-Air' and the Dynamic-Air systems both use a series of
'boosters' to inject additional air at intervals along the conveying line. These
BASIC PNEUMA TIC CONVEYING SYSTEMS
407
boosters, which are generally set to admit air only when required, may be
located at equal intervals along the pipeline or may be placed at strategic
positions only, for example just after pipe bends. It should be noted that, unlike
the various forms of by-pass system, these boosters add air to the conveying line
and therefore increase the conveying velocity.
References and bibliography
References
I. Dixon, G. Pneumatic conveying. in Plastics Pneumatic Conveying and Bulk Storage, ed. G.
Butters, Applied Science Publishers, 198 I.
2. Marcus, R.D. and Rizk, F. The reliability of long distance pneumatic transport. Conf on
Reliable Flow of Particulate Solids, CMI, Bergen, August 1985.
3. Mainwaring, N.J. and Reed, A.R. Mechanisms for gas-solids flows at low velocity in pneumatic
conveying pipelines. Proc. I Jth Powder and Bulk Solids Conf, Chicago, May 1986.
4. Hitt, R.J., Reed, A.R. and Mason, J.S. The effect of spontaneous plug formation in dense-phase
pneumatic conveying. Proc. 7th lnt. Powder and Bulk Solids Conf, Chicago, May 1982.
5. Krambrock, W. and Parekh, S. Pneumatic conveying of poor flowing abrasive or fragile bulk
materials. Proc. Pneumotransport 5, BHRA Conf., London, April 1980,419-442.
6. Maire, U. Low velocity pneumatic conveying of carbon black. Paper presented to Rubber
Division Meeting, Am. Chem. Soc., May 1984.
7. Moller, H., Pust, J. and Lubble, T. Turbuflow: a pneumatic conveying system with economical
power consumption. Bulk Solids Handling 5 (4) (August 1985) 789-794.
Recommended further reading
Kraus, M.N. Pneumatic Conveying of Bulk Materials. Ronald Press, New York, 1968.
Stoess, H.A. Pneumatic Conveying. Wiley-Interscience, 1970.
Dixon, G. Pneumatic conveying. In Plastics Pneumatic Conveying and Bulk Storage, ed. G.
Butters, Applied Science Publishers, 1981.
Kraus, M.N. Pneumatic conveying systems. Chem. Engg. 13 October 1986, 50-61.
13
Components of pneumatic
conveying systems
13.1 Introduction
In Chapter 12 the various types of pneumatic conveying system were
discussed, and attention is now turned to the components that go to make up
these different systems. In addition to the conveying line itself, which would
normally be of steel but may be alternatively of aluminium, plastic, glass or
rubber, the essential components of a pneumatic conveying system are the air
mover (for example, fan, blower, compressor or vacuum pump), the feeding
device, and the gas/solids disengaging device. In order to design and construct
a reliable and economic pneumatic conveyor it is essential to have a good
awareness of the different types of air-mover, feeder and disengaging unit that
are available, their advantages and disadvantages, and the criteria for their
selection. In this chapter the various designs of each of these components
commonly used in practical pneumatic conveying installations are described
and illustrated.
13.2 The air supply
13.2.1 General requirements
The selection of an air mover is one of the most important decisions to be made
during the design of a pneumatic conveying plant. It is often the largest single
item of capital expenditure and the potential conveying capacity of the plant is
dependent upon the correct choice being made. Air movers available for
pneumatic conveying applications range from fans and blowers producing
high volumetric flow rates at relatively low pressure to positive displacement
compressors, usually reciprocating or rotary screw machines, capable of
producing the higher pressures required for long distance or dense-phase
conveying systems.
The rating of the air mover is expressed in terms of the supply pressure
required and the volumetric flow rate to be delivered. The pressure of the air
supplied to a pneumatic conveying system will depend principally upon the
operating pressure-drop over the conveying line, although allowance should
be made for additional pressure losses, such as those in the connecting
pipework between the air mover and the conveying line, across the feeding
device (especially where a blow tank is used), and finally, across the filter unit.
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
409
The assessment of the overall system pressure-drop is discussed in the next
chapter.
The volumetric flow rate required from the air mover depends upon the
conveying velocity and the size of the pipeline. It should be noted that the
volumetric output of an air mover is normally expressed as 'free air delivered'
(or FAD). This is the volumetric flow rate at normal atmospheric pressure and
temperature, not at the actual delivery pressure of the machine. In fact, the free
air delivered will approximately correspond to the volumetric flow rate at the
suction port of the machine, or at the discharge end of the conveying line, in a
positive-pressure pneumatic conveying system. For a vacuum system the free
air delivered will be nearly equal to the volumetric flow rate at the suction
nozzle, or at the discharge from the air mover.
In the following sections the main features of some air movers typically
employed for pneumatic conveying duties are outlined.
13.2.2 Fans and turbo-blowers
Fans provide high volumetric flow rates at low pressures and are often used for
dilute-phase conveying. High product flow rates can be achieved with largediameter pipes.
In pneumatic conveying applications, the fans used are normally the radial,
flat-bladed type. Although fans are widely used on dilute-phase systems where
the chances of blocking the conveying line are small, they do suffer from the
disadvantage that their characteristic curve is relatively 'flat' (Figure 13.1)
which indicates that the volumetric flow rate of air produced is very dependent
upon the pressure against which they are working. Thus, if the solids feed rate
to the system should become excessive for any reason, causing the line pressure
drop to increase significantly, the air flow rate may become so low that solid
material falls out of suspension, with the risk then of totally plugging the line.
Positive displacement machines, for which the volumetric flow rate is largely
~
positive displacement blower
volume flow rate
Figure 13.1
Characteristic curves of low-pressure air movers.
410
BULK SOLIDS HANDLING
independent of the discharge pressure, are less likely to cause this type of
system failure.
Single-stage fans capable of delivering air at a reasonable pressure tend to be
rather large in diameter and pneumatic conveying applications therefore often
involve the use of smaller multistage machines. However, these machines are
still sensitive to fluctuations in back pressure and, except for very dilute, low-
Figure 13.2 A cutaway view of a typical regenerative blower (photo courtesy of CompAirReavell Ltd).
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
411
pressure conveying, the current trend is towards positive displacement Rootstype blowers for all normal pneumatic conveying applications involving
pressures up to about one bar gauge.
Fans may be used on both positive and negative pressure systems and also
on combined 'suck-blow' systems where, with light or fluffy materials, it is
sometimes possible even to convey through the fan itself.
For relatively low-pressure duties there may well be advantages in small
regenerative compressors that have recently become commercially available
(Figure 13.2). Although the efficiency of these machines tends to be rather low,
they do possess a characteristic more akin to that of a positive displacement
machine in that they do not display the very sharp fall in flow rate in response
to a rise in back pressure. A beneficial feature claimed for these blowers is that
they are less sensitive than Roots-type or sliding vane machines to erosive
wear from dust-laden air.
The multistage axial flow type of machine is manufactured only in larger
sizes, producing extremely high flow rates that are rarely, if ever, appropriate
for pneumatic conveying applications.
13.2.3 Roots-type blowers
The well-established Roots-pattern blower, developed from F.M. Roots'
original invention of 1859, is extensively used on pneumatic conveying
applications where the operating pressure does not exceed about one bar.
Greater pressures tend to result in deflection of the main shafts, which is
unacceptable because of the necessarily small clearances between the rotors.
However, it seems likely that in the near future Roots-type blowers capable of
working reliably to somewhat higher pressures will become available. As an
exhauster, this machine is also commonly used for negative-pressure systems.
The basic construction of the Roots blower, which is available in sizes
handling up to about 500m 3 /min of free air, is illustrated in Figures 13.3 and
13.4. Twin rotors (which usually have two straight lobes, but may have three)
are mounted on parallel shafts within a casing and rotate in opposite
directions, moving the air in a direction normal to their axes. Timing gears
maintain the relative positions of the rotors so that a small clearance exists
between them. As the rotors turn, air is drawn into the spaces between the
rotors and the casing, trapped, and discharged as each rotor passes the outlet
opening. It should be noted that although the Roots blower is a positive
displacement machine, no compression of the air occurs inside the blower
itself.
13.2.4 Sliding-vane rotary compressors
For medium- and high-pressure systems the sliding-vane type of rotary
compressor is well suited. These generally produce a smoother flow of air at a
412
BULK SOLIDS HANDLING
~
f intake
operating principle
Figure 13.3
A straight lobe rotary blower (Roots-type blower).
higher pressure than the Roots blower, and a single-stage machine is capable
of delivering more than 50m 3 /min of air at a maximum pressure of around
4 bar. Significantly higher operating pressures may be obtained from twostage machines. Oil-injection also permits higher working pressures (up to 10
bar), but this type of machine is generally not available in capacities greater
than about 6m 3 /min.
Figure 13.5a illustrates the operating principle of a simple sliding-vane
compressor. It should be noted that some form of cooling is essential, since
quite high temperatures can be reached as a result of the combined effect of the
vanes rubbing against the casing and the compression of the air between the
rotor and the casing. The cooling may be by water circulated through an
external jacket or by injection of oil directly into the air-stream just after the
beginning of compression (Figure 13.5b). As mentioned previously, the latter
method does permit higher working pressures, but an efficient oil separation
system adds to the cost of the plant.
13.2.5 Screw compressors
A relatively recent innovation for medium- to high-pressure operation is the
helical-lobe rotary or Lysholm screw compressor. This machine, illustrated
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
413
Figure 13.4 An example of an industrial Roots-type blower (cutaway view courtesy of Peabody
Holmes Ltd).
oi separator
oi SI..IT"C
(a) BaSIC
panem
(b) 01 injected machine
Figure 13.5 Sliding-vane positive displacement rotary compressors.
diagramatically in Figure 13.6, consists essentially of male and female
intermeshing rotors mounted on parallel shafts. Inlet and outlet ports are at
opposite ends of the compressor. Air entering one of the ea vi ties in the female
rotor becomes trapped by a male lobe and as the rotors turn this trapped air is
compressed and moved towards the discharge end. Continuing rotation of the
lobes causes the discharge opening to be uncovered so that the trapped air,
414
BULK SOLIDS HANDLING
discharge port
Figure 13.6 Helical lobe rotary compressor (Lysholm screw). Diagrammatic view showing male
and female meshing rotors.
now at minimum volume, is released into the discharge line. Note that like the
sliding-vane compressor, but unlike the Roots blower, compression of the air
takes place within the machine, the compression ratio being fixed by the design
of the rotors and the position of the inlet and discharge ports.
An interesting variant of the machine described above is the Zimmern
monoscrew type which is capable of operating at somewhat higher pressures.
The single rotor may be in the form of a cylinder or a disc cut with helical or
spiral grooves in which mesh the blades of two or more gate wheels. Air
entering the grooves as the rotor turns is trapped by the gate wheels and
compressed, eventually being released through an uncovered discharge port.
Although better known in refrigeration applications, the Zimmern monoscrew
has been produced as an air compressor.
Lysholm-type screw compressors are manufactured with capabilities
ranging from as little as 1 m 3 jmin up to more than 100m 3 /min and, with oilinjection, can develop maximum pressures of around 13 bar. As with oilinjected sliding vane machines, it is essential to remove the oil from the
compressed air and with large compressors the injection, separation and
filtration equipment represents a substantial proportion of the plant cost.
Nevertheless, commercially available screw compressor packages are now
competing strongly with reciprocating machines at the high-pressure end of
the pneumatic conveying market. Figure 13.7 illustrates a typical airprocessing package consisting of screw compressor and motor, air and oil
filters, oil separator and after-coolers.
13.2.6 Reciprocating compressors
The familiar reciprocating compressor (Figure 13.8) is probably still the most
widely-used machine for providing air for high-pressure pneumatic conveying
415
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
ai" flow
non-ren.m valve
intake filer
~->c:--...
-
Figure 13.7 Typical screw compressor plant. Layout diagram to show oil injection/separation
system and ancillary components.
Figure 13.8 A reciprocating compressor suitable for pneumatic conveying applications (photo
courtesy of CompAir-Reavell Ltd).
416
BULK SOLIDS HANDLING
systems, although screw compressors are a serious competitor where large
volumetric flow rates are required. Reciprocating compressors are available as
single-cylinder machines or with multiple cylinders arranged to give one or
more stages of compression, and they can be manufactured to give oil-free air
without the need for additional separation equipment. A compressor of this
type could thus be found to suit almost any pneumatic conveying application
in the medium- to high-pressure range. Even the disadvantage of a pulsating
air flow, usually associated with reciprocating machines, can be overcome by
selecting one of the modern small multiple-cylinder compressors such as that
in which several pairs of radially-disposed opposing positions are made to
reciprocate by the motion of a centrally-placed wobble plate.
13.2. 7 Vacuum pumps
Most of the air movers previously described (or suitable variations of these)
can be used on negative-pressure pneumatic conveying systems. However, the
most commonly used are Roots-type machines, operating as exhausters,
which are capable typically of holding a continuous vacuum of around
500 mm Hg gauge (360 mm Hg absolute). Higher vacuums can be maintained
by a Roots exhauster fitted with water injection, but it would be more usual to
employ a liquid-ring vacuum pump which can reach 600 mm Hg gauge
(1650 mm Hg absolute) in a single stage and over 700 mm Hg gauge in two
stages. Liquid ring pumps having capacities from about 1m 3 jmin up to
70m 3 /min are available.
A typical form of liquid ring pump is illustrated in Figure 13.9. As the
impeller rotates, the service liquid (usually water) is thrown outwards to form a
stable ring concentric with the pump casing. Since the impeller itself is
eccentric to the casing, the spaces between the impeller blades and the liquid
ring vary in size so that air entering these spaces from the suction port is
trapped and compressed before being discharged through the outlet port. The
suction port
Figure 13.9 A liquid ring vacuum pump. Diagrammatic view of a typical pump showing the
principle of operation.
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
417
liquid ring also performs the useful functions of cooling the compressed air and
washing out small quantities of entrained dust.
13.3 Feeding devices
Except for medium- and high-pressure systems using blow tanks, the product
feed is usually from atmospheric pressure (as, for example, from an open
supply hopper) to the conveying pipeline. This presents few problems when
feeding vacuum systems since the product feed is in the direction of the
pressure gradient. However, the product feed to a positive-pressure system
must take place against an adverse pressure gradient, and the resulting leakage
of air from the conveying line can, in certain situations, interfere with the
feeding process. A feeder must therefore be capable of introducing the bulk
solid reliably at a constant rate, even when there is a significant pressure
difference between the conveying line and the supply hopper. Also, it is
important that air leakage at the feed point is kept to a minimum, both to
prevent undue interference to the feeding process and to avoid unnecessary
reduction of the air available to convey the product. One further point to
observe is that the pressure-drop caused by the feeder should be as small as
possible. Some of the devices that have been developed to meet this
requirement will now be described.
13.3.1 Rotary valves
The rotary valve, also known as rotary feeder, rotary seal, star valve or rotary
air-lock, is probably the most extensively used device for feeding low-pressure
pneumatic conveying systems. It consists basically of a bladed rotor working
in a fixed housing (Figure 13.1 0). Product from the supply hopper continuously fills the rotor pockets at the inlet port which is situated above the
rotor. It is then transferred by the motor-driven rotor to the outlet where it is
prodJct feed
outlet port
Figure 13.10
Rotary valve ('drop through' pattern).
418
BULK SOLIDS HANDLING
air
air
+
product
air + product
(a) Drop-out box
Figure 13.11
(b) Venturi
Typical entrainment sections.
discharged and entrained into the conveying line. The ability to feed against an
adverse pressure gradient is achieved by allowing a flow of air (leakage) to take
place through the rotor casing clearance on both the product feed and empty
return pocket sides of the rotor.
The most commonly used design of rotary valve is the 'drop-through'
pattern in which the bulk solid being handled (which should be reasonably
free-flowing) is metered through the rotating valve and falls into a separate
entrainment section beneath. This entrainment section may be nothing more
than a simple 'drop-out' box (Figure 13.11 a), but an alternative configuration
that seems to be gaining in popularity is the venturi entrainment section
(Figure 13.11b). In the latter case, the reduced cross-section results in a higher
entrainment velocity and a lower pressure in this region, with a consequent
decrease in the air leakage back through the rotary valve. The net result is a
significant improvement when handling the finer, free-flowing types of bulk
solid.
A variation on the standard pattern of feeder, intended primarily for
handling granular and pelletized materials, where shearing of the product is to
be avoided, is the offset rotary valve (Figure 13.12). This is designed, usually
with a controlled supply of solids, so that the rotor pockets do not become full
and therefore the chance of material becoming nipped between the rotating
Figure 13.12
An offset pattern of rotary valve.
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
419
rotor
air---:::J:::::::::=t:::::::::::r-a;:ir;-:+:-;p~roduct
Figure 13.13
A rotary valve of the 'blow-through' type.
blades and the valve body is virtually eliminated. Another variation, intended
primarily for use with more cohesive materials that might tend to 'hang up' in a
standard pattern of rotary feeder, is the 'blow-through' valve (Figure 13.13). In
this device the conveying air passes through the rotor and purges the
discharging pockets, entrainment of product thus occurring actually within
the valve. Figure 13.14 illustrates some examples of modern, commercially
available rotary valves.
Before discussing the problems with and limitations of rotary valves it is
beneficial to have an understanding of how they work. The most simple
concept of the way in which these devices work is that the rotor pockets fill
completely with material fed to them by the supply hopper. Under such
circumstances the product mass flow rate m, for any rotor speed N is given by
the simple equation
( 13.1)
This equation represents the maximum possible throughput of a valve and is a
measurable quantity since the volume of one rotor pocket is denoted by V, n is
the number of rotor pockets and Pb is a characteristic bulk density of the
product being handled, which experience has shown may be approximated by
the 'poured' value obtained from static tests. This equation suggests that the
feed rate depends only on the rotor speed, as shown by the straight line in
Figure 13.15. However, when feeding a conveying line, the air leakage through
the valve can impede the product flow into the rotor pockets and thereby
reduce the feed rate. In extreme cases this can be a value much lower than that
predicted by equation ( 13.1 ). Since it is evident that both the rotor casing
clearances and system pressure affect the leakage, the feed rate depends in
some way on (i) the product being handled, (ii) the rotor speed, (iii) the rotor
casing clearances, and (iv) the system pressure. Consequently, valve performance is more likely to take the form of one of the curves shown in
Figure 13.15. Unfortunately, there is little data available in manufacturers'
420
BULK SOLIDS HANDLING
Examples of modern commercially-available rotary valves. (Top) Drop-through
pattern; (Bottom) blow-through pattern. (Photos courtesy of Rota Val Ltd.)
Figure 13.14
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
421
feed rate with
no air leakage
dependent on product,
rotor clearances and
system pressure
rotor speed -
Figure 13.15
Typical feed rate characteristics.
literature on the effect of these operational variables on feed rate, and so the
sizing of valves for a particular application has been, until recently, a matter of
experience and good judgement.
A second problem with rotary valves concerns the extent of the air leakage
itself. As previously discussed, this will principally depend upon the system
pressure, rotor clearances and the product being handled. Figure 13.16 shows
a typical relationship between system pressure and leakage rate for various
rotor clearances. A lack of knowledge about this leakage at the design stage of
such systems can obviously lead to fans and blowers being incorrectly sized.
When a blower is oversized, the conveying velocity of the solids is increased
and, if the conveyed product is abrasive, this increased velocity may cause
rapid wear and premature failure of pipe bends and fittings. If the product is
friable, the increased velocity may cause excessive product degradation.
Conversely, with an undersized compressor the air velocity may not be
sufficient to hold the solids in suspension, resulting in the possibility of a
blocked pipeline.
For the reasons outlined here, rotary valves are not generally used to feed
from atmosphere into systems which have a pressure above about 0.8 bar
gauge, since the leakage, with its attendant problems, can become excessive at
pressures greater than this. If the undesirable effects described above are to be
minimized, reliable information on the valve performance is required when the
422
BULK SOLIDS HANDLING
increasing rotor-casing
clearances in this direction
pressure gradient - -
Figure 13.16
Typical leakage rate characteristics.
conveying system is being designed. Simple procedures for estimating both
feed and leakage rates of typical valves have recently been developed [1, 2] and
if these are thoughtfully applied they contribute to reducing the 'judgement
gap' which exists when predicting valve performance.
A further limitation of rotary valves is that they are not particularly well
suited to handling abrasive products. Although they can be manufactured
with replaceable wear-resistant rotor blades and housing liners to enable
mildly abrasive products to be handled, it is not generally considered good
practice to use these feeders with products that have particle hardness greater
than 2 or 3 on the Mohs scale. Products harder than this can cause a rapid
increase in the rotor casing clearances, the consequences of which on system
performance have already been discussed.
For the majority of applications rotary valves perform perfectly satisfactorily. However, it is not uncommon for the valve to be blamed for poor
system performance and, in some cases, this has proved to be justified for the
very reasons outlined in this section. It is therefore worthwhile describing here
some of the salient design features which help to ensure satisfactory valve
performance.
Rotors normally take one of two forms; that is, 'open-end' or 'closed-end'. In
the 'open-end' pattern the blades are welded directly to the driving shaft, whilst
with the 'closed-end' type discs or shrouds are welded to the shaft and blade
ends to form enclosed pockets, as shown in Figure 13.17a. Although open-end
r:J.
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
/
/
/
~
closed-end (shrouded)
423
/
angled blades (for
grarular pro<ilcts)
(a) Rotor types
shaHow rOU1ded pockets
for cohesive pro<ilcts
normal pattern
replaceable blade t~s
for abrasive products
(b) Pocket configtxations
Figure 13.17
Various features of rotor construction.
rotors are less expensive they have several disadvantages. With more abrasive
materials, wear of the rotor housing end plates is possible since the product is
in constant contact with them. Also, they are not as rigid as the closed-end type
since they have only one edge secured to the drive shaft. The closed-end type
are more rigid and can be used with abrasive materials. However, they cannot
be used in the blow-through types of feeders shown in Figure 13.13.
There are basically two rotor pocket configurations in widespread use, and
these are shown in Figure 13.17b. The most common is the type which has
deep pockets and therefore maximum volumetric displacement. It is more
suited to handling free-flowing products. The rotor with shallow, rounded
pockets has a somewhat smaller volumetric displacement, but this configuration has been successfully used with the more cohesive types of product that
could tend to stick in deeper pockets. With abrasive products there may be
some advantage in fitting the blades with replaceable tips.
As air from the conveying line leaks through the valve, each rotor blade in
close proximity to the casing produces a drop in pressure in the direction of the
pressure gradient. Consequently, a method of reducing the leakage is to
increase the number of rotor blades. Obviously, there is a practical limit to the
number of blades that can be used in a rotor when handling a given product.
This constraint is largely dependent on the product itself, since increasing the
number of blades decreases the angle between them, and this is sufficient with
some products to prevent them from being discharged when presented to the
424
BULK SOLIDS HANDLING
outlet port. It is for this reason that the number of rotor blades is optimized
at between eight and ten on most commercially available valves.
The rotor clearances can have a significant effect on valve performance and,
in an attempt to minimize the effect of the leakage on the feed rate,
manufacturers make these clearances as small as possible. Clearances on new
valves are typically 0.075-0.15 mm, since clearances smaller than this would
add considerably to the cost of manufacture and may even lead to the rotor
binding in the housing due to deflection of the rotor and movement within the
bearings when subject to the applied pressure gradient. Some manufacturers
fit flexible elastomer/polymer wipers to the rotor blades so that they are in
contact with the housing (Figure 13.17b). However, this approach is generally
limited to low-pressure applications (less than 0.25 bar gauge) since the
leakage at pressure gradients greater than this can deflect the wipers and so
lose the advantages.
A technique which has been developed by manufacturers and users of rotary
valves as a practical solution to the problem of air leakage is 'venting'. This
involves the provision of an alternative means of escape for the leaking air, so
that it does not impede pocket filling. This is normally achieved by the
provision of vent holes in the valve casing on the empty pocket return side of
the rotor cycle, as shown in Figure 13.18. However, opinion is divided on the
effectiveness of the technique. Some manufacturers strongly recommend its
use in all situations where valves feed against pressure gradients. Others argue
product teed
·'·r]
)}:·~;t~
vented air
.
.
.
.
L
Figure 13.18
t
vented
ar
+
Valve venting.
ar
prod.ict
air + product
Figure 13.19
--
air
Venting techniques.
air + product
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
425
that, provided the rotor clearances are small enough, venting is unnecessary.
Evidence exists to support both of these opinions and the decision on whether
or not to incorporate venting usually depends on experience acquired from
installing equipment in similar circumstances. Since the vented air will
inevitably contain a carry-over of product, this is normally directed back to
the supply hopper or to a separate filter unit, as shown in Figure 13.19.
13.3.2 Screw feeders
The basic screw feeder, illustrated in Figure 13.20a, is rarely used to feed
pneumatic conveying systems since, unlike the rotary valve, there is little in the
design to satisfy the important requirement of feeding against an adverse
pressure gradient. However, by designing the screw with a decreasing pitch it is
possible to generate a plug of material within the barrel that effectively satisfies
this requirement. As the screw continues to rotate the plug is pushed into the
pipeline where it is dispersed and entrained in the conveying air
(Figure 13.20b). Screw feeders are generally suitable for handling cohesive
materials and an important advantage of a well-designed feeder of this type is
that the discharge into the conveying line is continuous. Furthermore, since
there is a linear relationship between the rotational speed of the screw and the
feed rate, the discharge can be controlled within close limits.
More sophisticated variants of the screw feeder have been developed for the
purpose of feeding a product against somewhat higher pressures. The Mono
pump (Figure 13.21 a) was originally conceived for pumping slurries but it has
been demonstrated to be useful for feeding fine particulate products into
conveying lines at pressures of up to 0.5 bar gauge, provided that the product is
initially aerated so that it enters the pump effectively in a fluidized condition.
Another device for use on similar applications is the screw-pump
(Figure 13.21 b) which is capable of operating successfully at conveying
pressures of up to 2.5 bar gauge and can therefore achieve reliable transport
over considerable distances. This feeder, which is best known under the name
Fuller Kinyon pump, although very similar versions are manufactured by a
(b) Decreasng pitch screw
(a) Slr(lle screw
Figure 13.20
Screw feeders.
426
BULK SOLIDS HANDLING
(a) Mono purrp
prod.ict
-
andai"
out
(b) FtJer-Khyon purrp
Figure 13.21
Two forms of feeder-pump.
number of different companies, is particularly common in the cement industry.
The product is fed from the supply hopper and is advanced through the barrel
by the impeller screw. Since the screw pitch decreases towards the outlet, this
compacts the material as it advances and propels it through a provided nonreturn flap at the end of the barrel and into a chamber, to which air is
continuously supplied through a series of nozzles. The air/solids mixture, at a
pressure of up to about 2.5 bar gauge, then passes into the conveying pipe
which depending upon the feeder size and the conveying distance, would
normally be in the range 75 mm-400 mm.
13.3.3 V enturi feeders
Since the basic problem with feeding positive-pressure systems is that the
leakage resulting from the adverse pressure gradient can interfere with the flow
of product into the conveying line, some improvement should be possible if the
pressure at the feed point is reduced. The venturi feeder (Figure 13.22) is
designed to achieve this by reducing the cross-sectional area of the pipeline at
the feed point so that the pressure in this region is lowered to that of the supply
hopper, with a corresponding increase in the velocity of the conveying air. In
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
427
product feed
air+
product
air
IIToat - region of reduced presStre
Figure 13.22
Venturi feeder.
this way the air leakage from the conveying line to the supply hopper is almost
eliminated and the product can flow more readily under gravity into the line.
In order that a sufficiently low pressure is maintained at the feed point
without the cross-sectional area becoming too small, the total pressure-drop
through the conveying line must be kept quite low. For this reason the use of
venturi feeders is usually restricted to applications where a free-flowing
product is to be conveyed at low flow rates over short distances. A further
constraint on the use of this type of feeder results from the high velocities that
are reached in the throat section since serious erosion can occur in this region
when abrasive products are being handled. Finally, it should be noted that the
flow of product to the venturi feeder must be controlled by an appropriate
metering device, such as a screw-feeder or belt-feeder, if blockage of the throat
is to be avoided.
13.3.4 Gate lock valves
These are probably the least used of all devices for feeding positive-pressure
conveying systems. They are also known as double-flap valves and doubledoor discharge gates. They basically consist of two doors or gates which
alternatively open and close to permit the passage of the product from the
supply hopper into the conveying line (Figure 13.23). These gates may be
motor-driven, cam or air-cylinder-operated, or may work under gravity. The
air which passes the lower gate from the conveying line is vented so that it does
\-,.
)'·-'---~
~-:· ..._;.::~7Figure 13.23
Operating sequence of a gate lock valve.
428
BULK SOLIDS HANDLING
not interfere with the product about to flow through the upper gate. As with
rotary valves, the blower or compressor should be sized to allow for this
leakage. Like the venturi feeder, care must be taken to ensure that the product
is metered into the gate lock since it will cease to function correctly if it
operates under a head of material, as would be the case if it was situated
directly beneath the outlet of the supply hopper.
To a certain degree the gate lock might be termed an intermittent feeder
since it discharges material between five to ten times a minute. In contrast, the
rotary valve has up to approximately 250 discharges per minute from its
pocketed rotor. This reduction in the number of discharges obviously means a
higher volume per discharge when comparable rates are handled. This can, in
turn, lead to a blockage in the entrainment region if the pipeline is not correctly
sized. This type of feeder has been used successfully with system pressures up to
0.4 bar gauge, and with appropriate materials of construction it is suited to
handling both pulverized and granular abrasive products.
13.3.5 Blow tanks
All the devices considered so far are capable of feeding a bulk solid into a
conveying line against an adverse pressure gradient. However, only the
Fuller-Kinyon pump can operate successfully against a pressure much in
excess of 1 bar gauge. Where it is required to convey a product in dilute phase
over a distance of more than about 300 m, or in dense phase over more than
about 50 m, it is likely that a high-pressure system will be required, and this
may be beyond the operating range even of the Fuller-Kinyon pump. As
explained in the previous chapter, feeding into high-pressure systems almost
always involves the use ofblow tanks, and these devices are capable of working
at pressures of around 7 bar gauge, or sometimes rather higher.
The blow tank itself is essentially a pressure vessel which is gravity-fed with
the bulk solid to be conveyed. The feed valve on the top of the vessel is then
closed and, with the valve in the conveying line also closed, the blow tank is
pressurized to the required conveying pressure. With the compressor still
operating the outlet valve is opened and conveying begins. Since the blow tank
delivers product to the conveying line in batches it is quite common practice to
use two blow tanks operating in sequence so that one is being recharged while
the other is discharging.
A particular advantage with blow tank systems is that the blow tank itself
serves as the feeder, and so the problems associated with feeding against an
adverse pressure gradient do not arise. However, since there can be a
considerable difference in pressure between the blow tank and the entrance to
the conveying line, this must be taken into account when evaluating the
requirements of the compressor. Another positive feature of blow tanks is that,
unlike the feeders already discussed, they are generally free of moving parts.
With the blow tank acting as the feeder, product degradation and erosion in
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
429
this region can also be reduced and so low grade blow tanks are often used in
low-pressure systems as an alternative means of feeding the conveying line.
However, a point that should be borne in mind is that, since the blow tank is
essentially a pressure vessel, it has to be designed and manufactured to an
appropriate pressure vessel code. Until recently such codes have been BS 1500
Part 1; 1958 and ASME 8. However, these have been largely superseded in the
UK by BS 5500: 1976, which is more stringent in terms of design, manufacture
and inspection requirements. A direct consequence of this is that blow tanks
can be very expensive when compared with the feeders described in the
previous sections.
Blow tanks are invariably classified into either 'top-discharge' or 'bottomdischarge' types. This terminology refers to the direction in which the contents
of the vessel are discharged (Figure 13.24). With bottom discharge the product
is gravity-fed into the pipeline and if the conical section is sufficiently
air • product
0
0
·..
air • product
(a) Bottom discharge
supplementary
a1r
(c) Bottom discharge with
supplementary air
Figure 13.24
discharge.
(b) Top discharge
porous membrane
(d) Top discharge with
supplementary air
Various blow-tank configurations showing aeration of the product to aid
430
BULK SOLIDS HANDLING
steep the contents can be completely evacuated. Top discharge is arranged
through an off-take pipe which is positioned above the base of the tank, and it
is quite common for this configuration to retain a certain amount of product
around the periphery of the bottom of the tank. This simple classification can
become confused by the considerable number of different configurations that
are used to admit air to the blow tank and conveying line. Ideally, all that is
required is to admit air into the top of the blow tank until it reaches the
pressure required for conveying. With the outlet valve open and the
compressor still running, the air passing into the conveying pipe carries the
product with it and so by this means the contents of the tank are gradually
discharged. In such a system the pressure in the blow tank is obviously related
to the product flow rate, and Figure 13.25a illustrates a typical relationship. It
should be noted that the curve will not pass through the origin since there
exists a finite (positive) blow tank pressure at zero feed rate. This represents the
pressure drop through the system with only air flowing. Such a graph enables
the designer to determine the blow tank pressure required to feed the product
at the desired rate.
With some products the method of admitting the air to the blow tank
described above is sufficient to feed and convey at the desired rates. However,
with others this has led to unsteady feeding, conveying below design ratings
and even blockages in the entrance to the conveying pipe. Consequently, it has
become almost standard practice to aerate the product in the region of the
entrance to the conveying pipe with a view to aiding discharge and giving a
air flow rate to blow tank
1.0
total air flow rate
//\
0.9
\
0.8
0.7
Q)
~
-o
X
Q)- - - -
.!!?
~
0
en
~
:;
.0
blow tank pressure(a) Typical relationship between
blow tank pressure and bulk
solid feed rate
Figure 13.25
total air flow rate(b) Typical relationship between air
and bulk solid flow rates
Blow tank operating characteristics.
COMPONENTS OF PNEUMATIC CONVEYING SYSTEMS
431
more uniform feed. With the bottom discharge tank this is achieved by
admitting air near the base of the cone, as shown in Figure 13.24c. With the top
discharge type (Figure 13.24d) the air is admitted through a membrane which
may be a porous plastic, porous ceramic or a woven belting material sandwiched between perforated plates. With this particular configuration it has been
shown that the height of the off-take pipe above the membrane can have a
significant effect on the feed rate. For this reason it is recommended that for the
finer, powdery types of product, this distance should be about 20 mm whilst it
is increased to about 40 mm when handling the more granular types of
product.
Experience has also shown that, with both of these configurations, a
supplementary supply of air just after the product had entered the conveying
line aids the conveying process. Unfortunately, the optimum proportions of
these air supplies (blow tank and supplementary) are ill-defined and it has
often required considerable skill on the part of the installation engineers
during commissioning to adjust the blow tank performance so that it will yield
the desired product flow rates. However, an insight into the relationship
between the quantities of these air supplies has emerged with recent
experimental data, which is shown in an idealized form in Figure 13.25b. This
shows the effect of the total air flow supplied to the system (blow tank and
supplementary air) on the product flow rate for various proportions of blow
tank to total air flow rates. The significant implication of this information is
that once the total air flow rate to convey at a given flow rate has been
determined, this then enables the proportions of the air supplied to the blow
tank and the supplementary tapping to be determined. For example, if it has
been determined that to convey X kg/s of product required Y kg/s of air, then
the intersection of these lines suggests that 80% of the air should be supplied to
the blow tank whilst the remaining 20% should be supplied to the supplementary tapping.
13.3.6 Entrainment devices for vacuum systems
The feeding of bulk solids into vacuum conveying systems is generally an
easier matter than feeding a similar positive-pressure system since the pressure
gradient is in the direction of the product feed and will in fact assist the flow of
product into the pipeline. Where the feed rate of the product must be
controlled, almost any of the feeders previously described would be suitable.
However, if the feed rate is not critical it is possible to use a much simpler, and
cheaper, device such as a slide- or gate-valve (Figure 13.26).
A distinct advantage of a vacuum system is that it can be used to reclaim
material from a 'free surface'; for example from a pile or from a bunker or ship's
hold. In these circumstances a suction nozzle of the type shown in Figure 13.27
would be generally used. As with a domestic vacuum cleaner, it is essential
when using one of these suction nozzles to maintain an adequate flow of air
432
BULK SOLIDS HANDLING
adjustable
air inlet
Figure 13.26 Slide/gate valve.
-conveying pipe
(a) Suction nozzle
conveying pipe
(b) Shovel type suction intake
Figure 13.27 Suction nozzles.
through the suction tube at all times, and to avoid filling the tube solidly with
the bulk material.
Many different types of suction nozzle have been developed over the years
but probably the most common pattern is that consisting of two tubes
arranged eo-axially as shown in Figure 13.28. The annular passage between
the tubes permits the air induced into the nozzle by the exhauster to entrain
particles into the flow entering the inner tube. Recent research [3] has
demonstrated that the relative positions of the ends of the inner and outer
tubes can have a significant influence on the effectiveness of the suction nozzle,
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
433
\ r6t\k~~: r
~~~i~~
K'<-:~ ~:?~ (;~
~i~'6.~~;. ."'r'i:.-·
·};..1-£~ \?-~i ~): ¥~;~
y:,,.,k!/J 'tt;r;,/ \"~~
'IL--:;t.''V.
~~f.~M1i~~~~~~
[a) Inner tube retracted
within outer tube
Figure 13.28
[b) Air flow throttled on
inlet to annulus
Cc) Inner tube extended
beyond outer tube
Co-axial tube suction nozzle showing typical modes of operation.
and therefore on the overall performance of the vacuum system, for a wide
range of different bulk solids. In order to achieve the highest practical solids
flow rates for any given air flow rate it is generally necessary that the inner tube
of the nozzle should project beyond the outer tube, as illustrated in
Figure 13.28e, The amount of the extension for optimum performance appears
to depend upon the nature of the bulk solid being handled: up to about 25 mm
gives good results with a 50 mm-diameter suction tube but more than this is
likely to result in the tube becoming blocked.
13.4 The pipeline
An extremely important part of any pneumatic system, but one which too
often receives insufficient attention, is the pipeline itself. There are many
materials from which the pipe could be manufactured, the commonest being
seamless mild steel, stainless steel and aluminium. For short, light-duty
pneumatic conveying plastic pipe may be considered, but care should be taken
to guard against hazards associated with electrostatic charging. For special
applications requiring, for example, a flexible pipe, various rubber compounds
are available.
Apart from the obvious need for physical strength when used on highpressure applications, the main criterion for the selection of a suitable pipe
material is the nature of the bulk solid to be conveyed. In the food industry, or
in other situations where rust contamination could be a problem, mild steel
piping should obviously be avoided. There are many examples of problems
arising with specific products: in the plastics industry, for instance, where the
internal surfaces of pipes handling low-density polyethylene are specially
434
BULK SOLIDS HANDLING
(a) Standard flanged type
(b) Sleeve-type allowing easy rotation
of installed pipe to equalize wear
Figure 13.29 Typical couplings for pneumatic conveying pipelines.
roughened to prevent the formation of the streamers of plastic film known as
'angel hair' [ 4].
Joints between sections of pipe are often butt-welded but it is a good policy
to design the system in such a way that appropriate parts of the pipework can
be easily dismantled in the event of a blockage occurring. Whatever method is
used for pipe jointing, it is necessary that two precautions be observed: one is
that the pipes are accurately aligned as any ridges can deflect the flow to cause
erosive wear, and the other is to ensure that electrical continuity is maintained
across the joint components in situations where electrostatic charging
represents a hazard. Simple welded or screwed flanges are a convenient and
common method of joining lengths of pipe, but there are currently on the
market several different patterns of compression-type sleeve coupling
(Figure 13.29).
There is frequently a need to change the path of a solids flow, from one
hopper which has become has become full, to another, for example. Obviously
this could be achieved by manually disconnecting the conveying line and reconnecting it to the appropriate point, but naturally manufacturers have
developed a variety of flow diverters to achieve the same effect. These diverters
are available in various forms, the flap valve and the slide valve illustrated in
Figure 13.30 being perhaps the most widely used. By their very nature, diverter
valves tend to suffer from the harsh service conditions and it is important that
they should not be placed in inaccessible locations.
Despite the fact that one of the main advantages stated for pneumatic
(a) Flap type
(b) Shde type
Figure 13.30 Diverter valves.
COMPO:-iEJ\TS OF PNEF:Vll\ TIC COSVEYlNG SYSiTMS
435
436
BULK SOLIDS HANDLING
conveying systems is their flexibility of routing, it is always desirable for the
conveying line to follow the most direct route from the feed point to the
discharge. Pipe bends are to be avoided, as far as possible, because they
represent a resistance to the flow of the bulk solid (and therefore add to the
overall system pressure-drop) and also, when abrasive products are being
conveyed, because they tend to be an Achilles heel in terms of erosive wear and
subsequent leakage. Where bends are unavoidable it is usually recommended
that they are of the 'slow' type, having a radius of at least five times the pipe
diameter. In situations where erosive wear of the bend is likely to be a problem
it is essential that flanges or couplings are used so that the bend can be easily
replaced. Strengthening the bends with welded pads or other forms of 'wearback' is common practice and a number of special designs of bend, claimed to
reduce wear, are commercially available (Figure 13.31).
13.5 Disengaging and collecting devices
The choice of gas/solids disengaging system to be used on any given
application will be influenced by a number of factors, notably the amount of
bulk solid involved, the particle size range, the collecting efficiency required
and the capital/running costs. In general, the finer the particles to be collected
the higher will be the cost of a suitable disengaging system.
Usually the choice is between some form of cyclone and a fabric filter, and
where fine particles are involved (that is, less than about 25 ,urn) it is likely that
only a fabric filter will give a satisfactory collecting efficiency. The loss of
pressure in the gas/solids separator is unlikely to be significant in comparison
to the overall system pressure drop, except perhaps in the case of fan systems.
However, methods of estimating the pressure-drop are given in Chapter 5,
along with descriptions of these components and guidance on their selection.
13.6 Notation
m,
N
n
V
Pb
Solids mass flow rate
Rotational speed (revolutions/second)
Number of rotor pockets
Volume of rotor pocket
Bulk density
References and bibliography
References
I. Reed, A.R. and Mason, J.S. Estimating air leakage through rotary valves. Bulk-Storage.
Movement, Control 3(3), (January/February 1977).
2. Reed, A.R. Estimating feed rates of rotary valves. Solids Handling 1(6) (November/December
1979).
COMPONENTS OF PNEUMA TIC CONVEYING SYSTEMS
437
3. Reed, A.R. and Mason, J.S. The effect of suction nozzle design on the performance of vacuum
pneumatic conveying systems. J. Powder and Bulk Solids Technol. 7(4) (1983) 9-14.
4. Dixon, G. Pneumatic conveying. In Plastics Pneumatic Conveying and Bulk Storage, ed. G.
Butters, Applied Science Publishers, 1981.
Recommende d further reading
Kraus, M.N. Pneumatic Conveying of Bulk Materials. Ronald Press, New York, 1968.
Anon. Industrial Reciprocating and Rotary Compressors: Design and Operational Problems.
Proc. I M echE Con[., London, October 1970.
Q
14
Pneumatic conveyor design
14.1 Introduction
In the two preceding chapters discussion has been restricted to general details
ofthe arrangements of pneumatic conveying systems and their components. It
is necessary now to give some more positive pointers to successful pneumatic
conveyor design.
It is probably still true to say that in industry pneumatic conveying of bulk
solids is widely regarded as something of an art. The specification of systems
and the selection of components tends to rely heavily upon the judgement
and practical experience of engineers who are familiar with the subject, and the
relatively small (but increasing) number of companies that specialize in the
manufacture and installation of pneumatic conveyors guard jealously the
knowledge that they accumulate.
Whatever the type of pneumatic conveying system to be installed, the design
decisions must centre upon the pipeline diameter and the size (and power) of
the air mover required. Amongst the many other design decisions to be made,
probably the most important concern the method of feeding the bulk solid into
the pipeline and the type and size of disengaging device to be used.
It is possible to find in the published literature many suggested approaches
towards the design of pneumatic conveyors, but none of these provides a single
reliable method for designing a complete system from a knowledge only of the
properties of the bulk solid to be conveyed. Certainly there has been, in recent
years, an improved understanding of the characteristics of gas/solids flow in
horizontal and vertical pipelines. There have even been papers reporting
specifically on the influence of bends and fittings. It is beyond the scope of this
book, however, to attempt a review of the different design methods available
and attention here is restricted to a discussion of some aspects of a design
approach that will enable a specification to be drawn up for a given
application with reasonable confidence.
In general, the designer would be presented with information on the
material to be transported, the mass flow rate required, the rough layout of the
conveying system and, possibly, the type of system (that is, positive-pressure or
vacuum, dilute- or dense-phase, and so on). The first design decisions then
concern the conveying velocity, the solids loading ratio (that is, the ratio of the
mass flow rate of conveyed solids to the mass flow rate of conveying air) the
diameter of the pipeline and the pressure-drop through the system, leading to
the specification of the air mover in terms of flow rate and delivery pressure.
The application and reliability of mathematical models is somewhat limited
PNEUMATIC CONVEYOR DESIGN
439
in the field of pneumatic conveying. As explained in Chapter 3, many
proposals have appeared in the technical literature for the modelling of
gas/solids flows in dilute phase, and even some for dense phase. However, none
of these has become accepted as sufficiently reliable for the confident design of
pneumatic conveying systems. In the case of dilute-phase flow, since the solid
particles are uniformly distributed within the gas stream, it seems reasonable
to suppose that a simple analytical approach might allow the relationship
between solids flow rate, gas flow rate and pipe size to be predicted with
sufficient confidence to enable a preliminary design of the system to be
undertaken. For dense-phase flow, the mechanism by which the solid particles
progress along the pipeline is so complex that there seems to be little chance
that any 'first-principles' modelling approach will really be useful.
In order to design a pneumatic conveying system with confidence there is
generally no alternative but to rely upon available test data for the bulk solid
concerned. Frequently this data can be derived from previous experience with
the same product, but if the product is a 'new' one and no information is
available on its handling characteristics in a pneumatic conveying system,
appropriate trials will have to be carried out in a pilot plant. Naturally the
design engineer must make a decision on how closely the test data should
parallel the actual installation that is to be designed. The extreme case of a fullscale 'mock-up' in which the actual bulk solid is tested might occasionally be
justified, but usually the trials would be undertaken in a test rig that is smaller
(either in terms of pipe size, or conveying distance, or both) and the results
scaled appropriately. It is always good policy to test the actual bulk solid
concerned, as even small differences in the physical properties of a material can
cause major differences in handling characteristics. An expensive mistake
could be made if, for example, a system successfully conveying cement is used
as the basis for designing one to handle, say, fertilizer.
In this chapter a general design procedure will first be outlined and then
more detailed consideration will be given to the determination of the
'conveying characteristics' of a bulk solid and the application of this data
within the design process. It should perhaps be emphasized at this point that it
is not the intention of the authors to set out here a definitive procedure for the
design of pneumatic conveying systems: for one reason, we do not have enough
pages available! However, it is hoped that there is sufficient detail in the
following discussion for it to be interesting, useful in giving an insight to the
design process and, in particular, to draw attention to some of the pitfalls that
may be encountered.
14.2 General design procedure
14.2.1 Conveying velocity and volumetric air flow rate
As air flows along a pipeline, the decreasing pressure resulting from the
440
BULK SOLIDS HANDLING
frictional resistance to the flow causes the air to expand. The average velocity
of the air across a section of the pipe must therefore increase in the direction of
flow so that in a pneumatic conveying system the lowest velocity normally
occurs at or near the point where the bulk solid is fed into the line. Clearly this
lowest velocity must be sufficient to transport the bulk solid without the risk of
blockages occurring in the system and, since the 'minimum transport velocity'
depends principally upon the nature of the bulk solid itself, it is usually the first
design parameter to be fixed.
Unfortunately the minimum transport velocities for different bulk solids are
not easily predicted since this parameter is influenced by many diverse
variables, including material properties such as particle size, density and
shape, cohesiveness and abrasiveness, and also (significantly) the solids
loading ratio. The only really satisfactory method of determining the
minimum transport velocity for a given particulate material is to carry out
tests on the material in a pilot plant having features that correspond as closely
as practicable to those of the plant being designed. Clearly this is where the
experience of the designer can be valuable, as he may have prior knowledge of
the conveying characteristics of the actual material or of a similar one.
As explained elsewhere in this book, there is a marked trend towards the use
of dense phase in preference to dilute phase for pneumatic conveying systems
because of the lower running costs and less severe effects on both the plant and
the conveyed bulk solid as a result of the lower velocities involved. However,
certain materials, especially those of a granular nature, cannot be conveyed in
a conventional dense-phase system, and the minimum transport velocity is
then determined by the point at which the particles begin to fall out of
suspension. For a wide range of materials this will occur at a velocity of around
16 mjs and this is a good value at which to begin the preliminary design of a
dilute-phase system. It should be understood, however, that with bulk solids
containing large lumps, especially if the density is high, the minimum transport
velocities may be very much greater.
For bulk solids capable of being conveyed in dense phase the minimum
transport velocity is typically around 5-10 mjs, but this is quite variable, and
there is really no alternative but to design from observed behaviour of the
materials concerned. In any case, for such materials, which generally tend to
have good air-retention properties, the minimum transport velocity depends
to a significant extent on the solids loading ratio. Conveying at higher values of
the solids loading ratio can often allow the gas velocity to be reduced, so
effecting a worthwhile saving in power consumption, but there is, of course, a
practical limit which can be determined only from conveying trials.
Once the minimum transport velocity has been determined, by whatever
means, it is recommended that a value twenty per cent higher should be used
for design purposes in order to provide a margin of safety against pipeline
blockage. Velocities greater than this are generally not advisable because of
the increased power and filtration requirements, the adverse effect (for most
PNEUMA TIC CONVEYOR DESIGN
441
products) on the solids flow rate and the possibility of excessive degradation of
the conveyed material and erosive wear of the system components.
It will be necessary, in due course, to calculate the volumetric flow rate of air
required ('free air' -that is, at normal ambient conditions) and this quantity is
related to the conveying air inlet velocity u81 , discussed above, by the following
equation:
(14.1)
where D is the diameter of the conveying pipe, p 1 and T 1 are the pressure and
absolute temperature at the inlet, and p0 and T0 are the standard ambient
pressure and absolute temperature. In SI units, taking Po = 1 bar and
T0 = 288 K, the relationship becomes
(14.2)
where p 1 is in bar absolute, D is in metres, ug 1 is in metres/second and t 1 is the
temperature in degrees Celsius, giving V0 in m 3/s.
Note that this value of V0 will be the volumetric flow rate of air required to
convey the bulk solid through the pipeline. The volumetric air flow rate to be
specified for the air mover must be larger to take account of'leakage' from the
rotary valve or other feeder or, in the case of a vacuum system, to take account
of any additional air ingress along the conveying line. For a positive-pressure
system fed by a rotary valve, an air leakage rate of 15-20% of the blower
output would be quite normal.
14.2.2 Solids mass flow rate and solids loading ratio
The specification for a pneumatic conveying system will generally include the
required solids throughput as the number of tonnes of the bulk solid to be
transported in one hour. The actual flow rate of the material along the pipeline
can then be determined according to the proportion of the time that the system
is actively conveying. Thus, in the case of a continuously-operating system, the
design would be based on the steady hourly rate through the pipeline, whereas
if the system selected is to operate batchwise (a single blow tank system, for
example) the pipeline must be sized for a higher rate than the specified hourly
rate to allow for non-continuous conveying. The ratio of the design flow rate to
the specified hourly rate will depend upon the type of batch system to be used.
Typical ratios would be about 1.25 for a twin blow tank system and about 1.5
for a single blow tank capable of conveying a one-tonne batch. Thus, if a single
blow tank system is to be designed for a rate of 40 tonne/hour, the pipeline
should be sized for a conveying rate of about 60 tonne/hour.
The ratio of the mass flow rate of the conveyed bulk solid to the mass flow
442
BULK SOLIDS HANDLING
rate ofthe conveying air, known as the 'solids loading ratio' or 'phase density',
is another design parameter that is difficult to predict with much confidence. In
so-called 'dense-phase' pneumatic conveying systems very large values of
solids loading ratio (</J) may be obtained-possibly up to several hundredsand in the extreme, <P approaches the value corresponding to the minimum
fluidizing condition. In fact, the conveying velocity and the solids loading ratio
are interrelated and it is perhaps a matter for debate which should be selected
first. To some extent the choice of solids loading ratio is dictated by economic
considerations and involves a comparison between the cost of the largediameter pipeline that would be necessary for a low value of </J, and the cost of
the compressor necessary to meet the greater pressure drop associated with
high values of </J.
Typical values of the solids loading ratio for dilute-phase systems would be
between 5 and 15. In the absence of more reliable information (for example,
from tests on a pilot plant) a reasonable procedure for the design of a dilutephase system is to begin by assuming a value of 10 for the solids loading ratio,
and then to adjust this figure upwards or downwards in order to match the
predicted pressure-drop through the system to the characteristics of the
blower or compressor used.
14.2.3 Pipeline diameter
Although it is not possible at this stage to make a final decision on the diameter
of the conveying pipeline, an estimate must be made in order to begin the
iterative procedure, involving the pipe diameter and the system pressure-drop,
which will lead to a preliminary design for a dilute phase system. As mentioned
above, the starting point is to take the solids loading ratio to be 10 and then to
calculate the air mass flow rate for the required solids mass flow rate. Knowing
the air flow rate and the conveying velocity, a suitable size for the pipeline can
be determined.
Thus, for the first estimate
(14.3)
where mg is the mass flow rate of air, Pg is the density of the air, ug is the
conveying velocity and D is the pipeline diameter.
Setting m,= 10 mg the above expression becomes
D_ (
m, )112
7.9pgug
(14.4)
where m, is the mass flow rate of solids. When using equations (14.3) or (14.4) it
should be appreciated that the density pg and velocity ug of the conveying air
should be taken at the same section of the pipeline. The 'pick-up velocity' is
PNEUMA TIC CONVEYOR DESIGN
443
usually the minimum value in the conveying line and, being at the upstream
end, would correspond to the maximum pressure and density. It is therefore
likely to be necessary to estimate the density using the anticipated delivery
pressure of the air mover.
The density of the conveying air can be calculated from the pressure p and
absolute temperature T using the perfect gas equation
(14.5)
where R is the characteristic gas constant which, for air, has a value of
287 Jjkg K. Thus, in SI units,
Ps = 287(273
+ t)
(14.6)
where pis in bar absolute, and t is the temperature in degrees Celsius, giving p 8
in kg/m 3 .
It must be stressed that, although for convenience the determination of pipe
diameter and pressure-drop are discussed separately here, in practice these
two variables should be considered together. Equation (14.4) gives a first
estimate of pipeline diameter which should be used to calculate a value for the
pressure-drop along the line at the required solids flow rate and conveying
velocity. If the pressure-drop is found to be excessive, a larger-diameter
pipeline should be selected andjor the solids loading ratio reduced. The full
calculation should then be repeated.
14.2.4 Pressure-drop
When calculating the pressure-drop through the conveying line it is advisable
to keep in mind the acceptable figures for the system in question. For example,
if the system is of the vacuum type the maximum practical value of the
pressure-drop is limited to around 0.6 bar (9lbf/in 2 ). If the pressure-drop
exceeds this value, the resulting low pressure and low density at the suction to
the vacuum pump or exhauster means that this component has to be large, and
therefore expensive.
In positive-pressure systems the limiting factor is usually the solids feeder.
As explained in Chapter 13, continuous conveying systems using a rotary- or
screw-feeder are generally restricted to maximum pressure-drop of around
1 bar (14.5lbfjin 2 ), although considerably higher values can be achieved if
special feeders, such as the Fuller-Kinyon pump, are employed. Still higher
pressures, up to around 7 bar (lOO lbfjin 2 ), can be accommodated in batch
systems using blow tank feeders.
The reliable prediction of pressure-drop in a gas/solids mixture flowing
along a pipeline is one of the major difficulties facing the designers of
444
BULK SOLIDS HANDLING
pneumatic conveying systems. In recent years a considerable amount of
literature has been published on the characteristics of two-phase gas/solids
flow, but there is, as yet, no technique for predicting pressure-drop that is both
reliable and convenient. Techniques that are simple enough to be readily used
(so-called 'rule-of-thumb' methods) tend to be rather uncertain, and, at the
other extreme, high-level mathematical models that are claimed to give
accurate predictions of pressure-drop are usually complex and inconvenient,
often requiring data on the particulate material that would not ordinarily be
available. The use of computers to assist in the design process, particularly
with regard to the calculation of conveying line pressure-drop, has naturally
generated some interest in recent years. For mainframe and minicomputers
sophisticated packages are available which may be configured for pneumatic
conveying applications, but this high-level approach is of more interest to
mathematicians and research workers than to the practising engineer.
Computer-aided design techniques for desk-top microcomputers offer more
immediate benefits, and a number of approaches have been presented in the
technical literature [ 1-3].
Methods of predicting the pressure-drop in a gas/solids mixture flowing
through a pneumatic conveying pipeline have been discussed at some length in
Chapter 3 (section 3.6.5) and there is little purpose in repeating the full
discussion here. The generally accepted approach for dilute-phase conveying
is to calculate the wall-friction pressure-drop occurring as the air flows, at the
required rate, through the pipeline on its own; and then to multiply the result
by an appropriate factor to allow for the presence of the bulk solid; and, finally,
to add on additional pressure-drops contributed by the various components
such as feeders, bends, diverters, and so on.
Thus, the wall friction pressure-drop in a flowing gas/solids suspension can
be written
(14. 7)
where the 'pressure loss factor' or 'solids friction coefficient' a is a complex
function of several different variables, as explained in Chapter 3. An approximate indication of the value of a can be obtained from the chart in Figure 3.22
(repeated here as Figure 14.1), which has been prepared from test results
reported for a large number of different products, but it will be noted that,
except at very low conveying velocities, a quick and convenient approach is
simply to make a equal to the solids loading ratio, </J.
Thus
(14.8)
The 'air-only' pressure-drop ~Pg can be determined using one of the
approaches outlined in Chapter 3. Methods of estimating the pressure-drops
due to the feeding device and the pipe bends are also given in Chapter 3.
In pneumatic conveying systems the gas/solids disengaging device is usually
445
PNEUMA TIC CONVEYOR DESIGN
100 1 - - 1--
:\\.
,\.'\.'\.
50
I \.\.'\.~
I \_~ ~
\_'\ ~ ~
-""'."-.: ::-:::::::
E
~ 20
a;
\
0
0
.§
~
"'
~
10
"'"~
""'""
5
.......
20
~~
-...____::
12
10
8
6
........
1---
4
~
2
0
10
20
30
40
50
conveying veloci1y (melres/second)
Figure 14.1
Values of coefficient a in equation (14.7).
a cyclone, a fabric filter unit, or a combination of the two. In the case of a
cyclone the pressure-drop is generally quite low, but on low-pressure systems
it may still be significant since the volumetric flow rate produced by the fan is
very sensitive to the total system resistance. Variations in cyclone design to
increase the collecting efficiency also tend to increase the pressure-drop across
it.
The pressure-drop across a fabric filter obviously depends principally upon
the size of the filter, particularly the total area of filter fabric and its resistance
to air flow. The length of time since the previous cleaning of the fabric will also
have an influence. In order that the filter unit should not be too large, and
therefore expensive, it may be necessary to accept that the pressure-drop
across it will represent a significant proportion of the overall system pressuredrop. Consequently, any increase in the resistance of the filter may have a
serious effect on the performance of the system and a regular cleaning routine
is essential.
Generally however, whether a cyclone or fabric filter is used, the pressuredrop across it should not exceed about 150 mm H 2 0 (0.015 bar), which may be
safely disregarded in the majority of cases.
Further discussion on the design and selection of gas/solids disengaging
devices can be found in Chapter 5 on dust control.
Once the overall pressure-drop has been estimated on the basis of a solids
loading ratio and pipeline diameter selected as explained in sections 14.2.2 and
14.2.3 it must be compared with the 'maximum acceptable pressure-drop'
previously decided upon. If the estimated pressure-drop is too great it will be
446
BULK SOLIDS HANDLING
necessary to select a larger pipeline diameter and repeat the calculation. It may
appear that reducing the solids loading ratio should also give a lower pressuredrop, but this can only be achieved by increasing the air mass flow rate (since
the solids flow rate is fixed by the system specification), which leaves no
alternative to increasing the pipeline diameter.
14.2.5 Stepped pipelines
It will have been noted that the rate of change of velocity, and therefore the rate
of change of pressure, increases as flow takes place along a pipeline. It may well
happen that, in a long pipeline, the conveying velocity becomes excessively
high with consequent degradation of the product or erosion of the pipe wall. If
the preliminary design study shows such an occurrence to be likely it is normal
practice to select a 'stepped pipeline' in which the pipe diameter is increased in
one or more stages. This not only has the effect of reducing the conveying
velocity but also reduces the pressure-drop along the line. Naturally care must
be taken not to increase the pipe diameter by too much in one step as it is
possible for the conveying velocity to be reduced to such an extent that
saltation occurs.
The calculation of pressure-drop in a stepped pipeline is somewhat more
complicated than the method outlined in this chapter, although the general
principles involved are the same.
14.2.6 Selection of the air mover
The commonest types of air mover used on pneumatic conveying applications
have been described in Chapter 13. The type selected for a given installation is
usually dictated by the kind of conveying system planned; for example, for a
high-pressure system a reciprocating or screw compressor, for a low-pressure
(positive) system a fan or Roots-type blower, or for a vacuum system a liquidring vacuum pump or Roots-type exhauster. Figure 14.2 illustrates the
approximate performance coverages of the main classes of air mover, although
it should be emphasized that this chart is intended as a guide only since in most
cases there are substantial overlaps in their ranges. In particular, reciprocating
compressors are found in a great variety of sizes and types, and models are
available to satisfy almost any operating condition shown on the chart.
Centrifugal (turbo) compressors, and especially the multistage axial-flow type,
are normally manufactured only in large sizes, handling very large volume
flow rates, and therefore rarely find application to pneumatic conveying
installations.
The volumetric flow rate of air ('free air delivered') and the delivery pressure
required are the two parameters that must be specified when selecting a blower
or compressor for a pneumatic conveying system. Manufacturers of these
machines will supply a chart showing their performance as a plot of delivery
447
PNEUMA TIC CONVEYOR DESIGN
0.05
fans
5
10
so
100
300
volumetric flow rate (FAD), m3/min
Figure 14.2 Coverage chart showing approximate ranges of operation of various types of air
mover on pneumatic conveying application. (Note that reciprocating compressors of suitable
design are available and may be used to cover almost any operating condition above a pressure of
one bar.)
pressure against free air delivered for various running speeds. Superimposed
on these operating characteristic curves are lines showing the power absorbed.
A typical performance chart for a Roots-type blower is reproduced as
Figure 14.3 and it is seen from this chart that locating the point corresponding
to the required delivery pressure and FAD allows the necessary running speed
and the resulting power consumption to be determined.
14.3 Summary of preliminary design procedure for dilute-phase systems
It will have been appreciated that a certain amount of iteration is unavoidable
when following this simplified design procedure in order to obtain an
acceptable balance amongst the various design parameters. To clarify this
point it is worthwhile here to attempt to summarize the design process as a
series of steps, which begin with an outline specification of the pneumatic
conveying system in terms of the required solids flow rate and the pipeline
routing (overall distance, number of bends, etc.).
448
BULK SOLIDS HANDLING
(i) Select suitable value of minimum transport velocity, say 15 m/s (referring
to section 14.2.1)
(ii) Select suitable value of solids loading ratio, say 10 (section 14.2.2)
(iii) Calculate air mass flow rate and estimate suitable pipe diameter
(section 14.2.3)
(iv) Estimate overall system pressure-drop (section 14.2.4)
(v) Consider whether this estimated pressure-drop is acceptable (that is,
within a suitable range of values for the type of air-mover proposed); if it
is, go to Step (x)
(vi) Select next larger or smaller size of pipe, as appropriate
(vii) Calculate new air flow rate required to give selected minimum transport
velocity
(viii) Calculate new solids loading ratio to give specified solids flow rate
(ix) Go to Step (iv) (re-calculate overall system pressure-drop)
(x) Estimate additional air requirement (for example, to include air leakage
from rotary valve) and thus determine total air to be supplied by air
mover, as 'free air delivered' (section 14.2.1)
(xi) Using performance characteristics of selected air-mover, determine exact
operating condition and power requirement (section 14.2.6)
14.4 Designing from available test data
14.4.1 Conveying characterisitcs
It should always be regarded as preferable to design pneumatic conveyors on
the basis of previously-obtained conveying data for the bulk solid concerned.
It matters little whether such data comes from experience of a working
industrial installation or from specially commissioned trials, although the
latter would naturally be expected to yield data in a more immediately usable
form.
It is generally most useful if the data relating to the handling of a particular
bulk solid are presented in the form of 'conveying characteristics', that is, a
chart showing the relationships amongst the solids flow rate, air flow rate,
pressure-drop and solids loading ratio. A typical set of conveying characteristics, in this case for powdered limestone ("' 75 11m) conveyed in a 125 mmdiameter pipeline, 80 m in length, is shown in Figure 14.4. The pipe route
includes a 20 m vertical rise and seven 90° long-radius bends. It is necessary
that full details of the conveying line are known because the conveying
characteristics plotted in this way, are specific not only to the bulk solid
concerned but also to the conveying system. A full performance chart similar
to Figure 14.4 would not be easy to obtain from an average industrial
pneumatic conveying system, but from a properly-instrumented test rig of the
type that would be used by a major manufacturer or by a specialized research
449
PNEUMA TIC CONVEYOR DESIGN
.......
3 5 7
10
power absorbed (kW)
15
20
25
30
.g"' 0.5 H---\-=~--+--~c----\!--~-t--'~--'1<--~-+--''\.
'5
c:
0
(J
Cl>
~ 0.4
.5
~~-.:....,-..t.::~_j3000 ~
~\:::::l~:-f~::-~s:::;=:~:;::j2500 i
"'
>
M~ 0.3
§
Cl>
~
•t;;
.Q
~ 0.1 1-~--...L
E
:J
0
>
0.1
0.6
0.4
0.2
a.s
0.3
pressure rise across blower (bar) tor atm. pressure at intake
0 .7
Figure 14.3 Typical performance chart for a Roots-type (straight-lobe) rotary blower.
and development laboratory, complete data can be recorded for almost any
particulate or granular bulk solid.
Several observations can be made from a first inspection of Figure 14.4.
Firstly, the range of solids loading ratios, up to a maximum of 10, suggests that
the system was working in a dilute-phase mode, and this is confirmed by the
fact that the lowest value of the conveying air velocity is 15 m/s. It should be
noted that the air flow rate on the horizontal axis is expressed on a volumetric
basis as 'free air', although an alternative is to use mass flow rate.
It is immediately apparent that a wide range of flow conditions could exist in
the pipeline to which Figure 14.4 relates. At an air flow rate of 15m 3 jmin
(FAD), for instance, the solids flow rate could be anything from zero up to 11.8
tonne/hour (for which the pressure-drop would be 0.8 bar) or more. Operating
with a greater air flow rate is generally not a good idea since a higher
proportion of the available pressure-drop will be needed to overcome wallfriction losses for the air flow, leaving less for the conveyance of solids.
14.4.2 Scaling for pipe size and conveying distance
For both dilute-phase and dense-phase conveying applications, conveying
characteristics obtained from trials on a pilot plant obviously give a great deal
of valuable information about the handling behaviour of the bulk solid
450
BULK SOLIDS HANDLING
concerned. However, it is most unlikely that the pilot plant will be of exactly
the same configuration as the system being designed, and therefore it will be
necessary to modify the conveying characteristics so that they show the
relationships amongst the solids flow rate, air flow rate, and pressure-drops for
the required conveying distance and an appropriate pipe diameter. Much of
the skill in designing a pneumatic conveying system is in this modification of
existing data so that it becomes relevant to the system being designed, not only
in terms of conveying distance and pipe size, but also in terms of the number of
bends and their geometry, vertical sections of pipe (up and down), operating
sequences (in the case of batchwise conveying), and so on. It is possible here
only to give an outline of the technique of'scaling' for pipe size and conveying
distance, but this should be sufficient for the reader to gain a general
understanding of the design method. Further information can be found in [4]
and [5].
Scaling the conveying characteristics for a specific bulk solid is best carried
out in two stages. The first stage involves scaling to the required distance, with
allowances for vertical sections and bends, and the second stage scales the
conveying characteristics in terms of the pipe diameter. Scaling with respect to
conveying distance is a fairly complex process and can result in marked
12
].....
j
conveying ar
velocity (mls)
15
8
0.8
:a
g
D
G>
~ 6
0.7.
~
8
.;;;
G>
3
t)
"'"'G>
CS.
~ 4
a.
"
-~
>-
2
G>
c>
0
0
0
10
15
20
25
30
voumetric air flow rate (free air) (m 3 /min)
Figure 14.4 Conveying characteristics for powdered limestone Pipeline: 125 mm diameter, 80 m
long, with seven long-radius 90° bends.
451
PNEUMA TIC CONVEYOR DESIGN
differences in conveying parameters. Significant changes can result in the
solids flow rate, solids loading ratio and the air requirements, all of which are
very much dependent upon the nature of the bulk solid concerned. In order to
illustrate the steps involved in scaling, reference will be made to Figure 14.5.
This is a set of conveying characteristics, presented in a similar way to
Figure 14.4, but relating to the dense-phase conveying of pulverized fuel ash
(PFA) in a 50mm-diameter pipeline lOOm in length.
In the first instance the conveying characteristics for the PFA will be scaled
up to a distance of 150 m. Now, provided that the extrapolation is not too
great, scale up of solids mass flow rate with respect to conveying distance can
be carried out with reasonable accuracy on the basis of a reciprocal law, that is
.
1
ms ocL
(14.9)
The product mass flow rate scale on Figure 14.5 is thus changed according
to the relationship
.
Lt .
m.2 = L2 m.t
24
(14.10)
180 150
20
].....
3.0
16
~
_g 12
2.6
~
2.2
-t;
1.8
"'aa>
g
a>
~
g
"'"'
~
8
1.4
0::J
"8
a
G>
~
3:
4
1.0
:
·~a>
8
0
0.6
0
0.02
0.04
0.06
0.08
0.1
ar mass flow rate (kg/s)
Figure 14.5 Conveying characteristics for pulverized fuel ash (PF A). Pipeline: 50 mm diameter,
lOOm long.
452
BULK SOLIDS HANDLING
so that when scaling from 100 m to 150 m, as in this example, all the product
mass flow rates are reduced by a factor of 2/3.
Now it is essential that conveying conditions, in terms of air velocities, are
the same for the two situations and therefore scaling must be carried out for
data points having the same conveying line pressure-drop and the same air
mass flow rate. Furthermore, the 'datum' conditions, corresponding to the
pressure-drop for air only flowing through the line, must be changed by an
appropriate amount to reflect the fact that, for the same inlet air velocity in a
longer pipeline, both the air flow rate and the pressure-drop will be different.
Figure 14.6 shows the result of scaling for distance, from the original 100 m
up to 150 m. It is immediately evident that over the longer distance the
maximum solids loading ratio is very much less.
When scaling for the size of the pipeline it will again be necessary to adjust
the position of the 'empty line datum' since, in order to maintain similar air
velocities, the mass flow rate will need to be in proportion to the crosssectional area of the pipeline. An acceptable degree of accuracy when scaling
for pipe size is obtained on the basis of proportionality between solids mass
flow rate and pipe cross-section.
I
u
rrsss
now rate (kgts)
Figure 14.6 Conveying characteristics for PF A. Pipeline: 50 mm diameter, 150 m long (Scaled
from Figure 14.5).
453
PNEUMA TIC CONVEYOR DESIGN
I
'-
.
-
·-
I
30
solids
loading
ratio
---,- !-·
- 1-
0
1-
-
c-
40
30
-
f- ·
~
1--
20
1-
tO
5
I F---.
ft~
I /
- 1- -
-
"!'><(~
I""
3.0
I
-
J
.1-.
/
60
-
r-
~ /
7'1'----.. ~ A' r-.....
~/ ~~~ ~
~ ~--__,
~D<
- c-
-
-
/'--.
I
80
-
~ ..........
.L
I
v!f
- '1 ~+
c- ·-
_!
I
.........
::±/~
::::::_ -....,..., ........ ~'.......
~
1::::::-<r-..
/~-t:-r-- ~ -;.......
it:
- --
~-f--.
-
-~- F-
-t-
:-
......
15
10
air mass flow rate (kg/s)
1-r-r-
2.6
g
22 -5
:::><
..........
..........
~
11>
, ia
.8
-,
~
.4
.s
:::::~ 1,Q_
l50
-~f:--r-e :::~
-~ -~
----
0
>-
11>
>
-- ~-- -;-.... 0
.6
20
Figure 14.7 Conveying characteristics for PFA. Pipeline: 75mm diameter, 150m long (scaled
from Figure 14.5, via Figure 14.6).
Thus
(14.11)
and the product mass flow rate scale on Figure 14.5 (or Figure 14.4, depending
upon the conveying distance required) is then adjusted using the relationship
•
D2
m.2 = ( Dl
)2
•
msl
(14.12)
Figure 14.7 shows the result of scaling up from the 50 mm-diameter line to
75 mm by first adjusting the datum condition and then changing the vertical
scale, increasing all product mass flow rates by a factor of2.25; that is, (75/50)2 •
The outcome of this somewhat complicated procedure is that, for a specified
bulk solid, the results of laboratory trials have been adapted to yield a set of
conveying characteristics which are vital to the reliable design of a pneumatic
conveying system that is required to transport the same bulk solid at the same
(or greater) rates over a longer distance. The required pipe diameter is
determined and a suitable operating condition can be selected, enabling the
454
BULK SOLIDS HANDLING
air mover to be specified in terms of air flow rate (FAD), delivery pressure and
size of driving motor (i.e. power).
14.5 Notation
A
D
L
rilg
ms
p
Po
P1
Apg
Aps
R
T
To
Tl
t
tl
~g
Vo
r:x
<P
Pg
Cross-sectional area of conveying line
Diameter of conveying line
Total conveying distance
Mass flow rate of conveying gas (air)
Mass flow rate of conveyed bulk solid
Pressure in conveying line
Atmospheric pressure
Pressure at conveying line inlet
Pressure-drop due to gas (air) alone in conveying line
Pressure-drop due to two-phase (gas/solids) mixture in conveying line
Characteristic gas constant
Temperature (absolute) in conveying line
Atmospheric temperature (absolute)
Temperature at conveying line inlet (absolute)
Temperature in conveying line
Temperature at conveying line inlet
Velocity of gas (air) in conveying line
Volumetric flow rate of air ('free air')
'Pressure loss factor' in equation (14.7)
Solids loading ratio ( = rils/rilg)
Density of conveying gas (air)
References and bibliography
References
1. Parameswaran, M.A. and Mukesh, D. Computer-aided design of a pneumatic conveyor, Chem.
Engg. World 13 (10) (October 1978) 41-46.
2. Woodcock, C.R. and Mwabe, P.O. An approach to the computer-aided design of dilute-phase
pneumatic conveying systems. Proc. Pneumatech 2 Conf, Canterbury, UK, September 1984.
3. Latincsics, N. Pneumatic conveyors: computer aided design methods. Proc. lOth Annual
Powder and Bulk Solids Conf., Chicago, May 1985.
4. Mills, D. Mason, J.S. and Marjanovic, P. The comparison of pressure drop in horizontal and
vertical dense phase pneumatic conveying. Proc. 3rd Conf. on Pneumatic Conveying, Pecs,
Hungary, March 1985.
5. Mills, D. and Mason, J.S. The influence of conveying distance on the performance and air
requirements of pneumatic conveying system pipelines. Proc. Conf on Reliable Flow of
?articulate Solids, Bergen, August 1985.
Recommended further reading
Anon. Pneumatic Handling of Bulk Materials. EEUA Handbook No. 15, Constable and Co.,
London, 1963.
PNEUMA TIC CONVEYOR DESIGN
455
Kraus, M. N. Pneumatic Conveying of Bulk Materials. Ronald Press, New York, I968.
Stoess, H.A. Pneumatic Conveying. Wiley-Interscience, 1970.
Wen, C.-Y. and O'Brien, W.S. Pneumatic conveying and transporting. In Gas-Solids Handling
in the Process Industries, eds. J.M. Marchello and A. Gomezplata, Marcel Dekker Inc., 1976,
89-134.
Dixon, G. Pneumatic conveying. In Plastics Pneumatic Conveying and Bulk Storage, ed. G.
Butters, Applied Science Publishers, 1981, 19-145.
Mason, J.S. Mills, D. Reed, A.R. and Woodcock, C.R. Pneumatic Handling of Bulk Materials.
Notes for 4-day post-experience course, Thames Polytechnic, London, 1986.
15
Air-assisted gravity conveying
15.1 Introduction
The three preceding chapters have been concerned primarily with pneumatic
conveying by pipeline, and consideration will now be given to a variation on
this technique in which the particulate bulk solid is made to flow along a
channel inclined at a shallow angle. Pneumatic conveying has several
advantages over other methods of transporting bulk solids, but it suffers from
two drawbacks. Firstly, the power consumption is quite high; and secondly,
especially when conveying in dilute phase, the solids velocity is relatively high
and may cause problems as a result of particle degradation and erosive wear of
the pipeline and system components. Both of these difficulties may be
minimized by conveying in dense phase, that is, with a higher ratio of solids to
air, so that the quantity of air used is smaller and the conveying velocity is
lower.
Air-assisted gravity conveying (or 'air-float conveying') can be regarded as
an extreme form of the dense phase method in which the predominant factor
causing flow is the gravitational force on the bulk solid. The technique is
essentially to maintain an aerated state in the bulk solid, from the moment that
it is fed into the upper end of an inclined channel, by the continuous
introduction of air (or other gas) at a low rate through a false bottom, made of
suitable porous material and fitted into the channel (Figure 15.1 ). Since the
bulk solid is kept 'live' by the trickle-flow of air, it flows freely down the slope,
even when the angle of declination is very small. The quantity of air used is
kept to the absolute minimum necessary to reduce the interparticle forces, and
the frictional forces between the particles and the internal channel surfaces,
sufficiently to allow the bulk material to 'flow'. The general principle of airgravity conveying is thus very simple and the method has the big advantage of
being essentially 'workable'; that is, a great deal of latitude is available in the
design of installations, and provided that a few basic requirements are met
they will generally operate without trouble.
It is not known when aeration of a bulk particulate solid was first used as an
aid to conveying, but one of the earliest relevant patents appears to have been
that of Dodge in 1895 [1] who used air, entering an open channel through slits
in the base, to transport coarse-grained material. However, significant
progress in the gravity conveying of aerated powders was not made until some
thirty years later when it was found that the method provided an excellent
means of conveying cement. The German company Polysius was a pioneer in
the development of air-assisted gravity conveying, but was followed into the
AIR-ASSISTED GRAVITY CONVEYING
457
bulk solid
feed
Figure 15.1
channel.
The principle of air-assisted gravity conveying: an aerated bulk solid flowing along a
field by the Huron Portland Cement Company of America which obtained the
first British patent in 1949. Huron's plant at Alpena, Michigan, was one of the
first to make extensive commercial use of this method of conveying and
employed 'Airslides', as they came to be called, at various stages of the
production process from grinding mill discharge to finished cement. The third
organization that played a prominent part in developing and establishing airgravity conveyors was the Fuller Company which manufactured them under
licence from Huron.
Although the air-assisted gravity conveyor first came to prominence for the
transport of cement~-and this is still one of the main applications-many
other types of material are now handled with relative ease, including such
diverse substances as fly ash, coal dust, plastic and metal powders, alumina
and sand. Typical of the large installations described in some detail in the
published literature are a 50 000-tonne storage plant and an 80 000-tonne
ship-loading plant, both handling alumina [2], and a Canadian aluminium
smelter capable of handling 160 000 tonnes of alumina per annum [3]. Various
sizes of conveying channel are used in these installations, one of the largest
being a 915 mm-wide channel which transports alumina from a surge hopper
to a main silo at a rate of 1500 tonne/hour [ 4].
Currently there are a number of different companies marketing air-assisted
gravity conveyors under a variety of different trade names, such as Airslide,
Fluidor, Whirl-Slide, Flow-Veyor and Fluid-Slide. Nevertheless, considering
the advantages that they can offer over other forms of bulk solids transport,
particularly in terms of low power consumption, the use of these conveyors is
not as widespread as might have been expected. To some extent this may be the
result of a lack of confidence on the part of the design engineer, since airgravity conveying remains something of an art!
458
BULK SOLIDS HANDLING
In order to avoid the pitfalls that do exist and to enable systems to be
optimally designed rather than over-designed, some understanding of the
phenomena involved in air-gravity conveying is desirable. Observation of a
particulate bulk solid being conveyed in this way will immediately suggest a
similarity to a liquid flowing in an inclined channel, but it is also evident that
the continuous supply of air that is necessary to maintain the liquid-like state
of the material has a close affinity to the gas-fluidization process. The present
study, therefore, extends the basic principles of fluidization introduced in
Chapter 3 to deal with the flow of fluidized solids. The design, construction
and operation of practical air-assisted gravity conveyors is discussed at some
length and finally consideration is given to a number of interesting variations
on the conventional air-gravity conveyor in which the transported material
flows along a horizontal or even an upward-inclined channel.
15.2 The flow of fluidized solids
It has been remarked previously that when particulate solids become
'fluidized' under the influence of a continuous upward flow of a gas they tend to
display many of the characteristics of liquids. Amongst these characteristics
are the ability to maintain a horizontal free surface and the ability to flow from
a higher to a lower level. Thus, for example, a powder fluidized in a vessel
would flow from a hole in the side of that vessel, and could continue to flow
through a horizontal pipe fitted to the hole, provided that this pipe was not so
long that complete defluidization occurred. If it were possible to keep the
powder in its fluidized condition as it passed along the pipe, the flow could be
maintained indefinitely.
Some methods of conveying particulate bulk solids in dense phase have
been discussed in Chapter 12, generally relying on a flow of high-pressure air
to keep the powder on the move. A method which comes closer to providing a
true fluidized flow is the Gattys 'trace-air' system which is just one of several
similar systems that are, or have been, commercially available and in which air
at a relatively low pressure is supplied continuously to the powder in the
pipeline through an internal perforated pipe running the whole length of the
conveying line. The motive force comes from a pressure-drop along the
conveying line created by pumping air in at the upstream end, as in
conventional pneumatic conveying by pipeline, but the pressures are lower
and the risk of blockage is smaller. An alternative system could have a
continuous portion of the pipe wall made of a porous material with additional
air being supplied from a separate duct external to the conveying line, and
combining this idea with the use of gravity of provide the motive force, a
remarkably economical method of transporting bulk solids can be conceived.
Figure 15.2 shows a different approach to the same concept of continuous
fluidized flow, which illustrates quite simply the fundamental principle on
which air-assisted gravity conveyors operate. Most free-flowing particulate
AIR-ASSISTED GRAVITY CONVEYING
459
(a)
Figure 15.2
Aeration of a particulate material to reduce the natural angle of repose.
materials display a natural angle of repose of around 35o to 40° (Figure 15.2a)
and in order to get such a material to 'flow' continuously, under gravity alone,
on an inclined surface it would normally be necessary for the slope of the
surface to be greater than this angle of repose (Figure 15.2b). Materials
exhibiting some degree of cohesiveness have much larger angles of repose and
often will not flow, even on steeply inclined surfaces, without some form of
assistance, such as vibration of the surface. The introduction of air to a bulk
powder, for example by supporting the powder on a plate made of a suitable
porous substance and allowing the air to flow upwards through it into the
powder, can significantly reduce the natural angle of repose. The powder will
then flow continuously from the plate when it is inclined at a very shallow
angle, which needs only to be greater than the so-called 'fluidized angle of
repose' of the material-for most free-flowing powders, around 2°-6°
(Figure 15.2c). This phenomenon of fluidized flow can form the basis of a
simple and reliable method of bulk solids transport if a channel is constructed
having a porous base through which air can flow from some form of plenum
chamber (Figure 15.1 ). It is of course an essential requirement that sufficient
460
BULK SOLIDS HANDLING
air flows into the powder in the channel to cause it to flow and therefore the
porous base must be of high enough resistance to ensure that when part of it is
clear of powder the remainder is not starved of air (Figure 15.3a). The other
essential condition to be met is that the downward slope is sufficient to permit
a steady continuous flow of the fluidized powder. Provided that these
conditions are satisfied, the air-assisted gravity conveyor would normally
prove to be a trouble-free and very economical method of transporting a wide
range of powdered and granular bulk solids.
The appearance of the flowing aerated powder in the channel can depend
upon a number of properties that together might be termed the 'flowability' of
the material, and also to some extent on the roughness of the channel surface.
Thus, a very free-flowing dry powder having a relatively low natural angle of
repose (that is, good 'flowability') would be likely to fluidize well, and in this
1
wt(1.:·
lit.f
~&!·~:
(a) Starting the flow: air velocity
into the stationary powder must
exceed Umf, even when a large part
of the porous membrane is uncovered.
porous membrane (distributor)
~~r~-~i·'--~~\~~~~~~~~~j
1r
plenum chamber
air
~ift:
:;;.>:.,·
>J'!.
.,,Ji;(~
,<'!; rl'!{A.
(b) Free-flowing powders become
fluidized and will normally flow
along the channel when the slope
is as little as 1
°
powder well fluidized
:;·~~~--.~~~ ..~ ";-..;:n,~~-r.~'l) ~~~~
-1"
::.-"1~
(c) Slightly cohesive powders that do
not fluidize well can often be
conveyed if the channel slope is
greater (up to about 10 O). The
powder effectively slides on a layer
of air trapped against the top surface
of the distributor.
Figure 15.3 The flow of aerated particulate bulk solids in inclined channels.
AIR-ASSISTED GRAVITY CONVEYING
461
state to flow smoothly along a channel inclined at as little as one or two
degrees to the horizontal (Figure 15.3b). Visual observation of the flowing
powder would show distinct liquid-like characteristics such as a smooth or
slightly rippled surface, a 'plume' set up from a partial obstruction to the flow,
and a 'standing wave' set up from a more substantial obstruction. In contrast, a
powder that is cohesive can show a markedly different behaviour in an airgravity conveyor. Very cohesive (sticky) materials are, of course, unsuitable for
conveying in channels in this manner. However, powders that are only slightly
cohesive can usually be conveyed provided that the slope of the channel is
greater; perhaps 6°-10°. Observation of these materials suggests that the
particles are not fluidized, but move virtually as a solid mass sliding along the
channel (Figure 15.3c). Irregular zig-zag cracks in the flowing powder bed and
the craggy appearance of its free surface suggest similarities to the channelling
and slugging behaviour that can occur in stationary fluidized beds-indeed
these cohesive powders could be expected to exhibit just such
characteristics-and the nature of the motion is very much akin to that
occurring in en-masse conveyors (Chapter 9).
It is not clear whether the improved 'flowability' that results from the
continuous aeration of powders results predominantly from the air filtering
through the solid particles and reducing the contact forces between them (thus
causing partial fluidization) or from the formation of air layers between the
bed of particles and the channel surfaces allowing slip to take place with the
consequent sharp reduction of the boundary shear stresses. Even with fine freeflowing powders there is some evidence for the latter effect (for example the
bubbling behaviour of a stationary fluidized bed is almost entirely suppressed
when the bed flows), but it seems probable that the former effect is
predominant with such materials.
15.3 Practical air-assisted gravity conveying
As has been previously explained, conveying on a downward slope has the
great advantage of gravity to assist the flow of the aerated bulk solid. This is
the conventional, low-energy application of air-assisted gravity conveying.
Figure 15.4 represents a basic air-gravity conveyor in which the conveyed
bulk solid flows continuously under gravity from the inlet to the discharge
point. Essentially the conveyor consists of two U-section channels (one
inverted) with the porous membrane clamped between them (Figure 15.5a). A
variety of different materials may be employed as the 'porous membrane',
some typical examples being woven cotton or polyester, sintered plastic or
ceramic tiles, and laminated stainless steel mesh (Table 15.1). Where the
channel is fairly wide and the porous membrane is not rigid (for example a
woven fabric) some additional support for the membrane, such as a wire grid,
may be required. The lower channel serves as a plenum chamber to which air is
supplied at one or more points depending upon the overall length of the
462
BULK SOLIDS HANDLING
solids feed
inspection
cover
porous
embrane
supply of filtered air
solids/
discharge
j
Figure 15.4 Arrangement of a typical air-gravity conveyor.
channel
plenum
chamber
inspection cover
(which may be glazed)
(a) Section of the conveying duct
(b) A side discharge box, one of the many components that can
easily be built-in to an air-gravity conveying installation
Figure 15.5 Construction of an air-gravity conveying channel.
AIR-ASSISTED GRAVITY CONVEYING
463
Table 15.1 Some features of materials commonly used as the porous distributor in air-assisted
gravity conveyors.
Material
Woven fabric
Cotton
Polyester
Asbestos
Sintered plastic
Sintered metal
Ceramic tiles
Woven steel laminate
Compound materials,
e.g. filter cloth
sandwiched between
perforated steel plates
Relative cost
Features
Light and fairly strong, but has little rigidity
and may need supporting in wide ducts;
performance may deteriorate if fluidizing air
or conveyed solids are moist.
As for cotton, but less susceptible to
Low
moisture; unsuitable for use at elevated
temperatures.
Particularly useful in high-temperature
Low
applications.
Has smoother surface and greater rigidity
Medium
than woven fabrics; appears very prone to
deterioration through accumulation of
atmospheric dust and fines in conveyed
material which cause decrease in air flow.
Hygienic (therefore useful in food industry);
High
gives good fluidization and can be made
with high degree of uniformity; but very
expensive.
Perhaps less convenient than other materials
Medium
in that tiles must be fitted together and
sealed, but widely used; good fluidization;
ceramic is brittle and subject to impact
damage, but is resistant to high
temperatures.
Qualities similar to sintered metal; resistant
High
to high temperatures.
Low to medium Combines good fluidization qualities
of fine filter cloth with strength
steel sheets; can be easily made to
any desired specification to
suit user's application.
Low
conveying system. The presence of the covered top channel renders the
conveyor virtually free from problems of dust leakage, but naturally it would
also operate satisfactorily as an open channel. In this form the device has been
widely employed for flow assisters mounted at the bottom of silos, bunkers,
railway wagons and lorries, and so on, enabling these containers to be made
with a virtually flat base and thus to have a substantially greater capacity.
Where the conveyor is covered it is necessary for the top channel to be
adequately vented through suitable filters. With short conveyors it may be
sufficient to rely on the air escaping with the powder from the outlet end of the
channel and then through the vent system of the discharge hopper, if one is in
use. If the conveying system is long, or if there is a possibility of the channel
outlet becoming choked with powder, it is better to vent from two or more
points between the inlet and the outlet. It is likely to prove useful to have
inspection or access ports fitted at convenient positions along the duct,
464
BULK SOLIDS HANDLING
especially in the region of the inlet and outlet and in other positions where
blockage may occur. In any case it is advisable to have a means of physically
cleaning out the channel since it is a peculiarity of air-gravity conveyors that
when the solids feed is reduced the flow becomes unstable and then stops.
Thus, the base of the channel cannot be completely cleared of the conveyed
material simply by shutting off the feed.
The air-gravity conveyor may operate with flooded feed from a hopper
where precise control of the solids flow rate is not required. The system is then
effectively self-regulating and, with free-flowing powders, there should be little
risk of the conveying channel becoming choked provided that its slope and the
flow rate of fluidizing air are sufficient. Alternatively, the supply may be from
some form of metering device such as a rotary valve or screw feeder. Another
commonly used technique for obtaining some measure of flow control is to fit a
gate or baffie in the conveying duct, close to the inlet from the hopper. Placing
a flow-regulating gate near the outlet end of the conveyor is generally not
advisable as the whole channel could well fill with powder backing up from the
gate. Problems would then occur with venting of the fluidizing air and with
erratic flushing of the powder under the gate as it opens. However, provided
that care is taken over the design of the venting arrangement and also of the
method of discharge control, the choke-fed air-assisted gravity conveyor can
prove to be a very useful device, allowing material to be drawn at will from any
of a number of outlets in what is effectively, a long fluidized header-tank. Solids
flow control at the inlet end, although basically more reliable, does present a
problem on long channels because of the considerable delay between making
an adjustment to the control gate and seeing the effect of this adjustment at the
lower end ofthe channel. In fact, where it is important to control the solids flow
rate within relatively close limits it becomes almost essential to install some
form of buffer hopper close to the discharge point.
Air-gravity conveyors are available from a number of manufacturers as a
range of standard bolt-together components which include straight and
curved sections of various widths along with 'accessories' such as flow
diverters, inlet and discharge ports, gate valves and scrap traps. One such
component-a flow diverter-is illustrated in Figure 15.5b.
Controlling the location at which a bulk solid is discharged from an airassisted gravity conveyor is likely to be much more satisfactory than
controlling the rate of discharge. Using appropriate bends, diverters and outlet
ports it is possible to construct quite complex systems. Figure 15.6 illustrates
an ingenious but simple solution to the problem of automatically controlling
the feed of materials to a stockpile. An overhead air-gravity conveyor
discharges the fluidized bulk solid down each of a succession of outlet spouts
until the rising level of the stockpile causes them to become blocked.
It has been stated that air-gravity conveyors are usually trouble-free in
operation, and whilst this is true, there are one or two ways in which problems
may arise. One potential source of trouble is the porous membrane that forms
AIR-ASSISTED GRAVITY CONVEYING
'·· \
465
\,,
\.,
Figure 15.6
spouts.
An air-assisted gravity conveyor feeding a stockpile through multiple discharge
the base of the conveying channel. There are many examples of installations in
which the same membrane has been in use continuously for a number of years,
but in other cases replacement is necessary at quite frequent intervals. There is
probably little that can be done about blinding of the pores in the top surface
of the membrane, but precautions can be taken against deterioration of the
underside by ensuring that the main air supply is adequately filtered.
A further precaution concerns the need for the porous membrane to
withstand a certain amount of ill-usage. It appears to be common practice for
operatives to attempt to relieve suspected blockages with the aid of an iron bar
or similar implement wielded against the outside of the channel or prodded
through an inspection port, with the not uncommon result that the porous
distributor is cracked (in the case of ceramic tiles) or punctured (woven fabrics).
Blockage of the conveying duct is unlikely to occur unless the porous
distributor is damaged or the nature of the conveyed material changes
drastically (for example, becoming wet), both of which would tend to cause
local, or complete defluidization of the flowing solid. Erratic flow in the
conveying channel is unlikely to be caused by the air-gravity conveying system
itself, unless the slope is too shallow or the bed depth is too great. It is more
probable that the feed to the channel would be at fault, for example, as a result
of arching in the hopper supplying the air-gravity channel.
15.4 Design parameters for air-gravity conveyors
15.4.1 Slope of channel
Experimental investigation of the influence of channel slope suggests that
there is an optimum value of the slope which depends principally upon the
466
BULK SOLIDS HANDLING
nature of the bulk solid being handled. Attempting to convey at a slope less
than this optimum value can result in the depth of the bed of bulk material in
the channel increasing excessively, even to the point where the channel
becomes completely blocked. Conveying at slopes greater than the optimum
value should not cause any problems, but does not yield any significant
advantage and does not make the best use of available headroom.
However, this optimum slope is not easy to predict without undertaking
tests with samples of the material in a small-scale channel. In general, for freeflowing materials a slope of around 3° should be sufficient, but more cohesive
powders may require 7o to lOo to ensure continuous trouble-free operation.
15.4.2 Conveying distance
Provided that the continuous downward slope can be maintained, there is
generally no limit to the length of conveying channel that can be used. Airassisted gravity conveyors of 100 m or more in length are not unknown. It is
necessary of course to arrange the air supply so that a uniform pressure exists
beneath the distributor, and in very long conveyors it is usual to provide air
inlets at several points along the length of the plenum chamber. It may also be
advisable to vent the main channel at several points to prevent the build-up of
an excessive air velocity over the top of the material being conveyed.
15.4.3 Width of conveying channel
The main parameter governing the capacity of an air-gravity conveyor is the
channel width. In the literature published by manufacturers of these conveyors, and in other sources giving basic design data, quantities described as
'typical capacities' are given as a function only of the channel width with little,
if any, indication of how such figures would be modified for different types of
conveyed material, and for different channel slopes and fluidizing air flow
rates. This is not as unreasonable as it first appears in view of the fact that,
provided the slope and air flow rate exceed the required 'minimum' or
'optimum' values for the particular material being conveyed, they will have
little influence on the solids flow rate.
A useful preliminary estimate ofthe width ofthe channel required for a given
application may be made by regarding as constant the average velocity and the
bulk density of the flowing suspension (although both are in fact functions of
the channel slope and fluidizing air velocity). Thus the width of conveyor (b)
required to handle a mass flow rate ms of a material having bulk density Pb is
given approximately by
rm
b _( _
e_s_
r.pbus
)112
( 15.1)
where r. is the operating aspect ratio, re is the expansion ratio of the conveyed
467
AIR-ASSISTED GRAVITY CONVEYING
3:
g
"'"'ro
E
"'
:2
0
"'
0.2
0.4
0.5
0.8
1.0
channel width (m)
Figure 15.7 Chart giving the approximate relationship between conveying capacity and channel
width for air-gravity conveyors operating at an aspect ratio of 0.5.
material (that is, the ratio ofthe bulk density ofthe unfluidized material to that
of the suspension) and u. is the average solids velocity along the channel.
Taking suitable average values of the quantities u., ra and r., and introducing
the particle density pP in place of the bulk density Pb• a convenient 'rule-ofthumb' may be proposed as
b
~
1.6(;;r'2
(15.2)
where m. in kg/sand pP in kg/m 3 gives bin metres. This relationship has been
used to plot the chart, Figure 15.7, which provides a quick reference for
determining the approximate channel size for a given application. (It should be
noted, however, that normal industrial practice would be unlikely to permit
the widest channels to operate at an aspect ratio as high as 0.5, and caution
should be exercised in this respect when using the above equations or chart.)
468
BULK SOLIDS HANDLING
15.4.4 Air requirement
In order to specify the air requirement of an air-gravity conveyor it is necessary
to establish the volumetric flow rate of the air through the porous base of the
channel and the pressure within the plenum chamber.
The plenum pressure is clearly a function of the resistance offered by the
porous base of the channel, but also depends upon the depth of the conveyed
material in the channel. If it is assumed that the conveyed material is fully
supported by the air it is possible to estimate the pressure on the upper surface
of the porous membrane for any required aspect ratio of the flowing bed.
Knowledge of the permeability of the porous base (that is, the air flow rate per
unit area per unit pressure difference across it) would then permit the pressure
in the plenum chamber to be estimated. In practice, however, it is difficult to
predict with any confidence an optimum value for this parameter because of
uncertainty over the actual pressure drop across the flowing bed of bulk solid.
As mentioned previously, it is essential that the porous membrane is of
sufficiently high resistance to ensure a uniform distribution of air into the
conveyed material, and typically the plenum pressure needed is found to be
approximately 250~500mm H 2 0.
The flow rate of air that must be supplied to the air-gravity conveyor
depends principally upon the length and width of the channel and the nature of
the bulk particulate material to be conveyed. The air flow may be expressed
conveniently in terms of the volume flow rate per unit area of the porous
channel base; that is, as a 'superficial velocity' of air into the conveyed bulk
solid from the chamber. The value of this superficial velocity that must be
maintained can be predicted approximately from a knowledge of the
fluidization characteristics of the bulk solid, although the slope of the channel
and the solids mass flow rate required will also have an influence. The
optimum superficial air velocity, at which the conveyor can be operated
economically without undue risk of stoppage of the solids flow is likely to be
between two and three times the minimum velocity at which the material could
be fluidized (umr; see Chapter 3). For very free-flowing materials on a relatively
steep incline an air velocity only slightly in excess of the minimum fluidizing
velocity may be sufficient, but for very fine powders up to ten times umr may be
needed. In addition to being wasteful of energy, operation at too high an air
velocity can cause problems as a result of fine particles being entrained in the
air stream leaving the surface of the flowing suspension. Therefore the designer
requires some knowledge, not only of the minimum fluidizing velocity of the
bulk solid to be conveyed, but also of the air velocity at which entrainment can
begin, which corresponds approximately to the terminal velocity of the fine
particles falling in stationary air.
Many methods of predicting umr for bulk solids are to be found in the
published literature (again, see Chapter 3). Figure 15.8 is a chart based on one
of these correlations for powders fluidized with air at a condition close to
AIR-ASSISTED GRA VJTY CONVEYING
469
'Cil
l
·€
0
a>
>
·a
10
ea
group A
:§
/I
i.
:::>
Ml !MUM FLUIDIZING
VELOCITY
(/)
50
100
mean particle diameter C /"ID)
Figure 15.8 Minimum fluidising velocity and terminal velocity for a bed of particles fluidized
with air at normal ambient conditions.
normal ambient. Also shown on this chart are approximate values of u1, the
terminal velocity of particles in free fall in still air. For a particulate bulk solid
of known particle size and density, Figure 15.8 allows a fairly reliable estimate
to be made of the minimum fluidizing velocity and, using the diameter of the
smallest particles in the material, the air velocity can be predicted at which
these fine particles may begin to be carried upwards from the surface of the
bed. Approximate ranges of the types of fluidization behaviour, as given by
Geldart's classification (Figure 3.13), are also shown on Figure 15.8, superimposed on the lines corresponding to the minimum fluidization condition,
thus helping to provide a useful prediction of the likely behaviour of a
particulate bulk solid in an air-assisted gravity conveyor.
R
470
BULK SOLIDS HANDLING
For a more detailed discussion of the various aspects of the design of airassisted gravity conveyors the reader is directed to [5].
15.5 Properties of bulk solids for air-gravity conveying
Almost any bulk particulate solid having good fluidizing characteristics will,
when suitably aerated, flow easily down an inclined surface, and can therefore
be transported satisfactorily in an air-assisted gravity conveyor. Although it is
often stated that being easily fluidizable is an essential requirement for
conveying in this manner, in fact, many materials having slightly cohesive
properties can also be conveyed. However, very cohesive (damp or 'sticky')
materials and powders of extremely fine particle size which 'smear' over the
channel surface and 'blind' the porous membrane are generally unsuitable for
air-gravity conveying.
A list of materials that can be handled by a particular type of conveying
system is often misleading because of the implication that those materials not
on the list may be in some way unsuitable. Nevertheless, a list is given here as
Table 15.2 with the intention of illustrating the wide range of bulk solids that
can be successfully transported in air-gravity conveyors and the wide range of
industries in which the system may be useful. It is perhaps of greater value in
appreciating the versatility of air-gravity conveying to study some examples of
actual applications of bulk solids transport by this method. Such information
can often be obtained from manufacturers of air-gravity conveyors but there
are also a number of useful references in the published literature to practical
installations handling various bulk solids and some of these are set out in
Table 15.3.
The work of Gel dart in classifying bulk solids according to their fluidization
behaviour has been discussed previously and a chart illustrating the ranges of
Groups A, B, C and D, (e.g. Figure 3.13 or Figure 15.8), provides a useful guide
to the suitability of powders and granular materials for air-gravity conveying.
In general, materials in Group B, which includes most powders in the mean
particle size and density ranges 40 to 500 11m and 1400 to 4000 kg/m 3 , are the
Table 15.2 Twenty common particulate bulk materials
that can be handled successfully in air-gravity conveyors
Alumina
Animal feedstuffs
Barytes
Bauxite
Catalysts
Cement
Fertilizers
Flour
Gypsum
Kiln dust
PVC resin
Potash
Pulverized coal
Pulverized fuel ash (pfa)
Powdered ores
Rockdust
Sand
Soap powder
Soda ash
Talc
471
AIR-ASSISTED GRAVITY CONVEYING
Table 15.3 Some sources of information on industrial application of air-assisted gravity
conveying
Material handled
Cement, fluidized and conveyed on woven canvas belting
in a trough inclined at about 4o
Hot metallic sulphide dust, fluidized on a porous
medium of refractory aluminium oxide
Alumina powder in a large Canadian smelting plant,
conveyed on porous tiles at a 2.2° slope.
(Conveying rate about 200 tonne/h in 500 mmwide channel.)
Alumina transported on various sizes of air-gravity
conveyor in ship loading and unloading plant.
Rockdust handled in bulk to reduce costs in mining
applications. ('Airslide' with 6° slope)
General information; and reference to sodium
tripolyphosphate and silica flour.
Various bulk solids conveyed on 'airslides' in
self-unloading railroad car.
Author(s) and
reference
Avery, W.M. [6]
Nordberg, B. [7]
Anon. [8]
Bushell, E. and
Maskell, R.C. [3]
Leitzel, R.E. and
Morrisey, W.M. [2]
Alston, G.L. [9]
Anon.,
[10]
EEU A
Handbook
Hudson, W.G. [11]
easiest to convey and will flow well at very shallow slopes. When the supply of
fluidizing air is shut off the bed collapses rapidly and flow stops, so that there
are unlikely to be any problems with air retention. Materials of larger particle
size and/or high density (Group D) can sometimes be conveyed in the same
manner, b Jt the quantity of fluidizing air tends to become rather large, and
other forms of transport, such as belt conveying, are likely to be more suitable.
Group A generally includes powders of small particle size and/or low density
which should flow well in an air-gravity conveyor; however, as a result of air
retention, the material may have a tendency to continue flowing for a time after
the fluidizing air supply has been shut off. Finally, Group C includes cohesive
powders that are difficult to fluidize satisfactorily because of high interparticle
forces resulting from very small particle size, electrostatic effects or high
moisture content. The dividing line between Groups C and A is very indistinct
and the only way of properly assessing the suitability of doubtful materials for
air-assisted gravity conveying is by practical experiment in a small-scale test
rig. As previously indicated, it may be found that apparently unsuitable
materials will, by a combination of 'flowing' and 'sliding', move continuously
along an inclined channel, provided that the slope and air supply are sufficient.
Although for a given bulk solid, the parameters mainly influencing its flow
behaviour are those that have already been discussed, there are several other
effects which can cause changes to occur during conveying. The most
significant of these are moisture, electrostatic charging and particle segregation. It is well known that changes in the moisture content of powders can
seriously affect their handling characteristics and this is especially true in the
case of fluidization and fluidized flow. Whilst a small increase in moisture may
1
472
BULK SOLIDS HANDLING
be beneficial in reducing the tendency of the material to hold an electrostatic
charge, too much moisture can cause normally free-flowing powders to
become so cohesive that they cannot be fluidized. Electrostatic charging can
have a similar effect and indeed can be a considerable hazard if the conveyed
material is potentially explosive.
The tendency for segregation to occur in fluidized beds has been mentioned
previously, and this tendency for the coarser particles to drift down towards
the distributor can also occur in flowing fluidized solids. Where the channel is
short and relatively steeply inclined there would be little opportunity for
segregation to occur, but in longer channels the problem may become
significant. In extreme cases a deposit of coarse particles may continuously
build up on the bottom of the channel until the solids flow ceases altogether.
15.6 Air-float conveyors for horizontal and upward transport
It has already been established, through the example of the air-gravity
conveyor, that a fluidized powder will flow along a channel, in the manner of a
liquid, provided that there is an input of energy to the powder sufficient to
maintain the flow. In view of the several positive features that air-gravity
conveying has to offer it is not suprising that there have been a number of
attempts to devise modifications to the basic system that would permit
material to be transported horizontally or on an upward slope. In order to
convey a bulk solid horizontally in an air-float system some additional source
of energy is required to propel the material along the channel. Perhaps the
most familiar device of this type is the one marketed under the name 'Jet
Stream' in which the base of the channel consists of a flat plate with a large
number oflouvred openings so that air enters from the plenum chamber with a
significant component of velocity along the channel (Figure 15.9). This system
works very well for transporting relatively large single items such as packets
and boxes, but rather less well for bulk solids. Although the angled air jets
should serve both to 'fluidize' and to propel the material along the channel,
Figure 15.9 Perforated plate distributor of the type used in the 'Jet Stream' conveyor: the spacing
of the openings, their shape and the percentage of open area may be varied to suit the material
being conveyed. (Typical dimensions are given in mm.)
AIR-ASSISTED GRAVITY CONVEYING
Figure 15.10
473
Stepped or multi-section conveyor for horizontal conveying [10].
high-pressure air
low-pressure air
porous membrane
(a) One form of Stegmaier"s air-jet conveyor
~-
19
I
(Ref.12)
0.5 --~250
~~-
(b) A typical slotted plate distributor : the slots extend the
full width of the con•,eying channel but their size and spacing
could be varied
(c) A combination of porous distributor and directional air-jets
Figure 15.1 l
Horizontal conveyors using air jets to move the bulk material along the channel.
474
BULK SOLIDS HANDLING
problems arise with backflow of particles into the plenum chamber and
degradation of friable materials as a result of the high velocity of the jets.
Furthermore, the specific energy consumption (that is, the energy consumption per metre length conveyed at a rate of one tonne per hour) is rather high.
Other proposals for horizontal air-float conveying included a stepped airgravity conveyor with 'air-lifts' at the end of each downward inclined section
(Figure 15.10), an air-jet conveyor with forward-facing nozzles at regular
intervals along the channel (Figure 15.11 a) and various designs incorporating
inclined slots across the full width of the conveying channel (Figure 15.11 b, c).
A number of attempts have been made to operate conveyors of the air-float
type on an upward slope. In fact, the devices mentioned above will move
particulate material up a slight incline, but not very efficiently. More ingenious
systems have been described in the literature which will work on an upward
gradient of around 10°-20° (Figure 15.12), but with the exception perhaps of
some specialized applications, these devices are unlikely ever to be commercially viable.
Although intended as a variant of the conventional downward-sloping airassisted gravity conveyor for handling 'difficult' materials, the 'Pneuslide'
conveyor (Figure 15.13) is worth mentioning here. This conveyor, which is
plenum chamber
(a) The 'Pneumatic Escalator' of Shinohara and Tanaka (Ref.13)
(b) The lsler conveyor, designed to operate by generating a pressure
gradient within the conveyed material (Ref.14)
Figure 15.12
Proposed methods of air-float conveying on an upward incline.
AIR-ASSISTED GRAVITY CONVEYING
Figure 15.13
475
Cross section of 'Pneuslide' and 'Pneudistributor' [15].
claimed to overcome some of the inherent disadvantages of the more usual
rectangular section channel with porous base, uses a perforated-pipe distributor of special design running along a V-bottomed channel. The purpose
of the V-bottom was to minimize the quantity of stagnant material held below
the distributor and, to ensure that a layer of particles remained above the
distributor, the lower edge of the discharge port from the channel is located
some 50 mm above the distribution pipe. The Pneuslide represents an
interesting development and in many applications its advantages of operation
at high temperature and elimination of clogging and backfilling could
outweigh the obvious disadvantage of stagnant material lying in the channel
beneath the distributor.
For a further discussion of these and other variants on the air-assisted
gravity conveyors, see [16].
15.7 Energy consumption of air-gravity conveyors
It must be admitted that air-assisted gravity conveying suffers from disadvantages, notably that the installation is somewhat less flexible than a pneumatic
pipeline system and the range of bulk solids that can be conveyed is rather
narrower than could be handled by some mechanical systems. However, such
disadvantages as the air-gravity conveyor has are largely compensated by the
high transport rates that can be achieved and the remarkably low energy
consumption when conveying moderately fine particulate solids on a
continuous downward slope.
It has been mentioned previously that the air supplied to the plenum
chamber of a typical air-gravity conveyor would be at a pressure of around
250-500 mm H 2 0 and the superficial velocity of the air through the porous
476
BULK SOLIDS HANDLING
base ofthe channel would normally not exceed 100 mmjs. A simple calculation
then shows that, for example, the maximum power requirement of a 0.5 mwide air-gravity conveying channel should be around 250 watts per metre
length. A channel of this width could be expected to have a capacity of at least
500 tonne/h so that the maximum specific power consumption is likely to be in
the region of0.5 W/m pert/h. Since the air requirement of air-gravity channels
is proportional approximately to their width whilst the conveying capacity is
more nearly proportional to the square of the width, wide channels have a
lower specific power consumption than narrow ones, provided that they
operate at full capacity.
The energy consumption of air-float conveyors operating horizontally or on
an upward incline is less easy to estimate. However, the various forms of air-jet
conveyor could be expected to require the same quantity of air for fluidization
as the air-gravity conveyors, plus an additional air-flow to propel the powder
along the channel. This 'additional' airflow can be several times that required
for fluidization so that the energy consumption of the air-jet conveyors tends
to be rather high.
15.8 Notation
b
rh.
ra
r.
Umc
ut
u.
Pb
Width of conveying channel
Solids mass flow rate
Conveying aspect ratio (defined as the ratio of the depth of the
flowing particulate bed to the width of the channel)
Expansion ratio of particulate bed (defined as the ratio of the
bulk density of the unfluidized material to that of the
suspension)
Minimum fluidizing velocity
Terminal velocity of particles in free fall
Average velocity of the conveyed material
Bulk density
References and bibliography
References
1. Dodge, J. Verfahren zum FortschaiTen von Materialien in Forderrinnen mittels Luftdruck
(Procedure for transportation of materials in conveying channels using pressurised air.)
DRP88402, 1895 (German patent).
2. Leitzel, R.E. and Morrisey, W.M. Air-float conveyors. Bulk Materials Handling, Vol.1, ed.
M.C. Hawk, Univ. Pittsburgh, Sch. Mechn. Eng., 1971, 307-325.
3. Bushell, E. and Maskell, R.C. Fluidised handling of alumina powder. Mech. Handling 47(3)
(March 1960) 126-131.
4. Butler, P. No-moving parts conveyor shifts dry powdered solids. Process Engg. August 1974,
65.
5. Woodcock, C.R. and Mason, J.S. Aspects of the design of air-assisted gravity conveyors for
AIR-ASSISTED GRAVITY CONVEYING
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
477
the transport of bulk particulate solids. Proc. 7Ist Annual AIChE Conf, Florida, November
1978.
Avery, W. Meet the Airslide. Pit and Quarry 41(2) (1949) 62-67.
Nordberg, B. Air-activated gravity conveyors. Rock Products, 52, August 1949, 115-124.
Anon. Hot dust is conveyed pneumatically from precipitators to furnaces. Eng. and Mining,
J., July 1954, 91.
Alston, G.L. Advances in rockdusting procedures. Mechanisation, January 1961, 46-48.
EEUA Handbook No.l5, Pneumatic Handling of Powdered Materials, Constable and Co.,
London, 1963.
Hudson, W.G. Why use pneumatic conveyors. Chem. Engg., Aprill954, 191-194.
Stegmaier, W. Pneumatic chute for the horizontal transport of powdered bulks. Bulk Solids
Technology 2(1) (Spring 1978) 47-55.
Shinohara, K. and Tanaka, T. A new device for pneumatic transport of particles. J. Chem.
Engg. of Japan 5(3) (1972) 279-285.
Isler, W. An air-slide type conveyor for horizontal and upward inclined transport. ZementKalk-Gips 10 (1960) 482-486 (In German).
Singh, B., Callcott, R.G. and Rig by, G.R. Flow of fluidized solids and other fluids in open
channels. Powder Technol. 20 (1978) 99-113.
Woodcock, C.R. and Mason, J.S. Air-float conveying of particulate bulk solids. Proc. Int.
Symp. on Fine Particles Processing, Las Vegas, February 1980.
Recommended further reading
Kraus, M.N. Pneumatic Conveying of Bulk Materials. The Ronald Press Company, 1968, 241-254.
16
Hydraulic conveying
16.1 Introduction
Hydraulic conveying of bulk solids, or 'slurry transport', involves the
conveyance of solid particles in suspension in a moving liquid. Although the
majority of commercially viable slurry pipelines have been constructed to
carry mineral particles in water, almost any combination of solids and liquids
could be possible provided, obviously, that the solid material is not dissolved
or affected in some other unacceptable manner by the carrying liquid. Hightonnage, long-distance transportation of coal, iron, copper, phosphate,
limestone and various other minerals in hydraulic pipelines is now a wellestablished commercial alternative to other modes of bulk solids transport
such as lorries, railway trains and barges.
The essential elements of a general hydraulic conveying system are
illustrated in Figure 16.1. Initially the bulk solid must be prepared, and this
may involve several stages of size reduction by milling and grinding, followed
by mixing with water (or other liquid) to an appropriate consistency. The
slurry is then held in storage tanks, and agitated to keep the solid particles in
suspension, before being pumped into the pipeline. Depending upon the length
of the pipeline, additional pumping stations may be required at intermediate
points. At the reception terminal it is usually necessary to remove most, if not
all, of the carrying liquid in a 'de-watering plant', after which the bulk solid
passes on to the next process.
One of the first reported applications of the conveyance of particulate solids
in hydraulic pipelines was in California around 1850 when gold-bearing sand
was lifted through some 10-20 m and flushed down inclined sluice boxes, but it
was some forty years later when a US patent was granted for pumping coal
slurry [1]. A number of short-distance systems were demonstrated soon after
this, and in 1914 the first medium-length slurry pipeline was carrying coal from
Thames river barges to the Hammersmith power station in London, the
distance involved being some 540m [1]. It was not until the 1950s that the
slurry pipeline really began to compete against other forms of transportation
for moving bulk solids at high rates over long distances, and in the next 30
years or so a large number of commercially operated pipelines began working,
ranging in length from a few miles to around 1000 miles, and handling a variety
of different bulk solid materials. Lists of important slurry pipelines have
appeared in several publications, for instance, [1]-[3], and only two
examples, representing landmarks in the development of hydraulic transport
of solids, will be described here.
. r- 1·: .:'
479
HYDRAULIC CONVEYING
terminal
facility
dry
solids
plp.loo - ·
~
r-----,~
carrier
liQ.Jid
Cw,ter)
1===91==~·
'
PIPELINE L _____ j PIPELINE
SLURRY
PREPARATION
MAIN
PUMP
INTERtvEDIATE
PUMP
DEWATERING
PLANT
dry
solids
carrier liquid
to waste,or
re-use
~
I
I____ ---~------------------------'
Figure 16.1
The essential elements of a hydraulic conveying system.
The first long-distance hydraulic pipeline for the transport of iron ore was
constructed in north-western Tasmania (Figure 16.2a) in the late 1960s to
carry the low-grade ore from the mine site at Savage River, a distance of 53
miles (85 km) to Port Latta on the north coast [ 4]. The terrain is rugged and
mountainous, rendering other modes of transport impractical, both from a
technical and economic standpoint. The selected route involved crossing
several deep river gorges, including that of the Savage River itself, which
necessitated suspending the 230 mm-diameter pipe 140 m above the river from
a 365 m long catenary. The annual throughput achieved with the pipeline is
about 2.3 million tonnes.
A pioneering development in the hydraulic transportation of coal has been
the 273 mile (437 km) Black Mesa pipeline in Arizona, USA. The pipeline,
which began commercial operation in 1970, is 450mm in diameter for most of
its length and transports coal at a rate of around five million tonnes per year. It
crosses a high desert plateau and four mountain ranges on its route from the
Kayenta mine in north-eastern Arizona to the destination in the southern tip
of Nevada (Figure 16.2b). Upward gradients are limited to 16%, principally to
avoid problems occurring as a result of particles falling back along the pipe
during shutdowns. Towards the end of the route the pipeline drops some
1070m in 12miles (19km), and in order to absorb the high pressure head
during this rapid descent the pipe diameter is reduced to 300mm.
Probably the biggest problem facing planners of long-distance pipelines
concerns the acquisition of rights of way. Legal difficulties in this respect have
caused a long delay to one of the most ambitious slurry transport projects ever
proposed, the 1400 mile (2300 km) American ETSI coal slurry pipeline
designed to carry 25 million tonnes per year through a 950 mm-diameter pipe
from Gillette, Wyoming, southwards to the Gulf Coast.
Of considerable interest recently, especially where the use of water presents
insurmountable difficulties, are proposals to develop slurry systems that
would use other liquids. The two combinations receiving greatest attention are
coal-in-oil and coal-in-methanol [2]. There seem to be few problems with the
480
BULK SOLIDS HANDLING
1, Port Latta
Savage
River
t.tne
The Savage River Pipeline in Tasmania
r--L!!~----1
I
The Black Mesa Pipeline in Arizona, USA
Figure 16.2
The routes of two of the world's major slurry pipelines.
flow behaviour of such slurries, although coal-methanol mixtures apparently have thixotropic tendencies which would result in higher pumping
pressures than are desirable. A big advantage of substituting oil or methanol
mixtures for the aqueous slurries is that the de-watering process is reduced or
even eliminated altogether since the entire slurry can be used as a fuel.
HYDRAULIC CONVEYING
481
The economics of slurry pipelining are interesting but quite complex with
many factors to be taken into account, most of them specific to the project
under consideration. In general, slurry transport has applications where:
(i)
(ii)
(iii)
(iv)
(v)
Large annual tonnages are to be handled
The transportation distance is large
The terrain is too difficult to allow either road or rail systems to be viable
Sufficient water is available
The preparation of the bulk solid is not costed solely against the transport
system but is necessary for a subsequent process
(vi) The bulk solid is not damaged or spoiled by slurrification and has
reasonable de-watering characteristics.
The numerous variables and project characteristics interact in a complex
way, however, to influence the selection of a transportation system and the
only effective approach to establishing the economic feasibility of a hydraulic
pipeline for a specific project requires estimates of cost based on an engineering
study of that project.
In this chapter only a brief overview of hydraulic conveying is presented.
However, there now exists a vast quantity of literature on this fascinating
subject and the reader wishing to undertake further study could begin with the
books listed on p. 493 and progress to the more specialized technical
papers, particularly those published in the proceedings of the Hydrotransport
series of conferences.
16.2 Components of a hydraulic conveying system
16.2.1 Pumps
Quite a wide variety of pumps are available for handling slurries, and a useful
survey of these can be found in [5]. These fall into two main categories:
reciprocating pumps, subdivided into plunger type and piston type, and
rotodynamic (centrifugal) pumps. They each have advantages and disadvantages, the most significant being that the reciprocating type, being a positive
displacement machine, can attain higher pressures (even to the extent of restarting flow in a blocked pipeline) whereas the centrifugal pump is capable of
passing much larger particles (up to 100 mm diameter or more) without serious
damage.
The selection of pumps for a slurry pipeline project would be governed by
three factors: the pressure required, the flow rate required and the nature of the
slurry in terms of the size of solid particles and their abrasiveness. Table 16.1,
from [6], summarizes the capabilities of the main classes of slurry pump on
hydraulic pipeline applications. The pressure requirement is the first factor
that dictates the type of pump to be used, since for pressures greater than about
45 bar the centrifugal machines must be ruled out. The choice between plunger
482
BULK SOLIDS HANDLING
Table 16.1 Performance capabilities of slurry pumps [6]
Type
Plunger
Piston
Centrifugal
Max. Working
Pressure
(bars)
240~275
170~210
40~50
Max.flow*
(m 3 /hour)
200
600
11000
Mechanical
Efficiency
Max. allowable
particle size
(mm)
85~90
2
2
150
%)
85~90
40~75
(*Note that these maximum flow rates can usually be obtained only at pressures much smaller
than the maximum shown)
plunger
con~~;png
Figure 16.3 The elements of a plunger pump.
I
Figure 16.4
A double-acting piston pump (fluid end).
pumps and piston pumps would then depend mainly upon the abrasiveness of
the slurry concerned (with the former being better for highly abrasive
products) and the flow rate required. Costs, however, especially in terms of the
number of pumps required (including those on standby), must be carefully
considered.
The plunger pump (Figure 16.3) and the piston pump (Figure 16.4) are
generally similar in construction. Both have a crankshaft which drives the
plungers or pistons through connecting rods and crossheads. The plunger-type
pumps are necessarily single-acting, but piston pumps may be either single- or
double-acting. Since abrasive particles trapped between the piston and the
HYDRAU LIC CONVEYING
483
cylinder wall would result in very high rates ofwear, it is usual when handling such
materials to employ plunger pumps in which the plunger is continuously flushed
with clear water during the suction stroke. Valves are usually of the automatic
type, designed to minimize the effects of erosion and to pass reasonable sized
particles (up to about 1.5 mm).
Figure 16.5 A centrifugal pump for slurry handling (pho to courtesy Warman International Ltd).
484
BULK SOLIDS HANDLING
Reciprocating pumps are used on both the Savage River and Black Mesa
slurry pipelines. The former uses four 450 kW trip lex plunger pumps, arranged
in parallel, two of them being variable-speed in order to allow some
adjustment of the throughput and to make possible a gradual start after a
shutdown. The maximum working pressure of these machines is 140 bar
(2000 lbf/in 2 ) and each delivers 88m 3 /hour. The Black Mesa pipeline has four
pumping stations each equipped with double-acting duplex piston pumps.
One station has four 1300 kW pumps, each rated for 320m 3 /hour at 110 bar,
and the others each have three 1120kW or 1300kW pumps, delivering
480m 3 /hour at the lower pressure of 76 bar. These pumps transport 670
tonnes/hour of coal at a concentration of 48% by mass, corresponding to a
volumetric flow rate of 960m 3 /hour [6].
Centrifugal pumps (Figure 16.5) are more commonly used and tend to be
the automatic choice for short-distance applications and on in-plant operation where the relatively low maximum working pressure (about 50 bar, for
multiple pumps in series) does not prove to be a limitation. In order to
minimize wear, centrifugal pumps are commonly lined with rubber, and this
places a restriction on the impeller speed and the particle size of a slurry, since
large particles travelling at high velocities can have sufficient inertia to cut the
rubber lining. Pumps for coarse-particle slurries are lined with wear-resistant
metal alloys and can operate at higher heads since greater impeller tip-speeds
are permissible. However, the need to pass large particles means that these
pumps are designed with impellers and casings having wide flow passages, and
the hydraulic efficiency tends therefore to be low.
A typical application of centrifugal pumps is on the Waipipi Iron Sands
project in New Zealand, which includes a 6.4 km land pipeline followed by a
2.9 km undersea section. There are three pumping stations, having ten
centrifugal pumps distributed amongst them, ranging in capacity from
190kW, 520m 3 /hour up to 600kW, 1460m 3 /hour. The smaller pumps,
arranged five in series in the main booster station and three in series on a
concentrator barge, have a maximum discharge pressure of 28 bar, whilst the
larger ones, mounted six in series on a ship-loading station, are rated at 46 bar
[6].
A system that has been developed for handling very abrasive slurries is
based on the use of 'lock-hoppers' (Figure 16.6). These allow conventional
multistage pumps to develop high heads with clear water whilst the slurry is
switched in and out of the lock-hoppers by sequenced valves. Another device
which has the same general objective of feeding the solids into the pipeline
downstream of the main or primary pumps, so allowing these to work with
clear water, is the jet pump (Figure 16. 7). The driving fluid, from a conventional
primary pump, flows at high velocity through the central nozzle and entrains
solids-laden fluid, mixing with it in the throat section. In order to obtain a
reasonable delivery pressure, the flow rate of the driving fluid is likely to be of
the same order as the entrained flow.
485
HYDRAULIC CONVEYING
SIIITY from
water rell.m
Figure 16.6 A lock-hopper system for use with abrasive slurries. Note: system is illustrated with
valves b, c, e and h open, and valves a, d, f and g closed so that lock-hopper A is discharging slurry
into the pipeline under the action of high-pressure water being supplied through valve e. Lockhopper B is filling through valve c. All the valves are reversed when lock-hopper A is empty of
slurry and lock-hopper B is full.
/
jet nozzle
diffuser
ni~ng tube
___
/_'-_ _ _ __
/
-
delivered
flui9____
Figure 16.7 The principle of the jet pump.
16.2.2 Slurry preparation plant
In its simplest form, slurry preparation consists of milling or grinding the bulk
solid down to a size suitable for pumping and then mixing it with the carrier
liquid before introducing it into the conveying pipeline. An important
486
BULK SOLIDS HANDLING
economic consideration relates to the proportion of the cost of slurry
preparation that has to be set against the transportation. Thus, if the bulk solid
needs to be milled to a small size for a subsequent process (as would be the case
with minerals extraction from ores, for instance) a fair proportion of the cost of
the mills can be assigned to this.
In all cases, slurry preparation will involve striking a balance between the
size of particles giving optimum slurry flow characteristics and the size needed
for any subsequent processes, which includes de-watering at the discharge end
of the pipeline. Thus, if the particles are extremely fine, de-watering will be
difficult, although the flow qualities of the slurry would be good. Coarse
particles, however, generally require higher conveying velocities (and therefore
cause higher energy consumption and greater rates of wear).
Size reduction of bulk solids is generally by crushing or grinding, with
modern practice being to reduce the size to about 2 mm in jaw or gyratory
cone crushers, with further reduction, if required in rod mills or ball mills. For
the Black Mesa coal pipeline, for example, the coal from the mine or stockpile
is first passed through a cage mill and then, after mixing with water, undergoes
further grinding in a rod mill to a size of 1200 Jlm.
The two most important variables in slurry preparation are the density of
the slurry and the top size of the particles since both affect the flow
characteristics. The usual practice is to prepare the slurry in the agitated
storage tanks to a slightly higher concentration than required, and then to
make final adjustments by the addition of clear water as it enters the pipeline.
Screening is the usual method of ensuring that oversized particles do not enter
the main pipeline.
16.2.3 The pipeline
The majority of operational slurry pipelines are of mild steel and, although the
first consideration when specifying the pipeline is that it should withstand the
applied pressure, attention must also be given to the effects of corrosion and
erosive wear. Where there are significant changes of elevation in a longdistance pipeline the variation of pressure can be substantial. Worthwhile
savings in the cost of the installation can then be made by using pipe sections of
reduced wall thickness on the high levels where the pressure is lower.
Typically, steel pipe for slurry pipelines will have a wall thickness in the range
5-15 mm. On the Black Mesa coal pipeline the 460 mm-diameter pipe has a
wall thickness between 5.6 mm and 11.9 mm, and the 230 mm-diameter Savage
River pipeline varies between 6.4 mm and 13.8 mm [ 1].
Other materials are used for slurry pipelines, including reinforced concrete,
abrasion-resistant steel and high-density polyethylene (HOPE), the latter
being particularly useful where corrosion is a problem. Linings of rubber or
plastic may be used to combat erosive wear when handling abrasive slurries.
Erosive wear of slurry pipelines is likely to become a problem when
HYDRAULIC CONVEYING
487
conveying velocities exceed about 3 m/s, especially where the conveyed
material is abrasive in nature. The mechanisms of abrasion and corrosion,
however, are very complex and beyond the scope of this book: further
discussion of the subject can be found in specialist sources such as [6] and [7].
16.2.4 De-watering equipment
Removal of the water, or other carrier liquid, at the discharge end of a pipeline
can be a major problem, and this alone can be the deciding factor in a slurry
pipeline feasibility study. In general, the finer the particles in the slurry the
more difficult (and, therefore, expensive) it will be to de-water.
There are essentially three processes involved in de-watering:
(i) Particle sedimentation, which may be either natural (that is, by gravity) or
assisted by centrifugal action
(ii) Filtration, where the water drains through a cake of the solid -again this
may occur naturally or with assistance by centrifugal action, pressure or
vacuum
(iii) Thermal drying.
Any or all of these processes may be involved in a de-watering plant, the
selection of the method depending upon the nature of the slurry to be dewatered, the final dryness required and, of course, cost considerations.
Sedimentation techniques can involve the use of various forms of dewatering screen if the size of the particles in the slurry is relatively large.
Separation of the fines can be assisted by washing the slurry over the screens
with additional water. Rapping or vibrating can also help to achieve the best
performance from the screens. Where the solid particles are too fine for dewatering screens to be effective, the slurry can be held in settling tanks so that
separation occurs, over a period of time, by natural sedimentation. In order
that the operation should be continuous, these thickening or clarification
tanks are usually constructed with a conical bottom which is swept by a series
of revolving rakes to direct the settled solids to a central outlet. Clear water is
withdrawn from the top of the tank.
The hydrocyclone is a device that is commonly used for liquid/solids
separation. In appearance and concept it is very similar to the dry cyclone used
for the separation of solid particles from a gas stream (see Figure 5.4), but the
construction is considerably heavier.
For centrifugal de-watering there are various forms of centrifuge commercially available, perhaps the most commonly used being the solid-bowl
centrifuge and the screen-bowl or basket centrifuge. Figure 16.8 illustrates a
typical solid-bowl centrifuge consisting of a rapidly rotating cylindro-conical
bowl and a screw conveyor section of similar profile that revolves concentrically within the bowl, but at a slightly different speed. The slurry is fed into the
centrifuge via the hollow central shaft and the solids form a layer on the inside
488
BULK SOLIDS HANDLING
i ure 16.8 A olid-bowl centrifuge.
Figure 16.9 Mode of operation of a rotary drum filter.
surface of the bowl by centrifugal sedimentation. The liquid leaves the bowl
over a weir-plate at the cylindrical end whilst the solids leave from the opposite
end, propelled by the rotation of the screw relative to the bowl. Adjustment of
the position of the weir plate allows the depth of the water layer in the bowl to
be altered, greater depth giving a clearer effiuent but increasing the fines
content and the moisture content of the de-watered solids.
The basket centrifuge or screen-bowl centrifuge is somewhat similar, but the
rotating cylindrical bowl is constructed of fine mesh, typically of 200-1000 Jlm
aperture size. Slurry enters the bowl axially at one end and is distributed over
the inside surface of the cylindrical screen. It is propelled along the bowl, either
by the action of a rotating screw conveyor or by an axial oscillation applied to
the bowl. The de-watering mechanism is thus essentially filtration, with the
fine particles that pass through the mesh being returned to the bowl for further
processing, and the caked solids being thrown off at the discharge end of
the bowl.
Vacuum and pressure filtration, particularly the former, are commonlyused ways of removing the water from a conveyed slurry. They offer a
HYDRAULIC CONVEYING
489
somewhat more gentle approach to the recovery of the solids and are therefore
better for fragile materials. The simplest form is the rotary drum filter in which
the filter cloth covers the surface of a cylindrical drum arranged with its axis
horizontal. The interior of the drum is evacuated as it rotates slowly with
about one-third of its surface immersed in the slurry to be de-watered. Liquid
passes through the filter and is collected in a filtrate tank whilst the solids cake
on the surface of the drum is progressively dried as the drum turns
(Figure 16.9). After about three-quarters of a revolution the de-watered solids
cake is removed from the drum by means of a scraper knife or by a temporary
reversal of air flow through one segment of the filter.
There are many variations on the theme of filtration, with the filter cloth
being arranged on plates or discs, for example, but their principle of operation
is basically the same.
16.3 System design
16.3.1 General design approach
A slurry pipeline can prove to be an acceptable method of transportation when
(i) The bulk solid to be transported is compatible with the physical restraints
of the state of the art
(ii) Economics favour pipeline transport over other modes
(iii) External restraints, related to the rights-of-way for example, can be
satisfied reasonably.
The physical restraints relate primarily to particle size and solids concentration. Thus, whilst it is true that virtually any combination of size and
concentration can be pumped, in order to design a system that will not wear
out the pipe at an excessive rate and that can be operated under predictable
and stable flow conditions, it is necessary to place fairly strict limits on size and
solids concentration.
Two modes of flow are generally recognized-homogeneous flow in which
very fine particles are carried in true suspension at high concentrations, and
heterogeneous flow in which there exists a significant concentration gradient,
often with large particles 'rolling' along the bottom of the pipe. Most longdistance slurry pipelines operate predominantly in the homogeneous flow
regime. Tailings pipelines, however, are often in the heterogeneous flow regime
simply because it is not practical or economical to perform any processing to
enhance their transportation characteristics.
On the other hand, for useful solid materials it is often economical either to
grind the product or to thicken it in order to improve its flow characteristics.
This approach has been the main feature of the development of slurry
technology. Thus, slurry pipeline design philosophy is generally based on
tailoring the slurry to be compatible with existing pipe materials, slurry
490
BULK SOLIDS HANDLING
pumps, and long distance oil and gas pipeline construction techniques, rather
than the development of new hardware to suit the slurry. Thus, a fundamental
understanding of slurry flow behaviour in a stable and controlled environment
was the basis upon which advances in the technology of slurry pipelines were
made.
The economics of slurry pipelines are 'site-sensitive' and so it is difficult to
generalize. One major variable in comparing transport alternatives is the
overall conveying distance. Since pipelines can often take a fairly direct route,
they are usually significantly shorter than rail or road routes which have more
severe grade and construction restrictions, or barge routes which have obvious
length and location restraints. In addition, generalized comparisons are
difficult where existing alternative transport modes are available. Some
general observations which can be made are as follows.
Annual tonnage. A throughput of one million tonnes per year (about 115 t/h
on continuous operation) or more is likely to be necessary if transport by a new
slurry pipeline is to be competitive with other transport modes. However, for
certain applications, such as transporting high-value minerals such as copper
from remote locations, annual throughputs of only a few thousand tonnes can
be commercially viable.
Distance. For pipelines that require slurry preparation and separation
facilities, a distance of 50 to 100 miles is usually necessary to 'spread' the cost of
the plant required to the end points. However for mineral pipelines, where no
additional process facility investment is needed, pipelines as short as 10 or 20
miles can be commercially viable.
Terrain and location. Slurry pipelines are often selected as the best mode of
transport where the terrain is difficult and the location is remote. Pipelines are
easier to construct in remote areas than roads and railways since they have less
restrictive grade requirements and can be installed at rates of several
kilometres per day by conventional long-distance pipeline construction
techniques. Also, since the pipeline can be buried and pumping stations can be
spaced 50-100 miles apart, remote operations and maintenance are relatively
simple.
External restraints. These can relate to the availability of water; ability to
acquire rights-of-way (crossing of competing railway tracks, for example); and
even environmental groups, which sometimes oppose slurry pipelines because
they tend to foster development of mines, power plant or other facilities in
conservation areas.
16.3.1 Flow characteristics and pressure-drop
An understanding of the rheological characteristics of slurries and, m
HYDRAULIC CONVEYING
491
solids concentration-
Figure 16.10
General form of relationship between slurry viscosity and solids concentration.
particular, the modes of flow that they exhibit when pumped through
pipelines, is crucial to the successful design of hydraulic conveying systems. As
mentioned previously, two distinct flow regimes can be conveniently
identified-homogeneous flow (non-settling slurries) and heterogeneous flow
(settling slurries). These have been described in more detail in Chapter 3
(section 3. 7.1) and at this point the reader should refer back to that and the
following sections for a discussion of the modelling of the different modes of
flow and the use of these models for the prediction of pressure-drops in
flowing slurries. The various correlations given, and the associated charts,
should enable pressure-drops to be determined with sufficient confidence at
least for a preliminary design study.
In practical slurry pipeline systems the critical variables, which are to some
extent interrelated, are the pumping velocity and the solids concentration. The
viscosity of the slurry is clearly dependent upon the concentration of solids,
but in general the form of the relationship is not linear (Figure 16.10). The
optimum working concentration for slurry pipelines is likely to be around the
'knee' of the curve in order to balance the requirements of maximum solids
throughput and lowest pumping power. The pumping velocity will also
influence the power requirement and for this reason, as well as to minimize
problems of erosive wear, the velocity should be kept reasonably low.
However, the velocity must not be so low that the solids begin to settle out of
suspension (assuming that the system is being designed on the basis of
homogeneous flow).
16.4 Recent developments
Probably the most important recent development in the field of hydraulic
conveying concerns the transport of coarse materials. Optimum slurry flow
characteristics require that the solids are in the form of fine particles carried at
high concentrations in the homogeneous flow mode. However, subsequent
handling of the material would often be easier if the bulk solid were not so fine,
and this is particularly the case with de-watering where, for coarse materials,
492
BULK SOLIDS HANDLING
the relatively simple process of screening would be quite adequate.
A number of installations handling coarse coal are already operational,
although these generally only cover short distances. There is considerable
interest, especially in Australia, in the long-distance transport of coarse
materials. It has been demonstrated that, by using a non-Newtonian carrier
fluid, coarse coal having a top-size of 20-25 mm may be transported at very
low velocities (1-2 m/s) with acceptable pressure gradients and specific
energies, and this work has more recently been extended to include mine-waste
materials having density about twice that of coal [8]. The carrier fluid used in
the experimental investigations is made from finely milled coal ( < 90 ,urn)
mixed with water in a concentration of about 50% by mass to give the required
Bingham plastic characteristics. It is pointed out that the application of this
technology to coarse mine-waste slurries is particularly attractive since the
underflow from the de-watering plant provides a convenient carrier fluid
having suitable Bingham-type rheological properties.
A development that is likely to have a considerable effect on slurry
transportation, especially of coal, concerns the use of slurry fuels in industrial
boiler plant. At a recent conference on the applications of coal/liquid mixtures
(CLM) it was reported [9] that in several countries of the world boilers are
being built or adapted to burn coal-water or coal-oil fuels, and research is
beginning to show that CLM fuels may have advantages over dry pulverized
fuels.
Other recent investigative work concerns the use of alternative carrier
liquids such as oil or methanol, as mentioned in the introduction to this
chapter and, in the light of the comments above, this could generate much
interest in the future. The use of small quantities of drag-reducing agents is also
being examined by some research groups. Significant reductions in pressure
losses have been shown to be attainable by the addition of soaps, polymers and
other substances [10].
References and bibliography
References
I. Zandi, I and Gimm, K.K. Transport of Solid Commodities via Freight Pipeline (Freight
Pipeline Technology; Volume 2). US Department of Transportation, Report No. DOT-TST76T-36, July 1976.
2. Link, J.M., Pouska, G.A. and Kirshenbaum, N.W. Mineral slurry transport-an update.
Proc. Int. Symp. on Fine Particles Processing, Las Vegas, February 1980, 282-298.
3. Zandi, I. Freight pipelines, J. Pipelines 2(1982) 77-93.
4. McDermott, W.F. Savage River Mines, the world's first long distance iron ore slurry pipeline.
In Bulk Materials Handling, ed. M.C. Hawk, Univ. of Pittsburgh School of Engineering, 1971,
216-238.
5. Thompson, T.L., Frey, R.J., Cowper, N.T.; and Wasp, E.J. Slurry pumps: a survey. Proc.
Hydrotransport 2, BHRA Conf., Conventry, UK, September 1972, Paper HI.
6. Wasp, E.J., Kenny, J.P. and Gandhi, R.L. Solid-Liquid Flow Slurry Pipeline Transportation.
Trans Tech. Publications and Gulf Publishing Company, 1979.
HYDRAULIC CONVEYING
493
7. Baker, P.J., Jacobs, B.E.A. and Bonnington, S.T. A Guide to Slurry Pipeline Systems. BHRA
Fluid Engineering, 1979.
8. Duckworth, R.A., Pullum, L., Addie, G.R. and Lock year, C. F. The pipeline transport of coarse
materials in a non-Newtonian carried fluid. Proc. Hydrotransport 10, BHRA Conf.,
Innsbruck, October 1986, 69-88.
9. Davies, G. Coal slurry fuels get closer. The Chemical Engineer, January 1986, 17.
10. Sauermann, H.B. Recent developments in hydraulic pipelines. Materials Handling News,
April 1982, 18-24.
Recommended further reading
Bain, A.G. and Bonnington, S.T. The Hydraulic Transport of Solids by Pipeline. Pergamon,
Oxford, 1970.
Baker, P.J., Jacobs, B.E.A. and Bonnington, S.T. A Guide to Slurry Pipeline Systems. BHRA Fluid
Engineering, 1979.
Wasp, E.J., Kenny, J.P. and Gandhi, R.L. Solid-Liquid Flow Slurry Pipeline Transportation. Trans.
Tech. Publications and Gulf Publishing Company, 1979.
17
Capsule transport
17.1 Introduction
In the preceding chapters (12-16) of this book, various aspects of the
transportation of bulk particulate and granular materials in pipelines have
been discussed. The concept was that if the bulk solid were to be fed
continuously into a gas or a liquid flowing steadily along a pipeline, the
particles would be conveyed by the fluid to the outlet end where they could be
disengaged from the carrier fluid in a suitable separation unit. An alternative
approach to the pipeline transportation of bulk solids, especially in cases
where, for some reason, it is undesirable for the conveyed material to come
into contact with the carrier fluid, is to enclose the bulk solid in cylindrical or
spherical capsules, of diameter only slightly less than that of the pipeline, and
then use the gas or liquid to propel these capsules from one end of the pipeline
to the other.
The term 'capsule transport' is used here to mean any system that involves
the transportation of cargo (usually, but not necessarily, bulk solid) in capsules
propelled by fluid moving through a pipeline. This definition could encompass
the familiar systems, often seen in department stores, hospitals and factories, in
which documents and small samples are transported in cylindrical containers
through small-diameter pipes, usually operating under a vacuum. The
definition could be extended to include the case where the bulk material is preformed (for example, by sintering) into relatively large solid cylinders or
spheres. Although the mechanism of transportation is very similar, these solid
cylinders or spheres should not, of course, be called 'capsules'.
Of the two distinct methods of capsule transportation-by gas (usually air)
and by liquid (usually water)-it was the former that was developed first and
was the first to be used commercially. Pneumatic capsule systems were first
built and demonstrated in England in the 1820s, although it was more than ten
years earlier, in 1810, that George Medhurst, an English engineer, had
suggested this method for the conveyance of letters and goods at high speed
through small-diameter pipes [1]. The first experimental system is believed to
have been that of John Valiance, which comprised a wheeled carriage 5! feet
(1.7 m) wide and 22 feet (6.7 m) long, running on rails through a tube 8 feet
(2.4 m) in diameter and 150 feet (46 m) long. Considerable development of the
concept of pneumatically-propelled capsules for the conveyance of goods and
personnel was undertaken during the mid-19th century by the Pneumatic
Despatch Company [2]. They were responsible for laying an experimental
CAPSULE TRANSPORT
495
Figure 17.1 An experimental pneumatic capsule pipeline laid alongside the River Thames,
London, in 1861 [3] (Illustrated London News).
tube, some 400 metres in length, along the bank of the River Thames at
Battersea in London (Figure 17.1). This tube was moved and extended to
550 m to run underground between Euston Station and a nearby post office,
carrying parcels in the wheeled capsules at speeds of about 7.5 metres/second
(Figure 17.2).
Various similar tunnels were constructed in London for the conveyance of
parcels and, in August 1864, a full-size passenger-carrying pneumatic railway
was demonstrated at Crystal Palace in London (Figure 17.3). Passengers were
conveyed in a wheeled carriage through a tunnel approximately 3 m in diameter
and 550 m long [2] but, since the journey was undertaken in darkness, the
effect of claustrophobia must have been considerable! Shortly after this a
similar underground system was constructed in New York with the intention
of'demonstrating the practicability of passenger conveyance by the pneumatic
method' [2]; however, it is doubtful whether fare-paying passengers were ever
carried.
There was little further progress towards the development of a pneumatic
capsule pipeline for the transport of passengers, but the Pneumatic Despatch
Company, and later the Post Office, built up a system of tunnels under London
for carrying letters and parcels. A similar system using a 450 mm-diameter pipe
2 km in length, has been operating in Hamburg, West Germany, since 1962,
and others have been developed in France, Japan and the USA [1].
In the use of pneumatic capsule pipelines for the transport of bulk solids the
Soviet Union seems to have made the most impressive progress. Systems either
in operation or under consideration (in 1978) included one for carrying ore at a
rate of four million tonnes per year over a distance of 6 km, and another to
transport broken stone a distance of 50 km at 2.4 million tonnes per year [6].
In Georgia in the Soviet Union there is a commercially-operated system
carrying gravel in trains of six capsules which travel at 15 m/s through a onemetre diameter pipeline [I]. This pipeline was 2.2 km in length, but a second,
some 50 km long and having a capacity of 2 million tonnes per year, was under
construction in 1980.
A system in Japan, consisting of a 600 mm diameter pipeline 1.4 km in
Wheeled capsules used in an early form of pneumatic pipeline for the transport of
parcels [4] (Illustrated London News).
Figure 17.2
zCl
r
0
z
>
"':I:
s
r
~
;><;
r
c::
Ill
I.D
"""
0\
A pneumatically-propelled passenger-carrying 'capsule' demonstrated at Crystal
Palace, London, in August 1864 [5] (Illustrated London News).
Figure 17.3
\0
-.J
""""
"'...,
~
;;l
>
zC/l
m
r
c::
C/l
n
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'1l
498
BULK SOLIDS HANDLING
length, having a capacity of 20 000 tonne/month, carries lime in trains of two
250 kg capsules [7].
In comparison with pneumatic capsule systems, hydraulic capsule transport
is a much more recent development, originating in Canada in the 1960s,
although it had been considered by the US Army as a means of supplying war
materials to China during World War II [8]. It is still very much an emerging
technology in transportation, and building on the research groundwork
undertaken by the Research Council of Alberta, in Canada, hydraulic capsule
transportation is now being extensively studied in the USA, Japan and South
Africa, and a number of technical papers on the subject have been published,
particularly in the BHRA 'Hydrotransport' series of conferences. However, the
majority of these papers appear to have been directed towards the theoretical
r-
~--
t
CAPSULE LOADNG
STO:RAGE STATION
(SI\)INGS)
I ~~::~~ry
capsule;;::!~: ~~AIN
~;;E!I;;:;;::::ir··--,
- ["~~-l--,
PIPELINE Lr' PIPELINE
1:_, __ , :
\
BOOS1ER(S) UNLOADNG CAPSULE
MAIN AIR
STAIDN
STORAGE
SUPPLy
CAPSULE RETURN
j
:_ ___________________ (e:2:.EY_ ~o_a~(ri!~ 9~ !l_f:1<!~1!el ~~L _!
Figure 17.4 The essential features of a pneumatic capsule transportation system.
and analytical aspect of capsule transport in hydraulic pipelines, and the
establishment of this method of transportation as an economically viable
alternative to other methods seems to be still some way off.
17.2 Capsule transport in a pneumatic pipeline
17.2.1 General features of a pneuma-capsule system
A typical pneumo-capsule transportation system (Figure 17.4) would include
the following essential features, each of which will be considered separately:
(i) the capsules, (ii) a loading station, (iii) the pipeline, with air supplied at
appropriate points, and (iv) an unloading station. For the long-distance
transportation ofbulk solids the pneumatic capsule pipeline offers a number of
advantages over alternative methods such as slurry pipelines, rail vehicles
and road vehicles. Possibly their most attractive feature in these days of high
fuel costs is a relatively low power requirement, an approximate figure for the
specific energy consumption being 0.6 kW per km tonne/hour. One reason for
this low power requirement is that, in contrast to road and rail vehicles, no
energy is expended in carrying the prime mover and its fuel. Another reason is
that there is a useful regenerative effect from capsules travelling downhill.
CAPSULE TRANSPORT
499
A second important advantage ofpneumo-capsule transportation relates to
the manner in which the bulk solid is carried, that is, enclosed in a container.
Since there is virtually no movement of the bulk solid particles, either relative
one to another or relative to their containing walls, the risks of both
degradation of the particles and abrasive wear of the system components are
almost entirely eliminated. Also, as the particles are not conveyed in the form
of a suspension in the air, the dust explosion hazard is minimal.
17.2.2 The capsules
In pneumatic pipeline systems the capsules are usually cylindrical in shape.
They comprise a container, wheels at each end for guidance and support, and
some form of seal to prevent excessive flow of air through the space between
the capsule body and the pipe wall (Figure 17.5). The capsule may be of the
closed type or the open type (that is, without any lid or cover) depending upon
the nature of the material being carried. The volume of material to be
transported in one batch can be increased by using larger capsules or, very
conveniently, by coupling together two or more capsules into a 'train'. The
optimum capacity of a capsule and the number to be coupled together should
be determined with a view to achieving maximum transport efficiency, taking
account of the loading conditions and despatch intervals, the needs of the
plant or process at the unloading point, the overall conveying distance, the
diameter of the pipeline and the radius of curves.
A practical size of capsule for a modern freight transport system would be
about 500 mm in diameter and 2.5 m long overall, giving a load capacity of
almost 0.5 m 3 . When carrying a high-density material the overall weight of the
loaded capsule could exceed 750 kg, and since the air in the pipeline offers
virtually no buoyancy it is essential that supporting wheels are fitted at each
end. The wheel-sets are typically either three or six wheels arranged at 120° or
60° intervals and mounted on a stiffly-sprung suspension which serves to
centralize the capsule in the pipe and also provides some shock-absorbing
capacity. A critical aspect of capsule design is that of the wheel assembly and,
in particular, of the wheels themselves. Reliability, wear and rolling resistance
are all important factors. Whilst steel wheels on a steel running surface are
probably best from the point of view of rolling resistance, plastic or rubber
tyres bonded 'to steel rims are much less noisy.
Figure 17.5 Typical wheeled capsule for use in a pneumo-capsule pipeline.
500
BULK SOLIDS HANDLING
Perhaps because it has been recognized that the wheels are almost
invariably the weakest part of the capsule there have been attempts to
eliminate them. One of the most interesting proposals is a system of magnetic
suspension so that there is no physical contact between the capsules and the
pipeline. The planned propulsion system in this case involves linear induction
motors, but the use of air to drive the capsules might be a feasible alternative
[9].
In general, bulk solids would be carried in closed capsules with automatic
loading and unloading. In a conventional capsule fitted with a long curved lid,
a useful arrangement is to fit one of the guide wheels at each end of the capsule
to the lid. This serves to keep the lid firmly shut whilst the capsule is in the
pipeline and provides a convenient means of opening the lid at the loading and
unloading stations.
The air seal is usually provided by a flexible skirt mounted between the
wheel assembly and the capsule body. This is slightly smaller than the internal
diameter of the pipeline in order to provide maximum aerodynamic thrust
with minimum friction of the capsule against the pipe wall. The aerodynamic
thrust, and therefore the velocity of the capsule, is clearly a function of the
proportion of the pipe cross-section occupied by the capsule and its flexible
skirt. In an interesting recent development, the seal was provided by an endplate fitted to the capsule, this end-plate being specially constructed to allow
the opening and closing of ports by remote control. In this way the
'effectiveness' of the seal can be adjusted, giving some measure of external
control of the capsule velocity [10].
The dimensions of the capsules are determined to some extent by the
internal diameter of the pipeline and the radius of curvature of the bends
(Figure 17.6). For any given pipe bend, the extremes of capsule size will range
from a very short capsule with diameter only slightly smaller than that of the
pipe, to a very long capsule of minimal diameter. Obviously neither of these
extremes is practical as the volume in each case approaches zero, but
somewhere between there will be an optimum value of the length/diameter
ratio (or 'slenderness ratio') for which the payload volume of the capsule is a
maximum. It is found [11] that, for a given pipe size and curvature, the volume
of the capsule body is nearly proportional to its length and the body weight is
nearly proportional to the cube of its length. There is therefore a practical limit
Figure 17.6
Relationship between the geometry of the pipeline and that of the capsule.
CAPSULE TRANSPORT
501
on the slenderness ratio that can be used, giving due consideration to the
structural integrity of the capsule, and a value of about 7 is recommended [11].
Except for relatively sharp bends (having a radius of curvature less than about
30 pipe diameters) the length of capsule to give maximum payload volume
would be too great for it to be structurally sound,-and therefore it is usually the
limiting slenderness ratio of about 7 that dictates the dimensions of the
capsules.
17.2.3
The pipeline
Since the pipeline is likely to be the single most expensive component in the
system it must be paid careful attention in order to limit costs. Although
pipelines of 1.5 m or more in diameter may be feasible, the practical range of
sizes is from 500-1000 mm. One manufacturer quotes suitable pipe diameters
according to the annual tonnage rates as shown in Table 17.1.
The pipe material would normally be of steel, but concrete offers a useful
cheaper alternative, and there is no limit to the length of the pipeline provided
that booster stations are incorporated at intervals, as necessary, to repressurize the air. The internal surface of the pipeline should be reasonably
smooth, as undulations or other irregularities will give rise to undesirable
dynamic forces on the capsule wheels and body.
It will usually be necessary to install two parallel pipelines, one for the
outgoing cargo-carrying capsules and the other for the return of the empty
capsules. However, it might be feasible on short-distance applications to send
loaded and empty capsules in alternate batches to and fro along the same
pipeline, and if it happens that the capsules are disposable on arrival at the
destination, obviously only a single pipeline would be required.
An important consideration when planning the route of the pipeline is to
ensure that curves are compatible with the capsules to be used. The minimum
acceptable radius of curvature will be determined by the proportions of the
capsule, as illustrated in Figure 17.6. However, as previously explained, the
capsule proportions are generally dictated by structural considerations and a
capsule built to the limiting slenderness ratio of about 7 is capable of
negotiating quite a sharp bend. A bend radius of about 30 pipe diameters
should be regarded as the tightest acceptable curve.
Table 17.1 Recommended pipeline diameters for a pneumacapsule system [12]
Transport rate
(million tonnes per year)
I
2
5
Pipeline diameter (mm)
600-1000
800-1200
1000-1400
502
BULK SOLIDS HANDLING
Figure 17.7
17.2.4
Pressure variation in a capsule pipeline.
The air supply
The air requirement, in terms of the supply pressure and the volumetric
flowrate, depends upon many factors, the most important being the length and
diameter of the pipeline, the number of capsules and their loading and rolling
resistance, and the pipeline gradient. The pressure of the air supplied to the
upstream end of the pipeline can be regarded as the sum of the pressure
required to overcome the wall friction resistance to the flow of air and the
pressure required to propel the capsules (Figure 17.7). The former is
determined relatively easily by well-established procedures, but the analysis of
the motion of a capsule in the pipeline and the determination of the associated
pressure-drop is more difficult. Detailed studies of this aspect of capsule
transport have been undertaken and published, for example [13], [14], but
further consideration of this is beyond the scope of this book.
As a result of the gradual fall in pressure along the pipeline there will be an
expansion of the air and, consequently, an increase in its velocity and in that of
the capsules. In order to operate a capsule transport system over long
distances it is necessary to install booster stations at intervals along the
pipeline. The spacing of these booster stations would be related to the
operating conditions of the system in terms of the velocity of the capsules and
the number of them in the pipeline. Furthermore, the lengths of sections
between booster stations might vary depending upon whether they are
predominantly uphill or downhill.
An important design feature of the booster stations is that they should allow
the capsules to pass through without interruption. Annular jet pumps similar
to those used in hydraulic capsule systems (Figure 17.10) have been tried but
tend to have a very low efficiency, and a more satisfactory form of booster
incorporates a flap-gate which shuts off the pipeline and so maintains a
pressure differential between adjacent sections (Figure 17.8). Although the
gate is normally kept closed by the adverse pressure differential across it, the
approaching capsule or, more precisely, the pressure wave travelling in
CAPSULE TRANSPORT
503
Sl.Wt 10
next section
Figure 17.8 Flap-gate booster for pneumatic capsule pipeline. Pressure ahead of approaching
capsule causes the flap gate to open automatically. Flap closes after capsule has passed.
advance of it, causes the gate automatically to open so that the capsule passes
through without making physical contact.
Because of the practical limit on the air velocities that can be allowed in the
pipeline there is no advantage in attempting to use very high pressures in order
to reduce the number of booster stations required. Roots-type blowers, or
machines having similar characteristics, are generally employed, providing air
at pressure of 0.5-0.8 bar. The critical aspect of the system design is then, as
explained previously, the spacing of the booster stations to maintain
movement of the required number of capsules at the required velocity.
17.2.5 Loading and unloading stations
Possibly the weakest link in a capsule conveying system is in the area of
loading and unloading. These functions require careful planning and involve
the use of reliable materials handling techniques to receive the empty capsules,
fill them, re-introduce them into the pipeline, receive them at the destination,
unload them and, finally, return the 'empties'. The dwell time is the most
critical constraint associated with the design of the terminal stations at each
end of the capsule pipeline since this affects the overall operating efficiency of
the system and the number of capsules that are 'active'.
In a typical system for handling aggregates, the design proposal called for
0.45 m 3 capsules to be automatically filled, accelerated under gravity and fed
into the pipeline at a rate of 220 per hour [15].
Various practical approaches to loading and unloading are possible, with
the capsules either moving slowly, bumper-to-bumper, along the main
pipeline through the terminal, or removed to some kind of branch track.
Where the pipeline is dedicated to one product, loading can generally be
achieved by using volumetric feeders, set to deliver a pre-determined quantity
of bulk solid into each capsule. The usual method of emptying the capsules
involves the use of a rotary unloader in which the capsules are rotated about
their longitudinal axis through 180° in order to discharge their contents into
receiving hoppers located beneath the track.
504
BULK SOLIDS HANDLING
17.3 Capsule transport in a hydraulic pipeline
17.3.1 General features of a hydro-capsule system
The transport of a bulk solid inside capsules in a hydraulic pipeline obviously
has many similarities with the pneumo-capsule transport system previously
described. The essential elements of capsules, pipeline, pumping and booster
stations and terminals are required in each system and they share many of the
advantages that capsule systems can offer in comparison to other forms of
bulk solids transport.
In comparison with pneumatic transport, hydro-capsule pipelining is a
relatively new technology, having been developed, largely in Canada, during
the 1960s. A substantial amount of information now exists in the form of
published technical papers, especially concerned with the hydrodynamics of
hydraulic systems. Information on the purely practical aspects, derived from
operational experience of existing installations, is rather less easy to find.
17.3.2 The capsules
For hydraulic transport systems the capsules are usually in the form of
cylindrical containers having a diameter of about 85% of the internal diameter
of the pipeline. Typically, the length of the capsule is about five times the
diameter. Other forms of capsule have been used, notably spheres which are
said to exhibit favourable transmission energy requirements for materials of
high density.
Some confusion has arisen over the use of the word 'capsule' to apply to
solid cylinders or spheres manufactured from the material to be conveyed,
although the hydrodynamic considerations will generally not be affected by
whether the 'capsule' is hollow or solid. Semi-rigid capsules or 'baggies'
represent another approach to the movement of bulk solids through hydraulic
pipelines; in this case the flexible container normally is disposable so that the
problem of returning empties is eliminated and a single pipeline can be used.
Since the density of the conveying fluid (normally water) is relatively close to
the effective density of the capsules, there is generally no requirement for the
capsules to be fitted with wheels.
An important consideration with hydro-capsule systems is the rate at which
capsules can be supplied and introduced into the pipeline at the loading
terminal. It is probably this factor more than any other which places a limit on
the economic viability of bulk solids transport by hydraulically propelled
capsules in comparison with slurry pipelines and with road and rail systems.
To illustrate this point it could be noted that a 200 mm-diameter slurry
pipeline should be capable of conveying an average bulk solid at a rate of
about one million tonnes per year; to match this capacity in a slurry pipeline of
the same diameter it is likely to be necessary to load one-metre-long capsules
at a rate of one per second [ 16]. Although it is possible to manufacture solid
CAPSULE TRANSPORT
505
cylinders or to fill hollow capsules at this rate, substantial equipment would be
required, which raises questions of investment costs and reliability.
17.3.3 The pipeline
One of the reasons why the hydro-capsule transport system has difficulty in
competing with conventional slurry pipelines lies in the need for two pipes
between the loading and unloading terminals-one to carry the loaded
capsules out, and the other to bring the empties back. It is not surprising,
therefore, that there has been considerable interest in alternative pipelining
methods that will permit the benefits of capsule transport to be obtained with
only a single pipe.
For the transport of coal it has been suggested [8] that over short distances
(less than 10 km) belt conveyors, lorries or coarse slurry pipelines may be more
economical than a double pipe hydro-capsule system, and for long distances
(more than 500 km) the fine slurry pipeline is likely to be the best option. Only
over the mid-range of 10 to 500 km might the double pipe capsule system be
competitive, but if a system could be devised to use just a single pipeline the
capsules look much more attractive.
On very short distance applications it could be feasible to pump the capsules
first one way and then the other through a single pipeline. However, the 'dead
time' while the empty capsules are returning represents a significant loss, and
the fleet size would need to be considerably larger to compensate for the
capsules temporarily out of service. Other approaches are to pack the bulk
solid to be conveyed in disposable or re-usable lightweight containers or bags
(the 'baggies' mentioned in section 17.3.2) or, alternatively, to mix the bulk
solid with a suitable binder and form it into spherical or cylindrical slugs so
that there is no container to return.
17.3.4 The water supply and pump system
The hydrodynamics of capsule motion is quite complex and will not be dealt
with in this book. Readers interested in this aspect of the subject can find much
to satisfy themselves in the technical literature, particularly the proceedings of
the 'Hydrotransport' series of conferences, some examples of papers being
listed as [17]-[20].
Probably the most important point to appreciate is that the capsules are
generally not wheeled and therefore, when loaded, will tend not to travel
concentrically in the pipeline. Furthermore, their longitudinal axes will not
necessarily even be parallel with the centre line of the pipe and the 'attitude' of
the capsules can vary between 'tail up' and 'nose up'. The flow rate of water
through the pipeline should be sufficient to ensure that the capsules are clear of
the pipe walls and this requires that the capsule velocity exceeds the value
corresponding to 'lift-off where the capsule adopts a nose-up attitude and rises
clear of the pipe wall [17].
506
BULK SOLIDS HANDLING
As with pneuma-capsule pipelines, in order to use a hydraulic pipeline to
transport capsules over long distances, means must be found of raising the
pressure of the carrying fluid at appropriate intervals. The main problem at
these 'booster stations' is to raise the pressure whilst allowing the capsules to
pass through with minimum disturbance and minimum reduction of their
forward motion. Since the capsule diameters are typically 85-90% of the
internal pipeline diameter, devising a booster pump that would allow the
capsule to pass straight through has proved something of a challenge to the
design engineers.
There are essentially two approaches which can be adopted: the first is to use
conventional pumps to raise the pressure of the water, whilst holding the
capsules in some kind oflock arrangement, and the second is to use a specially
designed pump through which the capsule can pass relatively undisturbed.
A very complete discussion of different forms of booster pump can be found
in [21], and only a few examples, representing each of the two approaches
mentioned above, will be briefly described here. A typical by-pass scheme, in
which a set of valves is manipulated to allow the capsules to by-pass the
booster pump, is shown in Figure 17.9. The operating sequence of this booster
is as follows:
(i) With valves 1, 6, 7 and 4 open (and the other valves closed) a series of
capsules is drawn into branch A under the influence of the centrally placed
pump and with the water circulating through the branches in the
directions shown in Figure 17.9a.
(ii) Valves 1, 6, 7 and 4 are now closed and valves 3, 8, 5 and 2 are opened.
Water now circulates in the reverse directions through branches Band A,
causing the capsules in branch A to be ejected into the conveying pipeline
whilst approaching capsules are guided into branch B.
(iii) Valves 3, 8, 5 and 2 are now closed, valves 1, 6, 7 and 4 are opened, and the
cycle is repeated.
This by-pass scheme is effective, but the fact that the capsules are stationary
for a time, and the considerable extra distance that the water has to be
pumped, mean that this form of booster is not very efficient.
A form of annular jet pump is illustrated in Figure 17.10. Water is drawn
from a point just downstream of the booster station and injected back into the
conveying line at high pressure through the annular nozzle. Although the
action of the jet pump increases the pressure of the water in the conveying line,
and does so without impeding the forward motion of the capsules, the device is,
unfortunately, very inefficient. Various other arrangements have been tried,
including annular axial flow pumps and linear electric motors acting directly
on the capsules rather than on the carrying liquid. The latter system seems to
be particularly attractive since each capsule would tend to behave as the
plunger of a plunger pump and a drive can be readily applied to the capsule in
either direction without mechanical or electrical connections.
Figure 17.9 A booster station, featuring a capsule by-pass arrangement, for a hydro-capsule
transport system.
(b) Capsule trail leaves Branch A, followilg trail enters Branch B
Branch A
(a) Capsule train enters Branch A, preceding train leaves Branch B
5
Branch A
"'""c
Vl
-.1
0
::0
...,
""
"'
0
z
>
::0
...,
m
r
n
>
508
BULK SOLIDS HANDLING
annular
diffuser
\
no~
/
capsule
IJ.lide
o,high-head
centrifugaii:JU11J
Figure 17.10
An annular jet pump.
17.3.5 Injection and ejection of capsules
Capsules can be fed into a pipeline by means of a lock-type injector similar in
arrangement to the by-pass scheme for booster stations shown in Figure 17.9.
At the pipeline exit the capsules come out of the pipe with the water in a
natural manner and no special effort is needed to eject them. Nonetheless, an
automatic system is needed to collect the capsules and to convey them to
terminal buildings where they are emptied of their contents, cleaned, and then
either stored temporarily or sent back through the return pipeline, with or
without another cargo.
17.4 Size of capsule fleet
An important consideration in the planning of a capsule pipeline, whether
pneumatic or hydraulic, is the total size of the capsule fleet that will be
required. This number must include the capsules in active service, plus an
appropriate number out of service, either for routine maintenance or on
standby against unplanned maintenance or breakdown. The following
analysis, based on that given in [11], shows an approach to the determination
of the size ofthe capsule fleet, which depends upon the capsule design (payload
and maintenance time) and the system operating conditions (line length,
running speeds, terminal turn-round times, annual throughput and operating
hours).
Now, considering the outgoing (loaded) line, if N 1 is the number of capsules
in the line of length L, and v1 is their velocity, they will be arriving at the
destination at a rate of v1 N tfLcapsules per unit time. Thus, if the mass of cargo
in each capsule is me, the instantaneous flow rate of cargo through the line
could be expressed as
(17.1)
Capsules will need to be returned to the loading point at the same rate, and
therefore assuming that the outgoing pipeline and the return line are the same
509
CAPSULE TRANSPORT
length,
(17.2)
where N 2 is the number of capsules in the line and v 2 is their velocity.
Thus
and the total number of active capsules in the pipeline is given by
Nv=N 1 +N 2
Le.
(17.3)
In terms of the required annual throughput mA (tonnes/year), the number of
active capsules can be written
(17.4)
where hA is the annual hours of system operation (that is, hours/year) taking
account of downtime for regular maintenance, shutdown at weekends, and so
on.
There will also be active capsules passing through the terminals and the
number of capsules thus involved will depend on the proportion of the total
cycle time that is actually spent in the terminals.
Now the time taken for a capsule to travel along the outgoing pipeline is
and for the return line
so that the total time in the pipeline is
( 17.5)
Then if the time spent in the loading station is ta and in the unloading station
510
is
th,
BULK SOLIDS HANDLING
the total cycle time is
tcycle
=
t.
+ t 1 + tb + lz
and the total number of active capsules in the system is
or
(17.6)
The capsule fleet size will exceed this total by some small number to allow
for standby in case of breakdowns.
17.5 Notation
hA
L
me
mA
m.
Nl
Nz
NP
Ntot
tl
t2
t.
tb
tcycle
Annual hours of system operation (hours per year).
Length of conveying line
Mass of cargo in one capsule
Annual throughput of bulk solid (tonnes per year)
Effective mass flow rate of bulk solid through pipeline
Number of capsules in outgoing (loaded) pipeline
Number of capsules in return pipeline
Number of active capsules in pipeline
Total number of capsules in service
Transit time for capsule in outgoing pipeline
Transit time for capsule in return pipeline
Time spent by capsule in loading terminal
Time spent by capsule in unloading terminal
Total time taken by capsule to navigate whole system (total
cycle time).
References and bibliography
References
I. Simper, J.l. and Baker, P.J. Pneumatic pipeline capsule systems-the future potential. Proc.
Pneumotransport 2, BHRA Conf., Guildford, UK, September. 1973, F4. 31-39.
2. Lee, C. E. The Pneumatic Despatch Company's Railways. Trans. Newcomen Society 45 (1974)
67-88.
3. Illustrated London News, 24 August 1861, 178.
CAPSULE TRANSPORT
511
4. Ibid. 28 February 1863, 213
5. I bid. I 0 September 1864, 276.
6. Alexandrov, A.M. Pneumatic pipeline container transportation of goods. Proc. Pneumatransport 4, Carmel-by-the-Sea, USA, June 1978, G5. 51-59.
7. Yoshitani, Y. Application of capsule transport system for raw material transport in steelworks.
Proc. Pipeline 78 Seminar, Univ. of Witwatersrand, South Africa, October 1978.
8. Liu, H. Capsule pipelines: potential and research direction. Proc. 4th Int. Symp. on Freight
Pipelines, Atlantic City, USA, October 1982.
9. Marcus, R.D. Pneumatic conveying update. Pneumatic Conveying Manual 1984, suppl to
South Africa Materials Handling News, 2-12.
10. Tsuji, Y., Morikawa, Y. and Seki, W. Velocity control in a capsule pipeline by changing the
area of the end-plate. J. Pipelines 5 (1985) 147-153.
11. Bunce, J.A. Capsules for pneumatic pipelines. Proc. Pneumotransport 4, BHRA Conf., Carmelby-the-Sea, USA, June 1978, G I. 1-18.
12. AI RAPID capsule-tube transport system. Brochure, Nippon Steel Corporation and Daifuku
Machinery Works Ltd., Tokyo, Japan.
13. Carstens, M.R. Analysis of a low-speed capsule-transport pipeline. Proc. Hydrotransport 1,
BHRA Conf., Coventry, UK, September 1970, C4. 73-88.
14. Tsuji, Y. Fluid mechanics of pneumatic capsule transport. Bulk Solids Handling 5 (3) (June
1985) 653-661.
15. Farahar, M.A. Transport of aggregates by the pneumatic capsule pipeline. Proc. Pneumatransport 3, BHRA Conf., Bath, UK, April 1976, A9 115-126.
16. Jensen, E.J. Capsule pipelining-the system and its potential. Proc. Hydrotransport 3, BHRA
Conf., Colorado, USA, May 1974, G I. 1-11.
17. Ellis, H.S. An analysis of the lift-off of pipeline capsules. Proc. Hydrotransport 4, BHRA Conf.,
Alberta, Canada, May 1976, Cl. 1-12.
18. Kruyer, J and White, L.M. Hydrodynamics for the design of a capsule pipeline. Proc.
Hydrotransport 4, BHRA Conf., Alberta, Canada, May 1976, C2. 13-22.
19. Polderman, H.G. Analytical and experimental studies on horizontal and vertical capsule
transport. Proc. Hydrotransport 6, BHRA Conf., Canterbury, UK, September 1979, 169-186.
20. Lazarus, J.H. Hydraulic transport of capsules in pipelines. Proc. lnt. Con[. on Pipeline
Transportation of Solids, Univ. of Witwatersrand, South Africa, 1981.
21. Lazarus, J.H. Booster pumps for hydraulic transport of capsules in pipelines. Proc.
Hydrotransport 6, BHRA Conf., Canterbury, UK, September 1979, 02. 187-200.
Index
abrasive materials
on belt conveyors 272
in bucket elevators 305, 308
in en-masse conveyors 323, 324
in hydraulic conveying systems 482,
484-6
in pneumatic conveying systems 385,
393,399,421-3,427,436
in rotary valves 421-3
in screw conveyors 347
in venturi feeders 427
in vibratory conveyors 375
abrasiveness 28, 275, 276, 305, 308, 323,
440
absorption
infrared 44
microwave 44
acceleration pressure-drop 135
acetylsalicylic acid (aspirin) 247
adhesion 30
aeration
in air-gravity conveyors 456, 459, 461,
470
in blow-tanks 430- I
in hoppers I 04, 188- 92, 197
in L-valves 81
in pipelines 122, 401, 403
in screw conveyors/feeders 344, 425
in vertical pipes 78
in vibratory conveyors 375
aerial ropeway 318, 331 - 3
aero-mechanical conveyor 327 - 8
air-assisted gravity conveyors 456- 77
air blasters 188- 91
air cleaners 211, 213 - 33
air-float conveyors 113, 456, 472-5
air injection 57, 122, 401 - 7
air knife 402
air retention 112, 122, 440, 471
Airslide 457
air-to-fabric ratio 229
alumina 44, 65, 206, 229, 245, 276, 352,
375, 457, 470, 471
aluminium 44, 235, 236, 245, 247
ammonium
chloride 276
nitrate 276, 352
phosphate 254
angle of repose 30-2, 63, 67, 80, 81,
160, 264, 275, 330, 459, 460
apatite 28, 29
apron conveyor 328- 31
arch
cohesive 41, 42, 55, 56, 63, 154,
155, 162, 177, 181, 190, 197, 198,
465
mechanical 41, 42, 56
Archimedean screw 335, 336, 338
Archimedes number 105 - 107
argon 249
asbestos 205, 206- 7, 382
asbestosis 205
ash 276, 306, 320, 347
aspect ratio 467, 468
asphyxiation 249
asthma 205
auger conveyor 337, 338-42
bacteria 204
bagasse 205, 375
bagassosis 205
baggies 504, 505
barge 478, 490
barley 276
barriers, explosion-proof 256
Bartknecht, W 253
barytes 352, 470
bauxite 276, 290, 470
belt conveyor 4, 65, 248, 256, 260- 97,
471, 504
acceleration of load on 287
drive arrangements for 268- 71
driving power in 267,281,284-8
idler less 290- I
loading and discharge of 272 - 3
mass of moving parts in 285 - 6
operation on incline of 264, 269, 281,
287
power unit of 271 - 2
shape factor in 278- 9
slope factor in 277, 280
belt weigher 180, 183
513
514
INDEX
belts 261-5, 282
cable 289- 90
cleaning 273- 4, 266, 288
cleated/profile 261, 262- 4, 304
creep in 270
jointing in 264
sag in 266, 267, 281-4
sandwich 293 - 4
sidewalls in 260, 261, 263, 265, 298, 304
speed of 260, 275-7, 281,
tension of 266, 269, 270, 275,
281-4
tracking (alignment) of 266, 276
troughing of 260, 265, 278-80
wear on 266
bending in silo walls 177
bend pressure-drop 129, 135-6
bends in pneumatic conveying
pipelines 124-5, 129, 135-6,
435- 6, 444, 448, 450
bentonite 352
beryllium 206
bin see hopper
bin activator 194- 7
Bingham plastic 144- 8, 492
Black Mesa 479- 80, 484, 486
Blaine constant volume apparatus 28
Blasius formula 132
blow tank 387, 393-8, 402-3, 408,
417, 428-31, 443
blower 110, 387, 390, 392,408,411,
421, 428, 441, 446
bonemeal 352
boosters 405- 7, 501, 502- 3, 506
Bowerhill-Parcey discharger 199- 200
bran 196
bridge see arch
Bridge Breaker discharge aid 197
British Materials Handling Board 178
Brownian diffusion 225
bubble-foam scrubbers 224
bubbling velocity, minimum 112
bucket elevator 298- 317
bucket filling efficiency of 314
centrifugal discharge in 300- I, 308,
315
continuous discharge in 301-2, 312
driving power of 315 - 16
explosions in 236, 251
loading of 308-9, 315
pivoted bucket in 303-4, 321
selection of 312- 13
speed of 300, 301, 304, 307, 312
Buhler 403 - 6
bulk density 7- 9
Bureau of Mines (US) 238, 248
Cable Belt conveyor
298- 90
caking 169-71, 231,487-9
calcite 28, 29
cancer 205
capacity factor (screw conveyor) 348,
349
capsule transport 380, 494- 511
carbon-black 204, 229, 375
carbon dioxide 249
carborundum 206
Carleton, A J 57- 9
Carman-Kozeny equation 87, 89
catalyst 11, 26, 470
cellulose acetate 385
cement 229, 276, 320, 324, 352, 375,
426, 439, 456, 457, 470, 471
centrifugal (turbo) compressors 446
centrifugal separators
cyclone 213 - 18
mechanical 213
centrifuge 487- 8
ceramic tiles 189
cereals 16, 347, 375
chain and flight conveyors 318- 34
chalk 276, 306
channel 47, 49, 64, 104, 139, 456-77
channelling 102, 110
charcoal 306
chickens 382
china clay (kaolin) 207, 276, 352
choke length (screw conveyor) 341
choking 123
Churchill formula 129
chute 49, 64- 74, 272
chute splitter 5
circular bin discharger 198 - 9
classification (size) 98
clay 276, 306
coal 11, 44, 101, 136, 138, 183, 204,
207, 229, 235, 238, 245, 247, 260,
306, 347' 352, 375, 397' 457' 470,
478, 479, 484, 486, 492, 505
coal/liquid mixture (CLM) 480, 492
cocoa powder 30, 44, 49, 235, 238, 245,
247
codes of practice
for electrostatic charging 258
for fabric filters 228
for hoppers 177- 8
coffee 229, 239, 247, 352, 375, 376, 382
cohesive materials
in air- gravity conveyors 459, 461,
466, 470, 471
in bucket elevators 305, 312
flow behaviour 30, 41, 49
in hoppers 41, 53, 56-8, 63, 154,
164, 168
in chutes 65
fluidization 112, 113
515
INDEX
pneumatic conveying 122, 423
in rotary valves 423
sampling 5
in screw conveyors 337, 347
sieving 16
voidage 8
coke 9, 276, 306
Colebrook formula 127
collecting efficiency
of cyclones 215- 18
of electrostatic precipitators 233
of fabric filters 224-6
of wet washers 221, 222, 224
colloids 141
composite hopper 156, 158, 176
compressor 408, 428, 442, 446
centrifugal (turbo) 446
Lysholm 412, 414
reciprocating 393, 414- 16, 446
regenerative 410- 11
screw 393, 408, 412- 15, 416, 446
sliding vane 411- 12, 414
Zimmern 414
computer-aided design 155, 444
concentration, minimum explosible 239,
246
concentrator rolls 265 - 6
conductivity 44
cone-and-quartering 4, 5
cone crusher 486
containment (of explosions) 246,
249-50
conveying characteristics 439, 448- 53
conveyor see under type, e.g. belt-,
pneumatic-, screw-, etc.
copper 173, 276, 294, 478, 490
core flow 54-5, 58, 154, 157, 166, 176
cork 205
corn starch 229
corrosion 486, 487
corundum 28, 29, 206
cotton 207
Coulter counter 16, 22- 4
coupling
eddy current 272
fluid 271-2
pipeline 434
cracks in silos 177
crushing 203, 209, 237, 486
Crystal ~alace railway 495
cube 11
cullet (glass) 352, 375
custard powder 236
cycle time (capsules) 509-10
cyclone
dry type 203,211,213-18,225, 381,
388, 436, 445, 487
collecting efficiency of 215- 18
explosions in 235, 249, 251
irrigated 220, 221 - 2
pressure-drop 216 - 19
uniflow 214-15
Darcy formula 87, 126
degradation
in air-gravity conveyors 456, 474
in capsule transport 499
in discharge chutes 272
in en-masse conveyors 321, 324
in micrographs 26
in pneumatic conveying systems 383,
385, 393, 399, 421' 428, 441' 446
in rotary valves 421
in vibratory conveyors 375
dense-phase flow 117, 122, 124, 136,
381' 383, 386, 393, 408, 428, 439,
442, 449, 456, 458
density bottle 9
density
apparent 10
bulk 7-9
particle 8 - I 0
depth filtration 224- 5
detergents 141, 352, 375
de-watering 376, 478, 481, 486, 487-9,
491
diameter
equivalent 11, 12
Feret's 12, 21
particle 12 - 25
projected area 12
sieve 12
Stokes 12
surface 11, 12
surface-mean 14
volume 11, 90
volume-mean 14
volume-surface-mean 15, 85, 90
diamond 28, 29
differential scanning calorimetry 246
differential thermal analysis 246
dilatant fluid 140
dilute-phase flow 117,118,123,129,
381, 386, 392, 409, 428, 439, 442,
444, 449, 456
discharge aids 56, 156, 164, 181, 186,
187-200
mechanical 198 - 200
pneumatic 188- 192
vibrational 192- 98
dispersed flow see dilute-phase flow
dispersion 9
distributor I 09- 11, 189
diverter 392, 434, 444, 462, 464
Dixon, G 120, 132, 137
Dodge, J 456
516
INDEX
dome 41
drag coefficient 92-8, 133, 149
drag conveyor 318- 20
drag reduction 129
drilling mud 145
drive factor (belt conveyors) 281-3
dune flow 117, 137
Durand equation 149
Dust Class 252, 253
dust
control of 203- 33, 417, 445
generation of 190, 203, 209, 272, 393
dust explosions 44, 235- 8, 499
dustability 208
Dynamic-Air 406
earth 306
eczema 205
electrical sensing zone see Coulter Counter
electron microscopy 16
electrostatic charging I, 16, 30, 31, 49,
112, 113, 224, 238, 248; 256-8, 433,
434, 471, 472
electrostatic precipators 211, 231- 3
elevators
bucket 298 - 317
screw 354-6
spiral (vibratory) 376- 8
elutriation 16, 17, 98
emery 206
en-masse conveyor 319, 320-5, 461
energy, minimum ignition 44, 238, 240,
241, 246, 248
entrainment 109, 116
equivalent lengths of pipe fittings 129,
130, 135
Ergun equation 90, 105
erosion, erosive wear
in blowers and compressors 411
in hydraulic conveying systems 483,
486, 491
particle hardness 28
in pneumatic conveying systems 383,
393, 396, 399, 421, 428, 434, 436,
441, 446, 456
ethylene glycol 21
ETSI pipeline 479
explosibility limits 239- 40
explosion hazard 235-59, 373, 380,
385, 499
explosion pressure 240, 241, 244, 246,
249, 250, 254
explosion rate constant 253
explosion tests 241 - 6
explosions see dust explosions
explosiveness 44, 172, 499
fabrics
for conveyor belts 261 - 4
for filters 226
for porous distributers 463, 465
face powder 11, 204
Factories Act (UK) 208
fans 387, 390, 392, 408, 409-11, 421,
445, 446
feeders 56, 155, 178, 180-7, 389,
417-33,443
apron 183 - 4, 272
belt 178, 180, 181-3, 272, 427
gate lock 427- 8
rotary (see also rotary valve) 183-4,
381, 387,417-25,443,464
rotary table 184- 5
screw 178, 180, 185-6, 199-200,
272, 337. 354, 387. 397. 425 - 6,
427, 443, 464
venturi 387, 426- 7
vertical load on 181, 358
vibratory 178, 180, 187, 272, 358-9,
365, 373
feed rate control 180
feldspar 28, 29
Feret's diameter 12, 21
fertilizer 227, 439, 470
fibrous materials 26, 388
filters 212, 224-32
in air-gravity conveyors 463
bag type 227- 32, 388, 445
cleaning 230- 2
collecting efficiency 224- 6
fabrics 226
in hydraulic conveying systems 487- 9
in pneumatic conveying systems 381,
388, 393, 425, 436
pressure-drop 229- 30
filtration 84, 203, 211, 224-32, 487,
488-9
filtration velocity 229
finite elements method for silo design
155, 178-9
Fire Research Station (UK) 238, 241,
248
fires 235
fish 382
Fisher sub-sieve sizer 28
flaky/flakiness 16, 17, 25
flap valve/ gate 427, 502- 3
fleet size (capsules) 505, 508- 10
flexible screw conveyor 339, 340
flocculation 138
flooding 55, 57, 184, 189, 195
flour 27, 30, 44, 49, 174, 196, 204, 229,
235, 245, 247, 347, 352, 381, 385,
470
flow factor (hopper) 63, 64, 165-8,
171, 174
517
INDEX
Flow Function (material) 42, 64, 164,
165-6, 168, 170, 171, 172,
fluid bed dryer 44, 256
Fluid-Schub conveying system 403 - 5
Fluid-Stat conveying system 406
fluidization 99- I 13, 458- 61, 468- 72
incipient (or minimum) 101, 104-9
fluidized bed 80, I0 I
fluidizing velocity, minimum 101,
104-9, 110, 442, 468, 469
fluorite 28, 29
fly ash 204, 229, 247, 352, 457, 470
frequency distribution 13
free air delivered (FAD) 409, 441, 446,
447, 448, 449, 454
free fall surface 77
free fall velocity see terminal velocity
friction
angle of internal 37, 60, 63, 67, 167,
174
angle of wall 39, 60, 166, 167, 174
coefficient of (belt conveyors) 281-2,
285-7
coefficient of internal 34
coefficient of wall 39, 51, 70, 73
conveyor belt/ drum 269- 70, 281, 284
factor
dense-phase 137
pipe 126- 9, 132, 147, 149
slurry 149
solids 132
in capsule systems 500
in pneumatic conveying line 440, 444,
449
in reciprocating conveyors 360
in screw conveyors 350
in vbratory conveyors 367, 369
wall 50, 60, 70, 122, 175, 400, 444,
449, 502
Fuller Co. 457
Fuller-Kinyon (FK) pump 425, 428, 443
funnel flow see core flow
gas
absorption of 28
evolution of 44
gassing up 81
gate-lock valve 427
Gattys conveying system 406, 458
Geldard chart/classification 112, I 13,
120, 469, 470
glass 136, 206, 229, 352, 375
gold 382, 478
grain 115, 236, 260, 300, 335, 337, 338,
341, 381
granular jump 68
graphite 207
grass seed 382
graticule 21, 22
gravel 306, 347, 375
gravity separators 211- 13
grinding 203, 209, 237, 248, 478, 485,
486, 489
gunpowder 385
gypsum 28, 29, 352, 470
hardboard fluff 27
hardness 11, 28
Mohs' scale of 28-9
Hartmann bomb 241, 243, 251
Health and Safety at Work Act (UK)
203, 208
Hedstrom number 145-7
helium 249
Herschel-Bulkley fluid 144, 145
heterogeneous flow 138, 139, 148- 50,
489, 491
high angle conveyor 294
Hogan discharge aid 195, 197-8
homogenous flow 138, 139-47, 489,
491
hoods, dust extraction 209- 10
hoppers 51 - 7
codes of practice for 177- 8
composite 156, 158, 176
core-flow 156, 157, 166, 171, 176, 177
design of 154-202
discharge from 56- 64, 178- 80,
187-200, 464, 465
explosion hazard in 235, 249- 53
flow in 47, 49, 51-6
geometry of 156-62, 172, 175-6,
188
mass-flow 156, 157, 159, 162, 166,
175, 176, 177
multiple-outlet 177
overall dimensions of 159- 62
plane flow in !57, 159, 168, 173, 175
pneumatic conveying systems and 380,
387-92, 397, 417, 425-8
shape of 156-9, 166, 175-6, 194
structural design of 176- 8
hopper/feeder interface 181, 184
horizontal tube apparatus 241, 244
Huron Portland Cement Co. 457
hydraulic conveying 138- 50, 478- 93
hydraulic radius 86
hydrocarbons, halogenated 249
hydrocyclone 487
hydrostatic pressure 50, 181
Hydrotransport conferences 481, 498,
505
ice 352
idler rollers 260, 265-8, 273, 285
catenary 265, 266
518
INDEX
impact resistant 266, 267
pitch (spacing) of 266, 282, 284
spiral pattern 266, 267
transition 268
inflammator 241, 244
ignition, prevention of 246, 248-9, 250
ignition energy, minimum 44, 238, 240,
241' 246, 248
237, 238-9, 241, 246,
248, 253, 258
ignition temperature, minimum 44, 238,
246, 248
impingement separators 212
inert gas 237, 249, 253, 336, 389
inertial separators 211 - 18
inflatable cushions/pads 190, 192
ingestion (of dust) 204
inhalation (of dust) 204-8
ignition source
injection
of air 57, 122, 401-7
of oil 412, 414
of water 416
insecticide dust 204
iron 207, 276, 478, 479
]-valve 79- 80
Janssen formula 51, 176
Japan pipe conveyor 292- 3
Jenike, A W
hopper design procedures of !54- 5,
177
'flow - no flow' criterion of 162-4
shear cell of 35 - 7, 40- I
jet pump 484-5, 502, 506, 508
JetStream conveyor 472
Johanson, 1 R 57-8, 63
kaolin 207, 276
kieselguhr 206
kiln dust 470
L-valve 79- 81
laser diffraction spectrometry 16, 24- 5
Lea and Nurse permeameter 28
limestone 207, 254, 276, 375, 448, 449,
478
linear induction motor 500, 506
lining
high friction 370
low friction 173 - 4
of pipelines 486
of pumps 484
liquid ring pump/compressor 416, 446
loading factor (screw conveyors) 347,
349
lock hoppers 484- 5
lorry 463, 478, 505
lumps, lump size
on belts 183, 275- 6, 281
in bucket elevators 30 I, 302, 305,
308
in pneumatic conveying systems
in screw conveyors 376
lungs, lung disease 203, 205
Lysolm compressor 412, 414
machine coefficient, dynamic
440
363-5,
368
magnesium 44, 235, 245, 247
magnetic suspension 500
mass flow 54-6, 58, 156, 167, 168, 176
material coefficient, dynamic 363, 364,
366
material factor (screw conveyors)
mayonnaise 141
measuring cylinder 8
mean diameter
surface 14
volume 14
volume-surface 15
Mechanical Handling Engineers
Association (UK) 281
Medhurst, George 494
median size 14, 110
mesh numbers 15, 18-19
metal powder 229, 457
mica 206, 352
micrograph 26
microscopy
electron 16
optical 12, 16, 21, 26
milk powder 229, 352, 375
milling
351
478, 485, 486
minerals, mineral ore
486, 490
138, 347, 478,
mineral slurries 141, 145
mixing paddles 348, 350
Mohr stress circle 34- 6, 42
Mohs' scale of hardness 28-9, 422
moisture
effect on flow behaviour l, 30, 41,
49, 154, 169, 171-3,275
effect on fluidization 112, 471-2
after de-watering 489
analysis of 43 - 4
balance of 44
inherent 44
sampling of 4
surface 44
Mono pump 425
Moody chart 127, 128, 147
National Fire Protection Association
(USA) 253
nitrogen 249
INDEX
nomograph
for equivalent lengths of pipe 130
for explosion vent areas 252
for hopper discharge rate
(Carleton) 59
(Zanker) 62
for hopper wall/valley angles 175
non-Newtonian flow 138, 139-48, 492
non-mechanical valve 79- 81
nuclear magnetic resonance 44
nylon 247
oats 352
oil injection 412, 414
ore 183, 276, 306, 470, 478, 479, 486,
495
overload factor (screw conveyors) 351
overpressure 52- 3, 177, 253
oxidation 235, 238
oxygen 237, 239, 246, 249, 389
packed bed 84- 91, 100, 102, 104, 119
packed tower 220, 221
packing 7-8
paint pigments 11, 26, 44, 204, 229
paints 141, 245
paper pulp 141
particle density 8, 9-10, 28, 130
particle hardness 11, 28- 9
particle shape 2- 3, 11, 25- 26, 112,
130
particles, size distribution of 10- 25, 98,
104, 110, 138 (see also size
distribution)
peas 352
peat 306
perlite 207
permeameter 27 - 28
personality test 2
pH level 138
pharmaceuticals 44, 229, 300
phase density see solids loading ratio
phase diagram
gas/solids flow 118-20, 122-4
liquid/solids flow 148
phosphate 138, 260, 276, 306, 478
photosedimentometer 18, 20
pick-up velocity 127, 442
pipe see rat-hole
pipe conveyor 291 - 3
pipette 5
plastics 44, 229, 375, 381, 457
plug flow 54, 75
Pneumatic Despatch Company 494
pneumatic conveying 84, 209, 380-455,
456
air movers in 409- 17, 446 - 7
explosion hazards of 235, 249, 256
519
feeders in 417-33, 441
gas/solids separation in 218, 225, 229,
436
high pressure systems in 392- 400
low pressure systems in 386- 92
low velocity systems in 400- 7
modelling of gas/solids flow in
116-37
pressure drop in 125-37, 443-6
stepped pipelines in 398, 446
system design for 438-46
vacuum conveying in 390- 2, 409,
416, 417, 431-3, 441, 443
pneumatic railway 495
pneumoconiosis 205
Pneumosplit 403- 4
Pneuslide 474- 5
Poiseuille equation 86, 142
pollen 204
polyethylene 239, 247, 352
polymer solutions 145
polypropylene 27
Polysius 456
pores 7, 10
porosity 7, 85
porous bed, irrigated 220, 221
porous media 84- 91
porous membrane/ distributor 109- 10,
461, 463-6, 468
potash 470
powder pump see blow tank
power law fluid (Ostwald) 140- 4
power requirement
of air-gravity conveyors 475- 6
of auger conveyors 341 -2
of belt feeders 183
of capsule systems 498
hydraulic conveying 491
of inclined screw conveyors 353- 4
of pneumatic conveyors 447, 448, 454,
456
of V -trough screw conveyors 349- 51
of vertical screw conveyors 354
of vibratory conveyors 374-9
pressure distribution 48, 71
pressure loss factor 129-33, 444
pressure rise, maximum rate of 240,
241, 244, 246, 251, 253
pressure piling 250
principal stress 34, 36, 53
probe, sampling 4
pseudoplastic 138, 140-3
pulse-phase conveying 401 - 3
pulverized fuel ash (PFA) 451, 470
pumps
jet 484 - 5, 502, 506, 508
reciprocating 481 - 2, 484
rotodynamic (centrifugal) 481, 483, 484
520
INDEX
PVC 21, 30, 352, 470
pycnometer, air-comparison
pyrites 276
quartz
9-10
28, 29
railway wagon 463, 471, 478
rat-hole 55, 56, 154, 155, 181, 190,
197
reciprocating compressor 414- 16, 446
reciprocating conveyor 360
regenerative effects 498
Research Council of Alberta 498
resonance, nuclear magnetic 44
respiratory disorders 205
rice 11, 352
riffler 5
Rigden constant volume apparatus
28
rockdust 470, 471
Roots-type blower/exhauster 392, 411,
414, 416, 446, 447, 503
rotary sample divider 5, 6
rotary valves
air leakage in 421-2
'blow-through' 419, 420, 423
'drop-through' 418, 420
explosion hazard in 248
explosion-proof 256
feed rate in 419, 421
for air-gravity conveyor 464
in pneumatic conveying systems
387-92, 397,417-25,441,448
offset 418
rotor clearance in 424, 425
venting by 424 - 5
roughness, pipe 127
rubber 375
sag
in conveyor belts 266, 267, 281 - 4
in en-masse conveyor chains 323
salt 11, 229, 347, 375
saltation 120, 148, 446
sampling 3-5
sand 21, 27, 30, 44, 49, 77, 78, 93, 229,
245, 260, 276, 313, 347, 352, 367,
375, 382, 457. 470, 478
sandwich belts 293- 4
Savage River 479- 80, 484, 486
sawdust 306, 352, 381
Schiller and Naumann model 93
scoop 4
screening 376, 486, 492
scraper chains 319
scratch tests 28
screw compressor 393, 408, 412-15,
416, 446
screw conveyors
auger 337, 338-42
centrifuge 487, 488
flexible 339- 40
industrial (heavy-duty) 342- 52
inclined 351 - 54
U-trough 337, 342- 54
vertical 352, 354- 6
screw flights 335, 343-4, 348, 350, 352,
355
screw pump 381, 387, 425
sedimentation 12, 16, 17- 18, 20, 91-8
in pipelines 138, 487, 488
segregation 3 - 4, 326, 382
in air-gravity conveyers 471, 472
by fluidization I 03
in hoppers 55, 171
in Selby coalfield 260
in vibratory conveyors 376
self-heating 238
self-unloading vessels 293
Semco conveying system 407
settling 91 - 8
hindered 91, 98-9, 139
sewage sludge 145
shaker conveyor 360
shape
hopper 156-9, 166, 175-6, 194
particle 11, 25, 27, 85, 112,440
shape factor 12, 26
shear cell 35-9, 40, 164, 170
annular 37, 38
for wall friction 40
Jenike 35-7, 39, 41, 170
Portishead 37, 38
rotational 37
torsional 37
translational 37
Walker 37, 170
ship unloaders
bucket-type 300
Simporter 294
Siwertell 355
shock loads in silos 177
sieve analysis 15, 16, Ill
sieve shaker 16, 17
Siletta discharge aid 194, 197- 8
silica 203, 205-7
silo see hopper
silo failure 52, 177
Simporter 294
Siwertell bulk discharger 355
size distribution, particle 3, 4, 10-15,
18, 19, 23, 24, 87, 98, 104, 110, 113,
138, 228
skimmer 213
slenderness ratio 500- I
sliding vane compressor 411- 12, 414
521
INDEX
slip ratio 134
slope factor
in apron conveyor 329
in belt conveyor 277, 280
slugging 102, 112, 122
slurry 138-9, 148, 172, 478-93
smoke 204
snubbed drive (belt conveyors) 269
soap powder 352, 470
soda ash 229, 276, 470
solids friction factor 132, 133
solids loading ratio 117, 386, 438, 440,
441-2, 443, 444, 446, 448, 449
Soli tube conveyor 292- 3
sparks 238, 241, 248, 256, 258, 385
specific energy 393, 474, 475-6, 492,
498
specific gravity bottle 9
specific surface 27, 84, 85, 87, 106
sphericity 26, 85, 91, 106, 107
spinning riffler 5, 6
spiral elevator 376- 8
spouted bed 113 - 15
velocity, minimum 115
spray chanber 220- I
spray scrubber 220, 222- 3
standing wave 461
starch 196., 236, 385
static electricity see electrostatics
steel 352, 375
stepped pipeline 398, 446
stockpile 464, 486
Stokes' diameter 12, 96
Stokes' law 93, 108
stone 306, 495
Storall bin discharger 199- 200
stress field 53, 164
stress
consolidating 63
Mohr circle of 34- 6, 42
principal 34, 36, 53
Sturtevant, B F 380
suberosis 205
'suck-blow' system 391, 392, 411
suction nozzle 409, 431 - 3
sugar 11, 30, 44, 49, 170, 205, 229, 235,
238, 245, 247, 276, 375, 381
sulphide dust 471
suppression (of explosions) 246, 253-6
surcharge
in chutes 72
on apron conveyors 330
on conveyor belts 275, 278
surface area 14, 26- 7, Ill, 235
surface diameter 12, 14, 26
surface-mean diameter 14
surface tension 172
surge wave 68
suspension flow see dilute-phase flow
switch 53, 176, 177
table sampler 5, 6
tailings 489
Takt-Schub conveying system 403
talc 28, 29, 205, 206, 352, 382, 470
Tasmania 479
temperature, minimum ignition 44, 238,
246, 248
tensioner 270- I, 282, 298
terminal velocity 92, 93, 95- 8, 109,
133, 139, 469
test sieves 16, 17
Thames Polytechnic 78, 120
thermal drying 487
threshold limit values 208
throw factor (vibratory conveyors) 363
tilting plate 40
time consolidation 168 - 71
time of storage 37, 43, 188
tin 207
titanium dioxide 207, 229
tobacco 204, 229, 375
topaz 28, 29
trace air conveying system 406, 458
trajectory
belt conveyor discharge 272
bucket elevator discharge 311 - 12
in vibrating troughs 362, 363
transport velocity, minimum 440, 448
tripper 273, 288
troughing angle, optimum 265
tubular drag conveyors 326- 8
Turbuflow conveying system 405
twenty-litre sphere apparatus 241, 245,
253
twin blow tank 396-8, 441
two-phase flow
gas/solids 116-37
liquid/solids 138- 50
U-trough (screw) conveyors
341-54
ultrasonics 44
337,
vacuum conveying 390-2, 409, 416,
417, 431-3, 441, 443
vacuum pumps/exhauster 408, 416-17,
443, 446
Valiance, John 494
van der Waals forces 224
velocity
deposition critical 149
minimum conveying 132, 386, 440,
448
fluidizing 101, 104-9, 110
spouting 115
522
superficial 99, 118-20, 123, 468, 475
terminal 92, 93, 95, 98, 109, 133, 139
venting
of air-gravity conveyors 463, 464, 466
of blow tanks 395 - 7
explosion relief 240, 246, 249,
250-3, 254, 255
in rotary valves 424- 5
vent ratio 251
venturi 418, 426-7, 428
venturi scrubber 220, 222- 4
vermiculite 352
vertical tube apparatus 241
Verti-lift 356
vibration 43, 459, 487
vibrators 112, 156, 192-8
rotary eccentric 193, 372-3
electromagnetic 193, 370, 373
vibratory conveyors 358- 79
Vibro-Bi-Plan discharge aid 197
viruses 204
voidage 7-8, 85, 90, 91, 98, 104, 106
void fraction 7
volume diameter 11, 26, 90
volume-mean diameter 14- 15
volume-surface-mean diameter 14, 15,
85, 90
Waeschle 403
Waipipi Iron Sands project 484
Warren Spring Laboratory 401
WASP (photosedimentometer) 19, 20
water injection 416
wear
in belt feeders 183
INDEX
on bends 436
in blowers 411
in bucket elevators 307
in chutes 272
on components 26, 28, 399, 441, 456,
499
in en-masse conveyors 323
in feeders 393, 423
in fittings 393, 421
in pipelines 26, 393, 399, 421, 434,
446, 456, 486, 489
on rotary valves 423
on vibrating troughs 363, 375
wet sieving 16
wet washers/scrubbers 211, 212,
218-24
wheat 247, 276, 342, 352
Williams J C 57, 58, 60
wood 44, 115, 235,245,247,276, 321,
352, 375, 385
wrap, angle of 269- 70, 282
wrap factor 281
yield locus 33, 35, 36, 39, 42, 170, 171
effective 37
time 37
wall 39-41
yield stress, unconfined 34, 37, 42, 162,
164
Zanker's Nomograph 61-3
Zimmern compressor 414
zinc 207
zipper conveyor 292
zirconium 207