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HD-A132 316
UNCLASSIFIED
MEASUREMENT OF VELOCITY DISTRIBUTIONS IN TURBULENT JETS USING A LASER DOPPLER VELOCIMETER<U) NAVAL POSTGRADUATE SCHOOL MONTEREV CA M D WESSMAN JUN 32
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NAVAL POSTGRADUATE SCHOOL Monterey, California
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THESIS MEASUREMENT OF VELOCITY DISTRIBUTIONS IN
TURBULENT JETS USING A LASER DOPPLER VELOCIMETER
by
Mark Donald Wessman
June 198 3 (••
Thesis Advisor: W. G. Culbreth
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Approved for public release; distribution unlimited
83 09 12 027
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Unclassified MCUWTV CLASSIFICATION 0' TMIS PAOC (*»m> Dmtm Kni*r.<0
REPORT DOCUMENTATION PAGE WAIT BCB1W
READ INSTRUCTIONS BEFORE COMPLETING FORM
I. OOVT ACCESSION NO, 3 RECIPIENT'S CATALOG NUMBER
4. TITLE f«M *u»*lf/.)
Measurement of Velocity Distributions in Turbulent Jets Using a Laser Doppler Velocimeter
S. TYPE OF REPORT ft PETRIOD COVERED
Master's Thesis June 198 3
« PERFORMING ORG. REPORT NUMBER
7. A4|TMOR<*>
Mark Donald Wessman
•• CONTRACT OR «RANT NUMBERf«J
». MRFOMUNO ORGANIZATION NAME ANO AOORESS
Naval Postgraduate School Monterey, California 93940
10. PROGRAM CLEMENT, PROJECT, TASK AREA A WORK UNIT NUMBERS
It. CONTROLLING OFFICE NAME ANO AOORESS
Naval Postgraduate School Monterey, California 93940
12. REPORT DATE
June 1983 IS. NUMBER OF PAGES
144 14. MONITORING AGENCY NAME A ÄOOMESÄflf 5ffmäi Äääi Confroll/ng Olllcm) IS. SECURITY CLASS. (at :hl. r.port)
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IT. DISTRIBUTION STATEMENT (ml ihm mkmtrmmt ~tit+4 Im Blmek 10. II <a!l»r»n, Ami Hmmmt)
»•. SUPPLEMENTARY NOTES
II. KEY WOPJOS (Cmttmmt an ra*«raa «Ms II mmmmmmmn) mmM Im+iHItr *r •>«<* numbmt)
Laser Doppler Velocimetry Turbulent Buoyant Jets Laser Anemometry
Turbulent Buoyant Plumes
so. ABSTRACT frnmmm •» war*« •/*• it M»M«T «•* immmtiir *r MMA BBBBBM
The theory of operation of Laser Doppler Velocimeters is discussed for both reference beam and differential Doppler modes. Current entrainment models for velocity distributions in vertical axisymraetric buoyant jets in a quiescent ambient are reviewed. A specific Laser Doppler Velocimeter is used to measure the velocity distribution found in a vertical, axisymmetric turbulent jet
(continued)
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Item 20. (continued)
discharged into a quiescent ambient and the results are compared to theory.
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Approved for public release; distribution unlimited
Measurement of Velocity Distributions
in Turbulent Jets Using a
Laser Doppler Velocimeter
by
Mark Donald Wessman Lieutenant Commander, United States Navy
B.S., University of Utah, 1971
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL June 1983
Author:
Approved by:
?3wV Trafen g&3& ___^
Thesis Advisor
Mäd=d&L£- Second Reader
an of Science and Engineering
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rrr- • ^ ." " • • • • .• 1 i ' > ••» • • -• i» i • -
ABSTRACT
The theory of operation of Laser Doppler Velocimeters is
discussed for both reference beam and differential Doppler
modes. Current entrainment models for velocity
distributions in vertical axisymmetric turbulent buoyant
jets in a quiescent ambient are reviewed. A specific Laser
Doppler Velocimeter is used to measure the velocity
distribution found in a vertical, axisymmetric turbulent jet
discharged into a quiescent ambient and the results are
compared to theory.
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."- -^ *^> j.^ .^ ••. ••;-•. "."V"»." •." • ~»," "." i" J" •' .'.•.» r^^^W^*»
TABLE OF CONTENTS
I. INTRODUCTION 11
II. LASER DOPPLER VELOCIMETRY 15
A. THE REFERENCE BEAM TECHNIQUE AND THE DOPPLER SHIFT 15
B. THE DIFFERENTIAL DOPPLER TECHNIQUE AND THE FRINGE MODEL 18
C. FREQUENCY SHIFTING 21
D. SIGNAL DETECTION AND PROCESSING 23
E. VELOCITY AND FRINGE BIASING 24
F. SEEDING OF FLOWS 25
III. CIRCULAR BUOYANT JETS 27
A. GENERAL PROPERTIES OF JETS 28
B. ENTRAINMENT MODEL FOR THE QUIESCENT AMBIENT 31
C. SUMMARY OF PREDICTED BEHAVIOR 36
IV. APPARATUS AND PROCEDURES 37
A. LASER DOPPLER VELOCIMETER OPTICS 37
B. THE LASER DOPPLER VELOCIMETER ELECTRONICS 41
C. THE COMPUTER AND SUPPORTING ELECTRONICS 45
D. THE SIGNAL PATH 46
E. THE FLUID LOOP 49
F. POSITIONING APPARATUS 50
R
• . • . •. - -
'•* s "VLT * .-•'.-•. -v.- -.• . • ..- - •....••.-.-. - - *'-*•*'—'•-"'-•'-•*-•-»*-•- •*- -r -'. T'II r.i • Hi ••>. »'• i"i.
T- •>3>*1. <^i~~!"*»r-^—"»r-t-;
G. DATA ACQUISITION PROCEDURES 51
H. DATA REDUCTION 56
V. CONCLUSIONS AND RECOMMENDATIONS 59
A. VERIFICATION OF THE GAUSSIAN PROFILE 60
B. THE GROWTH OF JET HALFWIDTH 61
C. THE DECAY OF CENTERLINE VELOCITY 61
D. THE ENTRAINMENT COEFFICIENT 63
E. THE JET OVERALL VELOCITY DISTRIBUTION 64
F. THE VARIANCE OF EXPERIMENT SEVEN 64
G. RECOMMENDATIONS FOR FURTHER STUDIES 65
H. SUMMARY 67
LIST OF REFERENCES 68
APPENDIX A. ANALYSIS OF ERRORS 70
APPENDIX B. TABULATED RESULTS 74
APPENDIX C. FIGURES 77
APPENDIX D. COMPUTER PROGRAMS 90
INITIAL DISTRIBUTION LIST 144
• . •. . •. - . . • • . ..•••-•.
*-*—*-•-• •' - • • - ' r •-'--• r
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1
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ill _!_». ii. UU I HI II pi pi p pi ii ,mm m <m •
LIST OF FIGURES
Fig. 1. Geometry of Doppler Shift Model 77
Fig. 2. Typical Reference Beam LDV Arrangement 78
Fig. 3. Fringe Model Interference 79
Fig. 4. Typical Differential Doppler LDV Arrangement- 80
Fig. 5. LDV Optics Arrangement <- 81
Fig. 6. Doppler Bursts 82
Fig. 7. Signal Flow Path 83
Fig. 8. Experimental Apparatus Fluid Loop 84
Fig. 9. Jet Velocity Profile 85
Fig. 10. Growth of Jet Width 86
Fig. 11. Velocity Decay of Jet 87
Fig. 12. Entrainment Coefficient 88
Fig. 13. Streamwise Jet Velocity Distribution 89
7*.
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Al.l,.t.W,.l.f.-.l.l.....,J.'..-..-, < J .-.^.. . ..- ..... ...^^ . ...... ... • - - __ • •... ^^
TABLE OF SYMBOLS
B Characteristic jet width (L)
D Jet discharge diameter (L) * 2
E Volumetric entrainment rate, dQ/dS (L /T)
1/2 F Densimetric Froude number, U /D{(gD(p -P/p )} ' o a o o 2
F. Local densimetric Froude number, U /{gB(P-P )/^L} L m a m m
f Frequency (Hz) 2
g Gravitational acceleration (L/T ) 3
Q Volumetric flow rate (L /T)
r Radial jet coordinate (L)
S Streamwise jet coordinate (L)
U Streamwise jet velocity (L/T)
v Velocity of particle (L/T)
GREEK SYMBOLS
a Entrainment coefficient
6 Angle of beam crossing, angle between lines of sight in reference beam mode.
# Angle between velocity vector and fringe pattern normal, angle between velocity vector and the scattering vector.
X Laser light wavelength (L)
P Density (M/L3)
8
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'.";.•-
SUBSCRIPTS
a Ambient condition
d Doppler shift a
m Evaluated at local jet centerline .;
o Evaluated at the centerline of the nozzle exit g
m
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m i ••, m.. i.i.i i.i,i'n".n'V'. »um i ipipa jaji IM.......... ;.» .
ACKNOWLEDGMENT
The author wishes to express his appreciation to
Professor William Culbreth of the Naval Postgraduate School
for his assistance and support during the conduct of this
research. Equipment funding was provided by the NPS
Foundtion Research Program.
•
10
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. •"*•*• "• .• ."•.--,'- ."-
•a^i.^1^^« ^ ^ - ,
I. INTRODUCTION
The study of the characteristics of turbulent jets and
plumes has become an item of widespread interest as the
concern for the environment has grown. An understanding of
how the velocity profile varies throughout ehe jet is
central to the development of knowledge of the behavior of
the jet with respect to heat and mass transfer, both
subjects of intense interest to the engineer or scientist
who must predict the impact of a discharge on the
environment. Further, changes in temperature or
concentration may someday have significance in non-acoustic
antisubmarine warfare applications.
Researchers have used a variety of techniques to study
turbulent jets and plumes. Qualitatively, the
characteristics may be disclosed through photographic
studies involving the injection of tracer dyes. For the
purposes of determining the widths of the plumes and their
trajectories, this technique is useful, but precise velocity
information or numeric data regarding the temperature or
concentration profiles within the fluid are not available
from this method. Velocity information, as well as
temperature can be determined using hot wire anemometry, but
this technique requires that a probe be inserted in the flow
11
I
i
— - - - ^MM
w^^^^^^^^^i^m^^^^p —p- ". .". I". .-.' .IT."
in order to obtain the measurement. The presence of the
probe is intrusive in nature and will invariably alter the
flow characteristics of the system. Similar objections
arise when the use of rakes of thermocouples, conductivity
probes, or any similar device is contemplated. For years,
however, no alternative existed and researchers were
required to make do, minimizing the effects of the
measurement devices if possible.
In 1964 [1] [2], it was noted that laser light in a flow
in which particles were present was scattered, and that the
scattered light was shifted in frequency by an amount
proportional to the velocity of the scattering particles.
Subsequent work developed the technique, known as Laser
Doppler Velocimetry or Laser Doppler Anemometry, with the
result that there is now a reliable, non-invasive method of
measuring fluid velocity in a variety of environments.
For the purposes of the present work, a commercial Laser
Doppler Velocimeter was obtained. The device was interfaced
with a Hewlett-Packard 9826 microcomputer for data
acquisition, a tank was constructed and a suitable nozzle
was installed for the introduction of a vertical submerged
jet of water into an ambient. Here the intent was to gather
data on a jet discharging to the quiescent medium of the
tank, and to develop the measurement procedures, interfacing
programs, and data reduction facilities necessary to analyze
the behavior of the jet. The results were compared to those
12
III! |BII| . II •••••• •!. ••.••. I. ' ' ' ' • • •!• •*• '• ii. >.i .•'. »••,•' ,l'ii I.I.III « .••• • » • •
obtained by earlier researchers under similar conditions
with the objective of validating the technique and ensuring
proper functioning of the system.
Data was collected at a variety of flow rates in
quantities sufficient to constitute a valid statistical
base. Raw data gathered by the microcomputer in conjunction
with the LDV electronics was transmitted via telephone line
to a Digital Equipment Corporation VAX 11/780 computer,
which was large enough to perform the required manipulations
to reduce the data to usable form. Results were expected to
be consistent with those obtained by other researchers
utilizing other methods.
Specific information to be gathered and compared was:
1. The jet center line velocity as a function of
streamwise coordinate and the velocity of discharge at
the nozzle axis.
2. The variation of jet characteristic width with
streamwise coordinate.
3. The rate at which the ambient fluid is entrained into
the jet, as characterized by the entrainment constant.
Information which was also gathered in order to
demonstrate the capabilities of the system included:
1. The mean velocity component normal to the streamwise
coordinate.
2. The turbulence intensities in the radial and
streamwise directions.
13
'v"-:V^^v,-^^,V''-^l''?^-'V:''-l.'-l'..^.''.>.l,l-l,.^.l>l,.>,lll"1?'-!'. ' .'. •• 'I 'Vl'_«lifiii»||.;t.-» ... i f py ._!•;»._..;
3. The mean Reynolds stress at the point of measurement.
The measurements were made using the LDV to gather data
in first the streamwise direction, then, after rotating the
plane of the beams, in the direction normal to the
streamwise coordinate. No attempt was made to take
instantaneous readings in the two directions simultaneously,
as this model LDV possesses no capability to do so.
As the data was gathered, the velocity information was
monitored on the screen of the microcomputer, which was
programmed to provide a display similar to that of a
spectrum analyzer. As each sample was received, the data
point was plotted, accumulating vertically with an abscissa
representative of the velocity. The resulting plot
represented the number of "hits" at a particular velocity
over the total sampling time. In general, the accumulation
of 100 or more points of data provided a distribution which
was Gaussian in nature, and which could then be saved on
flexible disk for further processing.
The ability to accurately determine mean velocity at
selectable points within the jet allowed confirmation of the
shape of the velocity profiles within the body of the jet.
This is of particular value as most models so far postulated
assume a Gaussian profile radially and that the centerline
velocity decays inversely with the streamwise coordinate
dimension. It was expected that these assumptions would be
verified during the course of the investigation.
14
£.«.,-„. ...... ... >-" --• . -. ...
rm**mrm~*-*mi~m*mmm!^'~^~*~^*'m^m^^^mmmmmrmmmr*+,i • . .L•, .H .,, p. , ,, ß .,.,.„.,.
II. LASER DOPPLER VELOCIMETRY
Laser Doppler velocimetry (also known as Laser Doppler
Anemometry), is a relatively new technique for the
measurement of velocities in fluids. It is dependent on the
wave mechanics of light in the medium of interest, but
requires no physical probe to be inserted into the flow, and
is, therefore, non-intrusive in nature. The method has been
used to measure mixing in chemical reactors, flow through
nuclear reactor fuel bundles, chemically reacting flows, and
flows in other environments where the geometry or the nature
of the fluid to be studied precludes the use of other
techniques. It has been used in both gases and liquids.
Drain [3] presents the theory and techniques of Laser
Velocimetry on an introductory level and covers the
currently used methods and processes in some depth. Only
those topics necessary for background or understanding of
the methods used in the present work will be discussed
here.
A. THE REFERENCE BEAM TECHNIQUE AND THE DOPPLER SHIFT
The Doppler shift is a well known phenomenon which has
been widely utilized in acoustics and in radar
applications. Because light is a form of electromagnetic
radiation, scattered light from particles in a fluid flow is
15
• i.i. i. • A1'.'' •-' W i «.»"' '».i.iijiiiu».»^^^w^_pi»i i .• j p .i.ni,. n
also Doppler shifted by an amount determined by the relative
velocities of the source, the particle, and the detector.
For a stationary source and detector, the amount of the
Doppler shift observed is a function of the half angle of
scattering and the component in the direction of scattering
of the velocity vector of the particle scattering the
light. As the geometry of the system is a known quantity,
the velocity of the particle can be obtained directly from
the Doppler shift frequency. This is the principle of
operation of the reference beam mode in Laser Anemometry.
Because of the speed at which light propagates, the
derivation of the Doppler shift must include relativistic
effects in order to be rigorous. Applying the equations of
special relativity and using the final approximation that
the velocity of the particle is very small compared to that
of light, the Doppler frequency shift can be shown as:
f. » (2v/x)cos*sin(«/2)
where v is the particle velocity, x is the wavelength of the
light, and 4 is the angle between the direction of
scattering and the particle velocity vector, and # is the
angle between the original beam path and the line of sight
from the particle to the detector. The scattering direction
is defined in Mie scattering theory as the direction of the
bisector of the obtuse angle formed by the lines from the
16
-*-*-• • - •-• •-, w. . -.v.- . . . ... -.-• • ,..^^_ . .-,,,
TTT,TT,7T^^^^T^'T^^^T^^T^^•9^^7'',^,^^,^^*f,"^"^,T* « • •—i—r"
•i!
source to the particle and the particle to the detector.
Figure 1 shows the geometry.
»^ In practice the Doppler shift frequency is very low in •i j$ comparison to the frequency of the laser light (32 MHz
Doppler shift at 10 m/sec for red light such as from a He-Ne
14 laser at a frequency of 4.7 X 10 Hz, a ratio of 7 parts in Q
10 ). Such a low variation in frequency is extremely
difficult to detect. Furthermore, the output frequency
response of most detectors is far lower than optical
frequencies. Accordingly, a technique must be used whereby
improved frequency response is obtained and the Doppler
shift more readily detected. Mixing Doppler shifted light
with light of the original frequency is a technique similar
to that used in superheterodyne radio and radar transmitters
to move signals to more favorable parts of the
electromagnetic spectrum. The light of the original
frequency is the reference beam from which the technique
takes its name.
VJhen two coherent (i.e., of a fixed phase relationship)
signals are mixed, the result is a signal with constituent
waves of frequencies corresponding to the sum and the
difference of the original frequencies. In optical detector
systems, the sum component is at a frequency much too high
for the bandpass characteristics of the system to process
and is thus filtered out. The difference signal, however,
17
k^^^^^ :v.v:---.y.v: :•:•.- ..._•
^^^•^^^ ^•^^
is at a lower frequency which is easily processed, and which
corresponds to the Doppler shift frequency.
Physically, the reference beam is generally split off of
the illuminating beam before it passes through the fluid.
It is redirected to be finally focused on the detector
pinhole, mixing with the scattered light from the main
beam. It is sometimes necessary to attenuate the reference
beam in order to assure similar intensities of the signals
at the surface of the detector.
The reference beam technique has been used with success
in a variety of applications. However, its applicability is
limited by a low signal-to-noise ratio which renders it less
useful than the differential Doppler technique. The
arrangement of a typical reference beam LDA is found in
Figure 2.
B. THE DIFFERENTIAL DOPPLER TECHNIQUE AND THE FRINGE MODEL
If two beams of coherent light, both of equal
intensities are crossed in the body of a moving fluid, light
scattered from the intersection volume will be shifted by an
amount equal to the difference between the Doppler shifts of
the light scattered from the individual beams. This shift
can be analyzed similarly to the case of the reference beam
method, but a simpler model is available to explain the
results obtained. This is the fringe model.
18
l'*1''' '•'' *''• ill "-r •* -* - - -•-». ..._.-....•• •!. Jl,
qw^^^^^^^^^w^^^w^w^^^^^ • I
The formation of interference fringes has been observed
using diffraction gratings, pinholes of specified
separation, and many other simple optical devices [4]. These
fringes are the result of constructive and destructive
interference between the wave fronts of the light where they
are coincident. The same result occurs when beams from
coherent sources are crossed in space. The maxima of the
light intensities resulting from the mixing are the bright
planes of the fringe pattern and correspond to the loci of
points at which the wavefronts are in phase. If the beams
are crossed at angle 9, the spacing of the fringes can be
shown to be given by:
d - X/2sin( 6 /2)
The fringes are parallel to the bisector of the intersection
angle of the beams. If a particle passes through the
pattern at velocity v, the scattered light will be modulated
in intensity at a frequency given by;
f, = (2v/x)cos*sin(»/2)
This is the differential Doppler frequency, and the process
is the basis of the differential Doppler method. Here * is
the angle of the velocity relative to the normal to the
19
•:
*
• «',., rf'- CmCm Cm. %:m% m.l'm •'• • . l'. 1- •"- «'. •?- t'.V. • ^ «". • - «',_,*- m". . _ . . » . . ,_. ., • *-*-••
• .- i - J^^^^^^^^^^*"^"^^^^*"«"1 •i •» i • •» •»•
fringe planes. Figure 3 depicts the geometry of the fringe
model.
The frequency of light scattered from the intersection
volume using the differential Doppler technique is
independent of angle. This fact allows collection of the
signal at any angle which is advantageous to the purpose at
hand. If the detector is positioned in the hemisphere
beyond the intersection volume from the laser or beam
source, the term "forward-scatter" is used. Conversely, if
the detector is on the same side as the source, the term
"backscatter" is used. Collection in the forward-scatter
mode provides greater signal strength while, if backscatter
is used at 180 degrees, the receiving optics can be combined
with the transmitting optics. Backscatter, however, is
limited by a much lower signal strength.
Light intensity across the beam fronts is not uniform,
but varies in a Gaussian manner radially. As a consequence,
the volume of intersection of the beams is ellipsoidal in
shape and the intensity of the fringes varies across the
cross-section of the intersection volume. This results in a
lower frequency modulation of the differential Doppler
signal which is called the pedestal. The pedestal is
unwanted noise and is usually removed by filtering before
signal processing begins.
A diagram of a typical differential Doppler arrangement
is found in Figure 4.
20
•.-•••Tb ••'•••• A' . .•,,;:..-^.'.':^',v..:..-'^'..'.'.-, . ...... •_.-.. -.-... _ _
m II • «> • I • < *> «i -I VI ^^^ • • i • i. • i »m » •» - | - t -m ••fi • «—^
C. FREQUENCY SHIFTING
As a particle passes through the intersection volume in
the differential Doppler mode, the light scattered is
modulated at the differential Doppler frequency
corresponding to the component of velocity of the particle
normal to the fringe planes. For flows in which the
direction of travel is always known, sufficient information
can be obtained to characterize the flow. In highly
turbulent flows where flow reversals are present or in
similar cases such as mixing, an ambiguity exists as to the
direction of flow. Furthermore, since the signal is
generated by the movement of particles with respect -to the
fringes, a zero velocity results in an absence of signal.
Both of these problems are eliminated through the use of
frequency shifting.
The technique of frequency shifting consists of altering
the frequency of one or both of the crossed beams by a fixed
amount. This can be accomplished by the use of mechanical
or electro-optical devices, the most common method being the
use of the electro-acoustic Bragg Cell.
When frequency shifting is used, the fringes will move
with a velocity determined by the frequency shift.
Directional ambiguity and loss of signal at zero velocity
are now eliminated, and the true velocity of the particles
may be determined by subtracting the frequency shift from
21
•''•'••••'• - -'* - i- lHll T| In - - • - - ' -- -• - - • •-•---•- . • . 1 • - . - J
'••'-.•'l'"^'.''.'.^''"""" .' -'•" .'- '- •^•l]-'..IM,l-",.^*^*T^Ul.» '••••••'•J'.'".• y t", i",i ,»••'••«.•. ....>.L.i.
the measured differential Doppler frequency, and then
proceeding with the computations as though no frequency
shift had been applied.
The Bragg Cell consists of a block of acousto-optic
material on one side of which a piezoelectric transducer is
affixed to impart the acoustic excitation to the block. The
acoustic waves traveling through the cell diffract the laser
light causing the it to be shifted in frequency by an amount
equal to the frequency of the acoustic wave. Successive
acoustic waves cause the signals to reinforce yielding an
improved efficiency in transmission. It has been found that
a shift frequency of about 40 MHz can provide 80% efficiency
and result in sufficient separation of beam orders to allow
for easy blocking and selection. In many currently used
systems, the plus first order beam is used at a 40 MHz shift
because the wavelength of the acoustic waves is comparable
to the diameter of the beams to be shifted.
Either one or two Bragg Cells may be used in frequency
shifting applications. Usually if one cell is used, a
downmix frequency of 32 to 35 MHz is used to reduce the
observed signal in frequency to a range where the frequency
response characteristics of the installed instrumentation
are better adapted to handle it. In the two Bragg Cell
technique one is usually operated at the most efficient
frequency for transmission {40 MHz is typical) and the other
operated at the amount of shift desired above the
22
•A •i
•
• -^—^—_~—•- - - - . _. . . .... .-..-.-.
.••.*•' '-'.' ^^^ff^^^^*m^m* ' ".' WP i"- '- •-•»^•«^^^»l^^^^^^^-»1. • • •!• M»"1." J."-* .• .. |.... •• . • .-T-v
reference. The net shift detected is the difference of the
two, providing selectable frequency shifting on the order of
magnitude of most flow measurement velocities encountered,
while maintaining optimum beam power.
D. SIGNAL DETECTION AND PROCESSING
The signal of interest in laser velocimetry is optical
in nature and is hence detected by means of optical
instrumentation. A photomultiplier tube or photodiode is
most often used as the primary djtector. Photomultipliers
provide inherent amplification features and have good
frequency response characteristics up to 10 to 100 MHz. They
are most responsive in the blue to green portion of the
spectrum but can be obtained with good response in the red
to infra-red regions. Photodiodes usually have no inherent
amplification attributes, but can be avalanched to provide
some multiplication. They are usually most sensitive in the
red to infra-red, although adequate sensitivity may be
obtained across the visible spectrum.
Signal analysis can be accomplished through a variety of
means. The method used is dependent on the type of
information required. For low Doppler frequencies, spectrum
analyzers can be used to provide frequency information from
the signals. Counter-tracker arrangements and
autocorrelators can be used to separate the noise from the
signal and to yield the frequency information. Any signal I
23
~L~M --. . i.i. i • .-. • ••^.. :..:•'. •'. --. -.••••• haaiaJia - - • -•-•-••. ..-.•. . .. . • .. .^. ._,. . • ^. . . . . ... .. .-...
:-.*.•.'.'•'.« !•• L.-.,-,^V-".,Jll,.M,J.-,-l.V- - •*' .3 "•w'.«.l"JI-Tl "'."••• ' " "• TT? ? *" .*" • •••• ": " *•-«V-.» •••' ' ..r^^Tr^i
processing arrangement must include provision for filters to
adjust the bandpass characteristics of the system to
maximize the signal-to-noise ratio. Low frequency filters
(high pass filters) are used to remove the pedestal while
low pass filters are adjusted to eliminate high frequency
noise such as that from thermal sources and photomultiplier
tube "shot noise".
For the present work, a counter type signal processor
was used to provide frequency information for each burst as
sampled. The processor used a high speed clock (250 MHz) in
conjunction with Schmitt triggers to measure the duration of
a burst of a fixed number of cycles. The frequency was then
obtained from the number of cycles measured and the time
required for the burst. Filtering was provided in the
apparatus before the counter tracker.
E. VELOCITY AND FRINGE BIASING
The results obtained by laser anemometry can be biased
in two principal ways. The first, velocity biasing, is the
biasing of the mean velocity by the disproportionate
inclusion of high frequency bursts over low. This occurs
primarily at low data rates when the registration of a data
point results from the passage of a single particle through
the intersection volume. In a flow with uniform particle
density, more particles moving at a high flow rate will pass
through the measurement volume than will particles moving at
24
-» .-,, i- -i * •«••-^-••-»—-•-^•-~- mr -
^w I ••I •• • I
I
low velocities. This is a consequence of a high velocity
particle having a higher probability of encountering the
intersection volume. If a sufficiently high data rate is
present that the data acquisition system samples at uniform
intervals at a rate much slower than the data rate, velocity
biasing is eliminated and the time average frequency will
yield the correct mean velocity. If such a high data rate
cannot be maintained, the data must be weighted with the
duration of each burst sampled. This will correct for the
low probability of sampling a low velocity particle.
The second biasing, fringe biasing, is a result of the
parallel nature of the fringes. If a particle passes on a
course parallel to the fringes, no signal will be
generated. Therefore, even though a significant number of
particles having a zero component of velocity in the
direction being measured can exist, only particles having a
non-zero component will be "seen". The use of frequency
shifting causes the fringes themselves to move and
eliminates the bias by generating a relative motion between
the particles and the fringes.
P. SEEDING OF FLOWS
Many flows of interest to the LDV user do not include
enough particulate matter to scatter the light and provide a
signal. In those cases, an appropriate seeding particle
must be chosen. There are two basic requirements for
25
9
i
• —-— ^ -" - •- - - • - - - • - . . . . ^ ^ .«••_•. . . . -
P"^^"7» L" .1 !'_•••
_v
• 1,1 .11,11 llljjll, I.I^JIIJI . L L •!.,1,1.I .1.1.1 I.I | | HI I • • ., ••,•,.! ju. <...».>•:•...... . 1. •. • •
scattering particles. First, they must follow the flow
sufficiently well to adequately represent the dynamics of
the system. Second, they must scatter sufficient light to
provide a good signal. Consideration must also be given to
special conditions such as high temperature or chemical
reactivity of the flows in the selection of the seeding
particles. The manufacturers of most commercial laser
Doppler velocimeters provide guidance in the selection of
appropriate particles for use with their apparatus.
26
w ^^^^^ ••••••
.->
3
III. CIRCULAR BUOYANT JETS
The characteristics and behavior of circular buoyant
jets have been the subject of many studies in the past four
decades. Most of these studies have involved not only
experimental observations but also mathematical model
development in an effort to accurately predict plume and jet
behavior under a variety of conditions. By far ih« most
widely utilized model is the entrainment model which
attempts to predict jet behavior based on integral equations
of continuity, momentum, and energy. Other approaches
utilized an analysis based on Prandtl's mixing length
hypothesis or on turbulence kinetic energy. Schlichting [5]
discusses these more traditional approaches.
The entrainment model has been used by numerous authors
in their studies, and general agreement on the forms of the
equations and constants involved has been reached. Gebhart
et al. [6] have provided a comprehensive discussion of the
various models and have employed a number of them for
comparative calculations. The models predict not only
trajectory and velocity behavior in jets but also deal with
the temperature and concentration fields found in jets in
uniform and stratified ambients, either quiescent or
flowing. For the present work only the information which
27
fl^T^^T^^T^1 I. •. !•' •l^^^^w^p^^^W'.i • i ,i .1 i m H m i
pertains to velocity distribution and jet growth will be
considered.
A. GENERAL PROPERTIES OF JETS
The physical extent of a buoyant jet can be divided into
three zones. The first, the Zone of Flow Establishment, is
that region in which the flow transforms from the
characteristics found in the nozzle to those of a free jet.
In this region momentum effects predominate and the
velocity, temperature, and concentration profiles found in
the flow field are typical of the nozzle itself. The flow
at the core of the jet is unaffected by the surrounding
ambient, and viscous shear effects act at the periphery of
the jet to initiate mixing with the surrounding fluid. The
Zone of Flow Establishment ends where the turbulent mixing
reaches the core of the jet.
The second region is the Zone of Established Flow. Here
buoyant effects and momentum effects of the jet are on the
same order of magnitude. Velocity profiles (as well as
those of temperature and concentration) are similar
throughout the region. Interaction with the ambient remains
through viscous shear at the boundaries and mixing proceeds
throughout the jet. The initial discharge conditions of the
jet play a progressively smaller role as the jet grows
toward plume-like behavior.
28
UP"! ••i •• ••-••- V- •"V "•-• -"T^T^TTT^I^^'^^T'^^'^J^'^^TT'T"
In the final region, the far field, momentum effects of
the jet are negligible and the behavior is influenced by
buoyancy effects. The jet is free to be convected passively
by the ambient. Diffusion acts as the jet loses definition
and becomes indistinguishable from the surroundings.
The terms jet and plume refer to submerged discharges
which have primarily momentum and buoyant behavior
respectively. A pure jet can be considered to be a
discharge of fluid of the same density as the ambient
injected at some velocity relative to the surrounding
fluid. A jet's behavior is determined by its momentum when
discharged and it reacts with the ambient only through
viscous shear at the boundary. Conversely, a pure plume can
be considered to be a discharge of fluid into an ambient of
significantly differing density injected at a low enough
velocity that momentum effects are negligible. A pure plume
may also be created by the injection of energy to the fluid
such as through immersion of a hot wire in the ambient. A
plume may be either positively buoyant or negatively
buoyant. Clearly, real world discharges are rarely either
pure jets or pure plumes. In this work the terms jet and
plume will be used interchangeably and will be understood to
apply to a discharge of a fluid into an ambient which will
be considered to be infinite in extent and which is not
required to have the same composition or properties as the
jet.
29
^^^^^^^^^^^m^^Hm*0Pf*ß**m**mmm* •.•.•.-••-•• •••.•••.• -^ .•. > . . ..,.,-
Ambients may be described as stratified or unstratified
as well as flowing or quiescent. A stratified environment
is one which possesses layers of fluid of differing
properties within its extent. Situations of interest
because of parallels in nature are those involving vertical
stratification of water either thermally or with respect to
salinity. In the laboratory, the environment stratified
with respect to salinity is the easiest to control and is,
therefore, the one usually studied. Here, however, the
object is to compare LDV measurements with theory.
Accordingly, the ambient of interest will be selected as
quiescent, unstratified water in the interest of
simplicity.
In addition to classification as jets or plumes,
discharges may be described by their angle of discharge with
respect to the gravity field. A vertical jet is one
discharged parallel to the gravity field (in either the same
or the opposite sense) and a horizontal jet is one
discharged normal to it. Obviously a jet can assume any
orientation, and the orientation may change over the flow
field if buoyancy is present. For the present work, the
vertical jet has been selected to provide for a stable,
predictable trajectory in the presence of buoyancy effects.
30
•
^^^^^^^^^••••»-p ." ." '
B. ENTRAINMENT MODEL FOR THE QUIESCENT AMBIENT
Morton et al. [7] were the first to use the entrainment
model which supposes that the rate at which fluid is brought
into the jet is proportional to the centerline velocity of
the jet and to the effective circumferential area of the
jet. Mathematically,
E a 2>rBU m
Here E represents the volumetric rate of entrainment into
the jet, B is some characteristic dimension of the jet yet
to\be defined, and Ü is the mean centerline velocity of the m
jet. This rate of entrainment must be equal to the rate of
change of volumetric flow within the jet or,
dQ/dS = E
Here Q is the volumetric flow rate and S is the streamwise
coordinate of the jet. The constant of proportionality
defining E is called the entrainment constant or entrainment
coefficient, a. Utilizing the notation thus defined, the
entrainment function becomes
E • 2JT«BU m
31
'"*""" —'' *'-»—>-- *•« .-..-• .-.I ,-.»• i , >, ,••,••, •. ...... .--.--.'--t-•.-'•-•. -m .-..•. _,"•_/ _.'•_ _-.-..
P'J.'J '» .•. '.• W P. •. • r^^^—W^^^P^*^^^*""^^—» • i •. • .i • •
The assumptions used in the solution of the equations
for differential modeling of the plumes are as follows:
1. The turbulent jet flow is steady.
2. Since the jet flow is fully turbulent, radial
molecular diffusion is neglected, compared to radial
turbulent transport.
3. Streamwise turbulent transport is negligible when
compared with the convective streamwise transport.
4. The variation of the fluid density throughout the flow
field is small compared to a chosen reference
density. Density variation is significant only in
buoyancy terms. (Boussinesq approximation).
5. There is no variation of other fluid properties
throughout the flow field.
6. Pressure is hydrostatic throughout the flow field.
7. The jet is axisymmetric. That is, throughout the flow
field there is no variation circumferentially of any
important parameter.
Most modelers have assumed a Gaussian profile for
velocity in the jet. That is, the velocity in the jet cross
section will vary as:
U • U exp(-r2/B2) m
2 Here B is twice the variance from the mean centerlme
32
{-.* -.' •«" •>•', -W" >.' m • . • .• ^ ' J- . ' , L - •-—»-.«-*• V>.-i..M* n n 1. V-Atfc -h ;..-.. Vb->V,-.•/••••• •..,••.. .. .- - . ...... . . .....-•.••.••;.••, -•»•-•-- . J
p«^!W^^^^^^^i -•-
• . • . * • •. "t "I r
velocity of the local velocity across the jet. Using this
definition, B can be seen to represent the radial coordinate
at which the mean velocity has decayed to 1/e of the mean
centerline velocity. B is therefore representative of the
nominal half width of the jet and is the quantity used in
the entrainment relations. A similar Gaussian profile has
been assumed for variations of temperature and concentration
to complete the models, but a spreading factor equal to the
square of the turbulent Schmidt number is added to the
denominator in the exponent. See Gebhart [6] for details.
In the Zone of Established Flow, which is of principal
interest here, buoyant forces and momentum effects are both
important. The relative importance of these quantities can
be represented by the value of the densimetric Froude
number, F. It is defined by:
F -U0/{gD(,a-,0)/,o}1/2
The importance of the initial momentum is given by the
discharge velocity U and the contribution of the buoyancy
force is represented by the density difference. It is a
measure of the velocity generated by the buoyant force.
Hereafter, the densimetric Froude number will be referred to
as simply the Froude number. In some models, I \e local
33
.-.•.-. •— •» • •. *.
-1 _ _•
•F"T ^f^PP^^^l^^p^•—-—i ^ ^""»
Froude number is used. It is defined as:
FT. • U /<gB( *-/>)//> } m a m m
Mathematical models using the entrainment function
provide prediction of velocity, concentration and
temperature profiles, trajectory, and jet width once the
entrainment constant is specified. The determination of the
entrainment constant has been empirical in nature, with
several researchers recommending specific values or forms
for correlations. While many of these have been formulated
for variable orientation or for flowing ambients, they will
not be addressed here; rather those relations germane to
quiescent ambients and vertical jets will be discussed.
Albertson et al. [8] conducted measurements in order to
verify mathematical models and to determine the value of the
entrainment constant. They found that for non-buoyant jets
(F =00), the appropriate value of a was 0.057. Other
researchers have been in basic agreement with that figure.
Albertson also found that the centerline velocity decayed as
1/S (that is, inversely as the streamwise coordinate) for
pure momentum jets and that the half width increased
directly as the streamwise coordinate. These dependencies
are consistent with the derivations involving mixing length
hypotheses found in Schlichting [5]. The assumption of the
34
/•y'iiVVvv' •' •-"."- "-. • . • V •. • '."• "- *-" "•' *-" *.'«••' •- •-' -
-.'>'.• i." •.• •.•«.»i." u.". • J •'-••. >. • ..« j"P»T^!*»^^^^^^^w^w-»?» '»"i »'
Gaussian velocity profile in the Zone of Established Flow
was also confirmed.
For pure buoyant plumes Abraham [9] proposed a value of
0.085. List and Imberger [10] and Fan [11] recommended 0.082
for the value of the entrainment constant for pure buoyant
plumes. Fan also recommended 0.057 for momentum jets.
In an effort to model jets which were neither pure
momentum jets or buoyant plumes, Morton et al. [7] proposed
that the entrainment constant be given by:
a a 0.057 + a2/FL
Hirst [12] proposed a value of 0.97 for a- and that the sine
of the angle of inclination of the jet to the horizontal
should be included on the correction term also.
Davis et al. [13] suggest the entrainment coefficient
be given by:
« = 0.057 + 0.083/F 0.3
They also measured the decay of centerline jet velocity with
streamwise coordinate as well as the growth of the jet
dimensions. Their apparatus discharged a saline jet
downward into fresh water, and they used hot film anemometry
for measuring velocity. No firm correlation was reached
with respect to jet growth because of the scatter of the
I
35
•
• •«-,- • • - - .-.-.•.•.•
» - , . .i. ..
.'.••• • •• • •• ' • " .' • Mi'inn.i.iii.i'iii.ii i ii iii n i n. ,ii n pfn wt p .• rmi .,-.L ^-^-.-
data. Their velocity decay data showed a decrease in the
* rate of decay with decreasing Froude number. This is
I consistent with the data from Albertson's studies for
infinite Froude number and that of Rouse et al. [14] who
reported that the centerline velocity for a pure buoyant
-1/3 plume decayed as S ' . Davis also verified the Gaussian
nature of the velocity distribution in the Zone of
Established Flow.
C. SUMMARY OF PREDICTED BEHAVIOR
Based on the foregoing, the jet behavior observed
through Laser Velocimetry is expected to be predictable.
Specifically, the jet is expected to grow in the half width,
B, at a rate proportional to the streamwise coordinate, S.
The centerline velocity is expected to decay at a rate
-1/3 proportional to 1/S for the pure momentum case and to S '
for the pure buoyant case. By fitting the observed jet
velocity field to appropriate power-law relations, an
expression for the volumetric flow rate Q as a function of
streamwise coordinate can be obtained. This expression can
then be differentiated with respect to S to obtain the
entrainment rate. As B and U are known, the value of the m
entrainment coefficient at any level can be calculated. A
mean entrainment coefficient can then be obtained for each
jet and compared with theory. Values of mean entrainment
coefficient are expected to vary between 0.057 and 0.082.
36
* *' '" ' * •' •*—*—•—i—'—•—*——•——*—*— ------ - - » - .•- - -.-.-»-.-. . .
»,»'i i • » •» HI i i ltimnni||HH!HI,|ili|il)>,l . . i u » r .- :- E—P
IV. APPARATUS AND PROCEDURES
I
I
The present work represents the first in a series of
studies investigating the characteristics of turbulent
buoyant jets using Laser Velocimetry. As such the present
research concentrated on the development and validation of
the technique. This leads to a developmental approach to
the use of the LDV and to the techniques of measurement
employed. Also, the LDV progressed through several
evolutionary stages during the course of the work as the
methods used were refined and problems with original
approaches were identified and corrected.
The information presented in this chapter is the result
of a number of changes to the original apparatus and
approaches to the employment of the LDV. It reflects the
form of the experimental arrangement and the method of use
which proved to be most effective in measuring the fluid
velocities.
A. LASER DOPPLER VELOCIMETER OPTICS
The LDV used in the present work was a TSI, Incorporated
model 9100-5 Laser Doppler Velocimeter. It is a modular
instrument which is intended to be user assembled with
components included as required for the application. All
components are mounted on an anodized aluminum base which is
37
:•* • . i. i. -ii • i • • ii • j • . . • • i - - - - - —. --._•-. _ - _ . ... . . _
*r*^^*^^^tmim*mimm^*m^*^^m^*!mmm^m*mmmmimim*mm • • • • • • •
equipped with mounting brackets for securing the modules to
the base. The optical modules are secured to each other by
the means of thumb screws and the entire assembly is mounted
on the base on rotating mounts which permit the choice of
angle of velocity component to be measured. Figure 5
presents a schematic representation of the LDV optical
assembly.
The laser unit is mounted in the lower part of the
extruded base. It is a Spectra Physics 15 milliwatt
Helium-Neon laser which operates in the continuous wave (CW)
mode. Power to the laser is furnished through a separate
power supply. The LDV is assembled with the laser unit
pointing away from the test section. The laser beam is
focused onto a front-surface mirror located in a housing at
the end of the base which reflects it to a similar mirror at
the top of the housing from which it is reflected in the
direction of the test section. Both of the mirrors are
provided with adjusting knobs which act through wedge
assemblies to permit alignment of the beam.
From the top front-surface mirror, the beam is focused
on an aperture located in the center of the after rotating
mount for the optics assembly. It then passes to a
prismatic beam-splitter module which separates the single
beam into two coherent beams of equal intensity which travel
in parallel paths down the base.
38
fc
I
<•> .••
A-'1"-* "*•' '•' '•" '•' V" ^"' •"••'• -^- • . ^—I «—• ^_^JLJ .._» . .. .'-. -.'.••'.•• . • . • • L ........
• ••• • -^^^^^^^^^^»^^•^•^»»-^
The two parallel beams then enter the frequency shifting
module. It contains two Bragg Cells, one in the path of
each of the beams. The Bragg Cells are acoustically
vibrated by electrical signals provided from a frequency
shift unit and power amplifier located remotely from the
base. One cell is driven at 40 MHz and the other at a
frequency above the first by an amount selectable by
pushbuttons on the frequency shift unit. Each Bragg Cell is
followed by a beam steering lens eccentrically mounted in
wedge assemblies. These lenses can be rotated to realign
the beams, to correct for the deviation introduced by the
frequency shifting process. In addition, the next module,
the beam steering module contains another such assembly in
the path of one beam. This is provided to assist in beam
crossing during final alignment of the device.
The next module, the receiving optics unit, contains
another rotating mount assembly. As the beams proceed
towards the test section, they travel through passages in
the outer portion of the assembly.
Following the receiving optics assembly a beam expander
is installed if the beam separation to be used was 50 mm.
If the beam expander module is omitted, the beam separation
is 22 mm. The latter was selected for the present work
because it provides a superior signal-to-noise ratio and a
smaller intersection volume with the selected transmitting
lens than does the 50 mm separation. This module is
39
•- * « .i;.-...i;....i:-i..-......,.,..,.•.._ ... . .»_.
• ».i mm m w •; i_i u_ii Pi_^wrP^^^^iwi^fi«^iy^i^w^
• .•
followed by a beam-stop assembly, a third and final rotating
T| mount and the transmitting/receiving lens.
The purpose of the beam-stop assembly is to block out
unwanted orders of the diffraction pattern created by the
Bragg Cells. The order used is the plus first order beam, in
which the proper difference in frequency exists. The
unshifted components (zeroth order) and those of higher
^| order must be blocked in order for a proper Doppler shifted
signal to be provided.
The lens used for this study has a focal length of 120
mm. Other sizes are available from TSI, extending in focal
length up to 600 mm for the model 9100-5. In the present
work, it was found that the increase in the length of the
intersection volume and the lowering of signal-to-noise
ratio which result from the use of the longer focal length
lens or greater beam separation degraded the quality of
measurement. Accordingly, the final configuration selected
was the 120 mm focal length lens with the 22 mm beam
spacing. Since 180 degree backscatter is the intended mode
for this device, the transmitting lens is also the receiving
lens.
The focusing action of the transmitting lens causes the
beams to cross, forming an intersection volume. Light
scattered from the intersection volume by particles flowing
in the fluid is gathered by the same lens and passed back
down the axis of the LDV. It is focused by a lens in the
40
p»—;—j—i—;—i—j—;—;—;—;—;—;—;—;—~—;—;rTT~rn—. j
receiving optics assembly on an aperture, then refocused by
another lens to the photomultiplier tube by way -of a
mirror. The aperture is located in a holder assembly and
can be changed providing larger or smaller size holes.
B. THE LASER DOPPLER VELOCIMETER ELECTRONICS
The optics assemblies, when properly aligned, cause the
image of the intersection volume of the two laser beams to
be focused on the detector surface of a photomultiplier
tube. This tube is powered by an external power supply
equipped with an adjustable gain control. It is also
provided with a self protection feature to prevent "cooking"
the tube should the light intensities encountered be greater
than appropriate for the selected gain. The photomultiplier
tube converts the variations in the intensity of the light
signal emanating from the intersection volume into a voltage
signal varying at the same frequency. This signal is the
raw Doppler signal from which the velocity can be
determined. Figure 6 shows typical Doppler bursts both with
and without the pedestal signal component.
The Doppler burst is caused by the variation in
intensity of the light scattered as a particle passes
through the laser beam intersection volume. Passage of a
single particle through the ellipsoidal volume illuminated
by the fringe pattern causes light to scatter, varying in
intensity at a rate corresponding to the rate at which the
41
w^mmmmmmm^^ar^mmr^mmm^^^mmmm^mrKm^^ Hwi P
••
bright fringes were encountered. The frequency of the
optical signal thus created is the differential Doppler
frequency, a knowledge of which permits computation of the
particle velocity. The envelope of the Doppler signal is
the total length of time occupied by one burst as shown in
Figure 6. A burst is defined as the signal generated by the
passage of one particle through the laser beam intersection
volume.
The photodetector output is sent to the Counter for
processing. It consists of three distinct sections; the
input conditioner, the timer, and the display section. For
the present work, only the first two sections were directly
employed.
The input conditioner's function is to take the raw
signal from the photomultiplier tube and generate either one
or two measurable envelopes for the timer to use, depending
on the mode of operation selected. The N-cycle mode was
used in the present work. In this mode, the input
conditioner generates a signal the envelope of which is of
the same duration as the Doppler burst consisting of N
cycles. Here N refers to the number of cycles which has
been selected on the front panel to be measured in a burst
from one particle passing through the intersection volume.
A second envelope is generated of time equal to that for N/2
cycles to pass. The N/2 cycle envelope is used to validate
the data during processing. These envelopes are generated
42
j.1 -.••.', • !*****9mm****9!**^r*^**m*mimmmmmm • •••• * • 'i.........
I*
1
through the use of Schmitt triggers and threshold detecting
circuitry. A full discussion of the electronics involved is
beyond the scope of this work. For further information
refer to the manufacturer's technical documentation for the
LDV [15].
In the total burst mode, which was not used in this
study, the input conditioner generates one envelope,
corresponding to the time of the total burst. Circuitry is
included to allow counting the number of cycles in the
burst. This mode is useful if the data rate is low and
correction for velocity biasing is required.
The input conditioner also contains filtering circuitry
for the removal of the pedestal component of the signal (the
low limit filter) and for the isolation of noise from the
signal of interest (the high filter). These are adjusted in
combination to provide a signal which is free of spurious
noise while still allowing enough of the signal to pass to
adequately measure the flow fluctuations. Additionally, an
amplitude limit control is provided. Its function is to
reject signals of greater than a specified amplitude. This
has the effect of eliminating signals from larger particles
which may not be adequately following the flow.
The final control on the input conditioner is a selector
which provides control of the number of cycles used in the
N-cycle mode and the minimum cycles required for a valid
burst in the total burst mode. Additional fittings include
43
i,.',' .•, .• 'rr^^^^^r^^^^^^^^^mmtmmmm^m^mmim^m^tr^m^mfmr^fi. T^^^T^^'^^TT^"^^
jacks for the photomultiplier output signal and filtered
output monitor for use on an oscilloscope.
The timer utilizes a high speed digital clock operating
at a frequency of 250 MHz and with a temporal resolution of
1 nsec When the envelope signal from the input conditioner
is gated into the clock, the time for the envelopes to pass
is measured. In the N-cycle mode, the time for N cycles was
compared to the time for N/2 cycles via a direct division.
If the deviation from double the N/2 time exceeds the
percentage selected by switch on the front panel the burst
is discarded. This comparison is not used in the total
burst mode.
On the front panel of the timer section output jacks for
the analog output and direct digital signal output are
found. Additionally, selector buttons and lights indicating
active values are found for the exponent to be applied to
the time signal in the interpretation formula. The
selection of the exponent value can be either manual or
automatic; however, when autoranging is selected, a stable
signal frequently can not be obtained. Accordingly, in the
N-cycle mode in particular, the LDV should be operated in
the manual mode once the magnitude of the exponent for the
current flow level has been experimentally determined.
Autoranging should be used in the total burst mode because
of the wide range of the numbers of cycles and the time for
the burst which will be detected.
44
• J • •."•,,-,lJ,'.'.".'J."?!yw*1 '•l•l••,,'T^*'^^^^^?^^^^»^^^^»*»T^^^*"'.^ IIHH-P
The front panel of the timer also contains a standard
ICC/Cannon 37 pin connector for transmission of control and
readout information directly to a digital computer. The
signals which are available via this connection are as
follows:
1. A 16 bit word consisting of a 12 bit mantissa and a 4
bit exponent representative of time for the burst.
2. An 8 bit word for the representation of the number of
cycles in the burst. This would be useful in the
total burst mode.
3. A one bit data ready signal for computer handshaking.
4. A one bit data hold signal.
5. A one bit single measurement per burst signal. This
can be used for control of some LDV functions from a
remote location.
C. THE COMPUTER AND SUPPORTING ELECTRONICS
The computer used to control data acquisition is a
Hewlett-Packard 9826 microcomputer. It uses a 16-bit word
length and is capable of communicating directly with the LDV
via an interface bus arrangement. Because of the 16 bit
word length, the data transfer arrangement used in the
present work is only appropriate for the N-cycle mode. This
is because there is no arrangement to hold data from the
digital word representing the number of cycles for later
input to the computer. Using the N-cycle mode, the number
45
' •» ' ' •'••-• ' • ' ' ',••'"•"'•' ••"-•••. • •_• > • 11 .1 .'1V.-J .^-l f ,• m ** ,1 rWTI -, . .•-;-..-^-
of cycles per burst to be measured is entered by the
operator at the computer console. This particular HP9826 is
fitted with a standard RS-232C interface and acquired data
is transmitted via modem to a larger computer for
reduction. In the interim, the experimental information is
stored on flexible disks.
For any work involving laser velocimetry, it is
essential that the operator be able to monitor the quality
of the signal being processed. For this purpose an
oscilloscope is irreplaceable. In the present work a
recording oscilloscope capable of dual trace operations and
with an operating range of up to 10 MHz was used. In
general for use in LDV applications, a frequency capability
of up to 100 MHz is desirable.
A frequency generator is required for setup and checkout
of the LDV electronics. It should be capable of up to 1 MHz
output and was sufficiently precise that a stable velocity
reading can be generated.
D. THE SIGNAL PATH
When a particle passes through the intersection volume
of a differential Doppler LDV, such as this one, the light
scattered in all directions is modulated at the differential
Doppler frequency. A lower frequency modulation due to the
variation in light intensity across the beams is also
present and constitutes the pedestal. The light scattered
46
**•"-—a—=—* * '•' '-1 • * ••- -•- - - -•••-. ... . . - . _-_-_ _ . . . . . ... . ........
". '\ •'•••' • ."- "JHJ»'. ••J»l»<.'^f<^^g^l»L«fi I P"^ I'D »I'll. • • !)•'. • . » ]•• mwm -i-n-» ,
K from the intersection volume is focused onto the !.\
photomultiplier tube by the receiving optics. The
photomultiplier tube converts this optical signal to an
electrical signal with a voltage proportional to the
intensity of the light. This photomultiplier tube output is
passed to the input conditioner.
On arrival at the input conditioner, the signal is first
checked by the amplitude limiting circuitry which eliminates
any bursts of excessive amplitude. For the purposes of the
current work, the amplitude limit was not set because the
quality of the data gathered indicated that no particles
sufficiently large to affect accuracy were being processed.
Next the signal is filtered, first by the high pass
filter which is set to eliminate the low frequency component
of the signal, the pedestal. The low pass filter next
removes components of frequency higher than its setting,
which eliminates shot noise in the photomultiplier tube and
thermal source interference. The signal is then ready for
processing by the Schmitt trigger system for generation of
the envelopes.
This new signal is passed to the timer where the leading
and trailing edges of the envelope are gated by the timer
and the signal representing the time of the burst is
generated. From here, the output is passed to the display
section and to the output jacks for the digital or analog
output. In the present work the signal was read off of the
47
-
'*'•••'- '-•• -•-•-^-U.'«l-.«:- M.. ./. ,.". ••.••.-•. r .-•. .: ^ • . . ...... .--.--.'.V.-I.V''. •".-.••*.•".•- _..... ...
I.." i.HI.Wj^^^^^W^^^^^^^^^^^^^* » » • • - T-
2»
37 pin connector in the front panel and processed by the
HP9826.
The signal received by the HP9826 is not directly
interpretable as the time, but yields the Doppler frequency
when used in the following formula:
f. - (N X 109)/(D X 2n"3) a m
Here D is the value of the mantissa of the 16 bit computer m
word, f. is the differential Doppler frequency, n is the
exponent part of the 16 bit computer word, and N is the
number of cycles in the burst, which is entered by the
operator on program initialization and set on the front
panel of the counter.
The computer program under which the process is
controlled applies the foregoing formula and computes the
velocity represented by the sample using the geometry of the
LDV and the following formula:
v = xf/{2sin(#/2)}
Position and orientation data, as well as temperature of jet
and ambient fluid, are entered manually during data
acquisition. All quantities are stored on disk in a logical
format which is directly transferred to the VAX mainframe
48
• mil i i.ii. ii i • i ij i. i • i i ii ^^
I J
computer via the telephone line. It is processed there
using statistical methods to extract the mean velocity, jet
half width, and entrainment coefficients. If desired, the
turbulence intensities and normal component of velocity can
be measured and processed using the computer programs
developed in the present work.
The flow of the signal is schematically represented in
Figure 7.
E. THE FLUID LOOP
The jet studied for the present work was generated in a
tank measuring 0.625 X 0.333 X 0.476 meters. The depth of
the water in the tank was 0.419 meters. The walls of the
tank were constructed of 0.00635 meters thick glass. Flow
was provided by a centrifugal pump via a control valve, a
heater and calibrated rotameter to a nozzle 0.003175 meters
in diameter. The nozzle was located in the tank 0.067
meters from the nearest wall, a distance of 21 diameters.
Temperature was monitored by two thermocouples, the
first embedded in the nozzle block for the measurement of
the temperature of the effluent. The other was located in
the bulk of the fluid in the tank for the measurement of the
ambient temperature.
Early experiments revealed that significant amounts of
heat accumulated in the tank from the injection of the
warmer water in the jet, with the result that the
49
• -- . __- ^J . . •__. -: . . I I -* ' - *-J
PT~ N- .-.-.-. > • , —: »•. » - - -.-.. . --»-•-- -*—- —T—r-, .—. - .- ............. . . • i. I ••».••.
temperature could not be held constant during the course of
an experiment. The situation was corrected by the
installation in the tank of a cooling coil connected to a
constant temperature bath. Subsequent to the installation
of the coils, the temperature remained constant in the tank
over the course of the experiments to within 1 degree
Fahrenheit. It should be noted that the presence of the coil
created temperature gradients in the tank, and a better
system of temperature control should be found for use in
experiments which may require more precise information on
the ambient temperature fields than was required in the
present work.
Early experiments also indicated that significant
circulatory effects were generated in the tank when flow
rates in excess of 40 percent of full scale on the rotameter
were used. Accordingly, flow rates below that point were
maintained for all later work.
Figure 8 is a schematic of the fluid loop used in this
work.
F. POSITIONING APPARATUS
Positional control and support for the LDV were provided
by a milling machine table from which the machine head had
been removed. This arrangement allowed the LDV to be
positioned reproduceably to within 0.0000254 m, (.001
inches), spatially. It was also sufficiently massive that
50
•*.'+.-* -A-•, i,v. v •• v ••• .•••• ....••• .•:..,.•.-.. A< 1 1 I » • I l * • : • I •_ .
^^^^^mm^mwi^*
vibration was minor, and could therefore be discounted as a
source of significant error.
While the movement of the milling machine provided good
control, some hysteresis was present in the left-right, and
fore-aft movements. This effect was minimized by always
approaching desired position in the same direction. Checks
of the method resulted in good accuracy being demonstrated.
G. DATA ACQUISITION PROCEDURES
Flow rates and trace locations for the data acquisition
were selected to provide similar conditions to previous
studies in order to compare results and validate the
technique. While an infinite Froude number initially
appeared to be the best choice, it was unobtainable with the
experimental apparatus. Relatively high Froude numbers, on
the order 200 to 500 were easily attainable and were hence
used.
The height of the first trace was selected to remain
beyond the accepted 6.2 diameters which delineates the Zone
of Flow Establishment (ZFE) from the Zone of Established
Flow (ZEF) in order to keep the expected velocity profiles
as nearly Gaussian as possible. Velocity traces were
obtained at regular intervals to ease positioning. The
number of points in the trace was selected to provide a wide
base on which the curve fit routines could operate, as was
the number of traces made in a given experiment.
51
-»————*—J-~-—»—«—^— *— ------ - ........
11 -• ••»• '•• •• .• • .• 1-^P^^^^^^^» —«—•—•.'•.-:
:•-•
For seeding of the flow field, several substances were
tried without success before powdered alumina was found to
provide very good reflectivity, uniform (relatively)
particle size, and good flow-following characteristics.
Also of concern was the abrasive characteristics of a
seeding particle in the centrifugal pump. The seeding
particle recommended by TSI is silicon carbide, but its
specific gravity is greater than that of alumina and its
increased abrasive qualities were believed to be potentially
prohibitive, as was its cost.
In preparation for data acquisition, the flowmeter was
calibrated using a graduated container and stopwatch.
Calibration curves were constructed and the data fit to a
cubic equation to allow computer determination of the exit
centerline velocity. Analytic expressions for the density
and viscosity of water were also utilized to provide
Reynolds number and Froude number data during computer
calculations.
The alignment of this Laser Doppler Velocimeter proved
to be extremely sensitive to changes in location of the base
and to changes in the angles of the Bragg Cells. While it
was not necessary to repeat the entire alignment process for
each experiment, it was essential that beam concentricity,
beam crossing and power maximization be checked if signal
quality deteriorated. Once beam crossing had been achieved
at one LDV orientation, the device was rotated 90 degrees to
52
. . •-••.•
,i M'V •. ••••;•» • . • . •.»!. i .PI, « i .t • • i fWfwpi J'-J •• •. !•. '•, ^ •. !•[ i IM » in m ,M... ... —„ _„..,, ^..-. -»—.—»—»-
assure that the beams still crossed and that the
intersection volume had not changed in its position relative
to the optics. The latter was easily determined by
positioning the intersection volume on a scatter plate,
marking the spot, and then rotating the barrel of the LDV.
If the laser light moved off the spot during the rotation,
realignment was necessary because of lack of concentricity.
Loss of beam crossing was apparent by a total loss of
Doppler signal.
Once calibration and alignment checks were complete, one
step remained in preparation for data acquisition. This was
the establishment of the spatial reference for the
intersection volume. The center of the nozzle exit was
chosen as the origin of the coordinate system. It was
located by finding the coordinates of the extrema of the
nozzle structure in all three directions and then applying
knowledge of the nozzle geometry to find the center. The
edges of the nozzle were found by observing the filtered
output of the photomultiplier signal on the oscilloscope.
When the intersection volume was precisely centered on the
knife edge of the nozzle, the signal observed on the
oscilloscope was a sinusoid of frequency equal to the
applied frequency shift. A maximum amplitude indicated the
center of the intersection volume was at the reflective
surface.
53
. . » . . . - -
1'-
I
'.•• '.- •«—=-^^—3-;
i
1
After initialization of the data acquisition program on
the HP9826, the LDV was positioned in the test section. The
frequency shift was selected so that the whole range of flow
reversals anticipated could be measured. For the present
work a frequency shift of 500 kHz provided excellent
results. Next, the low filter was adjusted to remove the
pedestal while observing the bursts on the oscilloscope.
Occasionally, the pedestal was not visible through noise in
the signal initially. In that case the high filter was
adjusted first to eliminate enough to see the Doppler
signal. Final filter adjustment was largely a matter of
judgement with respect to how wide the bandpass
characteristics should be set to pass the range of signals
characteristic of a turbulent flow.
After the signal quality had been optimized by the
filter adjustment, the data acquisition proceeded.
Provision has been made in the data acquisition program on
the HP9826 to display the "spectrum" of the velocity data
being accumulated. The display also can be be zeroed at any
time to erase accumulated data. The display was monitored
to observe the distribution of the velocities to monitor
data quality. If several peaks appeared, noise was present
(the distribution should be nearly Gaussian in shape), and
the filters were reset to narrow the passband. In some
cases, the setting intervals on the filters were not At
J • sufficiently fine to narrow the band in the frequency range
54
3
.-•
^^l^^VL^l.'>.,•/'^-l,^'A^.w^^^.'^''>^'^p•''>•,'-Vs'*-|,*.'J'.'•'*'^'•^v V-'1'.- '..*".'". <'."<•*»*.•. • .*•.•*»'-. • .•«-«•• •. • ,:.... l.,.•,.
I currently in use. In that case, a change in the value of
the frequency shift was appropriate, and the frequency- shift
and filters acted together to provide appropriate range.
When signal quality and the distribution of the
accumulated data indicated that good quality information was
being received, the operator stored the information at that
point and proceeded to the next. When to store data was
determined by the number of samples desired for the
statistical base and the quality of the signals being
processed. In the present work, the statistical base
desired was a minimum of 100 data points at each location.
Early experiments provided good experience in filter setting
and selection of the frequency shift, and little trouble was
experienced in later experiments in obtaining both good
signal quality and a Gaussian distribution of the velocity
spectrum during acquisition.
Several experiments could be conducted without the
necessity of completely reducing the data for any previous
ones. The time required to gather data on one velocity
component in a jet at five levels and seven to nine
positions on each level was about one day. The number of
points which were measured for each experiment was limited
simply by the time over which conditions remain constant in
the apparatus.
55
*~mrm~mmm
w
1
H. DATA REDUCTION
Computer programs were developed for data transfer and
reduction as well as the acquisition control process. These
programs were modularized to the extent practical in order
to provide maximum flexibility in application to later
research. Functionally, the programs can be classified as
acquisition, transfer, intermediate reduction, and final
reduction.
The acquisition program resided exclusively in the
HP9826. Its function was to automate the gathering of the
experimental data and to convert raw time data into
velocity. Additionally, the acquisition program recorded
the relative coordinates at which each sample was taken, the
orientation of the LDV for the data set, the flow meter
reading, the temperatures of effluent and bulk fluids, the
date of the experiment, and identifying information for the
data set. Its final output was a set of files on flexible
disk numbered by experiment number and data set within the
experiment.
Data transfer programs were necessary on both the HP9826
and the VAX computer. They acted in conjunction,
communicating over telephone lines to transfer the files
from floppy disk to internal storage in the mainframe. The
process was automatic and progressed without operator
intervention once program execution began as long as all
files to be transferred resided on the same flexible disk.
56
r
1
*•*> H ' 1 • . • ."' •-••»J-t-l.-l
If a particularly long experiment was spread over more than
w one disk, the operator reinitialized the process in order to I ;J change to the new one.
v The purpose of the intermediate reduction program on the -'I
VAX was to consolidate the information contained in the
separate data files associated with an experiment into one
file. In the process, the velocity data was processed
statistically, applying Chauvenet's criterion to reject data
values which deviated excessively from the Normal Error
distribution. This program preserved and recorded all
identifying data such as position and temperature, but
presented the output in the form of a single file which
reported the velocity data in terms of mean velocity and
turbulence intensity for the components measured at each
position. Because this program expected to find files for
streamwise and radial components in its input data set,
dummy files were included for the second component if
studies were conducted in the streamwise direction, only.
This was most easily done in the data acquisition phase of
the process.
Final data reduction was accomplished using a program
which was applicable to the study of axisymmetric jets in a
quiescent ambient only. It arrived at values of B, the jet
halfwidth, and U , the jet centerline velocity, by fitting
the data from each trace directly to an equation for a
Gaussian profile. The values of these quantities for each
57
—
6
1 EH 1
trace were then fitted to power law curves to arrive at
expressions for each as a function of the streamwise
coordinate.
The assumption of the Gaussian profile enabled easy
integration to obtain a simple expression for the volumetric
flow rate in the jet, Q, at each level as a function of
centerline velocity and jet half width. As each of these
was now a known function of the streamwise coordinate,
substitution and differentiation with respect to S yielded
directly an expression for the entrainment coefficient. The
coefficients obtained from the power fits were used to
compute local values of a and to arrive at a mean value and
standard deviation for use in comparisons.
The final reduction program also computed the values of
the exit Froude Number and Reynolds Number using properties
calculated from accepted analytic expressions. All results
were tabulated in program output including coefficients of
determination for curve fits and values of standard
deviation for quantities for which means were computed.
58
I^.^'.^'.t.'-.' " ••'••.-•,•• '"' '.','• •,•!?•' ' ""•' ' "P"'*t • •-•' •!•! • .. .......... . •
v»
1
4
V. CONCLUSIONS AND RECOMMENDATIONS
Ten experiments were conducted during the course of the
present work. Additionally, many sample traces were made
and trial measurements were taken for the purpose of
selecting the optimum seeding particle, optimizing filter
settings, and testing of the alignment of the LDV. Of the
ten experiments, the first six served to develop the
technique to be used and to debug both the apparatus and the
data acquisition computer program.
The final four experiments were conducted using the
procedures refined in the previous six and constitute the
trial set for comparison with previous work and validation
of the technique. Items of specific interest in these
experiments are the following:
1. The verification of the assumed Gaussian velocity
profile over the radial cross section of the jets.
2. The decay of the jet centerline velocity with
streamwise coordinate within the Zone of Established
Flow.
3. The growth of the jet through entrainment of the
surrounding fluid as demonstrated by the variation of
jet half width, B.
59
I
4. The mean entrainment coefficient for each jet, as
computed from the local values at each trace. level
measured.
Each of these will be addressed separately in the
following sections, and numeric results are tabulated in
Appendix B.
A. VERIFICATION OP THE GAUSSIAN PROFILE
Velocity traces were obtained by measuring five to ten
mean velocities across the diameter of the jet at various
downstream positions. Each trace's data was fit to a
Gaussian curve during the first step in the final data
reduction program. Figure 9 is a plot of one trace's least
squares fit curve and the data from which it was
constructed. This trace is typical of the data gathered,
and illustrates both the goodness of the curve fit and the
relative uncertainty as to the actual position in the jet at
which the measurements were made.
While the centerline of the jet nozzle is considered to
have been located quite accurately, examination of the data
for the Gaussian fits and the curves themselves provides
indication that the jet may not have been discharged exactly
vertically. This could lead to some error in the maximum
value of the centerline velocity obtained in lower traces,
but the error will decrease in higher levels of the jet due
•
60
\ .
^^^^w"^^"^•*^^»~*" • • - I'll. 1 j H ••••••%
to the spreading of the jet and the attendant decrease in
the rate of change of the jet velocity radially.
As can be seen from the sample trace, the assumption of
a Gaussian profile is valid to within the precision of
measurement possible in a turbulent flow.
B. THE GROWTH OF JET HALFWIDTH
Figure 10 presents the behavior of the jet width as a
dimensionless quantity plotted versus a non-dimensional
distance down the jet axis. Experiments 8 through 10 are
remarkably consistent, particularly at higher values of the
streamwise coordinate. The values of the data for
experiment 7 deviate in both slope and intercept for reasons
which will be discussed later in the chapter.
For comparison, the predicted value of the quantity B/D
using the relation proposed by Albertson [8] is plotted.
The results of experiments eight through ten indicate a
uniformly greater width than the model for jets of infinite
Froude number. This is to be expected in view of the
increased rate of entrainment which is predicted with
decreasing Froude number.
C. THE DECAY OF CENTERLINE VELOCITY
The decay of the centerline velocity found in the four
experiments is plotted in Figure 11, along with a curve
formulated from Albertson's model for infinite Froude
number. Once again, the data for the final three
61
!.•-.•->..••. .-.•• .,i.'4'..',' -•,-•.-.-•••"•. .-.-..,.:-.-:«•..... — .-..-.,.^........... ...... ... ., .... . .•-. ..... ..-.• .-. ,
^^^^m^^^m*^^^^^^^^^m^^^^^^^^^^^^^^^m*m* ••••-••. ••!••. -! •••• . . ,.,.,, .t...,.
experiments shows remarkable consistency, and that for
experiment seven deviates substantially.
The data for experiments eight through ten demonstrate a
decreasing rate of decay of the centerline velocity with
decreasing Froude number as evidenced by their slopes on the
plot. The slopes fall between the value predicted
(variation as 1/S) by Albertson for F = oo and by the
-1/3 variation as S ' predicted by Rouse [14] for F • 0. The
decrease in decay rate can be explained by the effect of
increasing buoyancy forces with decreasing Froude number.
The experimental data presented here is considered to agree
very well with theory.
Extrapolation of the plots of data in Figure 11 reveals
one more item of interest. The definition of the Zone of
Flow Establishment fixes the demarcation between it and the
Zone of Established Flow as that point at which turbulent
mixing reaches the centerline of the jet. At this point,
the centerline velocity will start to decay. Applying this
definition, the Zone of Established Flow can be seen to
start well before the 6.2 diameters predicted by Albertson.
The change is attributable to the increase in the
entrainment rate for a buoyant jet over the pure momentum
jet studied by Albertson.
62
.•uu'.-.'^'-.-',.-,. • • ..••^•i-i'v, -., .1.. .- . . . . . . -.,- ^ .....,-..;.
^^^^^^m^mmmi^^m—^9mim*mmm^mmimmB**m ^w—w~
D. THE ENTRAINMENT COEFFICIENT
Figure 12 plots the mean entrainment coefficients
determined in experiments seven through ten with a curve
computed from Davis's relation [13]. The values computed for
experiments eight through ten continue to conform to
predicted values while experiment seven deviates.
Examination of the values of entrainment coefficient
computed locally in the jets shows a decrease with
streamwise coordinate in all cases except for experiment
eight, where it remained relatively constant. For an
initially buoyant jet, the decrease in entrainment
coefficient with distance is expected as the local buoyancy
difference decreases. This is reflected in an increase in
the local Froude number and a decrease in a which is
predicted by all entrainment models. Experiment seven
exhibits this behavior even while not conforming to the
value predicted for the mean value of the entrainment
coefficient.
A comparison of the obtained local entrainment
coefficients with theory was not possible because of a lack
of local temperature data. However, the maximum entrainment
coefficient predicted by the model of Hirst [12] for the
four experiments is 0.061, a value applicable only at the
nozzle exit for experiment ten. At the earliest point
measured in experiment ten, a distance of eight diameters
downstream, the measured coefficient was 0.076. Since the
63
•».»..». i. h» i. i. i.i.r. a »•..••;:. I. •^.^•.i.r.,. .-. ...... .. . ... .... I - - - I .........
qpfPfM^PVPpHViapBaiMVWva« - •. • i«. • -. •
entrainment coefficient can not increase with distance, as
~ buoyancy forces are decreasing in that direction, data from
•y-i these experiments can be seen to be at variance with the " "w
model of Hirst.
M E. THE JET OVERALL VELOCITY DISTRIBUTION
I-;! Figure 13 is the distribution of velocity throughout the
}';_ jet measured in experiment eight. The plot was constructed
• using the coefficients of the curve fits for B and U and
>v the Gaussian velocity profile. It is representative of the
data obtained in all four experiments. On this plot the
P! variation of halfwidth and centerline velocity and the
Gaussian distribution of velocity with radial distance can "4 all be seen.
F. THE VARIANCE OF EXPERIMENT SEVEN *
Experiment seven was conducted with the highest exit
velocity of the four final trials. The flowmeter setting
for this set of data was forty percent of full scale, a
value which was estimated from earlier trials to be low
enough to eliminate the effects of recirculation in the
tank. The recirculation effects at higher velocity were
observable due to the presence of the alumina seeding
particles in the tank. It resulted in an ambient which,
instead of being quiescent, was coflowing with the jet
discharge. Entrainment coefficients in early trials were
significantly lower than expected, and the rate of jet
64
•J •I'.IV.V V V V / -| ,;.; . ." , fc^jB^a^iii^ MM
w^>^mmmmmmm-mm*mmmmm~mm*mm~m*^^~
growth and decay of centerline velocity decreased as a
result.
The phenomenon can be explained by considering the cause
of entrainment of fluid into the jet: viscous shear at the
jet boundary. The viscous shear is a function of the rate
of change of fluid velocity at the point in question, and
that rate of change is lower if the ambient has some
component of velocity in the same direction as the jet.
Reduced viscous shear results in reduced entrainment, which
in turn results in a decrease in the rate of decay of
centerline velocity as well as jet growth.
While no recirculation was apparent in the tank during
data acquisition for experiment seven, the behavior of the
jet indicates that some amount was present. Specifically,
the lower rate of decay of centerline velocity and the lower
growth rate of the jet dimensions indicates the lower rate
of entrainment into it. This is directly reflected in the
much lower values of a found.
G. RECOMMENDATIONS FOR FURTHER STUDIES
The length of the Zone of Flow Establishment is a topic
for which no predictive relations have yet been developed.
The Laser Doppler Velocimeter is a tool which can be
effectively used to study flow field changes during the
transition from establishing to established flow. It
possesses the ability to be positioned precisely and will
65
;*.-«*• • • »• i i • i.-.i. j ; j ...••;••:.. -..i . .- . . _ . , . j__^ j ^_, , . . . . _^
"!.-'«• • • • I .ill q.i«!H. ^11 »'I.IMI, 1^ lim,!,!!',!,!!!.»!!!!!.,! j.,. -... ~~-—~- .-.-: • •
not affect the flow characteristics because of its
non-intrusive nature. Further, the intersection volume can
be made small enough through the selection of the proper
combination of beam spacing and focal length to provide
extremely fine spatial resolution of measurements.
The body of literature on turbulent buoyant plumes in
cross flow environments currently in existence assumes axial
symmetry of the jet. In fact this is not the case. The LDV
can be used to fully characterize the flow field in this
environment. For this use, however, a very fine spatial
grid will have to be studied in order to yield the third
component of velocity through the use of the continuity
eguation. This requirement renders an exact knowledge of
the trajectory of the jet mandatory in order to optimize the
measurement procedure. The trajectory of the jet could be
determined by dye injection or by investigation of the
temperature field to determine in advance the grid of
positions at which the velocity should be measured.
Temperature data throughout the jet would also be useful in
developing exact correlations involving the local Froude
number, which would be a more appropriate quantity than the
exit Froude number in characterization of local behavior
within the jet.
In consideration of the apparent differences reported in
this report with the model of Hirst, further studies on
buoyant jets discharged into a quiescent ambient should be
66
'•,'''''1'ti:i'1'1 '' »•'•*• »' » '"• *•"" • ••••'• •»--*-• -- •--.- ... _ -. _• _ . . _
WV w«m
•
conducted to confirm the difference and to propose an
improved value for a-, Hirst's empirical constant in the
relation for entrainment coefficient as a function of Froude
Number. To accomplish this with accuracy, a larger tank and
improved system for flow control should be installed to
improve reproduceability of the settings and provide for a
more nearly infinite ambient into which the jet may be
discharged. A larger tank would also obviate the need for a
system for the removal of heat from the tank, thus removing
the artificial temperature gradients introduced to the
system by the coil. A system for measurement of the
temperature field should also be installed to provide for
determination of the local Froude number.
H. SUMMARY
The Laser Doppler Velocimeter is a viable and accurate
tool for measurement of the velocity distribution in
turbulent buoyant jet3. The studies conducted during the
present work showed good agreement with the results obtained
by other methods in separate studies. Inaccuracies in the
results can be attributed to non-availability of specific
data (e.g. local temperature) or to imprecision of the
positioning mechanism or metering devices used, and not to
the LDV itself.
67
l-.*r--._..*.«• T' - - - - . - > - - »- » - • - *J
m mi i Mm^^m^9mi i i i in ,..,.,.,, .,.«•
LIST OF REFERENCES
1. Yeh, Y. and Cummins, H.Z., "Localized Fluid Flow Measurements With an He-Ne Laser Spectrometer", Appl. Phys. Lett., pp. 176-178, 1964.
2. Cummins, H.Z., and Yeh, Y., "Observation of Broadening of Rayleigh Scattered Light", Phys. Rev. Lett., Vol 12, pp. 150-153, 1964.
3. Drain, L.E., The Laser Doppler Technique, Wiley 1980.
4. Hecht, E. and Zajac, A., Optics, pp. 278-325, Addison-Wesley 1974.
5. Schlichting, H., Boundary Layer Theory, 7 ed, pp. 729-755, McGraw-Hill, 1979.
6. Gebhart, B., Hilder, D.S., and Kelleher, M. "The Diffusion of Turbulent Buoyant Jets", to be published in Advances in Heat Transfer, v. 16, 1983.
7. Morton, B.R., Taylor, G.I., and Turner, J.S., "Turbulent Gravitational Convection from Maintained and Instantaneous Sources", Proceedings of the Royal Society
L-; of London, v. A234, pp. 1-23, 1956.
8. Albertson, M.L., Dai, Y.B., Jensen, R.A., and Rouse, H., "Diffusion of Submerged Jets", Transactions ASCE, v. 115, pp.
9. Abraham, G., "Horizontal Jets in Stagnant Fluid of Other Density", Proceedings ASCE, Journal Hydraulics Division, v. 91(4), pp. 139-154, 1965":
10. List, E.J., and Imberger, J., "Turbulent Entrainment in Buoyant Jets and Plumes", Proceedings ASCE, Journal Hydraulics Division, v. 99(9), pp. 1461-1474, 197T.
11. Fan, L.H., and Brooks, N.H., "Numerical Solutions to Turbulent Buoyant Jet Problems", California Institute of
r.G Technology, W. M. Keck Laboratory, Report KH-R-18, 1969.
12. Hirst, E.A., "Buoyant Jets Discharged to Quiescent Stratified Ambients", Journal of Geophysical Research, v. 76(30), pp. 7375-7384, 1971.
Ml *
68
•ppfW^^^JFW^^P^ • J—•—
V.
1 ."-. &«
i
*
t.
13. Davis, L.R., Shirazi, M.A., and Siegel, D*L*' "Measurement of Buoyant Jet Entrainraent from Single and Multiple Sources", Journal of Heat Transfer, v. 100(3), 1978.
14. Rouse, H., Yin, C.S., and Humphreys, H.W., "Gravitational Convection from a Boundary Source , Tellus, v. 4, pp. 201-210, 1952.
15. TSI, Incorporated, Instruction Manual, Model 1990 Counter Type Signal Processor for Laser Velocimeter.
16. Holman, J.P., Experimental Methods for Engineers, 3 ed, pp. 44-51, McGraw-Hill, 1978
69
yyyr>!BBWffi!"PW"wpw||p|*!P!|"!y?*i!|ffP^ -.:
APPENDIX A
ANALYSIS OF ERRORS
Error analysis for the present work is accomplished in
three levels. The first of these is the determination of
the precision to which basic quantities such as spatial
location and time can specified. Where available, the
tolerances reported in the manufacturer's specifications for
the device have been used as the source. If the quantity
can not be determined from the technical documentation, the
precision has been estimated from the fineness of scale or
reference used in the operation of the equipment. The basic
quantities and their estimated error are as follows:
1. Time (Counter-Tracker), 1 nsec
2. Time (flowmeter calibration), 0.1 sec.
3. Volume (flowmeter calibration), 5% of the quantity
measured (1000 ml)
4. Spatial location, 0.001 inches (2.54 X 10 ' meters)
5. Beam separation at the transmitting lens, 0.1 mm.
6. Focal length of the transmitting lens, 0.05 mm.
-12 7. Laser light wavelength, 5.0 X 10 m.
For the second level of analysis, the uncertainties of
the variables which were computed from formulas involving
70
;••?, the basic quantities were estimated using the method of
Kline and McClintock [16]. The uncertainties are:
b-:,, 1. Radial position in the jet (left to right), 0.110 mm.
\\
I 2. Streamwise position in the jet, 0.110 mm.
3. Radial position in the jet (in and out), 0.205 mm.
4. Mean flow velocity, (flow meter), 5% of the scale
reading.
5. Beam crossing half angle, 0.000819 radians.
6. Frequency of the Laser Doppler signal, 62.5 Hz at a
signal frequency of 1 MHz.
7. Particle velocity, 0.032 m/sec at a signal frequency
of 1 MHz, corresponding to a velocity of 3.50 m/sec.
or approximately 1% of the velocity.
For the third level of analysis, the root mean square
error between the curve fit computed values and the input
data values for U and B, both at the trace to trace level m
and throughout the jet was computed. The standard deviation
was also computed for the value of the mean entrainment
coefficient. The error of the predictive equations in
reproducing the data was on the order of ten percent of the
value of the data point.
The percentage error expected in the values of the
measured velocity using the LDV is seen to be less than one
percent. The quantity is very sensitive to the precision of
the alignment of the optics. The dominant factor in the
computation is the error in beam separation distance.
71
K
K £i&
Accordingly, it should be noted that extreme care must be
taken while crossing the beams to move only in a direction
perpendicular to the plane in which the beams lie. Movement
within the plane of the beams will alter the crossing angle
and subject the measurement process to substantial systemic
errors.
The reproduceability of the positioning data is
considered to be good, but the uncertainty of the actual
position of the intersection volume in the jet itself is
considered to exceed the values quoted for spatial
accuracy. The reason for this is the indication of a
deviation from vertical of the jet trajectory by as much as
one degree. Accordingly, the radial location reported for
the jet data points is considered to be truly accurate to
within no better than one millimeter. This is considered to
be the principal cause of error in the fitting of the data
to Gaussian curves.
The probable presence of circulatory effects in the tank
can be considered to be the primary cause of the deviation
of the data for experiment 7 from predicted behavior. It
should be noted that an "inversion" of the behavior of both
centerline velocity and jet growth occurred in the body of
the jet. Specifically, the centerline velocity increased
from one level to the next, and the half width decreased.
Given the accuracy of the LDV in determining velocity, it is
considered that the trend accurately reflects the actual
72
^»•• • .•'•'• • '• •
R:
i behavior of the flow field and that the change was the
result of forces external to the jet itself. Similar- local
inversions of the expected trends were observed in jets of
;.\ earlier experiments in which recirculation within the tank
was clearly visible.
Eg
:•' 73
:-.--.-. .---. ..<.-..-.-.-.-- • -. . -.-.- .- .- - -...,-.-- . .. .. . ......
• Eg
itt
1
Cfr
APPENDIX B
TABULATED RESULTS
Tabulated below are values of interest which were
obtained from the curve fitting routines. The local values
of the centerline velocity and jet half-widths are computed
~M using the Gaussian profile assumptions. They were in turn
fitted to the power curves yielding the equations given.
The coefficients were then used to compute the value of the
entrainment coefficient.
Experiment 7
Exit Froude Number 456 Exit Reynolds Number 7836 Nozzle Exit Centerline Velocity 2.54 m/sec
B(mm)
3.97 5.79 9.55 8.74 12.88
r-J
Coefficient of Determination
*• U - .116S"*""*' .852
••;
S (mm] U (m/sec) m
25.4 .806 50.8 .725 76.2 .415
101.6 .457 127.0 .333
Power curve fit equation
U • . m 116S" .549
B • .0505S* 699 .934
Mean entrainment coefficient .049 Standard Deviation .012
74
!''•".•'•'"•• •>••••••••?'
Experiment 8
Exit Froude Number 365 Exit Reynolds Number 7004 Nozzle Exit Centerline Velocity 2.22 m/sec
S (mm! U (m/sec) m B(mm)
25.4 .983 3.05 50.8 .543 6.59 76.2 .376 9.45
101.6 .457 12.02 127.0 .236 16.70
Power curve fit equation Coefficient of Determination
U = . m 0408S" -.867 .996
B • .1327S1 023 .996
Mean entrainment coefficient .073 Standard Deviation .007
Experiment 9
Exit Froude Number 317 Exit Reynolds Number 5954 Nozzle Exit Centerline Velocity 1.91 m/sec
S (mm) U (m/sec) m B(mm)
25.4 .680 3.92 50.8 .534 5.80 76.2 .327 9.24
101.6 .260 12.94 127.0 .196 17.82
Power curve fit equation Coefficient of Determination
U = .0429S-*783 m .944
B = .HIS'940 .965
Mean entrainment coefficient .072 Standard Deviation .008
75
^r»y»
Experiment 10
Exit Froude Number 239 Exit Reynolds Number 5123 Nozzle Exit Centerline Velocity 1.59 m/sec
S (mm) U (m/sec) B(mm) _ m_ ___„,_
25.4 .527 3.78 50.8 .427 6.17 76.2 .275 9.24
101.6 .203 13.90 127.0 .173 14.93
Power curve fit equation Coefficient of Determination
U = .0409S"'726 .940 m
B = .0974S'897 .983
Mean entrainment coefficient .069 Standard Deviation .009
76
i^vv;,;v.-Vv.-.--•:-•>•••. ,•• • - •: •.••:.-.
TTT •-'* ',• '•,".'.' • • •, U'.— .,» ••"••• . • ,• ,H. 1 , • , I I • I11 ll'i !• 'I .• . • • . • . I J .•'.».
APPENDIX C
FIGURES
PARTICLE SOURCE
SCATTERING VECTOR I OBSERVER
VELOCITY VECTOR
Figure 1. Geometry of Doppler Shift Model
77
'.••.-V.-VVVV"vV" •-.-..,• . -- • - • - - -• i - - • • i ix
i '."•'71 '."•' '.^- '.* ."• !s" ."-.' .' •' • » • I "T^Tf^T^^^^^^^
'
•
»I • . • | - Jw . •
BEAMSPLITTER
A LASER y-
FILTER
Figure 2. Typical Reference Beam LDV Arrangement
78
-•"-• -••-'»'-''••••••'• ;r'ii-'- -:- --iiY ' tLt-..l.,r.,-.i.Mi>iJj^^.>ixj^.J.;.-... • • *j_ ._• —i-*
1^^^^^^^^^^^^^*^.'."_.. . '•.". :\ ••. *•. :-;• .-.•'••: • . -•-
Figure 3. Fringe Model Interference
79
«-• •-• -: •-' •- - - --'----- - - •-'•-•-•• •.....• i ••»••> • •—•—^-^-^^-^^•*-*~«^«*«
f^^r • -•••»' •• 1 » " " i i i I pi ji ^^^rmm. i • j • • ... . .
DETECTOR
Figure 4. Typical Differential Doppier LDV Arrangement
80
i- - • • «."-.• •„• •.' -.'•.' -.' •„• -,•' • •/ .• •.' •.' .• •' • .• •. '. "-.'-v*.* .«* •<* J> »•• ^ «r i* «' •• •• »' I»', i i •" .iT «' » •!• •' • •
-P. i... .> 5 l'.U" J . !•.•.'•'. ' - - -. • - "—'
BEAM PATH OUTBOUND
BEAM PATH INBOUND
FOCUSING LENSES
8 7
n-Ni v
LASER
1 I
I If
2 I
\
/
1. APERTURE AND REAR ROTATING MOUNT
2. BEAMSPLITTER MODULE
3. FREQUENCY SHIFTING MODULE WITH BRAGG CELLS
4. BEAM STEERING MODULE
5. RECEIVING OPTICS ASSEMBLY
6. BEAM EXPANDER
7. BEAM STOP ASSEMBLY
8. TRANSMIT/RECEIVE LENS
9. PHOTOMULTIPLIER TUBE
Figure 5. LDV Optics Arrangement
81
- - ^ • - AJ^ - • - •'- *', • ••••_• «.-w. • • • - - • - - --—-——a--
m ,j • I . • I. !• I '.' »V U1, II . !•• I» *'. '•*. •* ' »V V. tf J*. V,»."
i
i
i -. r
Fig 6. Doppler Bursts o
o CO
o pi-
O Ö > o
CM i
O CO
I o
With Pedestal
-T 1 1 1 1—i 1 1 1 i i 1 r -i 1 1 1 r—i 1 i
0.0 1.0 2.0 3.0 Time
o •*•
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+* O O O > o
o •
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I o
Without Pedestal
T 1 i i l 1 1 1—i 1 1 1 i i 1 r
0.0 1.0 2.0 3.0 Time
4.0 5.0
i—'—i—i—•—i 4.0 5.0
• pi >. i. • «. I', vm'. ?^^i^^3 ii 11 i.ii • .^ »'•.'• .'.«.«—r . W . - ' i". • •—= • C"
2i
FILTERS
INPUT CONDITIONER
I SCHMITT
TRIGGER CIRCUIT
1 J
TIMER
PHONE LINE
^T HP9826
Figure 7. Signal Flow Path
«•*
««(f!WWf«ff5ff wm i •••--.. ..
:-:•
••:•
i -•
•
DRAIN
PUMP
M Figure 8. Experimental Apparatus Fluid Loop
84
mm ^^^w .". v". *»., «•. i; i.. i,
-.-
V
Si
•
O o CO
2 o © E
o o CO
Fig 9. Jet Velocity Profile
r in mm
85
fT« V l','^V'A'''.^,*'',V^. .'-"A' KmV* J .*-'*-"' .»'.'^1 • >".;l'."." 'T'T^^^^^rT^T' .• !• !"•! •! •!•••' - . - » - -T -
1 Fig 10. Growth of Jet Width
*
1
•:-:
5*10" 10' 1(f Dlmensionless Axial Distance, S/D
86
w^1 mm • » • ' • W>.' i •.»i" L" i« «;• ••"••• '"'!"-'.'-".,-"-;':;-•*.'-"• ..•"".- »."*•• '-• *•• '^.T.^.yif.
i Fig 11. Velocity Decay of Jet
•
v
; J
I
y.
5M0 101 itf Dimensionless Axial Distance, S/D
87
SV
*
nwmrwpufi •,•»•. v. t,' v. i".
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Fig. 12 Entrainment Coefficient
-".•
<D <D
— o
© O »
C o es w
CM
o .
LEGEND Q Experimentally Determined
— Davis et al.
i i i i i ' ' • ' i i i—i i i
200 250 300 350 400
Froude Number
-*—r-1-
450 500
88
^^^^ J . . •—5-
> ' f.:.«
N Fig 13. Streamwise
Jet Velocity Distribution
r:
••••."iii"»*
89
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a
i APPENDIX D.
c.
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INITIAL DISTRIBUTION LIST
No. Copies
1. Library, Code 0142 2 Naval Postgraduate School Monterey, California 93940
2. Dr. Paul J. Marto 1 Department Chairman, Code 69 Department of Mechanical Engineering Naval Postgraduate School Monterey, California 93940
3. Dr. William Culbreth, Code 69Cb 4 Department of Mechanical Engineering Naval Postgraduate School Monterey, California 93940
4. Dr. M. D. Kelleher, Code 69Kh 1 Department of Mechanical Engineering Naval Postgraduate School Monterey, California 93940
5. LCDR Mark D. Wessman, USN 1 USS Cayuga (LST 1186) FPO San Francisco, California 96662
6. Defense Technical Information Center 2 Cameron Station Alexandria, Virginia 22314
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