MIXING & AGITATION
IN THIS eBOOK
This eBook, created in conjunction with Cleveland Mixer,
is the ultimate resource for engineers looking to increase
mixing or blending efficiency and performance. Get familiar with the 9 most common mixing scenerios, then utilize
the handy calculations to properly understand and size
agitators. Lastly, review the impeller options and identify
which is best for your applications.
T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Content Inside
Mixing Process Classification
An in-depth discussion of the nine major classifications of mixing problems ranging
from simple blending, to crystallizations, extraction, and complex chemical reactions.
Basic Design Calculations
The major calculations required to properly understand and size and agitator. Includes horespower, bulk velocity, and shaft critical speed equations among others.
Mixer Impellers
Short review of the major types of impeller designs available, typical flow patterns,
and application examples.
Retrofitting with Hydrofoils
Describes how cost reductions or process improvements can be accomplished with
“flow efficient” Hydrofoil impellers.
About the Source
Cleveland Mixer designs and manufactures mixers and
agitators for a variety of industries, including chemical processing, food processing, pharmaceutical,
personal care, and water/wastewater treatment.
Since 1939, Cleveland Mixer has provided
solutions and technical expertise to their
customers, supplying them with the durable
equipment and ease of maintenance they need to
achieve their process goals.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Mixing Process Classifications.
BLENDING OF MISCIBLE LIQUIDS
Blending of miscible liquids is a simple physical mixing consisting of combining two or
more materials until the particles, portions, or drops of each of the components are disseminated within each other satisfactorily. The degree of mixing or intimacy of the particles is a matter of subjective judgement as to what is necessary. Specific data required
include:
•
The relative proportions of the liquids to be blended
•
The time available to obtain the final blend
The evaluation of the time available is quite important as it has a considerable effect on
mixer horsepower. Input horsepower is selected to give a certain number of batch turnovers in a given time period. By extending the time period, input horsepower can be
decreased, or conversely, increasing the input horsepower will decrease the blend time.
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The number of batch turnovers required to achieve a satisfactory blend is extremely variable. For example, 12 turnovers should blend readily miscible liquids of similar viscosity and density, such as alcohol and water. However, as many as 36 turnovers may be
required for readily miscible liquids of widely different viscosities, such as glucose and
water.
SOLIDS SUSPENSION
Solids suspension is also a simple physical mixing job involving suspending insoluble
solids in a liquid. Specific data required include:
•
Percentages of solids, particle sizes, and setting velocities in feet per second
•
Ease of wetting of the solids (See also Dispersion)
•
Type of suspension required, either (a) uniform suspension of all particles, or (b)
off-bottom suspension of all solids
Type of suspension is extremely important in mixer selection as illustrated in the following
example:
Assume a vessel with working volume of 3,000 gallons containing light liquid with 20%
insoluble solids, of which 1/3 are 10 mesh, 1/3 are 40 mesh, and 1/3 are 200 mesh.
Settling velocities of the largest 1/3 is 10ft. per minute. Horsepower required for various
types of suspension is:
•
Uniform Suspension 7½ HP
•
Off-bottom Suspension 3 HP
DISPERSION
Dispersion is usually defined as the mixing of two or more non-miscible liquids, or solids
and liquids, into a pseudohomogeneous mass which is more or less stable as measured
by its life before noticeable separation occurs. This can cover a wide range of product
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
types from slurries to heavy dispersions, such as pigment pastes, caulking compounds,
etc. Power input per unit volume can vary widely. Conventional propellers or turbines at
typical propeller and turbine speeds are adequate in some applications. In others, higher
speed impellers introducing higher shear and greater intensity of agitation are desirable
to satisfy the dispersing problem in a reasonable time period. Some dispersing applications can be routine, others may require experimental data to determine the best type of
mixer. Additional data required include:
•
Type of dispersion (liquid-liquid, solid in
liquid, gas in liquid)
•
Relative amounts of each phase
•
Viscosity of final product (if known),
together with details on temporary or interim viscosity conditions which are more
extreme than initial or final conditions
•
Rate of addition of one component into
another, and in which order
•
If solids are present, some expression as
to ease or difficulty of wetting. Some materials which are of a light, fluffy nature,
tend to float on the surface of a liquid,
whereas others may tend to form agglomerates which resist complete wetting. Both
conditions require greater intensity of
agitation to complete the dispersion
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
•
Time available to create the dispersion. Where the solids content
is low, solids easily wettable,
and agglomerates do not form,
the application and horsepower
requirements are similar to solids
suspension. A change in time
available has very little effect on
horsepower levels since the material is usually dispersed as rapidly
as it is added. In more difficult
applications horsepower levels
and available time usually have
a definite relationship due to the
need not only for high shear, but
for adequate turnover
•
Fineness of dispersion required
to be produced by the mixer. This
applies to solids in liquids dispersions and is usually designated as
micron size of particles. Some dispersions are considered complete
when merely smooth in appearance; others may require reduction of agglomerates to certain
maximum micron size. Agglomerates formed after initial entrainment of solids may be reduced
rather easily up to a point, after
which further reduction becomes
exceedingly slow with conventional horsepower levels. Under
this condition, if time is critical,
a special high horsepower, high
shear, high turnover mixer will be
required. If subsequent processing for particle reduction in other
types of equipment, such as roller,
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sand or colloid mills, is planned,
must consider the viscosity factor as an in-
this should be stated since it will
herent part of the dissolving problem. Input
simplify the dispersing job re-
power levels may run to 100 HP or more
quired of the mixer.
per 1000 gallons, with high shear being
DISSOLVING
Dissolving generally refers to the dissolving
of a solid in a liquid. Here the requirement
is to provide a good flow rate of liquid
past the surface of the solids. In general,
for readily soluble crystalline materials, the
type of agitation which provides initial wetting and suspension of all solids will satisfy
the application. In those cases where solids are difficult to dissolve or where faster
dissolving is desired, higher horsepower
levels are required.
desirable. Where long dissolving times can
be tolerated, lower horsepower levels can
be used. Actual times will depend upon
the material involved, the temperature and
particle size.
An easy dissolving application is salt solution make-up, as in preparing a 20% sodium chloride brine in a 2000 gallon tank at
temperature of 150° F. This will require one
horsepower. On the other hand dissolving
1% carboxy-methyl-cellulose in 2000 gallons of water where final viscosities could
run as high as 7500 cps. will require 7½
A different type of dissolving problem is en- to 10 hp. Starch cookers using turbine mixcountered when the solids are non-crystalers are a good example of dispersing and
line materials such as natural and synthetic
rubbers, solid resins, and other commercial
polymers. These materials first soften and
become quite sticky. These particles tend
to agglomerate into larger masses or to
adhere to the vessel walls. The solution increases in viscosity as dissolving proceeds,
with final viscosities becoming extremely
high in solutions having high solids content. Dissolving applications of this type
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dissolving. At a point in the cooking cycle
•
Percent of solids in solution
the starch is changed from a slurry to a
•
Physical characteristics of initial
viscous solution and passes a peak viscos-
products, interim changes, and
ity before it is finally diluted. Mixer must be
sized for the viscosity at the peak.
For example, for a 1000 gallon starch
batch at 12,000 cps. peak viscosity, 3
hp would be satisfactory. At 80,000 cps.
the final product
•
Temperature
•
Solubility
•
Permissible dissolving time
peak viscosity, 7½ hp will be necessary.
CRYSTALLIZATION
Another example is dissolving of crumb
Crystallization is the reverse of dissolving
rubber in organic solvent. Final viscosities can easily reach 500,000 cps.,
1,000,000 cps., or higher depending
upon solids content. Dissolving can be
accomplished slowly over several hours
time at moderate horsepower inputs with
and is accomplished either by cooling a
saturated solution to deposit out crystals, or
by heating a solution to drive off the solvent. The agitator selection usually resolves
itself into (1) a heat transfer application
necessitating good flow of the solution past
large diameter, low speed impellers. Power the heat transfer surfaces and (2) satisfactory handling of the crystals being formed.
levels in the range of 25 hp per 1,000
gallons are typical. Dissolving time can be
reduced by up to 80% by sharply increasing power input and providing high shear
in addition to high fluid turnover. Power
levels in this instance will be in the range
of 200 hp per 1000 gallons.
Data to be provided in dissolving applications should include:
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The problem of handling crystals usually dictates the choice of an impeller system. Some
crystals are sensitive to fracture and must be agitated gently. Other crystals may tend to
form on cooling surfaces and must be actually scraped off by the impeller. Some crystallizers in continuous flow may be designed to concentrate crystals at the bottom of the
vessel for draw-off. Other applications may require that the crystals be maintained uniformly in suspension. In other crystallizers, the solids may deposit out to the extent that
the fluidity is impeded because of the high percentage of solids in suspension.
In general, crystallizers fall into three basic types. The first is a conventional vessel with
either jacket or internal coils or both. The impeller is usually a low speed type to provide
good volumetric flow rates at moderate to low velocity. This type is useful for friable, easily damaged crystals, or where solids content builds up to a high level.
The second is a conventional vessel fitted with a draft tube in addition to a jacket or
coils. The draft tube provides positive flow control which prevents short circuiting of the
desired flow pattern. Usually higher speed impellers such as propellers are used. This
type is useful where crystal size is not important or not affected by the higher shear type
impeller.
A third type is a vessel used with pusher type impellers such as helical ribbons or gates
running in close proximity or actually scraping the vessel wall or heat exchange surfaces
to continuously remove the crystals from these surfaces as they are formed.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Additional data required for crystallization
agitation requirements are as follows:
•
General description of the pro-
A typical example is as follows:
A 15,000 gallon crystallizer is equipped
with a central draft tube and used for form-
cess with particular emphasis
ing solids at 25% maximum by weight,
upon progressive changes in
settling velocity up to 5 ft. per minute, with
crystals and slurry characteristics
crystals being continually drawn-off at the
as crystallization proceeds
tank bottom. Here motion only of the solids
•
Sensitivity of crystals
•
Temperature and pressure of
is desired, since a higher solids concentration at the draw-off point is necessary.
system
•
Description of heat transfer surfaces
•
Nature of crystals, whether they,
should be maintained in suspension, or permitted to settle.
•
Specific gravities of crystals and
of liquor, particle size of crystal,
settling velocities.
•
Crystal formation rates and
method of forming; i.e., do they
form as slurry or do they deposit
out on heat transfer surfaces.
A 10 HP axial flow impeller to provide motion only of solids would be suitable.
However, if uniformity of crystals in suspension is desired for other reasons, 15 HP
would be required.
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HEAT TRANSFER
Heat transfer applications involve either heating, or cooling, or merely maintaining a
uniform temperature. The latter is the easiest application, with heating next, and cooling
usually the most difficuIt. In processing, heat is transferred by conduction from the wall
of the vessel or surface of the internal heating elements to the contents of the vessel. As
the contents are agitated, heat is carried throughout the mass by convection. Mixing thus
speeds up conduction from heat transfer surfaces, and helps promote heat transfer by
forced convection.
Heating and cooling applications are best handled by providing an adequate flow of
fluid past the heat transfer surfaces, with proper measures taken to insure good top to
bottom turnover of the tank contents. This flow pattern will provide good exchange of
fluid between the center of the tank and tank wall resulting in reasonably uniform temperature of tank contents.
Heat transfer applications may be considered similar to blending. Consequently, for
low viscosity liquids, conventional propeller and turbine mixers are generally used. One
qualification on horsepower levels for low viscosity applications is that, unlike blending,
a point can be reached where an increase in input horsepower does not have any pronounced effect. For higher viscosity liquids, larger diameter lower speed impellers are
usually necessary to obtain the desired flow pattern, with accompanying increases in
horsepower similar to that required in higher viscosity liquid blending.
Complete data on all the contributing factors in a heat transfer agitator application are
often difficult to obtain. As much data as are available should be furnished and should
include the following:
•
Tank dimensions and details of tank jacket and/or coils
•
Whether heating, cooling, or merely maintaining an existing temperature is rePage 11
T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
quired. Time available for heating
or cooling
•
•
•
or more of the other types of agitator appli-
be handled as solids suspension
cations such as blending, dissolving, solids
problem. If so, give details as in
suspensions, heat transfer, extraction, or
solid suspension applications
gas dispersion, depending upon which of
Viscosity of fluids at the temperaDetails on heating or cooling me-
these promote the reaction. Complete data
as requested under the specific applicable
operation should be furnished.
dia, temperature of batch at start
Some chemical reaction applications are
and at end of cycle
difficult to classify from that standpoint of
Specific heats and conductivity of
tank contents
•
Reactor agitators are usually treated as one
Are solids present which must
tures to be encountered
•
CHEMICAL REACTION
Is the process material susceptible
to decomposition at the temperature of the heating medium or can
it solidify at the temperature of the
cooling medium
the type of mixing operation. For example,
the reaction of a gas with a liquid promoted by a solid catalyst in suspension usually
involves gas dispersion, solids suspension,
and heat transfer. Applications of this type
are usually evaluated in pilot plant equipment, and pilot plant mixing data should
be made available to the mixer vendor.
These data should include (1) input horsepower per unit volume (2) the geometrical
relationship of the pilot vessel and mixer
and (3) the peripheral speed of the mixer.
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EXTRACTION
In mixing applications, this is defined as
the separation of one or more components
of a mixture by the use of a solvent liquid.
In all these systems, agitation is used to
improve extraction rates by increasing contact areas and mass transfer coefficients.
High shear and high turnover are gener-
At least one of the components must be
ally provided to disperse the phases in
are formed during and following the ex-
However, washing and precipitive extrac-
immiscible with or only partly soluble in the liquid-liquid extraction and in leaching with
extractive liquid so that at least two phases horsepower levels similar to dispersion.
traction process. Extraction operations are
tion usually require only mild agitation simi-
commonly broken down into the following:
lar to blending. Extraction can be carried
•
of vessels. The continuous countercurrent
Liquid-liquid extraction, in which the
mixture treated is a liquid and the
two phases formed are both liquids
•
Leaching, in which one or more
components of a solid mixture are
removed by liquid treatment
•
Washing, which is similar to leaching except that the solids removed
are usually present only on the solid
surface rather than throughout the
solid phase
•
Precipitive extraction, in which a
homogeneous liquid system of two or
on in a single stage vessel, or in a series
extraction column has become of interest
in recent years because it can handle fairly
high flow rates through relatively small mixing areas with a speed-up in process flow
rates.
Extraction processing requirements are so
varied depending on the operation to be
conducted that it is impractical to attempt
to tabulate specific data required. Usually
it is best to try to classify it under one of the
other operations such as solids suspension
or dispersion.
more components is caused to split
into two phases by addition of a third
component
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
GAS DISPERSION
Gas dispersion refers to any operation in
which an incoming gas is intimately distributed throughout a liquid mass, usually with
resultant chemical reaction. The following
features are desired in setting up equipment for this operation:
•
Radial type turbines are preferred
to give a combination of shear
and radial discharge pattern
•
•
normal ungassed liquid level. Under conditions of high gas input and/or low tank
pressure the batch may expand considerably resulting in a reduced batch specific
gravity. In order to use the maximum horsepower capability of the mixer during the
gassing period (when it is needed), twospeed motors are sometimes used to permit
operation of the agitator at reduced speed
when that batch is in an ungassed and
A sparger ring for gas introduc-
denser condition. The impeller is then sized
tion below the bottom impeller is
on the basis of fully loading the mixer
preferred over an injection tube
when the batch is in a gassed and lower
Tanks should be tall and narrow
density condition.
in configuration to provide the
The following generalizations can be made
greatest residence time for the
gas, and should be fully baffled
•
expansion space be provided above the
Multiple impellers are recom-
regarding gas dispersions:
•
the horsepower requirement to
mended
Impeller systems are designed for relatively
high fluid discharge velocities in order to
obtain equal gas dispersions
•
horsepower required for identical
out the liquid. This will retain the gas in
greater contact surface between the gas
and liquid phases. The liquid in the vessel
will expand by the volume of gas entrained
and it is therefore necessary that adequate
Increasing the vessel operating
pressure tends to decrease the
disperse the gas into fine bubbles throughthe liquid as long as possible and provide
Increasing the gas input increases
gas rates
•
Increasing the operating temperature increases reaction rates, but
also increases gas volume by
vapor expansion, thereby increasPage 14
T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
ing the horsepower requirement necessary to produce an equivalent gas dispersion at lower temperatures. The increased reaction rate may offset the need
of equal gas dispersion with its higher horsepower requirement
•
The gas dispersion required is a function of the mass transfer rate. A given time
cycle can be attained by a high mass transfer rate with relatively small surface
area contact (large bubbles) or by a slower mass transfer rate and a high surface area contact (small bubbles). The horsepower requirement is determined
by the gas bubble size needed to give the desired performance. Horsepower
increases with increasing surface area requirements
Apart from the above factors influencing horsepower inputs is the relative dissolving rate
or reaction rate between gas and liquid. Some gases absorb or react rapidly-particularly
in the initial stages of the reaction. Others are considerably slower to react. The slower
reacting applications require a finer gas dispersion and therefore greater horsepower
input.
Data relating to gas dispersion are as follows:
•
Tank details, including all dimensions
•
General description of process with indication of reaction rates, if available
•
Batch size
•
Tank operating pressure and temperature
•
Volume of gas input in SCFM
The following examples indicate how reaction rate can affect horsepower input levels:
Vegetable oil hydrogenation goes easily but halogenation of an organic in a FriedlCrafts reaction can be quite difficult. A vegetable oil hydrogenator might require about 1
hp/1000 gallons, whereas a halogenator might be in a range as high as 10 hp/1000
gallons.
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Basic Design Calculations.
In the process of selecting an agitator system, many calculations must be performed to insure that the process requirements can be met and that the unit selected is mechanically
sound. Some of the basic equations are discussed below.
Reynolds Number:
NRe=
10.7 Sg N D2
µ
NRe = Reynolds Number
Sg = Specific Gravity of Fluid
N = Rotational Speed (RPM)
Reynolds Number (NRe)
NRe is a dimensionless number that characterizes
the fluid regime at the impeller. By definition, it is
the ratio of inertial forces to viscous forces, and is
used as a correlating parameter for impeller Power
Number (NP) and Pumping Number (NQ).
D = Impeller Diameter, In.
µ = Viscosity, Cp.
Fig. 1
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Proximity Factor
Power Number vs.
Reynolds Number
Power Number NP
100
The most neglected power correction factor is the proximity correction (Fig. 3). For
A - 6 - Bladed Radial
B - 4 - Bladed Axial
C - 3 - Bladed Hydrofoil
10
Proximity Factor
A
B
1
F
C
0.1 Viscous
1
Transition
10
100
1000
Turbulent
10000
Reynolds Number NRe
Prox.
2.0
1.5
Fig. 2
Reynolds Number (NP)
NP versus NRe curve as shown in Fig.2.
At Reynolds Numbers above 10,000, the
Power Number is constant (in a baffled
tank). At Reynolds Numbers below 10, the
Power Number has a linear inverse relationship with a slope of minus one.
With these established curves, we can determine the proper value of NP for any set
of operating conditions (speed, diameter,
RADIAL
1.0
D
0.8
0.6
C
0.1
0.2
0.3
0.4 0.5
0.7
1.0
1.5
C
Each series of impellers has a characteristic
specific gravity, and viscosity).
AXIAL
100000
D
Fig. 3
axial flow impellers, the proximity correction results from closing the outlet of the
impeller. The proximity increases the power
as a function of ratio of off-bottom clearance to the turbine diameter.
With radial flow impellers, we are restricting one of the two inlets resulting in initial
unloading as the impeller is brought closer
to the bottom. The power increases fairly
rapidly at C/D ratios less than .3.
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Motor Horsepower
Impeller Horsepower
P=
P
NP
N
D
Sg
NP N3 D5 Sg
(1.52)(1013)
= Impeller Horsepower
= Impeller Power Number Corrected
for Proximity & Reynolds Number
= Rotational Speed (RPM)
= Impeller Diameter, In.
= Fluid Specific Gravity
Fig. 4
P
Hp =
(EFF) (% LOAD)
Hp
P
EFF
% Load
= Motor Horsepower
= Impeller Horsepower
= Reducer Efficiency
= Motor Loading (90% max.)
Fig. 5
Impeller Horsepower
Primary Flow
The power required to drive a mixing impeller has been empirically determined
QP =
in water for fully baffled tanks, correction
factors have been developed to correct for
other conditions. The power requirement
QP
NQ
N
D
is primarily a function of the impeller design (NP), the operating speed (N) and the
impeller diameter (D). The specific gravity
is a direct multiplier on power.
MOTOR HORSEPOWER (HP)
To insure that a given mixing impeller can
operate at the design speed under design
conditions, we must be sure adequate motor horsepower is available. In addition to
impeller horsepower, we must also account
for reducer losses and for possible process
upsets.
=
=
=
=
NQ N D3
231
Primary Flow (GPM)
Pumping Number
Rotational Speed, RPM
Impeller Diameter, In.
Fig. 6
Another important impeller calculation is
primary flow, or the impeller displacement.
The pumping number is primarily a function
of the impeller design, however, correction
must be made if the impeller is not operating in the fully turbulent regime. (NRe >
10,000, see Fig. 7). The operating speed
(N) and impeller diameter (D) also enter
the calculation as shown (Fig. 6).
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MECHANICAL DESIGN - SHAFTS
Pumping Number vs.
Reynolds Number
One undesirable feature of a rotating impeller is the hydraulic side force which is
Pumping Number
generated. This side force affects the design of the auxiliary equipment, such as
the shaft, reducer, and seal, as well as the
102
103
104
Reynolds Number
105
106
support structure.
Shafts: Basis of Design
Fig. 7
Hydraulic Side Force:
Bulk Velocity
VB =
F = K N1.67 D3.53 Sg
Qp
F
K
N
D
Sg
7.48 A
VB
= Bulk Velocity, ft/min.
Qp
= Primary Flow (GPM)
A
= Cross Sectional Area of Tank (ft2)
Bulk velocity is a measure of flow used to
relate relative amounts of mixing.
Fig. 8
Bulk Velocity
Bulk velocity is a measure of relative agitation. It is defined as unit of flow per unit of
vessel cross-sectional area (see Fig.8). No
factor is included for varying vessel geometries, so it is most valuable when considering applications with similar ratios of batch
depth to vessel diameter.
=
=
=
=
=
Hydraulic Side Force (Pounds)
Constant (Geometry Factor)
Rotational Speed (RPM)
Impeller Diameter (Feet)
Specific Gravity
Fig. 9
The basic equation (Fig. 9) is based on
center mounted agitators in fully baffled
tanks. The geometry factor (K) is constant
for a given impeller under given mounting
conditions. The values of K,as well as the
powers of N and D have been empirically
determined for various conditions. Typical
values of K for several impellers are shown
below. It must be remembered that these
values increase rapidly for off-center mountPage 19
T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
ing, less than four baffles, vortexing condi-
hydraulic side force at maximum for the
tions, or conditions where tank internals
mounting condition specified and the maxi-
are not symmetric about the impeller.
mum anticipated torque.
Typical 4-blade
axial flow turbine
Typical 4-blade
Typical K Values
Non-Vortex
Vortex
0.0005
0.0025
0.0010
0.0050
radial flow turbine
Shafts: Basis of Design
Torsion and Bending:
d3 =
16
�Ss
(FL)2 + (Torque)2
Since the hydraulic side force has been empirically determined, many equations exist
d
= Minimum Shaft Dia. (Inches)
Ss
= Allowable Shear Stress
F
= Hydraulic Side Force (Pounds)
L
= Shaft Length (Inches)
Torque= Pound-Inches
and are currently in use by various manufacturers and users. As long as a proper
balance is struck between the allowable
shear stress and the hydraulic side force, a
properly designed shaft will result. The use
of low shear stress to compensate for low
hydraulic side force may cause underde-
Fig. 10
Another major area of concern in agitator shaft design is shaft critical speed. The
sign in the other support structures.
critical speed is related to the weight, its
Fig. 10 shows a standard formula for cal-
complexity of equations used to solve for
culating the required size of power transmission shafting. The shaft diameter is a
function of the combined loading (torsion
location, and the stiffness of the shaft. The
critical speed increases rapidly as the number of steps in the shaft increases. Most
critical speed calculations involve some
and bending) and the allowable stress. The form of approximation to reduce the comshaft is normally designed to handle the
plexity.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
different in diameter than the reducer shaft,
Shafts: Basis of Design
or 2) a single stepped shaft with the upper
diameter equal to the reducer output shaft
Critical Speed Calculation:
NC =
1
NC
dA 1
L
E
a
R
=
=
=
=
=
=
S
C
We
WB
=
=
=
=
146.4 dA2
E
(RS-1)c
[(L+a)L+ L ][4.13WL + W ]
3
L
e
B
First Shaft Critical Speed (RPM)
Upper Shaft Outside Dia. (Inches)
Shaft Length (Bearing to CL Impeller)(Inches)
Modulus of Elasticity
Bearing Span (Inches)
IA A is Upper Shaft Moment of Intertia
IB B is Lower Shaft Moment of Intertia
Weight Factor S = 1 for 316, 304 & C.S.
Lower Shaft Length (C > .75L)
Equivalant Weight (Pounds)
Pounds Per Inch of Lower Shaft
L1
lower bearing to centerline of the lower
To insure safe operation, the actual operating speed should be less than 60% of the
calculated critical speed. When an appropriate stabilizer ring or stabilizing fins are
employed, the shaft may be operated up to
W2
L1
least 75% of the overall shaft length from
impeller.
L2
Equivalent Weight (We)
We = W1 + W2 ( L2 )3...
diameter and the lower shaft length is at
W1
80% of shaft critical speed.
The equations presented are Cleveland Mixer’s standard equations, which are used in sizing mixers. The
constants and correction factors are generally empiri-
Fig. 11
The equation in Fig. 11 is used to calculate
cal and, therefore, are not absolute but may vary from
vendor to vendor as might some of the empirical equations.
the shaft critical speed for a single stepped
shaft. It allows for solid or hollow shafts. All
weights such as impellers, couplings, etc.
are transferred to the end of the shaft by
the equivalent weight equation. This equation is the one which would normally apply
to either 1) an unstepped shaft which is
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Mixer Impellers.
A mixer is any mixing element which is driven by auxiliary equipment, such as shaft,
speed reducer, and electric motor to provide mixing action.
Mixers are generally categorized by the flow pattern they produce relative to the shaft
centerline or the impeller axis in a fully baffled tank. Further, breakdown is based on
relative shear produced. The resulting divisions are: axial flow, radial flow, hi-shear, lowshear or high flow, and specialized impellers (those which are normally used in unbaffled tanks).
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
AXIAL FLOW IMPELLERS
Propeller
Hydrofoil Impeller
The primary types of axial flow impellers
are the propeller, pitched blade turbine,
and the hydrofoil designs. The propeller
is restricted to small mixers because of its
weight. The pitched blade is used when a
balance of flow and shear is required. The
hydrofoil offers the best high flow design.
Both are built with cast hubs and bolted
Pitched Blade
blades in larger sizes.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Fig. 1A
Fig. 1B
Fig. 1C
AXIAL TURBINE FLOW PATTERNS
The flow pattern produced by a typical axial flow impeller is shown above. When the
vessel is fully baffled and the agitator is center mounted, excellent top to bottom motion
is produced, resulting in good mixing (see Fig. 1B). If the baffles are removed (Fig. 1A),
swirling and vortexing result, mixing becomes very poor and the hydraulic forces on the
impeller increase dramatically. The flow pattern can be improved by moving the agitator off center (Fig. 1C). This will restore most of the top to bottom motion; however, the
hydraulic side forces remain high and if the impeller passes very close to the wall, the
force may become cyclic.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
RADIAL FLOW IMPELLERS
Typical radial flow impellers are shown
at left. Both provide more shear and less
flow per unit of applied horsepower than
the axial flow designs. They are commonly
used on dispersion applications involving
pigments and/or fillers.
The 6 blade design is known as the Rushton
turbine, and is often used on gas disper-
Radial 4 Blade Impeller
sions. The center disc prevents channeling
of the gas up the shaft.
Radial 6 Blade Impeller
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Fig. 2A
Fig. 2B
Fig. 2C
RADIAL TURBINE FLOW PATTERNS
Fig. 2 shows typical flow patterns produced by radial flow impellers. Fig. 2B shows the
flow pattern in a fully baffled tank. Note the tendency to form two agitation zones, each
of which has good top to bottom mixing but reduced interaction between zones. Again,
removing the baffles (Fig. 2A) results in a simple swirling motion, producing little agitation, poor mixing, a vortex, and much higher than normal hydraulic forces. Although
not shown, off-center mounting will provide somewhat better mixing with high hydraulic
forces.
Fig. 2C shows two radial impellers in a fully baffled tank. This situation can be used to
provide a degree of staging. If some degree of control from inlet to outlet is required, this
configuration can be used along with proper location of the inlet and outlet to provide
some control of residence time and reduce short circuiting.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
SPECIALIZED IMPELLERS
Two of the most common specialized impellers are shown at left. Both are primarily
used in high viscosity liquids and produce
flow by displacement with very little shear.
These specialized impellers produce bulk
mixing.
The specific type of impeller to be used is
a direct function of the material characteristics and process requirements, with a final
judgement between types which will work
based on economics.
Helix Impeller
A Side Note On Tank Baffles:
Historically, four baffles, spaced 90 degrees apart, have been considered “standard” with baffle width decreasing as
viscosity increased.
The lack of a radial flow component in the
discharge from hydrofoil impellers results
in (a) less swirling and (b) lower hydraulic
side force.
As a result, hydrofoil designs are operated
very successfully with three baffles, spaced
120 degrees apart.
Anchor Impeller
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Retrofitting With Hydrofoils.
A mixing impeller is used to transfer energy to a fluid system in order to achieve a desired process result.
The power transmitted by the impeller produces flow and head components. The head
term can be further resolved into static head and viscous shear.
“Flow-controlled” mixing applications may be defined as those where the desired process result is directly related to the flow. Examples include most blending, solids suspension, and heat transfer applications.
For many years, the impeller of choice for these jobs was pitched blade turbine, PBT. As
the cost of electrical power increased, the need for “energy efficient” impellers became
obvious.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
PROCESS CONSIDERATIONS
RETROFITTING
The process advantage of the Hydrofoil
There are two primary reasons why retrofit-
impeller lies in its ‘’flow efficiency;” that is,
ting a mixer might be considered:
the ability to maximize the flow produced
per unit of applied power.
A. To achieve the same process result at
a lower operating cost. We assume that
To demonstrate the benefits of a Hydrofoil
equal flow translates to equal process re-
retrofit, we use the following Pumping and
sults, and look for an impeller comparison
Power Numbers:
at constant Q and N. Simple algebraic
Impeller
Hydrofoil XTF3
Pitched PBT
NQ
0.55
0.79
manipulation tells us that:
NP
0.30
1.30
XTF3 Dia. = (1.128) (PBT Dia.)
We will restrict our discussion to the turbulent range of Reynolds Numbers, where NQ
and NP are constant.
Q=
where: N =
D=
Sg =
µ=
Impeller Power
(NP)(N3)(D5)(Sg)
(1.52) (1013)
(231)
relate to an increase in productivity. For
process, or an increased throughput for a
continuous process. Now our impeller com-
Reynolds Number:
(10.7)(Sg)(N)(D2)
NRe=
µ
Impeller Flow
(NQ)(N)(D3)
same operating cost. Here the savings will
example, a shorter blend time in a batch
The equations of interest are:
P=
B. To obtain a better process result at the
parison is at constant P and N, and:
XTF3 Dia. = (1.341) (PBT Dia.)
hp
gpm
Impeller speed, RPM
Impeller diameter, inches
Fluid specific gravity
Fluid viscosity, cps
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Hydrofoil retrofitting example:
A plant has three 15,000 gallon slurry tanks in a continuous process that operates 24
hours per day, 335 days per year. The existing mixers each have 30 hp motors, 53”diameter PBT impellers operating at 84 rpm. The mixer shafts are 3” diameter by 150” in
length. Wetted parts are 316ss. The slurry specific gravity is 1.15 and the viscosity is 20
cps.
Case A.
The present level of agitation is satisfactory, but the plant would like to reduce operating
cost. The plant electrical rate is 7¢/kilowatt-hour. We determine that the present mixers
each produce a flow of 42,800 gpm and draw 24.4 impeller horsepower.
Now consider the retrofit Hydrofoil:
•
XTF3 Dia. = (1.128) (53) = 60”
•
XTF3 Flow = 43,200 gpm
•
XTF3 Power Draw = 10.5 hp
The retrofit will provide equal flow at a savings of 13.9 hp per mixer. The electrical cost
savings will be $5,835/year/mixer or $17,500/year total.
As part of the retrofit, the plant could go to 15 hp motors in order to operate at more
reasonable points on the efficiency and power factor curves.
The total cost for Hydrofoil impellers, motors, starters, and installation should not exceed
the first years cost savings.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
Case B.
Consider the same three tanks. The pilot plant has run tests with Hydrofoil impellers that
resulted in an equivalent leaching efficiency at a 12-15% increase in process throughput rate. The Hydrofoils were operated at the same power levels as the original pitched
blade turbines.
A constant P and N retrofit:
•
XTF3 Dia. = (1.341) (53) = 71”
•
XTF3 Flow = 71,600 gpm
•
XTF3 Power Draw = 24.3 hp
Here the cost of Hydrofoils and installation can be compared to the profits resulting from
increased production.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
MECHANICAL DESIGN
CONSIDERATIONS
Hydrofoil impellers produce true axial flow,
while pitched blade turbines discharge at
45 degrees from the axis. Because of this:
•
Hydrofoils can be run at greater
off-bottom distances and still provide good bottom mixing
•
In our example at constant flow, the 60”
XTF3 weighs less that the 53” PBT. In the
constant power example, the 71” XTF3
weighs more than the 53” PBT so critical
speed must be checked. We find that the
critical speed ratio is higher than good
design permits. Our options are:
•
will meet the design requirements.
Less radial flow component results
In this case that would be a 69”
in less side force and lower bend-
diameter XTF3 with P = 21.0 hp
ing moments
Also, torque loads are reduced at constant
flow and are the same at constant power.
This means that the main mechanical design consideration, when retrofitting, is
the shaft critical speed, and the variable is
Determine the largest XTF3 that
and Q = 65,700 gpm
•
Locate the original 71” XTF3 high
enough up the shaft so critical
speed is no longer a problem. In
this case, raising the impeller 18”
would result in a safe design
impeller weight.
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T H E P L A N T E N G I N E E R ’ S G U I D E T O A G I TAT I O N D E S I G N A N D F U N D A M E N TA L S
CONCLUSION
For many industries, mixing and blending are critical pieces of the process. Before selecting your next mixer, be sure to take all the factors in this eBook into consideration.
Choosing the right mixer can mean the difference between optimal blending efficiency,
and some seriously undesirable results.
Be sure to work with a knowledgeable and experienced vendor to ensure you achieve
the blending results you need in the most efficient way possible.
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