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EXPERIMENTAL STUDIES OF TURBULENCE
IN LIQUID-SOLID FLOWS
by
W~TER FRANKLIN BOHLEN
B.S., University of Notre Dame
(1960)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF
PHILOSOPHY
at the
MASSACHUSETTS INSTITUTE OF
TECHNOLOGY
AND THE
WOODS HOLE OCEANOGRAPHIC INSTITUTION
August 1969
Signature of Author
__
Department of Earth and Planetary
Sciences, August 25, 1969
Certified by
Thesis Supervisor
Accepted by
Chairman, Departmental Committee
on Graduate Students
WTind en
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EXPERIMENTAL STUDIES OF TURBULENCE
IN LIQUID-SOLID FLOWS
by
WALTER FRANKLIN BOHLEN
Submitted to the Department of Earth
and Planetary Sciences on August 25,
1969 in partial fulfillment of the
requirement for the degree of
Doctor of Philosophy
A series of laboratory experiments were performed to
ascertain the extent and manner of turbulence modification
induced by low concentration suspended loads of near neutral
buoyancy. Hot-wire measurements of the fluid velocity field
of free surface flows were obtained in a specially designed
flume recirculating a dielectric liquid and 0.5 mm diameter
spherical plastic particles. In the fixed Reynolds number
flow (16,800) the data obtained at six different concentration levels, ranging from 0 to 3.5% by volume, indicate
that the presence of particles produces substantial turbulence changes. Even at this low level the mean velocity
profile shows an increasing gradient near the bed and sharp
deviation from a logarithmic profile. The rms level of
each of the velocity components u', v' and w' increases,
indicating a general rise in turbulence intensity. The
Reynolds stressju'v' increases, and its maximum value shifts
away from the bed. The overall scale of turbulence appears
to remain unchanged.
The data indicate that offhand neglect of suspended
particle presence is an oversimplification. There is a
similarity between these data and those obtained under adverse pressure gradients. Some effort is made to clarify
the altered turbulence production mechanism, and some future experimental work is proposed.
Thesis Supervisor: John B. Southard
Title: Assistant Professor of Geology
I
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TABLE OF CONTENTS
ABSTRACT ............................................
LIST OF FIGURES ....................................
LIST OF TABLES .................................... 6
ACKNOWLEDGEMENTS ...................................
7
I.
8
II.
III.
INTRODUCTION
....................................
PREVIOUS WORK ................................ 13
EXPERIMENT .................................
20
The Experimental Apparatus
The Turbulence Flume .....................
21
The Instrument Carriage .................
28
The Data Acquisition System .............
30
The Flow Liquid .........................
38
..............
39
The Experimental Particles
40
The Concentration Sampler ...............
The Experimental Procedure
Flume Flow Characteristics ..............
42
Voltage-to-Velocity Conversion ..........
46
...........
50
..............
57
Data Reduction Considerations
Concentration Measurements
Summary ................................... 58
IV.
RESULTS AND CONCLUSIONS
Concentration Measurements
.....
.......... 68
Mean Velocity Comparisons ...............
70
Turbulence Intensity .................... 76
Reynolds Stress ......................... 82
Power Spectra and Scaling ...............
84
Auto Correlation Function
Discussion
REFERENCES
..............
.........................
APPENDIX A
Venturi Flowmeter Calibration
...............
97
APPENDIX B
Hot-Wire Anemometer
......... ...............
102
APPENDIX C
Computer Programs
........... ...............
107
APPENDIX D
Equipment and Material Specif ications
BIOGRAPHICAL SKETCH
................
.
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116
120
5
LIST OF FIGURES
Fig. 1
Turbulence Flume Outline Drawing
.......
22
Fig. 2
Turbulence Flume Overall View ..........
23
Fig. 3
Scissors Jack
Fig. 4
Twin Swivel Links
Fig. 5
Filtration System ....................... 27
Fig. 6
Instrument Carriage Assembly
...........
29
Fig. 7
Data Acquisition System ................
31
Fig. 8
Concentration Sampler
..................
41
Fig. 9
Cross-Stream Velocity Profiles
.........
44
Fig. 10
Mean Velocity Comparison ...............
45
Fig. 11
Coordinate System ....................... 48
Fig. 12
Anemometer Frequency Response
Fig. 13
Energy Spectrum ......................... 55
Fig. 14
Suspended Particle Concentration
Fig. 15
Mean Velocity Comparison
Fig. 16
Velocity Defect Comparison
Fig. 17
................ 24
..........
...................
.... 25
..........
52
.......
69
...............
71
.............
73
Rms of Velocity Fluctuations
Clear Liquid Run ..............
77
Rms of Velocity Fluctuation
Liquid-Solid Runs .............
78
Fig. 19
Turbulence Intensity Comparison ........
81
Fig. 20
Reynolds Stress Comparison .............
83
Fig. 21
Normalized Power Spectra ...............
85
Fig. 22
Power Spectra
Logarithmic Plot ..............
87
Auto Correlation Curves
@ y/D = 0.572 .................
89
Fig. 18
Fig. 23
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LIST OF TABLES
Table 1
Summary of Experimental Hydraulic Data .....
61
Table 2
Tabulated Experimental Results .............
62
IllllllliYilll
ACKNOWLEDGEMENTS
I wish to express my sincere thanks to Professor John
Southard for his continuing help and patience in the execution of this study.
In addition the critical comments of
Professors Perkins, Mei and Mollo-Christensen and Dr. David
Ross were appreciated.
Any experimental project requires a nearly endless
variety of support.
Of special note, however, must be the
high quality of services provided by the departmental machine
shop under the supervision of Mr. Paul Gabriel and the extremely talented artisans of the RLE glass shop under Mr.
Larry Ryan.
Without their assistance, the experimental
apparatus could not have been constructed.
Also the feed-
back provided by numerous discussions with fellow graduate
students and the care exercised by Miss Karen Barker in
the typing of this thesis is greatly appreciated.
...And
then there is Elisabeth who waited.
The computations were done on an IBM 360/65 at the
M.I.T. Computation Center.
This work was supported by the
National Science Foundation under grant No. GA-1582.
I~__
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I.
INTRODUCTION
"That which is far off and exceedingly deep,
who can find it out....?"
Ecclesiastes
In studies of fluid flow mechanics one need not go far
afield to encounter complex unsolved problems.
For over
fifty years scientists and engineers have attempted to place
the dynamics of sediment transport and other liquid-solid
flows on a firm theoretical basis.
Despite these efforts
this problem area is still best described as an art rather
than a science.
The roots of the difficulty are readily
To quote Batchelor (1966),
apparent.
If I were asked to name the areas in fluid
mechanics which are most frustrating from an
all-round point of view, that is taking account of
the conceptual, experimental, and analytical
difficulties I should put high on the list first
the general problem of turbulence and secondly
the Lagrangian aspects of fluid flow. Both of
these areas are involved in the motion of small
particles in turbulent flows...
However, Batchelor was quick to point out that this level
of complexity is for some investigators an attractive feature; those who thrive on simultaneous frustration and
elation are well served.
Providing a challenging research area, studies of
transport mechanics in various free streams and jets find
application in a variety of scientific and.engineering
problems.
In each the investigators attempt to correlate
the mode and amount of material transported with measured
parameters of the flow field.
Studies by oceanographers
and marine geologists on regional sediment transport, by
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9
hydraulic engineers asked to predict beachfront erosion of
the filling of navigable channels, by ecologists and biologists concerned with the dispersion of air pollutants
and aerosols, by industrial engineers designing transport
systems for coal, paper pulp, etc., and by chemical engineers of the many diffusion and catalytic processes involved
in commercial production---all face basically the same
problem.
The highly nonlinear and time-dependent nature of
the governing equations together with an imperfect understanding of the physics of the interactions involved precludes unique analytical solutions.
Nevertheless these
studies have produced empirical solutions for specific cases
and a fairly detailed qualitative picture of the transport
process.
It has become clear that the individual features
of this process are closely interdependent.
To determine
the macroscale properties it is not enough to detail and
sum the microscale components.
take place.
Selective interactions often
To examine some of these features in more
detail I wish to confine this discussion to the transport
of natural sediments and to noncohesive materials in particular.
Observations iadicate that a bed of loose, noncohesive
grains will tend to react in a well defined and repeatable
manner when subject to shearing flows.
Initially at rest,
the particles show no tendency to move in very low velocity
flows, whether laminar or turbulent.
With an increase in
mean velocity, slight movements are observed at separated
locations on the bed.
This "threshold of motion" is ill-
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defined, and has been liLtle studied.
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ill,
It is unclear whether
the motion is the result of a general flow instability or
simply a localized feature, possibly a simple lift or
drag force on the individual particle.
Further increase in the velocity produces general agitation and motion of the surface particles.
This level is
marked by the onset of fully turbulent shear flow, the
scattering of particles by the apparent impingement of
turbulent jets or eddies, and the start of deformation of
the initially plane bed into sediment ripples.
Material
transport, either by rolling or saltating (i.e. small hops),
remains restricted to the bed surface.
This "bed load" is
the predominant transport mode for most natural regimes.
Necessarily, development of a rippled bed surface
In turn, the
will tend to modify the mean velocity field.
resultant accelerations and decelerations will effect the
evolution of the bed.
An accurate description of the growth
rate of these bed features requires a careful evaluation
of the local velocity field and the resultant boundary
shear stress.
However, even with the required measurements
in hand, it remains to apply the data within the framework
of a coherent physical model.
This problem has been addressed
by numerous investigators (Benjamin, 1959; Kennedy, 1963).
Their results are not entirely satisfying.
While sufficiently
accurate for some specific cases, their efforts do little
to quantify bed-form evolution and subsequent velocity field
modification.
Although Smith (1969) has recently presented
some more promising results, this area remains largely a
fundamental unknown in the transport process.
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11
Continuing to increase the mean velncity (but with the
flow remaining subcritical) increases bed deformation, induces longer wavelength, large amplitude, features or dunes,
and results in the transport of noticeable amounts of sediment above the bed as a suspended load.
This suspended
material tends to further complicate the transport mechanics.
The already complex boundary conditions are aggravated by
a concentration gradient, flow viscosity increases, momentum
transfer will be subject to variations due to particleparticle collisions, and the structure of fluid turbulence
will be modified as a function of suspended sediment concentration.
In short, the problem initially posed as a
single-phase flow with variable boundary conditions must now
be posed in terms of two-phase or liquid-solid dynamics.
Although this aspect is often neglected (being justified
in terms of the low suspended concentration) it is becoming
increasingly apparent that certain properties of the velocity
field are sharply modified by extremely low suspended loads.
Offhand neglect may be an oversimplification.
Further increase in the mean velocity will reveal few
additional complicating features.
Bed forms will continue
to change, becoming plane at some high shear velocity.
The
suspended load increases and, in the presence of a freesurface, supercritical flows induce surface waves and the
resultant bed forms termed antidunes.
The latter features
represent an additional influence on the velocity field.
For the most part however, these problems represent an extension of the lower velocity conditions.
Seemingly if a
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comprehensive model for subcritical flow was available,
it could be made to serve for supercritical conditions.
This brief review of the qualitative features of the
transport process points clearly to three prominent problem
areas.
First, what determines the threshold of motion and
what is the nature of the forces involved?
Second, what
are the dynamics governing the onset and evolution of bed
forms?
Third, how does the presence of a suspended load
influence the structure of fluid turbulence in shear flows?
These areas form integral parts of the total transport process, and are to some extent mutually dependent.
This inter-
dependence is especially strong for the latter two areas,
since any variations in the velocity field are necessarily
reflected in the boundary shear stress and subsequently
the bed profile.
Accurate interpretations require careful
evaluation of the character and extent of turbulence modification produced by a suspended load.
Such a study in
turn must recognize the existence of two mutually interacting fields of random motion:
bulence fields.
the particle and fluid tur-
Only in the limit, as particle diameter
approaches zero, do the measured properties of each become
identical.
The fdllowing investigation concentrates on modi-
fications produced in the fluid turbulence field in hopes
of clarifying one of the complex interactions involved in
the transport process.
II. PREVIOUS WORK
In reviewing the literature available on past efforts
to assess flow modifications produced by suspended loads,
one is confronted by a vast array of methods, results, and
conclusions.
Each investigator seems intent on proposing
and supporting a new theory rather than clarifying or extending previous research.
As a result it is difficult to ar-
rive at a concensus of opinion on any one feature of this
complex problem, a problem constrained first by the lack of
a unified theory governing the structure and mechanics of
turbulent shear flow and secondly by disagreement over the
mechanism responsible for the suspension of particles.
The difficulties remain not for the lack of effort; as
early as 1906, Einstein (1906) hypothesized that particles
suspended by a free stream would modify the energy balance.
To estimate quantitatively the increased energy dissipation,
he introduced the concept of an "effective viscosity" as a
function of suspended particle concentration.
The simple
partition of energy suggested by these laminar flow studies
was soon questioned, however, when turbulent flow applications
were attempted.
Gilbert (1914) published the results of an experiment
designed to measure changes in stream flow resistance for
various concentrations of suspended sediment.
Contrary to
the expected results, the data revealed increases in stream
mean velocity with fixed bed conditions and increasing suspended load.
This study, which suggests that a model pic-
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14
turing dissipation of flow energy only through bed-form
resistance and work to transport sediment is over-simplified,
pointed out the need for a more detailed understanding of the
dynamics of clear-liquid turbulence and its relationship to
particle suspension.
An empirical relationship governing the vertical distribution of sediment suspended by turbulent flows was first
published by O'Brien (1933) and later expanded by Rouse (1937).
The work applied the theoretical concepts of turbulence developed by Taylor (1921) and Prandtl (1925) for clear fluids
to sediment laden flows.
Briefly, it assumed that fluid
and particle motions were identical and that therefore the
diffusion of sediment is analogous to the diffusion of momentum.
Under steady flow conditions, the upwards diffusion of sediment across a given level must be equal to the amount falling
under gravitational forces.
With given conditions of shear
stress and mean velocity it is straightforward to derive a
governing differential equation.
Although based on several questionable assumptions, the
close correlation between the predicted distribution of suspended sediment and field and flume data suggests that the
proposed process was not very far from the truth.
In particu-
lar, attention was focused on the vertical component of the
turbulent velocity field as the agent responsible for particle
suspension.
Further attempts to quantify the suspension pro-
cess led directly to detailed studies of flow modification.
Until the experimental work of Vanoni (1953) the presence
of a suspended load, of normal field concentration, was as-
sumed to have little effect on the turbulent flow properties.
Kalinske and IIsia (1945), for example, in their work with
silt-size particles, noted that suspensions in excess of 11%
by weight are required before there is modification of the
fluid velocty field.
Generally, considerations have been
based only
the assumption that the overall flow remains
Newtonian.
.he presence of sediment was related simply to
changes in viscosity rather than to any changes in flow
dynamics.
The mean velocity profile was invaribly described
by using the logarithmic velocity defect law:
UI - U 2 _ 2.3
U*
k
loglo Y2/y
with U 1 and U 2 velocities at height yl and Y2 respectively
U*
= the shear velocity =
to = the bed shear stress
P
= the fluid density
In the analysis of a series of free-surface channel flows,
Vanoni noted a consistent decrease in the von Karman constant
k with increasing suspended load and a general departure of
the velocity from a logarithmic profile in the wall region.
He concluded that the decrease in k indicates a reduction in
turbulence energy level (or intensity), an effect particularly
noticeable in the high concentration area near the wall.
Subsequent studies by Einstein and Chien (1955) and Vanoni
and Brooks (1957) have supported these original results.
Despite these carefully reasoned studies, the exact relationship between the von Karman constant and the turbulence
energy level remains open to question.
While certainly in-
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16
dicating some modification in the turbulence field it is not
clear that decreases in k represent necessarily a decrease
in energy level.
Some investigators have even tended to dis-
count completely the importance of turbulence as a primary
suspension mechanism.
Bagnold (1954), combining some incisive physical reasoning with clever experiments, asserted that particle collisions
provide the vertical stresses responsible for suspension.
Citing the principle of least effect, he maintained that a
collection of grains under shear will tend to rearrange themselves so as to minimize internal shear stress.
According
to Bagnold, the resultant dilation thus produces an excess
pressure at the bed while the fluid turbulence is damped by
the high shear resistance.
Although Bagnold was able to provide some experimental
support for the "dilation pressure" and preliminary observational
evidence for damping of turbulence, the importance of grainto-grain collisions is still in doubt.
Recent experiments by Southard (1967) have been designed
to study the exact nature of the excess normal stress noted
by Bagnold.
Lagrangian measurements of neutrally buoyant
particle trajectories, in a rotating annulus, promise to provide a sensitive measure of momentum flux thus allowing assessment of the extent of grain collisions and the source of the
observed wall pressure.
Efforts to evaluate the nature of turbulent entrainment
and the extent of flow field modification produced by the presence of suspended particles are hampered by difficulties in
1111111
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17
making direct measurements and the near impossibility of any
substantial theoretical analysis.
Elata and Ippen (1961), using a Prandtl Tube and a capacitance gage pressure transducer, made turbulence intensity measurements in channel flows transporting neutrally buoyant
plastic particles.
Contrary to the expected result, their
data showed turbulence intensity increasing with suspended
load while the von Karman constant decreased and the mean
velocity deviated sharply from the zero concentration profile.
A model was suggested showing particle-flow interaction taking place primarily in the vicinity of the boundary layer.
Using the structure of turbulent shear flow proposed by
Townsend (1956), they suggested that the presence of particles
upsets the flow equilibrium through increased production of
small scale eddies and the resultant increase in eddy viscosity.
Such imbalance would modify the momentum transfer throughout
the flow and produce the indicated changes in the mean velocity profile.
Interaction would be a maximum in the area
where the turbulence length scales (eddy sized) were approximately equal to the particle diameter.
the density contrast
SED
/sL1dO
is
This suggests that
of secondary importance
and that particle size, shape, and volume concentration were
the more relevant parameters.
Concurrently Kada and Hanratty (1960), studying the
diffusion of potassium chloride solutions in fully turbulent
pipe flows, also found particle size and the slip velocity
(i.e. the relative velocity between particle and fluid) to
be the factors governing flow modifications.
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18
The hydraulic characteristics of liquid-solid flows
suggested by these studies were examined in more detail by
Daily and Chu (1961) and later by Daily and Roberts (1966).
Isolating first concentration effects and then particle size
effects, they concluded that fine particles primarily produce
changes in the boundary layer region by suppressing the laminar sublayer.
This results in an increase of centerline velo-
city (pipe flows), producing sharper mean velocity profiles.
Coarse particle suspensions tend to display blunter profiles
indicative of improved momentum transport due to grain collisions.
Theoretical verification of these experimental results
has been limited.
While individual particle motions in a
turbulent stream have been described with some success,
notably by the work of Tchen (1947), Saffman (1956), and
Batchelor (1965), a general, quantitative description of
flow modifications produced by a suspended load is lacking.
;
By deriving energy and acceleration balance equations,
Hino (1963) was able to predict the effect of various suspended
particle concentrations on the von Karman constant and the
turbulence intensity.
For neutrally buoyant particles the
the results were in close agreement with the experimental data.
For higher density contrast, the method indicated extremely
little turbulence damping over a wide range of concentrations
and a rapid increase in eddy dissipation.
These latter re-
sults still require experimental varification.
Although this work represents a significant step towards
quantifying basic liquid-solid flow characteristics, it also
19
points to the continuing need for additional experimental data
on the structure of turbulent shear flows and the extent of
changes produced by suspended loads.
20
III.
EXPERIMENT
The following experimental investigation has two primary
aims:
1)
development of a laboratory experimental system
sufficiently reliable to insure accurate, repeatable
measurements of the structure of fluid turbulence in
liquid-solid flows using standard hot-wire anemometers;
2)
employment of the system to observe the effects
produced by an increasing concentration of neutrally
buoyant particles in fully turbulent, free-surface
channel flows.
21
The Experimental Apparatus
THE TURBULENCE FLUME
Figure 1 shows in outline and Fig. 2 the overall view
of the turbulence flume used for this study.
While built
along the lines of a standard tilting-recirculating flume,
this facility incorporates features designed specifically
for turbulence studies using hot-wire anemometers.
The four meter tunnel is supported by a section of
aluminum channel braced along each side by smaller aluminum
channels and at each end by adjustable support braces.
This
combination insures a rigid, planar surface.
The support beam rests on four resilient shock mounts
which in turn are fastened to two aluminum tables.
One table
is supported by a scissors jack (Fig. 3) and the other by
twin swivel links (Fig. 4).
The entire structure is sup-
ported by stainless steel legs bolted to a heavy wooden base.
The jacking arrangement allows the flume to be tilted and
then locked in place.
This, together with the mass of the
tables and the rigidity of the legs, provides a very secure
support system.
%
The rectangular channel and divergent end sections were
fabricated using standard window glass (thickness 0.635 cm).
Pieces were hand selected from stock to be flaw-free, and
then cut to shape and edge finished.
using Dow Corning building sealant.
All seams were filled
The channel rests on
a Neoprene pad glued to the support beam.
Lateral constraint
22
SCALE
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ELEVATION
LEGEND
1.
Drain and Filtration Tap
Resilient Shock Mounts
13.
Adjustable Support Brace
2.
Aluminum Support Beam
Dayton 1/2 H. P.
VariDrive
14.
Glass Channel Test Section
3.
Scissors Jack
Labawco Centrifugal Pump
15.
Convergent Entrance and
Diffuser Section
4.
Standing Liquid Manometer'
Safety Catch Box
16.
Aluminum Side Supports
5.
Venturi Flowmeter
Ball Type Dump Valve
6.
3. 8 cm. Return Line
Modified 15 cm.
FIG.
1.
Glass Elbows
TURBULENCE FLUME OUTLINE DRAWING
S''' ~': '
ci .\
FIG. 2.
ti:
TURBULENCE FLUME OVERALL VIEW.
FIG. 3.
SCISSORS JACK
FIG. 4.
TWIN SWIVEL LINKS
26
and vertical support is provided by four pairs of adjustable
aluminum angles.
In combination with three internal spreaders,
these serve to fix and hold the inside channel dimensions
at 20 cm x 10 cm.
At each end of the channel modified glass elbows effect
the transition from rectangular to circular cross section.
These mate with 4:1 reducers which lead into the 3.8 cm return line.
The elbows, reducers, and return line are all
This composite glass construction
Pyrex acid-waste piping.
makes for easy cleaning and provides a system capable of circulating a wide variety of liquids.
The return piping loop is broken near the downstream
end of the tunnel to provide acess for the circulating pump.
This pump and its associated drive unit is bolted directly
to the wooden base.
Flexible Tygon tubing provides coupling
into the return line as well as providing a degree of vibration isolation and the freedom required to tilt the flume.
,
The centrifugal pump used in this study was designed
with large impeller clearances to permit the pumping of
slurries and abrasive materials.
In combination with a
mechanical variable-speed drive, it has performed well over
a moderately wide range of particle concentrations and flow
rates.
There is virtually no evidence of impeller wear or
of damage to the particles.
Mass flow rates are measured by a Venturi flowmeter
placed in the return line.
Pressure differences across the
nozzle are sensed by a standing liquid manometer which is
open to the atmosphere.
By applying the calibration data
VALVE
NURO
INLINE
FILTER
VALVE
RETURN
I1
5 GALLON
PYREX
STORAGE
CARBOYS
VALVE
SIPHON
LiNE
MALGENE
ASPIRATOR
CGAR OY
TO FLUME
'IG.
FiLTRATION
5.
S YUl~ EWl
VACUUM,
obtained under controlld conditions
(see Appendix A)
these
values are easily converted to flow rates.
A prime requisite for successful hot-wire velocity
measurements is that the flow liquid be free of room dust
and lint.
These materials tend to coat the wire and offset
the calibrations.
To minimize this possibility, the rec-
tangular channel was fitted with weather stripping and a
set of dust-tight lids.
In addition a tap in the return
line was fitted with a small control valve to permit removal of the liquid through an in-line filter.
The filtered
liquid could be returned to the tunnel by siphoning or be
stored in glass carboys for future use (Fig. 5).
Particles
were retained in the tunnel by a fine screen over the suction port.
To reduce the possibility of spreading liquid spills
due to rupture of the channel or return line, a safety
catch box was constructed.
A large (2.54 cm) ball valve
discharges into this box for situations requiring rapid
flume drainage.
THE INSTRUMENT CARRIAGE
Figure 6 sho's the instrument carriage assembly in place
on the flume.
The unit was designed to replace one of the
covers so that the tunnel remains dust-tight.
The carriage and vertical feed ride on a cross-stream
slide supported by a pair of longitudinal slides bedded into
the Plexiglas base.
The milled access allows a longstream
travel of 46 cm and a cross-stream traverse of 20 cm.
The
FIG. 6.
INSTRUMENT CARRIAGE ASSEMBLY
30
base is supported by three pairs of adjustable legs resting
on the aluminum channel.
Once leveled, the assembly is locked
in place with C-clamps.
The requirement that the tunnel remain sealed necessitated a rather unusual longitudinal drive.
A worm and wheel
gear pair drives two hard rubber rollers, one at each end
of the assembly.
These rollers alternately take up or let
out a thin Teflon sheet which is attached to the instrument
port on the cross-stream slide.
In this way the carriage
may be moved in the longstream direction without uncovering
the access.
The carriage position may be read to the nearest
0.1 cm by means of a steel rule fixed to the assembly base.
Cross-stream position is also determined using a steel
rule.
Mounted on the instrument port, it allows position
measurements to the nearest 0.1 cm.
The instrument housing on the vertical feed has been
designed to accomodate a variety of probes.
These extend
through a Plexiglas port on the cross-stream slide and have
full vertical and transverse freedom without disturbing
the dust-tight integrity.
Vertical position is measured to
the nearest 0.001 cm with a vernier scale mounted on the
carriage.
THE DATA ACQUISITION SYSTEM
Figure 7 shows schematically the system used to measure,
record, and analyze the structure of fluid turbulence in
various liquid-solid flows.
In detail, this system con-
sisted of the following equipment:
STAGE
I
CONSTANT TEMP.
HOT
WIRE
ANEMOMETER
FLOW CORPORATION
MODEL
HOT
WI RE
E
PRORE
VARIABLE
FI LTER
ANALOG -
DIGITAL
DIGITAL
COM PUTER
KROHN HITE
CONVE RTER
MODEL 3202
DEC
PDP-8S
900-A
DEC MODEL
ADO8-A
OSCILLOSCOPE
DIG ITAL
VOLT
METER
NLS
TEKTRONIX
MODEL 502
PUNCHED
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X-3
TAPE
--
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2
PAPER
TO
PUNCHED
PAPER
TAPE
COMPUTER
CARD
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IBM
MODEL
DATA
PROCESSED
DATA
DIGITAL
TAPE
IBM
OS
047
ACQUISITION
FIG.
7.
SYSTEM
360
CALCOMP
PLOTS
The Velocity Probe
Hot-wire probes mounted on the instrument carriage constitute the actual velocity sensors.
The possibility of high
mechanical stresses due to particle-wire collisions required
the use of unusually heavy elements.
Kovar wire (0.00381 cm
diameter) was selected to provide the required durdbility
while maintaining moderate sensitivity and frequency response.
Two probes were constructed:
a two wire, horizontal
X-array (Probe no. 1) and single wire inclined at 45 degrees
In each, stainless steel
to the vertical (Probe no. 2).
tubing (30 cm long x 0.341 cm o.d.) was terminated by an
insulating cap.
Pairs of long needles bedded into the cap
served as the wire supports.
Needle spacing on Probe no. 1
established a wire aspect ratio
(length/diameter) of 120
while spacing on Probe no. 2 resulted in a ratio of 93.4.
No insulating coating was required on the wire or their supports since all experiments were made in a dielectric medium.
The Hot-Wire Anemometer
A two-channel, constant-temperature anemometer (Flow
Corp.) was used to excite the hot-wire probes and to sense
the variations in rate of flow past the wire.
The operating
principles of this kind of apparatus are well known (Corrsin,
1963) and will be described only briefly.
A heated wire placed in a free stream of fluid will be
cooled as a function of the rate of heat transfer at its
surface.
This heat transfer depends on
1)
flow velocity
2)
temperature difference between wire and fluid (i.e.
the overheat ratio)
3)
physical properties of the fluid
4)
dimensions and physical properties of the wire
(Hinze, 1959).
Hot-wire anemometry usually attempts to correlate fluctuations in the cooling rate with fluctuations in the velocity
field.
However, even with the remaining parameters known
and constant an exact functional relationship is difficult
to derive.
King (1914), assuming potential flow and continuum
dynamics, developed a theoretical expression for the heat
transfer from a wire.
Using a rotating arm, he verified
the results experimentally and arrived at an expression which
can be written as
<
(1 -+
where:
_
(1)
I
- current through the wire.
R
- total electrical resistance of the wire
w
after heating.
- electrical resistance of the wire at the
g
fluid temperature.
e - a conversion constant (See Hinze, 1959).
R
k
1
- heat conductivity of the fluid.
- wire length.
RO - wire resistance at some reference temperature.
6 - temperature coefficient of electrical
resistivity of the wire.
- fluid density.
Cp - specific heat of the fluid at constant pressure.
d
U
- wire diameter
- total velocity
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34
Eq. 1 may be written in its more standard form
S A* 85
(2)
where the constants A and B are simply dependent on the
physical properties of the wire and liquid.
The rather idealized assumption of flow conditions and
temperature distribution and the questionable experimental
methods used by King have prompted numerous additional inDespite extensive effort the essential form
vestigations.
of the equation derived by King remains unchanged.
Kramers (1946), for example, studied in detail the
nature of heat transfer from a wire.
With the exception of
modified expressions for A and B his equation has the same
form as Eq. 2.
More recently, Collis and Williams
(1959) experimentally
investigated the mechanism of heat transfer.
Their work ex-
tended from low velocities, where free convection effects
may predominate, up to the range where vortex streets form
The experiments lead to the fol-
in the wake of the wire.
lowing expression:
/A/
where
)
-
(3)
- Nusselt Number (a dimensionless heat transfer
coefficient)
Tm - mean temperature between stream and wire
N
T, - surface temperature of the wire
A&B
n
R
- constants dependent on the wire and fluid properties
- coefficient dependent on the flow velocity
- wire Reynolds number.
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35
The equation indicates the complicaLed functional dependence
of the heat transferred on the fluid and wire properties
as well as on the velocity.
Noteworthy is the use of a
variable exponent n rather than the fixed exponent (0.5)
employed by King.
Although representing a significant improvement in
reliability, the form of Eq. 3 does not readily lend itself
to applied hot-wire anemometry.
A series of investigations
described by Richardson and McQuivey (1968) incorporated the
work of Collis and Williams and showed that for continuum,
incompressible flows the relationship between heat loss
and mean velocity could be written
2
Z
n(4)
which is noticeably similar to Eq. 2 but incorporates the
variable exponent n.
&
In practice Eq. 4 is only slightly less difficult to
apply than Eq. 3.
While the wire current I and the resistance
values are easily measured, the constants A and B are best
obtained by individual calibration rather than by calculation.
This is complicated by the fact that the exponent n shows
a marked dependence on flow conditions.
Collis and Williams
found that it could range between 0.3 - 0.45.
In an attempt
to eliminate this difficulty, Eq. 4 was used in the present
experiment simply as a guideline for a computer curve fitting routine.
u
III
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36
Under calibration or experimental conditions,
the
electrical output of the hot-wire anemometer provides the
information necessary to solve the left-hand side of Eq. 4
directly.
The wire "cold" resistance R
can be read on
the front panel after balancing an internal bridge.
The
"hot" resistance Rw is fixed for liquid flows at 1.1 Rg .
This insures an overheat ratio k of 1.1.
In the constant temperature mode of operation the electrical resistance of the heated wire is held constant.
An
electronic feedback network in the bridge circuit corrects
any fluctuations in the wire temperature.
The feedback
current I is passed through a fixed precision resistor.
The resultant drop provides the voltage available at the
anemometer output.
The response of this system, in combination with a
wire compensation circuit, insures a frequency response
many times higher than suggested by the inherent time constant of the uncompensated sensor.
The right-hand side of Eq. 4 contains the unknown velocity U and constants A, B, and n.
The constants were deter-
mined using a calibration procedure described in Appendix
B.
The values together with the resistances and the over-
heat ratio, were then used to determine the relationship
between output voltage and velocity.
The Monitors and Filter
As shown in Fig. 7 the anemometer output was monitored
using a digital voltmeter and a dual-beam oscilloscope.
The voltmeter displayed the DC level while the oscilloscope
was used to set the feedback gain, and to monitor the level
of voltage fluctuations and the filter output.
The variable filter (Krohn-Hite) was used in a lowpass mode to eliminate that portion of the output signal
produced by system vibration and electronic noise (-60 hz).
In addition the moderately sharp cut-off provided an upper
frequency limit.
This was used in selecting a data sampl-
ing rate (see Data Reduction Considerations).
The Digital Recording System
The voltage output from the variable filter was processed in a single channel analog-to-digital converter
(Digital Equipment Corporation Model AD08-A).
Using the
technique of successive approximation, this unit produced
a ten-bit binary work representing the analogue of the input
signal.
System accuracy was 0.1% of full scale, +1/2 of the
least significant bit (quantizing error).
The buffer register of the A-to-D converter was sampled
using a small digital computer (Digital Equipment Corporation PDP-8S).
Since the size of core memory available
(4096 12-bit words) precluded statistical computations, this
unit served simply as a data storage system.
The program
used (see Appendix C) allowed selection of a variable scan
rate and the acquisition of 2556 samples.
The record length
was thus dependent on the scan rate used.
Output from the PDP-8S was via teletype and a punched
paper tape unit (ASR-33).
Tape format was in ASCII (8)
code punched at a rate of ten characters per second.
Data Conversion and Processing
All data processing was performed on an IBM 360/65 system (IBM Manual A22-6821-7).
Since direct input of paper
tape data was not possible on this machine, all tape was
converted to punched cards.
The cards, each with 12 samples,
served as raw data input to the processing programs.
programs are tabulated in Appendix C.
The
All data reduction
considerations were based on a series of preliminary experimental runs (see Data Reduction Considerations).
THE FLOW LIQUID
All experimental runs were conducted in silicone oil
with a kinematic viscosity of 1.0 centistroke (for physical
properties see Appendix D).
This stable dielectric liquid
was selected because it
1)
permits the use of uncoated hot-wire sensors.
This
eliminates the possibility of coating damage due to
a
particle-wire collisions and increases the frequency
response of the sensor.
2)
is available in a viscosity which simplifies Reynolds
number similarity to water flows.
3)
eliminates the need for "wetting" the particles.
4)
reduces attraction between particles due to sur-
face charge.
5)
eliminates the possibility of algal growth which
often develops in water flows.
6)
is safe to handle and will not react with the plastic
particles.
These features in combination with its on-
39
the-shelf availability tend to offset its relatively
high cost.
THE EXPERIMENTAL PARTICLES
Expandable polystyrene particles (Sinclair-Koppers,
Dylite F-40-C) were selected for use in the experiment.
This material contains 5-8% by weight of a volatile, saturated
paraffinic hydrocarbon.
When heated above 770C the hydro-
carbon acts as a "blowing agent" causing the particles to
expand.
Careful metering of the heat applied allows control
of the expansion.
This technique was used to produce particles
with a specified density.
For the neutrally buoyant case, particles with a specific gravity of 1.05 were first expanded using steam.
Care
was taken to insure uniform heat distribution so that the
particles remained spherical.
Next an effort was made to
determine the relationship between particle size and density.
Floting samples of differing nominal diameter in a container
of flow liquid indicated that only particles from the 30 mesh
(U.S. Sieve Designation) screen possessed the desired density
range; smaller particles were too heavy, larger particles
were too light.
After sieving each expanded lot, the selected particles
were handculled using a double flotation process.
This
tedious routine finally yielded spherical particles with a
specific gravity range of 0.817--0.84 at 250 C and a nominal
diameter of 595 micron.
THE CONCENTPAT ION SA MPIER
Figure 8 shows the apparatus used to sample the concentration (by weight) of suspended particles.
A section
of stainless steel tubing (0.318 cm o.d. x 0.0279 cm wall)
was shaped to form the probe.
Mounted on the instrument
carriage, it is connected to a 50 ml centrifuge flask by a
length of surgical tubing and a glass petcock.
Samples are drawn by siphoning.
The adjustable stand
allows the pressure head to be set so that the flow rate in
the probe is equal to the local fluid velocity in the channel.
Two balances were used in weighing the samples:
an
Ohaus (Model 310) beam balance, with an accuracy of 0.01 g,
and a Sartorius digital analytical balance, with an accuracy
of 0.001 g.
FIG. 8.
CONCENTRATION SAMPLER
42
The Experimental Procedure
FLUME FLOW CHARACTERISTICS
Prior to the experimental runs, a careful study of the
flow characteristics of the turbulence flume was performed.
The instrument assembly was clamped in place spanning
Stations 150-200
(an arbitrary location near the end of
the test section).
After calibration, hot-wire Probe no. 1
was removed from the test port and mounted on the instrument
carriage.
The channel was then filled to a depth of 3 cm
with clear silicone oil and carefully leveled.
The hot-
wire probe served as a point gage.
The requirement that all experiments be conducted under
fully turbulent subcritical conditions with no loose bed
was most simply met by maximizing the pump discharge just
short of the onset of impeller cavitation.
This resulted
in the following flow characteristics:
Discharge
Q=1100 cm3/sec
Running Depth
D=2.84 cm
7:1
Width/Depth Ratio
Rh=2.22 cm
Hydraulic Radius
Mean Velocity
Reynolds Number
Froude Number
U=Q/A=19 cm/sec
R=U4R =17,800
F=U
Liquid Temperature
=0.36
T-250 C
No effort was made during this initial study to use an
algorithm for the conversion of hot-wire voltage to velocity.
For the qualitative information required, the mean velocity
based on discharge was sufficiently accurate.
A preliminary traverse over the cross-section at Station
198.5 revealed noticeable unsteadiness in the mean flow,
most likely the result of return line and entrance condition.
This unsteadiness required the installation of a honeycomb
baffle in the diffuser section.
This baffle was constructed
from plastic drinking straws (20 cm long x 0.318 cm i.d.)
filling the channel entrance and held in place by a Plexiglas wedge.
The cross-stream profiles shown in Fig. 9 indicate that
in combination with the 4:1 expansion and the convergent section the baffle effectively eliminates flow irregularities
produced in the return line.
The slight asymmetry at Sta-
tion 185 (y/D=0.562) was caused by an uncorrected thermal
shift in the hot-wire calibration.
Figure 9 also shows that over a large portion of the
channel cross-section the flow is essentially two-dimensional,
i.e. varying only with depth and cross-stream position.
This
characteristic was considered essential for the proposed
experiment and was the reason for the choice of the high
width-to-depth ratio (7:1).
The indicated long-stream development of the vertical
velocity profiles proved to be the result of a slight nonuniformity in running depth.
ing the channel slope.
This was eliminated by modify-
The resulting profiles at Stations
185 and 198.5 were found to be identical (Fig. 10).
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' , I- -. I--,-,
_ ''''
F---I
.-,
,
.
,
,
I
,
,
,
r-f, ,
_
__,_ _-_I_- :____._
--- '' -.-I
-I
-- -;L,4 -I
-.---+
__
__-__
J-f-'
- _[
'1_ __, _-!j_'_'__ - ::, I I 7L __ -- l-,
-1-1-1- i- _-1. --4F_'_,,1
___,I- -- ,--,'
j
I
Ji-i
11
-'-,
_
,l__LL_ _l
I
- , -1_,_1
-1,
1 _F
,
1
,-i
IF
,
_' _ 444 ' ___
-, 'I'll
,L ,__,LrlI
I
,
__
I
,l
I
__L'
_!
_
r
_7
____
-,
U
..
- __
__
.1
11
__
--______
____
__-_
--___
__
-_____
_,
-__
----_ ___ _--- -.- _____ _ -I-__-__ ------_
I ____,:
''
- -4-- -,-I,-i -_ --iii- -]:L-,, , -. FTrI I
=1 __L_.1.1-11
_
- _=
I
- ' -ii
-- ---I---- 71-- --,-.tr
-
.- t -
, ,
_L'_
--I
-
-
I,_ ___: _-,
I
-
-.- - ,
-. _- - -,
-I- i- F I
I
I
- I
I ,-,
I
I-,-!-:-1 4
13 r,,
- -1-1 L -1
1- T7
-
,
____
____
- ,
- - l-,
-
- -
tt
--I
-I
I
__ ,
--f 1t i
_,
- I_
-,
I -I_P
_J__ll____il_1___l____.__
-,_ - , - __ I- , 11
,
_ ,
___: ,
_,
_11 - .
,
. , L
:
I L
_
-
I-L
-,-L
,
-_ __ __TF_-
__ -:- _.- J. __:_. -1 - - ___T_,
, _ I I:
--
_
--
, ____.. I___ 11 -- -, -T '
, I
_
_ __-i--l
-
-------
:-,
--__ -,-,--,-I-
- _
-,,,,-,-F!..-
_
,-'
*
, , I
-
I
-
--- -. __ ,--- - __
____
I - - __ i-l- --- ,--7__ __
__:
I - -_i _ __ ,_____ - . ___
1+--- I- _L__j L
__
__- --IF .__ -
-
-
-- .
__- _'
74
I-
,-.
- , I I
_
-
I
__
On the basis of these preliminary studies, Station
198.5 was selected as the test section.
Here operation
near the channel centerline provided a fully turbulent regime
with a velocity profile that is uniform and two-dimensional
in the mean.
In addition, this station was sufficiently
far upstream to assure freedom from possible exit effects.
VOLTAGE-TO-VELOCITY CONVERSION
Before establishing the data-reduction criteria it was
necessary to develop a routine for converting the anemometer
output voltage to velocity.
The method proceeds from the assumption that the heat
transfer and therefore the output voltage is directly related
to the flow velocity.
The remaining variables, including
the physical properties of the wire and fluid, are known and
constant.
The voltage-velocity dependence for each wire of Probe
no. 1 was obtained using the procedure described in Appendix B.
The data indicate that the calibration curves can
be closely approximated by a series of straight lines.
Over
each linear segment the transfer coefficient n will be a
constant.
If the mean velocity of the experimental run is
known, the proper value or values of n can be selected from
the tabulation in Appendix B.
Combining this with the
derived values of A' and B' allows computation of the cooling velocity U given the output voltage E using the formula
E2=A'+B'Un
(5)
("piece-wise")
This algorithm and the linear
IIIIIIY
. _______.
...
_
approximation
was employed in the main computer program (Appendix C) for
all voltage-velocity conversions.
It remains to determine the relationship between the
cooling velocity U and the individual components of the
velocity field.
If, as shown in Fig. 11, the velocity field is described
in terms of a mean velocity U and fluctuating components
u', v', and w',
then a wire placed perpendicular to the
mean flow will be subject to a total cooling velocity U
with a magnitude given by
U2= (U+u') 2+(v') 2+(w') 2
(6)
Expanding Eq. 6 and rewriting yields
=1+ -- +U
U
+
U
(7)
U
U
Measurements in the turbulence flume at a Reynolds number
of 17,800 indicated that U was some 20-40 times larger than
the fluctuating components.
For most studies, therefore,
the quadratic terms in Eq. 7 can be neglected.
The output
voltage can be considered to be simply a function of the
mean velocity U and its first order fluctuations u'.
In practice, when the turbulence level u'/U is low,
the heat transfer is assumed to be governed by the mean flow
field alone.
The small turbulent fluctuations are said to
have little or no effect on the heat transfer.
Studies by
Sandborn (1962) have indicated this to be true over most
~
~_YYIII
YYIIIYYIIYIIY
IYII
ll
1Yillll
~ IIIYIIIIIIIIYIIYI
llflmmm---
48
FIG.
11.
COORDINATE
SYSTEM
FREE SURFACE
CHANN EL FLOWS
49
ranges of interest.
If the wire is perpendicular to the mean flow, then
this assumption allows the mean velocity to be computed
directly using Eq. 5 and the DC level of the anemometer
output.
Also, since the velocity fluctuations are assumed
to have no effect on the heat transfer, the same expression
(i.e. Eq. 5) can be used to compute u' by making use of the
instantaneous voltage output.
This technique was employed
in all experimental runs to determine U and u'.
The vertical and cross-stream fluctuations v' and w',
and the Reynolds stresses u'v' and u'w', could be determined
by making use of the angular sensitivity of the hot-wire.
Implicit throughout the above discussion is the assumption that only velocity components normal to the wire axis
GeBsner (1964) has shown that this
exert a cooling effect.
characteristic can be used to determine the Reynolds stress
and the mean square fluctuating velocities in a manner that
is -independent of wire calibration.
For wires oriented at
45 deg. to the mean flow he derived the following expression:
-2
M
= U12
2
w72
u 'v' = u
u'w
M
= u2
=
2
A-B
MA+B
2
u2
xz plane
M)(M
(2
A+B
B
A
2MA+B (MA+MB)
(M
(8)
xy plane
MA+B
- M2)(M
A
22MMA+B
B
2
A+B
-- W(MAMB)
(9)
+
M2)
A-B
+ M
xy plane
(10)
x
(11)
)
A-B
xz plane
50
where MA and MB are equal to the rms voltage output with the
wire oriented at +450
(subscript A) and -450
to the mean flow and MA+B and MA-B
(subscript B)
equal the rms of the sum
and difference of the A and B outputs respectively.
These equations were designed for use with matched
wires and were shown to work as well for single wire rotation as for a fixed X-array.
The latter feature was of
use in this experiment since limitations imposed by the
single channel data-acquisition system precluded use of
an X-array.
As a result, all data were provided by a single
wire placed alternately at ±450 to the mean flow.
Probe
no. 1 was used in the xz plane, and Probe no. 2 in the xy
plane.
The "Gessner" reduction program (Appendix C) combines
the data obtained using the perpendicular wire with that obtained using inclined wires and provides as output the Reynolds stress u'v', u'w', and the mean square fluctuations
2
and w'
2
.
of v' and w',
No effort was made to obtain the actual values
since the rms values are of primary interest.
DATA REDUCTION CONSIDERATIONS
Any data acquisition and reduction system is inherently
a source of signal distortion.
Electronic noise and lack
of response in combination with algorithm and sampling errors often produce a result that is a poor analogue of the
natural process under investigation.
The system characteristics of the hot-wire anemometer
were measured under actual operating conditions.
Heated and
IYYIIYYII
iiiIIIIYIYIIIYI
~--I'-
MMNuIli,
51
immersed in
silicone oil, the wire was subjected to a square
wave signal produced by an internal calibrator.
The re-
sponse of the feedback loop to this 10 my pulse was measured
on the oscilloscope and is shown in Fig. 12.
As provided
in the operating instructions, the upper frequency limit
F
of the system can be computed by determining the time
interval At (in psec) required for the signal to reach the
3 mv level from its peak value and substituting this into
the formula
C75
(12)
Fig. 12 shows At to be approximately 1.0 msec and the upper
frequency limit therefore to be 275 hz.
The results were
identical for all wires.
This calibration procedure was conducted under zerovelocity conditions.
At higher flow rates the response will
be slightly increased, thus insuring a sufficiently high
frequency level for the proposed turbulence experiments.
The electronic noise of the anemometer system, which
appears as "hash" on the oscilloscope trace (Fig. 12),
proved to be negligible.
Its 5 mv level is below the resolu-
tion of the A-to-D converter.
Also, preliminary runs in-
dicated an expected signal-to-noise ratio of 10 for the
fluctuating voltages and 400 for the DC signal level.
Such values assure accurate signal discrimination.
With the exception of the inclined-wire data, all
voltages were converted to velocity before analysis.
It is
52
FIG. 12.
ANEMOMETER FREQUENCY RESPONSE
Scale
Voltage = 10 mv/cm
Time Base =
0.5 msec/cm
recognized that the voltage-to-velocity algorithm discussed
in the previous section is likely to introduce a finite
error because of the linear approximation and the use of
first-order heat transfer theory.
Estimations based on
previous investigations (Sandborn, 19.62) and on the calibration data indicate that this error can be kept smaller
than 1-2% by selecting small linearizing intervals and flows
with low turbulence levels.
If not amplified by sampling
or other analysis errors, this is a modest value.
Prior to any processing, all voltage data were converted from their continuous analog form into a series of
discrete digital values.
This quantizing process, because
it necessarily involves some approximation, may introduce
errors in both the amplitude and the time or frequency
domains.
The degree of amplitude error is governed by the
accuracy of the A-to-D converter.
For the system used
this was quoted at 0.1% of Full Scale ±1/2 of the least
significant bit.
The resultant error can usually be ig-
nored.
Accurate reproduction of the spectral character of the
analog signal by its digital representation is determined
by the sampling rate.
When a continuous signal F(t) is
sampled at a rate of l/T samples/sec, frequency components
in the resultant digital record greater than f/T radians/sec
cannot be distinguished from those in the 0-f/T range.
This
folding or "aliasing" of the frequency spectrum can be el-
iminated by selecting a sapl ing int erval At such that
At=1/2F n with the "Nyquist" or cutoff frequency Fn chosen
such that there is no significant spectral energy above
it.
The selection of this value for the proposed experiment
was based on a series of preliminary-runs.
Examination of the anemometer output during these
runs revealed a noticeable spectral peak around 60 hz.
On
the assumption that this was a product of pump vibration
and electrical pickup, the peak was eliminated by lowpass filtering.
Then as a check, a qualitative spectral
study was made using a selected cut-off frequency of 40 hz
and sampling rate of 80/sec.
The results, shown in Fig. 13, indicate that the bulk
of turbulent energy lies below 15 hz and that it approaches
zero as the 40 hz limit is approached.
This decay tends
to support the assumption as to the source of the 60 hz
peak.
S
The 40 hz cutoff and the resultant 80/sec sampling
rate was used in all subsequent experimental runs.
With available core memory in the PDP-8S computer set
at 2556 words, choice of sampling rate automatically fixed
the single-pass tecord length.
Using a rate of 80/sec,
this was approximately 32 sec, providing an attainable
frequency resolution Af of 0.0391 hz.
To a great extent
these values determine the accuracy of the statistical
computations.
Particular attention was given to the re-
liability of the energy spectrum and its dependence on
record length.
-
~----------
II
D
FIG.
13.
ENERGY
SPECTRUM
PRELIMINARY
RUNS 11-12
--
CLEAR
':j
I.0 cs
H
LIQUID
SILICONE OIL
R= 17,800oo
_TJ
uJ
K
s"I'
SC-I
L,.5
I
13.5
~_
I
---~I
22 5
FREQUENCY LHZ3
I
27 .O
I
31 .5
-I
I
LIC .5
56
For 2N real data points XO;Xr1...,X
2 N-1,
the scientific
subroutine RHARM (IBM Manual H20-0205-3) uses the Fast
Fourier Transform (Cooley and Tukey, 1965) to compute the
real coefficients a 0 ,al,...aN-
1
and bl,...,bN-
1
in
_
where j=0,1,...,2N-l
This method is used in the main reduction program (Appendix
c).
A plot of (ak2 +bk 2 )/Af for each frequency component
represents the raw "periodogram", an indication of the
spectral distribution of energy density.
However, since
each of these points has only two degrees of freedom (Bingham
et al.,
1967), this plot is a rather poor spectral estimate.
Reduction of the large error bars, with a fixed record
length, requires either additional runs and the formation
of an ensemble, or sacrifice in frequency resolution by
averaging over a number of adjacent points in a single
record.
Whichever method is selected, the increase in de-
grees of freedom is a simple multiple of two, e.g. the
average of five points has ten degrees of freedom.
The procedure used in the turbulence experiments allows
a combination of the above options based on the requirements of each individual run.
At each vertical location where spectral information
is required, two 32-sec records are obtained.
Representing
a compromise necessitated by the slow speed of the PDP-8S
output punch, these data can be averaged over the ensemble
or the individual record in a manner designed to provide
optimum reliability with suitable frequency resolution.
For example, the spectra of several preliminary runs represented ten point averages resulting in a resolution of
0.391 hz and giving each point 40 degrees of freedom.
CONCENTRATION MEASUREMENTS
The average weight concentration of suspended particles
was used to set the initial conditions for each liquidsolid run.
Particles were added to the known volume of oil
in the flume in carefully weighed amounts.
Then, at the
completion of each run, after computation of the mean
velocity profile, measurements were made to obtain the actual
concentration over the vertical.
The concentration sampler was used to obtain three 50 ml
samples at each of six vertical locations.
Use of the velo-
cify data allowed the internal flow rate of the probe to be
set equal to the local fluid velocity at each point.
Next, total weight (liquid + particles) was determined
for each sample.
and weighed.
The particles were then separated, dried,
The'resultant weight concentration could be
converted to volume concentration by using the relationship
% By Volume = 0.80 (% By Weight)
This relationship is governed by the packing density, and
was determined by observing the volume increase in a graduated vial caused by the addition of a known weight of experimental particles.
SUMMARY OF THE EXPERIMENTALT
PROCEDURE
Each experimental run proceeded in the following fashion:
1)
The turbulence flume was filled to the selected operating
depth with a filtered and weighed amount of silicone oil.
Depth and surface checks were performed using hot-wire Probe
no. 1 as a point gage.
2)
A weighed sample of neutrally buoyant particles were
introduced and the average weight concentration calculated.
3)
In still liquid, the null resistance R n of each hot-wire
was measured and the ambient temperature recorded.
During
the experimental run, pump and frictional heating caused
a slow increase in liquid temperature.
This was carefully
checked and Rn adjusted to maintain an overheat ratio of
1.1.
4)
With the wires heated, the feedback and compensation
networks were tuned.
5)
The circulating system was started and the pump speed
adjusted to provide the required discharge.
This discharge
was constant for all experimental runs.
6)
The flow depth was measured and channel slope adjusted
to insure uniform flow.
7)
The instrument carriage was fixed in place at Station
198.5 and the probe positioned on the channel centerline.
(All primary experimental data were obtained at this location.)
The recorded raw voltages represent the following
measuring sequence:
a.
With hot-wire Probe no.1 perpendicular to the mean
flow, two 32-sec records were taken at each of six
locations along a vertical.
b.
Next, Probe no. 1 was placed first at +45 and then
In each position the
-45 degrees to the mean flow.
resultant output signal was sampled for 32-sec, with
the measurements being repeated at each of four vertical locations.
c.
Then Probe no. 2 was mounted on the instrument
carriage and used to take
±450
measurements at the same
vertical locations as in step b.
8)
The experimental data was processed as follows:
a.
All punched paper tape output was transferred to
punched cards.
b.
The volatge data from step a of the measuring
sequence (above) were converted to instantaneous velocities uh using a voltage-to-velocity algorithm.
After
this step, the main computer program was used to calculate:
The mean velocity
Uh
A-,
(14)
with N = the number of samples
The root-mean-square velocity
The auto-correlation function
with j=1,2,3,...representing the
number of time lags
60
The Fourier coefficients ak and b k in
sbKle
s 7rj
/
)Nk
(17)
with j-0,1,2,3,...,2N-1
c.
The data obtained in steps b and c of the measuring
sequence were not converted to velocities; instead
the respective rms levels were used in the Gessner
Reduction Program (Appendix C) to yield the Reynolds
stresses u'v' and u'w' and the cross-stream velocity
components v' and w'.
9)
After computation of the mean velocity gradient, the
actual concentration of suspended particles was determined
using the concentration sampler.
10)
At the completion of the experimental runs, the hot-
wire calibration was repeated in order to evaluate any shift
in the wire constants A' and B'.
TABLE 1
SUMMARY OF EXPERIMENTAL HYDRAULIC DATA
RUNNING DEPTH
D = 1.748 cm
CROSS-SECTIONAL AREA
2
A = 35.52 cm
CHANNEL SLOPE
S = 0.00421 cm/cm
DISCHARGE
Q = 1000cm 3/sec
LIQUID PROPERTIES
= 0.818 gm/cc
o
V = 1.0 x
10 - 2
HYDRAULIC RADIUS
Rh = 1.491 cm
DISCHARGE VELOCITY
Up
CHANNEL REYNOLDS NUMBER
R
SHEAR VELOCITY
u
FROUDE NUMBER
F
Q
=
UD4Rh
V
28.15 cm/sec
-
16,800
gRhS
=
Uo = 0.680
Fg D
@ 25 0 C
cm 2 /sec
= 2.480 cm/sec
_,,,.~-P~.
l- - -..
"..~l**.'"'"YI"
~~l^yuar~ruar~^
.i
riir~ur;r^
*-
^ii-ilu
TABLE 2
TABULATED EXPERIMENTAL RESULTS
RUN
DESIGNATION
Clear liquid
U
0.716
NC 0
0.572
0.430
0.287
0.143
0.057
U0o
cm/sec
cm/sec
27.340
25.5
J--X 102
U.
Ivp2 x10 2
U,
2
x10
Ju 2
1*
5.01
0.525
27.828
5.34
0.559
25.267
5.43
25.694
5.31
0.556
24.749
6.16
0.645
26.670
6.63
0.694
25.359
7.34
25.420
6.94
2.981
7.82
22.311
7.92
18.592
7.05
17.647
6.76
5.39
7.43
5.16
7.175
0.568
0.768
u v
'Jo
2
X0
11.12
18.97
0.726
8.352
7.62
0.818
21.88
0.830
7.20
0.738
0.708
17.71
YIII i--u"
II
~.i(L~ESIYIY~EII~I~IIl~~"""ii~i~-iirYt-i
i n-I-. rjnriir?-'.F?3h~rmi~d"~~?T1
~.-- 'i .T
TABLE 2
CONTINUED
U
RUN
DESIGNATION
NC 1
0.716
0.572
0.430
0.287
0.143
0.063
Tu
cm/sec
cm/sec
26.182
25.5
=-Ux102
Uo
J2
27x102
Uo
-
x10 2
u
4.88
0.511
26.243
4.94
0.517
25.420
5.47
25.725
5.61
0.587
24.566
5.92
0.620
24.780
6.16
0.645
23.80
6.56
23.652
6.63
21.671
7.23
21.427
7.36
21.396
8.34
21.884
8.91
5.50
6.57
5.59
6.78
0.572
0.687
-r
Uo
x10 4
12.04
16.37
0.694
8.21
7.23
0.757
19.97
0.770
7.611
7.97
0.873
0.933
19.55
TABLE 2
CONTINUED
u
RUN
DESIGNATION
NC 2
0.716
0.572
0.430
0.287
0.143
0.080
u
cm/sec
cm/sec
24.475
25.5
7x102
Uo
2
--
U
x10 2
JT2
-- i x10 2
u2
U0
4.84
0.507
26.060
5.42
0.567
25.694
5.97
24.144
6.01
0.629
23.164
6.04
0.633
23.073
5.97
0.625
22.524
6.89
22.799
6.74
20.543
7.09
20.634
6.96
20.208
8.305
19.385
7.67
6.03
6.98
6.04
6.96
u v X104
--
0.625
0.721
xl0
13.91
17.11
0.705
7.11.
7.20
0.742
15.45
0.729
8.65
8.70
0.869
0.802
14.59
I/I_____XI____IYXLFX_--___li-L
___-~--
-- ---L_)
-~--------
TABLE 2
CONTINUED
RUN
DES IGNAT ION
NC 3
U0
/ D"
u
cm/sec
cm/sec
0.716
25.725
25.5
0.572
0.430
0.287
0.143
0.080
x10
'-~
U.
2
&v22
j
Uo
xl0 2
22
- xl0 2
Uo
Uv
u*
"U*
5.14
0.538
25.938
5.28
0.552
25.176
6.08
24.658
6.02
0.630
24.201
6.30
0.660
23.713
6.32
0.662
22.738
6.97
22.646
6.65
21.488
7.60
21.366
7.65
18.928
8.07
19.354
7.60
6.02
7.35
6.45
7.27
0.636
0.730
Sx10
Uo
14.50
16.31
0.697
7.54
8.10
0.795
17.92
0.801
8.13
8.17
0.844
0.795
18.13
44
TABLE 2
CONTINUED
RUN
DESIGNATION
NC 4
y
2
2
i2
/D
U
cm/sec
U
cm/sec
Ju' 2 0
U x
0.716
24.749
25.5
5.58
0.584
25.572
5.61
0.587
24.597
6.41
24.323
6.10
0.639
23.408
6.70
0.701
23.439
7.08
0.741
22.006
7.48
22.494
7.30
20.726
7.81
20.421
7.55
18.775
7.90
17.434
7.75
0.572
0.430
0.287
0.143
0.080
x10 2
Ul
6.15
6.95
U
x102
6.40
qu
U*
0.671
0.783
U'v
U.
2
_
xl04
15.54
13.01
0.764
7.63
0.817
16.56
0.790
8.15
0.827
0.811
14.25
TABLE 2
CONTINUED
RUN
DESIGNAT ION
NC 5
Y
0.572
0.430
0.287
0.143
0.080
2
2
cm/sec
25.5
6.08
0.636
24.627
6.21
0.650
24.444
7.10
24.505
7.02
0.735
24.231
8.07
0.844
24.353
7.67
0.802
22.433
8.16
22.250
7.77
19.964
8.14
20.025
8.04
21.610
9.82
18.745
8.65
D, cm/sec
0.716
2
2
-21
U0 x10
U
24.414
U
J
U.
x10
7.32
7.89
U.
u---
x10
10
6.92
7.77
xl04
St-x1
0.743
0.854
19.58
21.96
0.814
8.02
7.88
0.852
21.42
0.842
8.59
8.64
1.02
0.906
17.99
IV. RESULTS AND CONCLUSIONS
Concentration Measurements
Hot-wire measurements were obtained at six different
mean values of suspended load.
The initial run (NC 0) was
performed in clear silicone oil and serves as the reference
for each subsequent run.
Concentration gradients for the
liquid-solid runs are shown in Fig. 14.
Run designations
NC 1 to NC 5 are in order of increasing mean concentration.
Each linear plot represents a best fit (by eye) to the raw
No effort was made to average or to produce a least-
data.
squares fit.
The noticeable departure of each of the concentration
gradients from a constant value is caused by the slight
variations
(~2%) in particle density.
The deviation from
neutral buoyancy produces a particle assemblage with a finite
fall velocity and results in maximum concentration values
at the bottom boundary.
To estimate the average fall velo-
city the transit time for each of 75 particles falling in
a large-diameter, graduated column of silicone oil was measured.
The assemblage average was 0.371 cm/sec @ 240 C.
In addition to the obvious mass variations in the vertical, the suspended load also produces an increase in flow
viscosity.
The relative magnitude can be estimated using
/-with
CO = volume concentration
-=
kinematic viscosity @ CO
-7= kinematic viscosity @ CO=0
(18)
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an expression originally derived by
ilers
(1941) for laminar
flows but holding with sufficient accuracy for many turbulent,
liquid-solid flows (see Fig. 15, Elata and Ippen, 1961).
Solving Eq. 18 over the concentration ranges indicated in
Fig. 14 (0-3.5%) shows the maximum change in viscosity to
be roughly 8%, with a 1% variation over an individual run.
Efforts to support these calculations with direct measurements were unsuccessful.
The slight viscosity changes were
below the viscometer resolution and resulted in widely
scattered, inconsequential data.
There is no doubt, however,
that the flow dynamics remain completely Newtonian in behavior at the low suspended concentrations employed in this
experiment.
Mean Velocity Comparisons
A comparative plot of the mean velocity profiles over
the vertical is shown in Fig. 15.
The sampling locations
were confined to the central region of the flow to insure
hot-wire measurements free of surface or bottom boundary
effects.
In addition, efforts to extend the measurements
close to the bed during the liquid-solid runs were hampered
by the tendency of the particles to lodge beneath the wire.
As a result, close proximity measurements were possible only
in the clear-liquid case.
The remaining profiles extended
to within one or two particle diameters of the bed.
It is apparent that the presence of a suspended load
produces rather marked effects on the mean velocity structure.
Over the measured region, increasing concentrations
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result in a general flow deceleration.
the volume discharge remains constant, that the external
region of the flow must concurrently experience an acceleraThese results are qualitatively similar to previous
tion.
experimental data for small particles (Daily and Roberts,
1966).
Of note, however, is the fact that the suspended
concentrations used in this experiment are substantially
lower than those of previous investigators.
Daily and Roberts,
for example, report findings obtained at 15% concentrations,
while Elata and Ippen (1961) worked with volume concentrations up to nearly 30%.
That rather large variations are
observed at low concentrations in this experiment is believed to be the result of the increased sensitivity afforded
by the use of a hot-wire anemometer.
This instrument hope-
fully would represent some improvement over the standard
Pitot tube.
An exact analytical description of the mean velocity
profiles, valid over the entire range of suspended particle
concentrations, is difficult to derive.
As shown in Fig.
16, the clear-liquid profile is for the most part adequately
described by a logarithmic law of the form
Um - U
u*
with
-2.3 log y
k
(19)
Ym
Um = mean velocity @ ym
U = mean velocity @ y
u* = Shear velocity
k = von Karman constant
Some slight departure is noted as the boundary layer region
is approached.
Laufer (1951) found this transition point
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near y = 30-7/u* which in this experiment with u* = 2.480
cm/sec gives y = 0.1209 cm and a y/D = 0.0692.
This is in
fair agreement with the data of Figs. 15 and 16, although
additional points near the boundary are required for an
accurate check.
One should note that this boundary layer
thickness is of the order of two particle diameters--a point
which may be of some importance in later discussions of
turbulence modification.
With increasing suspended load the mean velocity deviates rather sharply from the clear-liquid profile.
Over
the linear regions in Fig. 16 the variation can still be
described by a logarithmic function with decreasing values
of the von Karman constant (ranging from 0.385 to 0.240).
At higher concentrations, however, this single-parameter
fit must give way to more complicated multiple-parameter
functions.
Elata and Ippen (1961), by extending the rea-
soning used by Prandtl
(1925) in his "mixing length" theories,
introduced an additional function f 2 dependent on the concentration gradient.
Um
um- U
u*
Substitution into Eq. 19 yields
-2.3
-23 log
log Y + f2(Co;
k
~Ym Ym
)
(20)
with CO = volume concentration at y/ym
Although, as noted in their report, this equation serves
to present experimental data in some plausible form, the
required graphical determinations introduce wide scatter.
As a result the general applicability of Eq. 20 is unclear.
Increased confidence seems to require some check of the vali-
75
dity of the assumptions used in its derivation.
In turn
such information can be provided only by a far more detailed
understanding of the structure of turbulence in liquid-solid
flows than is presently available.
Some partial insight
into this problem can be provided by the mean velocity profiles themselves.
The trend displayed in Fig. 15 seems indicative of a
general reduction in vertical momentum transport with increasing suspended load.
The initially blunt turbulent
profile is tending towards the sharper laminar profile.
This would seem to support the hypothesis that turbulence
damping is to be expected at high particle concentrations.
Such reasoning, very much in vogue until recently, overlooks the fluctuating components of the turbulent velocity
field.
As detailed by Townsend (1956), the structure of
turbulent shear flow is a function of the interaction of
these components with the mean velocity.
A reduction of
fluid momentum close to the boundary is not necessarily
correlated with a general reduction in turbulence level.
Indeed, Schubauer and Klebanoff (1951), studying boundary
layers in adverse pressure gradients, found increasing
reduction in momentum to be correlated with increasing
turbulence levels.
It seems clear that any effort to assess
turbulence modifications must study not only the mean velocity field but also its fluctuating components.
AM
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76
Turbulence Intensity
Figs. 17 and 18 show the vertical distribution of the
longstream velocity fluctuations relative to the shear velocity u*.
The clear-liquid profile displays a steady in-
crease in rms level as the boundary is approached.
The
characteristic peak near the bed is indicative of the region
of maximum turbulence production and the general dominance
of viscosity in this region.
Again a reduced sampling inter-
val is required to delimit the maximum accurately.
The behavior of the rms levels with increasing suspendedparticle concentrations is shown in Fig. 18.
A general re-
structuring of the distributions is evident.
Initially there
is a slight reduction throughout the vertical and an indication of some turbulence damping.
With increasing sus-
pended load, however, the trend is definitely towards increasing turbulence intensity.
Although difficult to dis-
cern, there is the suggestion of a much less rapid increase
in ,the wall region ( y/D = 0.15) than further out.
With
the exception of NC 5 each of the intervening rms levels
is below that of NC 1 at the bed sampling point (y/D = 0.080).
In the light of these results and because so much importance is placed on the accurate measurement of turbulence
intensity, two possible sources of error should be discussed.
Any hot-wire probe operating in a liquid-solid flow is
subject to collisions between the particles and the wire.
Prior to the experimental runs it was reasoned that if the
wire survived, these collisions would produce high frequency
components in the output signal (very similar to "strumming"
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the wire).
These anomalies should be above our range of
interest (0-40 hz) and could therefore be filtered out.
At the start of the experimental runs it became evident
that this was not entirely the case.
Visual examination
of the oscilloscope trace revealed that simple low-pass
filtering still permitted vibration components to pass.
Particle-wire collisions apparently result in a rather
broadband introduction of energy.
Admittedly this energy
level is quite low, particularly at low suspended loads.
If the concentration was carried beyond 5%, however, there
is a possibility of significant error.
At the concentrations employed in this experiment the
errors introduced by particle-wire collisions were deemed
negligible.
Their cumulative effect was very much smaller
than the energy levels of the velocity field.
If this were
not the case, it would seem that in regions of high concentration, i.e. near the boundary, and therefor
increased
collisions, the rms levels would be substantially higher
than further out.
As has been indicated, this is not the
case.
The second possible source of error involves the shear
velocity u*.
There is some indication (see Discussion)
that increasing particle concentrations may result in decreased boundary shear stress <.
Any such reduction would
necessarily imply a reduction in the shear velocity (since
u
=
) and would result in some errors in the data points
shown in Fig. 17 and 18.
The constant u* value used in the
normalizing of each of these points was dictated by the slope
of the free surface.
Within the measurement accuracy
attainable this remained constant over each of the liquidsolid runs.
This possible source of error was also disregarded
ty would only result
since any reduction in shear velo
This in turn would
in an increase in the normalized
ies.
tend to reinforce the previous f,
gs that rms levels
were increasing with increasing
.-ended particle concen-
trations.
A comparative plot of the rms levels for each of the
fluctuating velocity components u', v',
Fig. 19.
and w' is shown in
Each point has been normalized using a selected
mean velocity value U O (see Table 2).
The accuracy of the v' and w' levels is somewhat below
that of the u' measurements.
As shown in Goldberg (1966)
a slight angular misalignment can cause rather substantial
errors in X-array measurements.
Viewed qualitatively how-
ever, the comparison plot displays some rather interesting
features.
The behavior of each component is similar.
With de-
creasing relative depth (y/D) there is a gradual increase
in intensity, with a peak value near the bed.
The lateral
fluctuations w' display a more gradual increase, while the
u' and v' values are nearly identical.
In liquid-solid
runs NC 1 through NC 5 there is a steady increase in the
rms level for each component above y/D = 0.15.
Closer to
the boundary and relative to the clear liquid run, this
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consistent increase is noted only at the higher concentrations.
These variations clearly indicate that the pre-
sence of a suspended load does not simply produce a redistribution of turbulence intensity (for example, increasing u' levels with decreasing v' or w' intensity) but rather
results in a general increase in turbulence intensity,
implying some substantial alteration in the turbulence production mechanism.
Reynolds Stress
The changing levels of turbulence intensity discussed
in the previous section are reflected in the plot of Reynolds
stress u'v' shown in Fig. 20.
For the clear liquid run
there is a close correlation between the level of maximum
turbulence intensity and peak Reynolds stress.
The pro-
duction appears to be induced by the interaction of these
virtual stresses with the local mean velocity gradient,
both displaying maximum values in this region.
With increasing suspended load, the point of maximum
stress tends to move away from the bed.
The peak values
are noticeably altered, and there is a general reduction
in gradient.
The steady increase in Reynolds stress at
y/D = 0.572, combined with the increasing velocity gradient,
implies increased production at this level.
Conversely the
reduced near-bed values (runs NC 2 through NC 4) very likely
indicate a reduction in turbulence production.
As was
indicated above, these facts are weakly evidenced in the
plots of turbulence intensity.
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Although the data presented in Fig. 20 are instructive,
additional points are required to allow accurate determination of the point of maximum Reynolds stress.
Also the
measurements, apparently the first in liquid-solid flows,
Despite these weaknesses
require corroborative support.
it is quire clear that the presence of suspended particles
in quite low concentrations markedly alters the turbulence
structure.
Power Spectra and Scaling
The frequency distributions of the longstream velocity
fluctuations u' are shown in Fig. 21 (in viewing plots, note
that all clear-liquid runs are grouped in a single plot
and subsequent liquid-solid runs are grouped by relative
depth).
For each experimental run, 15 points of a two-
member ensemble were averaged to provide a spectrum with
60 degrees of freedom and a frequency resolution of 0.5865 hz.
The Calcomp plots represent the normalized power spectrum
F(n), where
FC"n) =
~
4~
(21)
and therefore
with n
= frequency
P(n)=
Af =
u12 =
an,bn =
power spectrum
frequency resolution of the raw periodogram
mean square velocity @ y/D of interest
ensemble average Fourier coefficients
Each plot clearly displays a dominant low-frequency content
with the bulk of the energy lying below 20 hz.
Qualitatively,
85
FIG. 21.
NOR4ALIZED POWER SPECTRA
CLEAR
LIQUID
0.572
/D
HZJ
SFRFUELNCY
Ll
F/D Z 0.430
g a
9
13 -5
35 L,
FREIUENCY
-
22 t
27 [1
,
,
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,In ,
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Uc
Y/
=
0.287
D
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S
9 0
13-5
A j[
FBEQUENCY
5
(hZJ
22
27 .0
31 5
3G.U
Q .,
',[i
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D
.U
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1 [I
FREBUENCY tHZI
:11
U.
l,1r
Y/ 0.063
D
27.0
FREOUENCY
tHZ
i3 5
YI.U
j
Y/ =0.572
D
Il3
NC I
I
9 .0
22 .5
1 '.0
13.5
271.0
3 .0
31 .5
405
FREOUENCY (HZ)
NC 2
I
-. 0
-1
I
13.5
I
9.0
4 .5
I
1I
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27 .0
22 .5
1e i.
FREQUENCY
SI
31 .5
I
30 .0
10.5
16 .0
0.
(HZ]
Li
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(HZ)
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NC 4
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1 .0
I
FREQUENCY
22.5
I
27 .
I
1 .5
I
(HZ]
NC 5
I
-. 0
14.5
l
9.0
Il
13 .5
,
1 .0
FREOUENCY
22 .5
(HZ]
II
27.0
I
31 .5
35.0
10.5
Y/ =0.430
D
Li
NC I
1.5
.U
1.0
I90
F[EQUENCY
22.5
27.0
31.5
3G U
L.5
(HZ)
NC 2
s-
t .5
9 0
135
15
I
FREDUENCY
5
(HZ>
22
27 0
31 5
3U
.5
Li
I-)l
NC 3
270
31 .5
NJ.0
.0 .5
FFIEUENCY UMZ)
Li
Li
NC 4
4-f
2:
IA5
,9
0
13 5
li .0
FFEOUENCY
I
27_0
22
I
31
I
3 C1
I
11IL
.5
(HZ)
NC 5
.
,,5
9
I
13.5
1
1 .0
22
5
FFEGUENCY (HZ)
27.0
31
5
35.UI
I.5
Y/ 0.287
Li
IJD
NC I
l
L .5
9 U
13. 5
-I
11.
I
.5
22
-
27 I.0
31 .5
36 0
go
36._
Liu .5
FREQUENCY (mZ)
LU
NC 2
-.-
S.5
90
1395
1 .Al
22 .
27.0
31 5
FBEUUENCY (hZ)
LU
NC 3
LU
I_90
...
19
i---
11!
-- -~ - -- - I
1
I
i
5
10
13-5
I
18.1
2.
7.
1r
i
22.5
I
27.0
19
31.
0
31
-
i1
5
.l
1
40 5
FREQUENCY (HZ)
LU
LU
u_ -l
NC 4
I
.1
4 .5
9 0
15
13
151i,
22 .5
27.0
31
3
1U
0 .'
31 .
In .5
FREQUENCY (HZJ
NC 5
L:
I_
U
.5
9
i
13 5
li 1.
22.
FREQUENCY (FIZI
27 .,
31
Y/D= . 14 3
D
LU
NCI
I-
u .5
9. 0
13.5
1
.0
FREQOUENCT
I
27 .0
22 .5
--------- I
1 .5
1
3i.0
10.5
1
IG .0
10 .5
(HZ
LJ
NC 2
I
!
2-
cl.
S
II
.
..
S
q
11 '1
13 .0
27.0
22.5
5t .5
FREQUENECY (HZ)
L.I 2
LJ
NC 3
In
I
I
L .5
I
90
-
13.5
-~
~
1B.0
1~
22.5
27
L...5
0
I .5
FREQUENCY (HZ
=r
Li
NC 4
LA3
Il,_
.00-
5.5
9 0
13.5
18 .0
22 .5
27 0
31 .5
M .0
1 0.
FREQUENCY (HZ)
NC 5
LI
C3
.. . ..
.5
i.
.
i_
. _
13.5
10A
FREQUENCY
22-5
(HZ)
r
27.0
T
31 5
t
35.0
.
-0.5
Y=0.080
NC I
LU(
.
.5
9 .t
1 3 .5
If
FREQUENCY
22
b
27 _
31 .5
. U_
(HZ)
LU
1.0
I..-
NC 2
-~
t.5
.
9.0
13.5
15.X
FREQUENCY
22 b
27.0
31 .5
3GU
O.
(HZ)
LJ
LU
NC 3
U-
-
5 .0
9.
3.
1 6. a
22 .5
27 -0
31 .5
36 .0u
ao
FREQUENCY (HZI)
Li
Ch
NC 4
(0
.0
.5
3
13 5
15.0
22
5
27 .0
31 5
35 .U
U
0 .0
36 .0
0.5
FREQUENCY (HZ)
NC 5
45
9.0
13.5
1 .0U
22-5
FBEQUENCY (HZj
27.0
315
the spectral character of each remains essentially unchanges for all experimental runs.
At the higher concen-
trations there is a suggestion of increased high-frequency
components, particularly at 0.572 and 0.430.
This feature
is possibly indicative of increased production of smallscale turbulence or improved distribution in the outer flow
regions, but a definitive finding must wait on longer records
or larger ensembles and the resultant increase in accuracy.
To study the spectral decay characteristics of the experimental runs, the data plotted in a linear fashion in
Fig. 21 were replotted on log-log paper.
results is shown in Fig. 22.
A sample of the
The overall characteristics
of the curves in this comparison plot appear to be nearly
identical.
The steadily increasing negative slope varies
from -0.5 at the low frequency end to -6 at the high frequency extreme.
Quite similar in shape to those obtained
by Raichlen (1967) in water flows, each curve passes rather
ra idly through the -5/3 or Kolmogoroff region and displays
the dominance of viscous effects above 10 hz.
The variation in high-frequency energy content from
clear liquid to NC 5 conditions is apparent.
This suggests
that some truncation error was produced by limiting the
high concentration liquid-solid runs to a 40 hz cutoff
frequency.
Efforts to analyze this error by studying
changes in the rms level at higher' filter settings revealed
no noticeable increase.
The truncation error, if any,
must be quite small.
The single point hot-wire measurements precluded direct
87
--4
481-
4
IIH'
V
-14T
+
.+t4t-
6
4--
-
-
,,~1
,, ...±
+L
JB
I-1
Z8
IT-
IK
1:--L I.,I
-T ,,__--
4 -
"
4-----+ -I6
i
T4~
Tl
V
~
i
2+
FFT
-P
TV
41
HlTH --
.
ll
I F.
I Id- i -k- +-4
ilt~
H4~~'1
'
-i-1- - H I
I!
IJ
4
14+-
-_ jj
T
.
"Alt
T
4
64
4
-
-H
-,
Ai
I
+-
-
+
4+--T
i
-,..
l]--
:
4i
,
810
16
I
aItT
A
L
FI
$
4--
-
I4
10
1
i
+,-
I -!.
'
8
± I
-
IO'
+
1-
3
I- Ll,
v
If a curve fitting routine,
turbulence scale determinations.
after the manner of Laufer (1951) or Raichlen (1967), is
used with the data of Fig. 21, the close similarity between
these curves forces the conclusion that there was no change
in turbulence macroscale with increasing suspended load.
While this indeed appears to be the case, support for these
results, as well as the additional
(independent) determina-
tion of microscale variations, requires more data or, ideally,
simultaneous multiple point measurements.
Autocorrelation Function
A study of the autocorrelation function for each experimental run revealed the same degree of similarity evidenced by the power spectra.
plotted in Fig. 23 is typical.
The behavior of the example
Such a result further tends
to support the hypothesis that only slight changes in turbulence scale resulted from the increasing suspended loads.
Using the area delimited by the characteristic sharp decline
near the origin and the first zero point (0.5 sec) as a
measure of the macroscale, Fig. 23 shows that only at NC 5
is there a suggestion of a significant change in scale.
Although admittedly this is a rough estimation, owing to
the periodic variations present beyond 0.5 sec., it is
believed to be valid, since this external flow region
(y/D = 0.572) should be especially sensitive to any significant increase in small scale eddy production.
Nearer
the boundary such changes could be masked by the already
dominant small-scale turbulence.
89
+1
CLEAR
..............
.
.........
....
...
. ..
.....
.
.
.....
..
...
-I
+1
NC I
N. St.
Ir........
Z
o
.
.........
,............
...
........ I.......... ...
...
..... ...........
..
-I
+'
-............
..I
"...........
...... .... ..... ...
NC2
-
H
--""
---.... ....
+1
+1
+I
0
-j
.
0. ..
II..
_ .=................J....
. ......
..
.
.• .
I _•....................... .
NC
NC
5 0
NC 2
14
................
...................
-. J
..
...........
LuI
<
1
_
o.
.
. ....
S...
..
.........
........
.... .
+'
/
...
.......-
. . ...
.
...............
...
NC 5
.I..I
-- i "'"
..... •..........
~
.
~~~...
..
.
.
..
.
2
040
.. J....... ,.......
.
.
I.
.
.
.
.....
OF LAGS
tO30NYMBER
20
-lO1
...
.
50
60
ODELA
FIG. 23
70
80
90
100
10
20
TIME
AUTOCORRELATION
Y/D =O 572
30
r
40
.50
(sec)2k
CURVES
60
70
60
90
200
Discussion
Perhaps the most significant result of this experimental
investigation is that there are substantial alterations of
the turbulent flow characteristics at low suspended particle
concentrations.
The departure of the mean velocity from
a logarithmic profile, the general increase in turbulence
intensity, and the variations in momentum transport all
occur at suspended load levels not far above those encountered
in many natural regimes.
These findings clearly indicate
that in most instances offhand neglect of suspended load
effects will be an oversimplification.
What is needed is
a simple analytical description of the observed phenomena
which could be systematically included in the derived equations of motion.
This in turn requires a more detailed
understanding of the physics of turbulence production in
liquid-solid flows.
Towards this goal, can the experimental
results be of any assistance?
It seems apparent that the presence of particles induces an additional source of stress over and above the
usual pressure, viscous, and Reynolds stresses.
Moreover
it was observed that the action of the experimental particles
indiced a change in flow characteristics quite similar in
form to the observed longitudinal variations in adverse
pressure gradient flow.
In a gradual linear gradient, for
example, a comparison of results over a section far upstream
of any separation point shows the same trend in mean velocity (Schubauer and Tchen, 1961), a similar increase in rms
levels (Schubauer and Klebanoff, 1951), a general increase
91
in Reynolds stress with peak levels moving away from the
bed (Goldberg, 1966), and the concurrent small change in
energy spectra (Moses, 1964).
While it is not suggested
that the presence of particles induces an adverse pressure
gradient per se
conditions),
(clearly precluded by the uniform flow
the turbulence modifications in
each case are
strikingly similar and limited use of the analogy might
be instructive.
Within a model based on such an analogy it seems improbable that particle presence produces the observed turbulence changes simply by increased production of smallscale eddies.
As suggested by Elata and Ippen (1961), this
mechanism was supposed to be a function of scaling similarity
between particle diameter and the viscous sublayer thickness.
This is an intuitively pleasing construct, but, as noted
above, not evidenced in the spectral data.
Moreover, such
matching is hard to envision in adverse pressure gradient
flow where similar turbulence changes are noted.
Rather it is suggestive to reason that the suspended
particles exert primary influence through their effect on
the gradient of mean velocity.
The flow retardation noted
in Fig. 15 resultq in increased shear and increases u'v'
correlation.
In turn the
interaction of the increased
Reynolds stress u'v' and the mean velocity gradient results
in increased turbulence production as indicated by the
higher rms levels.
Such a mechanism could produce a higher
energy turbulence field with little change in spectral
character.
Since optimum effects would be produced in the
region of maximum turbulence production, it is reasonable
to assume that particle diameter would still remain a significant parameter in combination with flow Reynolds number,
suspended concentration and the mean velocity gradient.
The density contrast
SE./jL1XI
serves only to determine the
concentration gradient.
This is admittedly a rather simplistic line of reasoning.
Mean velocity gradient, Reynolds stress, and turbulence
intensity are pictured as independent variables, when in
fact they are mutually interdependent.
Nevertheless the
experimental results indicate that the proposition is not
entirely specious.
The increasing levels for each variable
are clearly observed, and although it remains to be shown
that the primary particle effect is through the mean velocity gradient, this feature is the easiest of the three to
work with in terms of a descriptive or predictive model.
*
A clarifying study would proceed first to improve the
quality of the spectral record.
A tenet of the above
proposition is that no significant increase in high frequency
energy is noted at the higher particle concentrations.
Next a visual study of the boundary layer region
(cf. Kline et al., 1967) in liquid-solid flows could provide an insight into the character of the near-wall velocity
gradient and the nature of the stresses introduced by the
particle presence.
Both could be used to provide a check
on the applicability of the adverse pressure gradient
analogy and the functional dependence of the turbulence
93
production on particle size and concenLration in various
Reynolds number flows.
As in the case in the majority of turbulence investigations and particularly liquid-solid flow studies, the results of this experiment are difficult to generalize.
How-
ever, the clarity of the data and the reliability of the
apparatus are encouraging.
A continuing systematic study
of this problem appears to be quite possible.
In combina-
tion with the information provided by the above investigations, this approach promises to permit the development of
a sufficiently accurate model for most field applications
and at the same time yield the necessary additional insights into the mechanics of turbulence in liquid-solid
flows.
REFERENCES
Bagnold, R. A., 1964, Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under
shear, Proc. of the Roy. Soc. of London, Vol. A225,
No. 1160, pp. 49Batchelor, G. K., 1965, The motions of small particles in
turbulent flow, Proc. of Second Australasian Conf. on
Hydraulics and Fluid Mech., pp. 019-041.
Benjamin, B. Brooke, 1959, Shearing flow over a wavy boundary,
Jour. of Fluid Mech., Vol. 6(2), pp. 161Bingham, C., Godfrey, M., and J. W. Tukey, 1967, Modern
techniques of power spectrum estimation, I.E.E.E.
Transactions on Audio and Electronacoustics, Vol. AU-15,
No. 2, pp. 56-66.
Collis, D. C. and M. J. Williams, 1959, Two dimensional
convection from heated wires at low Reynolds number,
Jour. of Fluid Mech., Vol., 6(3), pp. 357-384.
Cooley, J. W. and J. W. Tukey, 1965, An algorithm for the
machine calculation of complex Fourier series, Math.
Computation, 19, pp. 297-301.
Corrsin, S., 1963, Turbulence: Experimental methods, Handbuch der Physik, Vol. VIII/2, Ed. C. Truesdell, SpringerVerlag, Berlin. 696 pps.
Daily, J. W., and T. K. Chu, 1961, "Rigid particle suspen' sions in turbulent shear flow: some concentration
effects", M.I.T. Hydro. Lab. Tech. Rpt. No. 48.
Daily, J. W. and P. Roberts, 1966, Rigid particle suspensions
in turbulent shear flow: size effects with spherical
particles, Tappi, Vol. 49(3), pp. 115-125.
Eilers, H., 1941, Kolloid-Zeitschrift, 97, pp. 313Einstein, A., 1906, Ann. Physics, Vol. 19, pp. 286Einstein, H. A. and Ning Chien, 1955, "Effects of heavy
sediment concentration near the bed on velocity and
sediment distribution", Univ. of Calif., Inst. of Eng.
Res., Berkeley, Calif., M.R.D. Sediment Series No. 8,
76 pps.
Elata, C. and A. T. Ippen, 1961 "The dynamics of open channel
flow with suspensions of neutrally buoyant particles",
M.I.T. Hydro. Lab. Tech. Rpt. No. 45, 69 pps.
Gessner, F. B., 1964, "A method of measuring Reynolds stresses
with a constant current, hot-wire anemometer", A.S.M.E.
Bulletin No. 88, 9 pps.
Gilbert, G. K., 1914, "The transportation of debris by running water", U.S. Geological Survey Prof. Paper 86.
Goldberg, P., 1966, "Upstream history and apparent stress
in turbulent boundary layers", M.I.T. Gas Turbine Lab.
Rpt. No. 85, 45 pps.
Hino, M., 1963, Turbulent flow with suspended particles,
Jour. of Hydraulics Div. Proc. of the A.S.C.E. HY 4
pp. 161-185.
Hinze, J., 1959, "Turbulence", McGraw-Hill Book Co., New
York, 586 pps.
Kada, H. and T. J. Hanratty, 1960, Effects of solids on
turbulence in a fluid, Amer. Inst. of Chem. Eng. Journal,
Vol. 6(4), pp. 624-630.
Kalinske, A. A. and C. H. Hsia, 1945, "Study of the transportation of fine sediments by flowing water", State
Univ. of Iowa Studies in Eng. Bull. No. 29, 30 pps.
Kennedy, J. F., 1963, The mechanics of dunes and antidunes
in erodible bed channels, Jour. of Fluid Mech., Vol.
16(4), pp. 521-544.
King, L., 1914, On the convection of heat from small cylinders
in a stream of fluid, Phil. Trans. of the Roy. Soc. of
London, Series A, Vol. 214, pp. 373Kline, S., Reynolds, W. C., Schraub, F. A., and P. W.
Runstadler, 1967, The structure of turbulent boundary
layers, Jour. of Fluid Mech., Vol. 30(4), pp. 741-773.
Kramers, H., 1946, Physica, Vol. 12, pp. 61Laufer, J., 1951, "Investigation of turbulent flow in a
two-dimensional channel", NACA Report No. 1053, 20 pps.
Moses, H., 1964, "The behavior of turbulent boundary layers
in adverse pressure gradients", M.I.T. Gas Turbine
Lab Report No. 73, 41 pps.
O'Brien, M. P., 1933, Review of the theory of turbulent flow
and its relation to sediment transport, Tran. of Amer.
Geophys. Un. 14, pp. 487-491.
Prandtl, L., 1925, See Goldstein, S. "Modern developments
in fluid dynamics", Vol. 1, p. 205, Oxford Univ. Press,
N. Y. 1938.
Raichlen, F., 1967, Some turbulence measurements in water,
Jour. of Eng. Mech. Div. Proc. of the A.S.C.E., EM2
paper 5195, pp. 73-97.
Richardson, E. and R. S. McQuiuey, 1968, Measurement of
turbulence in water, Jour. of the Hydraulics Div. Proc.
of the A.S.C.E. HY 2, pp. 411-429.
Rouse, H., 1937, Modern conceptions of the mechanics of
fluid turbulence, Trans. of the A.S.C.E., pp. 535Saffman, P. G., 1956, On the motion of small spheroidal
particles in a viscous liquid, Jour. of Fluid Mech.
Vol. 1(15), pp. 540Sanborn, V., 1962, Application of the hot-wire resistancetemperature transducer to the measurement of transient
flow quantities, Transactions, A.S.M.E. Symposium on
Measurement in Unsteady Flow., pp. 54-60.
Schubauer, G. B. and P. S. Klebanoff, 1951, "Investigation
of separation of the turbulent boundary layer", NACA
Report No. 1030, 20 pps.
i
Schubauer, G. and C. M. Tchen, 1961, "Turbulent flow",
Princeton Univ. Press, Princeton, New Jersey, 122 pps.
Smith, J. D., 1969, "Studies of nonuniform boundary layer
flows", Univ. of washington, Dept. of Oceanography,
Ref. A69-7, RLO-1752-13, 119 pps.
Southard, J. B., 1967, Momentum transport in turbulent flow
between concentric rotating cylinders, Science, Vol. 156,
Spp. 1725-1727.
Taylor, G. I., 1921, Diffusion by continous movements, Proc.
of the London Math. Soc., Ser. 2, 20, pp. 196-211.
Tchen, C. M., 1947, "Mean value and correlation problems
connected with the motion of small particles suspended
in a turbulent fluid", Martinus Nyhoff, The Hague.
Townsend, A. A., 1956, "The structure of turbulent shear
flow", Univ. Press, Cambridge, 315 pps.
Vanoni, V. A., 1953, "Some effects of suspended sediment on
flow characteristics", State Univ. of Iowa Studies in
Eng. Bull., 34, no. 426, pp. 137-158.
Vanoni, V. A. and N. H. Brooks, 1957, "Laboratory studies of
the roughness and suspended load of alluvial streams",
Report No. E-68, Sedimentation Lab., Calif. Inst. of
Technology, Pasadena, Calif.
APPENDICES
APPENDIX A
Venturi Flowmeter Calibration
Fig. Al shows the principal features of the Venturi
flowmeter used in the turbulence flume.
Measurement of the
volume rate of flow is governed by the equation 1
Qactual =
cz
(?-)
/ /
where:
(I)
Qactual = volumetric discharge
= discharge coefficient
Cd
At
= inlet
A2
g
P1
= throat area (Fig.Ai)
= acceleration due to gravity
= pressure measured at the inlet
(Fig. Al)
= pressure measured at the throat
(Fig. Al)
= specific weight of the flow
liquid.
P2
y
area
(Fig.Ai)
Calibration of a flow meter consists of determining the
discharge coefficient.
Normally, if the meter is constructed
using the guideline established by the American Society of
2
Mechanical Engineers , the coefficient can be read directly
from tabulated values based on inside dimensions of the
flowmeter and the discharge.
In this case calibration was
1.
Spink, L. K., Principles and Practice of Flowmeter
Engineering, The Foxboro Corporation, Foxboro,
Massachusetts, 9th Edition, 1967, 575 pages.
2.
Fluid Meters, Their Theory and Application, Report of
The American Society of Mechanical Engineers
Research Committee on Fluid Meters, 5th Edition,
1959.
_ ~_~____I_
_ __CP~
15 cm
PRESSURE
NO.2
PRESSURE TAP
SINO. I
TAP
3,. cm
2
AI
9.5
J.I
FLOW
5.7 en
DIRECTION
0o
co
FIG.
VENTURI
Al
FLOWMETER
required since the inside diameter (3.8 cm) was slightly
below the smallest tabulated value (~5 cm).
Individual
calibration of a meter should also increase the attainable
measurement accuracy.
Calibration Procedure
Measurements of the pressure drop across the flowmeter
as a function of the discharge were made with the meter
placed in a piping section exactly similar to the flume
return line.
Water from the laboratory supply flowed through
the section and into a calibrated container.
The discharge
was measured using a stopwatch (gallons/minute) while an
open manometer indicated the Venturi pressure drop.
A
precision steel rule was used for the head measurements (cm).
Rewriting Equation I,
E
For the meter used,
~[
Az
=
AJ(II)
A, = 11.35 cm 2
A2 =
Using P=fgh=yh and hl-h
2 =Ah,
2.85 cm 2
Equation II becomes
(with Ah in cm and Q in cm3 /sec, also, 1 gallon = 3790 cm 3 ).
Sample Calculation
@ 7.4 gpm and Ah = 12.50 cm
Z-9
(16)
100
Calibration Results
Fig. A2 shows the results of a series of runs with
discharges ranging from 1 to 12 gallons per minute.
The
series was performed with the pressure taps aligned along
the side of the test section.
This configuration assured
the absence of air bubbles in the manometer line and minimized
the possible accumulation of particles in later liquidsolid runs.
Early scatter in the data points was eliminated with
the addition of a honeycomb baffle placed in the entrance
to the test section.
Consisting of plastic drinking straws
(20 cm long x 0.318 cm i.d.), this baffle was also placed
in the flume return line and used in all experimental runs.
After several test series it became apparent that the
discharge coefficient was very close to unity except at
low flow rates (<4gpm).
In order to insure fully trubulent
flows in the rectangular section, the discharge would have
had to be several times this value.
Therefore, for our
purposes the discharge coefficient was taken equal to unity.
After determining the discharge coefficient it remained
necessary to compute and tabulate pressure head versus discharge for flows df one-centistoke silicone oil.
This simply
required a correction for the density difference, since the
viscosity effect was negligiblel
Since / silicone oil = 0.818 gm/cc @ 25'C, Equation III
can be rewritten
e?,is
eutoispot
i
i.
o
f(IV)
This equation is plotted in Fig. A3 for various flow rates.
101
1.0
0.9
IZ
0.0
QS
0.7
w
FIG.
VENTURI FLOWMETER
CALIBRATION
A2.
WITH
IL
H2 0
O C..
0.6
w
0
HONEYCOMB
24 C
of
0.5
0.4
0.3
0.2
0.1
I
0
I
I
r
2
3
4
I
5
7
6
10
9
8
II
12
-
13
DISCHARGE
gallons per minute
2000
FIG.
1800
VENTURI
A3.
DISCHARGE
FLOWMETER
VS.
PRESSURE
HEAD
1600
I.OcsSILICONE
OIL
ofat 25* C
1400
1200
g
*
zE
on-s
U
C') u
1000
Goo
800
600
400
200
-
I
0
10
20
30
40
I __
--50
I
6070
I
-
~
80
HEAD (Alh)
cm
I
I
90
100
110
J
120
130
BAFFLE
102
APPENDIX B
Hot-Wire Anemometer Calibration
Beginning with
where I
= wire feedback current
Rw = hot wire resistance
Rg = wire resistance @ fluid temperature
A & B = constants dependent on wire and fluid properties
U
= cooling velocity
n
= heat transfer exponent, dependent on flow conditions
one could write
I 2 Rw
= Rw(Rw-Rg)(A / BUn)
(VI)
= Rg(k)(k-l) (A / BUn)
(VIa)
with k = overheat ratio= Rw/Rg
which leads to
f2 = A' / B'Un
(VII)
with E equal to the mean level of anemometer output voltage
and A' and B' representing the values of A and B modified
by the constant resistance and overheat values.
Under the assumption of a known or constant n measurements of E versus flow velocity under controlled conditions
would permit determination of A' and B'.
however, is dependent on flow conditions.
true for X-array operation.
The exponent n
This is especially
The small vertical separation
of the wires causes noticeable free convection effects at
low flow rates.
103
The following scheme was used to overcome this difficulty.
Measurements of output voltage E as a function of mean
velocity U were obtained by using the flume return line as
a calibration tunnel.
The filter tap (see Fig. 1) was
fitted with a sealed gland to permit insertion of the hotwire probe.
The DC output from the anemometer at various
flowrates was read using a digital voltmeter (Non-Linear
Venturi pressure drop was used as a measure of
Systems).
the discharge, and centerline velocity in the pipe was assumed
to be
U = V
A*
where U
V
A*
(VIII)
= mean velocity
= discharge
= cross-sectional area corrected for
displacement thickness
The location of the test port some 45 pipe diameters downstream from the Venturi insured flow characteristics that
were steady and well developed.
Cross-stream measurements
confirmed this assumption.
Each wire of Probe no. 1 was calibrated using the above
procedure.
The data plotted in Fig. B1 and Fig. B2 were
obtained with both wires heated and alternately placed at
right angles to the mean flow at the pipe centerline.
To obtain the value of the exponent n,
B2 were used to graphically determine dE/dU.
Figures Bl and
The values
were then plotted versus mean velocity of log-log paper
(Fig. B3).
The slope of these curves is simply related to
n, since differentiating Eq. VII to eliminate A'
So6(IX)
ez
IT
2F-
leads to
104
Taking logs,
YU
(X)
indicates that the slope is proportional to n-1.
A sharp dependence of n on the velocity is apparent.
Only with flow rates greater than 60 cm/sec does n maintain
a constant value over a wide range of velocities.
This fea-
ture was used in calculating A' and B'.
Using the exponent value selected from the high-velocity
portion of the curve, B' was calculated using Eq. IX.
This
value was assumed to be constant over the entire calibration
range.
While this may not be entirely correct, the exact
variation of B' is of academic interest only, since at this
point the procedure becomes entirely an effort to fit the
available data to Equations IX and VII.
The value of the exponent n was computed for various
velocity ranges by substituting B' into Eq. IX and making
use of the graphical values of dE/dU and the available
calibration data.
A' was calculated by substituting B' and n into Eq. VII.
Its value was found to be essentially constant over the calibration range.
The results of these computations are tabulated in
Table Bl.
The agreement between the measured calibration data
and values computed using the derived constants is shown
in Fig. B4.
One would expect the fit to be excellent except
in the very low velocity range, where buoyancy effects pro-
105
duce anomalous results causing the voltage-velocity curve
to approach zero in a fashion poorly reflected by the extrapolation.
106
3.0p
FIG.
B1.
CALIBRATION
WIRE
/
,
DATA
NO.1
SdU
X-ARRAY
KOVAR
WIRE
1.0 CS
SILICONE OIL
K= 1.1
/
/
10
60
30
VELOCITY
CM/SEC
30
VELOCITY
CM/SEC
90
107
-i
SI,
;.[
t
-i
.d."
T
_
_I1
-
1.0
.
dU
......
.....................
T....
.71:
j
/s
.P
YJ7.---C-------Ct
WIRE NO.
"i"
::
WIRE 4 140
.i:
0
0
FIG.
cm3
-umsc
CALIBRATION
cm/soc
CALIBRATIONS
DATA
CALIBRATION
WIRE NO.I
90
U
B3.
DATA
WIRE NO. 2
X-ARRAY
KOVAR WIRE
1.0 CS
SILICONE
I-ARRAY
OIL
KOVARWIRE
LO CS SILICONEOIL
K* 1.1
/
key:
+ COMPUTED
.
* MEASURED
key: . MEASURED
+ COMPUTED
/
0.
o
o
VELOCITY
o
FIG. B4.
so
VELOCITY
CM/SEC
CM/SEC
DATA COMPARISONS
o
o
108
TABLE B1
HOT-WIRE CALIBRATION CONSTANTS
WIRE
VELOCITY
n
A'
B'
3.45
7.26
3.60
7.10
cm/sec
No. 1
50 - 90
0.45
35 - 50
0.43
29 - 35
0.40
12 - 29
0.37
7.5 - 12
0.30
45 - 90
0.43
20 - 45
0.41
12 - 20
0.37
7.5 - 12
0.30
No. 2
109
APPENDIX C
COMPUTER PROGRAMS
110
The Data Acquisition
Language:
Program
Pal III Symbolic Assembler (See Digital
Equipment Corporation Manual 8-3-S)
Loading Sequence See DEC Manual DEC 08-NGCA-D
The PDP-8 Console Manual
*0232/ VARIABLE SCAN RATE A-D CONVERSION PROGRAM W. F. BOHLEN
TCF
KCC/CLEAR ALL FLAGS
BEGIN, CLA
TAD MCNT
DCA CNTR
TAD TOLL
DCA STORE
TAD K
DCA CLEAR / 6
TAD OUT
DCA SPAS/ INITIALIZE
CLEAR, TAD LOOP
DCA BAG/ RESET LOOP
ADCV
ADSF
JMP .-1
ADRB/ A-D CONVERT
STORE DATA
DCA I STORE/
ISZ STORE
ISZ BAG
JMP .-1/ VARIABLE LOOP
ISZ CNTR
JMP CLEAR
CLA
TAD MCNT
DCA CNTR
TAD TOLL
DCA STORE/ REINITIALIZE
TAD L
DCA DATA
DATA, TAD I STORE
ISZ STORE
JMS SSPRNT/ SIGNED DECIMAL PRINTOUT SUBROUTINE (8-23-U)
JMS I WHIZ/ TYPE A SPACE SUBROUTINE (8-19-U)
ISZ SPAS
JMP ./ 5
CLA
TAD
DCA
JMS
ISZ
JMP
OUT
SPAS
I KID/
CNTR
DATA
CARRIAGE RETURN-LINE FEED SUBROUTINE
(8-19-U)
ill
MCNT,-5000
CNTR, 0
K,3710
TOLL,2000
STORE,0
OUT, -15
SPAS,0
L,1710
WHIZ, TYSP
KID,TYCR
/ OR WHATEVER VALUE IS SET IN BY HAND
LOOP, -50
BAG, 0
PAUSE
The following routine was employed to change the length
of the variable loop and therefore the scanning rate:
Load Address
0315
Depress Exam
0417 should appear in the memory buffer
Key in the desired loop length, e.g.
Record Length 64 sec. key 7310 for sampling rate of 40/sec
32 sec.
-
7545
-
-
-
-
-
-
- 80/sec
12.8 sec.
-
7710
-
-
-
-
-
-
-200/sec
Load The Starting Address
Press Start....
0232
112
MAIN REDUCTION PROGRAM
C
C
C
C
C
C
C
C
C
THIS PROGRAM COMPUTES MEAN AND RMS VELOCITY9
THE FOURIER COEFFICIENTS AND THE AUTOCORRELATION
COEFFICIENTS FOR TURBULENTFREESURFACE,
CHANNEL FLOWS. IT IS DESIGNED TO REDUCE
DATA OBTAINED USING HOT-WIRE ANEMOMETRY
IN FLOWS OF ONE CENTISTOKE SILICONE
OIL. BOTH WITH AND WITHOUT SUSPENDED
PARTICLES..
.IMENSIONF(26CC),A(2600),R(5CC),INV(300),S(3CO)
JN=5
V= 10
SET UP LCCP FCR CATA RPEACIN
5 JA= 1
6 N=JA+ 11
READ (5,21) (E(I), I=J4,')
IF (E(N) .EQ. C.) GO 10 7
JA= JA412
GO TO 6
7 WRITE (6,31) N
CC 10 I=1,
E(I)=E(1I)/412.
C
C
C
10 CCNTINUE
CHECK TEN POINTS CF TFIS CENVEPSICN
WRITE(6,22) (E(I),I=1,1C)
CCNVERT VCLTS TO VELCCITY
DC 14 I= 1,N
E(1)=( (E( I) "2+3.45) /7.26)442.702
14 CONTINUE
WRITE (6,32)
140 WRITE (6,23) (E(1),I=1,10)
SET UP MATRIX FCR COPPLTING AUTCCCRRELATICN FLNCTICN
DC,19 I=1,\
A( I )=E( I)
19 CONTINUE
L=400
CALL ALTO (A,N,L,R)
CO 200 J=1,400
BPITE (6,39) J,R(J)
R(J)=R(J) *10.* 3
2C0 CONTINUE
WRITE
C
(7,30) (R(J),J=1,4CC)
hRITE CUT PEAN ANC PS
R (I1)=R(1) IC.
R (1)=SCRT (R(1))
hRITE (6,28) R(1)
VBAR=C.
CC 13 I=1,N
VBAR=VEAR4E( I)
13 CONTINUE
B=N
VELCCITY
.
--------------------
113
IV C LEVEL
1, MOD 2
(6,24) VBAR
REMUVE MEAN AND SET
CC 16 I=1,N
DATE =
MAIN
6(-C7C
10/52/1
_ RITE
C
UP fVfRix F-Ui
FC
RIER ANALYSIS
E(I)=E(I)-VBAR
16 CONT INUE
DO 17 I=1,2048
A( I )=E( I)
17 CONTINUE
CALL RHARIV(AtVINV,S, IFEPP)
WRITE (6,25) A(1),A(2)
WRITE (6,26) (A(I),I=3,2048)
J=2
DO 18 I=3,2C47,2
! (I-J)=iA(I) ''24A(I+1)' '2
10.*
t 3
A (I-J )=A(1-J)
18
C
90
60
21
22
23
24
25
26
27
28
30
31
32
34
3;
J=J+1
CCNTINUE
WRITE CUT FOURIER COEFFICIENTS AND PLNCH C(N) SCLARED
WRITE (6,27) (A(I),I=1,10)
WRITE (7,3C) (A(I),I=1,1C16)
-RITE (7,34) N
JN=JN- I
IF (JN .EQ. 0) GO TO 6C
GO TC 5
STOP
FORMAT (12F6.1)
FORMAT (1CFIC.5//)
VELCCITY CHECK'//1CF1C.5//)
FORMt'AT ('
FORVAT (' TEMPCR.L VEAN VELCCITY'//F1C.5/)
FORMAT (' A(C)=',FIO.5,1CX,' [(C)=',FlC.51//)
(6X,Fi0.5))
FORMAT (4(lOX,' A(N)',IC),' P(N)')/i
SCLAREC'//10F1C.5//)
C(N)
FORMAT ('
FORMAT (' RMS VELCCITY'//FlC.5//)
FCRMAT (8F10.8)
11,' N=',16/ )
FORMAT (
FORMAT (' WIRE NO.1'/)
FCNMAT (16/)
FORMAT (2(' J=',14,lOX,' CCRRELAIICN CCEFFICIENT=',FIC.8)//)
Ef\D
-----------------------------------------------------------------------------------------
----------------------------------------------------
-----------------------------------------------------------
-------------------
114
IV
G LFVFL
4
5
6
7
10
1,
12
5)
13
60
14
15
3
DATE = 69170
MAIN
THIS PRCGRAV CCVPUTES REYNOLDS STRESS VAKING
USE OF AN ALGCER ITf- TPAI IJS INDEPLNDEtT
CF THE WIRE CALIBRATICN
DATA IN USE OBTAINE[ LSING A SINGLE
WIRE ORIENTFE AT +AN[)- 45 DEGRFES TO
THE vEAN FLCt.
,C(2600),D(2600)
DIMENSION E(26,00)n ,A(2600),B(2600)
K=4
READ (5,24) UGNE
JN=)
JA=1
N=JA+1
RFAC (5,2r) (E(I ),I=JA,I)
IF (E(N) .EQ. C. ) GC TC 7
JA=JA+12
GG TC 6
0O0 10 I=1,N
E(l)=E(I)/412.
CENTINUE
XSU=0.
Cn
11
MCD
GESSNER REDUCTION PROGRAM
11
I=ltN
XSUP=XSU +E( I)
CONTINUE
F=N
XBAR=XSU'/F
CO 12 I=1,N
Et I )=E( I )-XBAR
CONTINUE
FSTAPLISF THE C OMPUTATICNAL
JN=JN+1
,JN
GO TO (5C,60)
C0 13 I=1,\
A(I )=E(I)
CONTINUE
GU TC 5
DO 14 I=1,N
P(I)=E(I)
CCGNTINUE
00 15 1=1,25C0
C(I)=A(I)+F{(I)
0 (I)=A(I)-f3( I)
CONTINUE
ARMS=0.
BRMS=.
CR'l S=1.
CR'S=C.
DO 16 1=1,25CC
ARM'S=ARS+ (A 1 )V-*2)
ARRAYS
13/33/¢9
115
IV C LEVFL
C
I,
Mnc
,
MAIN
DATE = 69170
BRRVS=BP S+(P( I )*2)
CRMS=CP S+(C(I )-'*2)
*2)
DRMS=CRPS+(C(TI)
16 CONTIINUE
ARMS=SORT (ARMS/25CO.)
BRVS=SQRT (eRMS/25C0,)
CRMS=SQRT(CRMS/25 0.)
CRMS=SOPT (CRMS/25O0.)
WRITE (6,21) APVS,BRPMS,CRVS,CRMS
USE THE COMPUTED VALUES TC SOLVE FCR THE REYNGLCS STRESS
*2) ),,( (CRMS*'-2 )+(DRMS**2)
RNUM=( (ARVS*2 )-( RPRVSI
2 )+ PRMS*,2)))
((A RV S
2
RDOCV= 2 (( CRMS
R STR F S=UC NE ( RNM, RDOGM)
hRITE(6,22) 8STRES
VSQ=UCNF*'((DRNS/CRMS)**2)
Vh ITE (6,23) VSQ
K=K-1
IF (K .EQ. 0) GC TC 3
GC TC 4
3. STCP
20 FOR AT (12F6.1)
ARVS=',F11.e//' BRMS=',F11.8//' CRMS =',F11.8//
21 FCRWAT(iHI,'
1 ' DRrS=',F11.,//)
22 FORVAT (' REYNCLDS STRESS=',F11.8//)
MEAN SCUARE WPRIME=',F11,8//)
23 FORMAT ('
24 FORWAT (F10.8)
END
13/33/39
116
APPENDIX D
EQUIPMENT AND MATERIAL SPECIFICATIONS
1.
Circulating Pump
Manufacturer:
Type:
Labawco Pumps, Inc.,
Belle Mead, New Jersey
Centrifugal
CAPACITY
Gallons/Minute
35
34
33
30
27
18
12
2.
SPEED
rpm
1.50
2.45
3.05
4.60
6.10
9.15
10.50
3450
If
'I
'I
II
if
II
ii
Drive Unit
Manufacturer:
Type:
Motor:
Speed Co ntrol:
3.
HEAD
Meters
Dayton Electric Manufacturing Co.,
Chicago, Illinois
Mechanical Vari-Drive
1/2 Horsepower Capacitor Motor
115/230v 60cycle 1725 rpm
Adjustable Pitch Pulleys and Deepcog Belt, speed adjustable
705-4230 rpm
Composition of Kovar
Manufacturer:
The Driver Corporation
Nominal Composition
Ni......29%
Co......17%
Fe......54%
Resistivity ................300 ohms/c.m.-ft.
Temperature Coefficient
of Resistance........... 0.003 ohm/ 0 C
Meltina Point............. 1430 0 C
Tensile Strength..........90-100 x 103 psi
Magnetic and somewhat subject to corrosion
117
4.
Flow Liquid
Dow Corning Corporation
Midland, Michigan
D. C. 200 Silicone Oil
Manufacturer:
Material:
Specifications
Viscosity @ 25 0 C - 1.0
Flash Point - 100 0 F
Pour Point - -123 0 F
Specific Gravity @ 77 0 F -
0.818
Viscosity Temperature Coefficient - 0.37
Coefficient of Expansion - 0.00134 cc/cc/oC
Refractive Indes @ 77 0 F -
1.382
Surface Tension @ 770 F - 17.4 cyne/cm
Thermal Conductivity @ 770 F - 0.00024 gm-cal/sec/
cm2 /oC.cm thick
Boiling Point - 305 0 F @ 760mm
Specific Heat - 0.348 cal/gm/oC @ 40 0 C
Dielectric Constant - 2.18 @ 102 hz
5.
Experimental Particles
Manufacturer:
Material:
Sinclair-Koppers Company
Pittsburgh, Pennsylvania
Dylite Expandable Polystyrene
F-40-C
Specifications
Specific Gravity Unexpanded - 1.02-1.05
- 0.82-0.84
Expanded
Size (Unexpanded)
Sieve Ana )is (U.S. Standard)
Volatiles
6.
on No. 30 - 60% max. (by weight)
on No. 40 - 70% max.
3% max.
on No. 45 on No. 50 - 0.5% max.
(% weight) - 6.0-6.5
Analog-To-Digital Converter
Manufacturer:
Type:
Digital Equipment Corporation
Maynard, Massachusetts
ADO8-A
Specifications
Analog Input:
Voltage - 0 to/ 10V (standard)
'Impedance - 1,000 ohms (standard)
Resolution - 1 part in 1024 (10 my)
118
Accuracy - 0.1% of Full Scale + 1/2 Least Signi-
ficant Bit
Temperature coefficient -
0.5 mv/oC
Operation temperature - 0 to 500 C
Conversion Rate - 100 khz maximum
Digital Output - A 10-Bit Binary Number
7.
Variable Filter
Manufacturer:
Type:
Krohn-Hite Corporation
Cambridge, Massachusetts
Model 3202
Specifications
Range - 20hz-2Mhz
Passband Gain - Unity (Odb)
Attenuation Rate - 24 db/octave
Maximum Attenuation - Greater than 80db
Output Hum and Noise - Less than 100 pv
8.
Digital Voltmeter
Manufacturer:
Type:
Non-Linear Systems
Palo-Alto, California
Series X-3 Multi-purpose Digital
Voltmeter
Specifications
(on the 10v range)
Resolution - 10 my
Accuracy - 0.1% LSB / 1 digit
Scan Rate - 3 samples/sec
9.
Hot-Wire Anemometer
Manufacturer:
Type:
Flow Corporation
Watertown, Massachusetts
Model 900-A
Specifications
D.C. Accuracy
Voltage
0.1% or 0.1 my
Hot Sensor Current
0.1% or 0.01 ma
Cold Sensor Resistance at 1 ma
0.1% or 0.01 ohms
Fluid Temperature(50ohm sensor)
0.1% or 0.03C
Fluid Velocity
1% or 0.1 fps
119
D.C. Mctcr
Resolution
Voltage
0.05% or 0.05 my
Hot Sensor Current
0.05% or 0.005 ma
Cold Sensor Resistance at 1 ma
0.05% or 0.0025 ohms
Fluid Temperature (50ohm sensor)
0.05% or 0.015'C
Fluid Velocity
0.5% or P.01 fps
Output 1,
Cd
Voltage
0.002% e
.02 my
Hot Sensor Current
0.002% ox 0.002 ma
Cold Sensor Resistance at 1 ma
0.0025 ohms
Fluid Temperature (50ohm sensor)
0.015 0 C
Fluid Velocity
0.01% or 0.001 fps
in
10.
1 kHL
Viscometer
Manufacturer:
Type:
Brookfield Engineering Laboratories
Inc., Stoughton, Massachusetts
LVT Series
S Specifications
Accuracy - 1.0% of Full Scale
Sensitivity - 0.2%
Reproducability - 0.2%
120
BIOGRAPHICAL SKETCH
The author was born in Tarrytown, New York on June 21,
1938 and raised in nearby Dobbs Ferry, New York.
After receiving a Batchelor of Science degree from the
University of Notre Dame in 1960, he entered the U.S. Navy
and served for two years as a shipboard engineering officer.
In 1962 he joined the staff of the Woods Hole Oceanographic Institution as a research assistant in the Geophysics
Group, and participated in several scientific cruises studying oceanic thermal structure and methods to measure it
continuously from an underway ship.
In November of 1963 he joined the staff of an oceanographic consulting firm located in Washington, D. C.
For
the next year he was engaged in the design and construction
of a mineral prospecting ship and participated in its first
cruise.
&
At the completion of this project he returned to Woods
Hole and joined the second leg of the International Indian
Ocean Expedition aboard the R. W. ATLANTIS II.
This cruise
ultimately led to his enrollment in M.I.T. in September of
1965.
The author is a member of the Marine Technology
iety,
the American Geophysical Union, and the Society of Sigma Xi.
In October of 1967 he married the former Elisabeth Pope
of Silver Spring, Maryland.