Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1983

Measurement of velocity distributions in turbulent

jets using a laser doppler velocimeter.

Wessman, Mark Donald.

Monterey, California. Naval Postgraduate School

http://hdl.handle.net/10945/19880

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Dudley Knox Library. NPS

Monterey. CA 93943

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISMEASUREMENT OF VELOCITY DISTRIBUTIONS IN

TURBULENT JETS USING A LASERDOPPLER VELOCIMETER

by

Mark Donald Wessman

June 198 3

Thesis Advisor: W. G. Culbreth

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Measurement of Velocity Distributions inTurbulent Jets Using a LaserDoppler Velocimeter

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Master's ThesisJune 198 3

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Mark Donald Wessman

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Naval Postgraduate SchoolMonterey, California 93940

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It. SUPPLEMENTARY NOTES

'*• KEY WORDS iContinue on rewerae aide II neceeemry and Identity by block number)

Laser Doppler VelocimetryTurbulent Buoyant JetsLaser Anemometry

Turbulent Buoyant Plumes

20. ABSTRACT (Continue on reveree aide II neceaaary end Identity by block number)

The theory of operation of Laser Doppler Velocimeters isdiscussed for both reference beam and differential Doppler modes.Current entrainment models for velocity distributions in verticalaxisymmetric buoyant jets in a quiescent ambient are reviewed. Aspecific Laser Doppler Velocimeter is used to measure the velocitydistribution found in a vertical, axisymmetric turbulent jet

(continued)

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discharged into a quiescent ambient and the results arecompared to theory.

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Measurement of Velocity Distributions

in Turbulent Jets Using a

Laser Doppler Velocimeter

by

Mark Donald WessmanLieutenant Commander, United States Navy

B.S., University of Utah, 1971

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLJune 1983

1Mi

Dudley Knox Library, NPS"erey, CA 93943

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.

TABLE OF CONTENTS

I. INTRODUCTION 11

II. LASER DOPPLER VELOCIMETRY 15

A. THE REFERENCE BEAM TECHNIQUE ANDTHE DOPPLER SHIFT 15

B. THE DIFFERENTIAL DOPPLER TECHNIQUEAND 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 QUIESCENTAMBIENT 31

C. SUMMARY OF PREDICTED 3EHAVI0R 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

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

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

TABLE OF SYMBOLS

B Characteristic jet width (L)

D Jet discharge diameter (L)

2E Volumetric entrainment rate, dQ/dS (L /T)

1/2F Densimetric Froude number, U /D{(gD(p -P I p )}o ^ a o o

2F T Local densimetric Froude number, U /{gB(p -p) I P. )

f Frequency (Hz)

2g Gravitational acceleration (L/T )

3Q 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

Angle of beam crossing, angle between lines ofsight in reference beam mode.

^ Angle between velocity vector and fringe patternnormal, angle between velocity vector and thescattering vector.

X Laser light wavelength (L)

P Density (M/L3

)

SUBSCRIPTS

a Ambient condition

d Doppler shift

m Evaluated at local jet centerline

o Evaluated at the centerline of the nozzle exit

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

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 the 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

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

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 centerline 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

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

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

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)a

where v is the particle velocity, X is the wavelength of the

light, and is the angle between the direction of

scattering and the particle velocity vector, and e 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

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

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

14laser at a frequency of 4.7 X 10 Hz, a ratio of 7 parts in

g10 ) . 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.

VThen 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

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

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 6, 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 )cos4sin($/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

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

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

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

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 detector. 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

23

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

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.

F. 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

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

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 the 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

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

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

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

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 oc 2nBUm

Here E represents the volumetric rate of entrainment into

the jet, B is some characteristic dimension of the jet yet

to>be defined, and U is the mean centerline velocity of them J

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 = 2»raBUm

31

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(-r 2/B

2)m ^ '

2Here B is twice the variance from the mean centerline

32

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:

P = U /!gD(,a-P

o )/po }

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, the local

33

Froude number is used. It is defined as:

F. = U2/{gB( P-Pm )/Pm )L m 3 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

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 = 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* 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

35

data. Their velocity decay data showed a decrease in the

rate of decay with decreasing Froude number. This is

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

-1/3plume 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

-1/3proportional 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 them

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

IV. APPARATUS AND PROCEDURES

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

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

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

followed by a beam-stop assembly, a third and final rotating

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

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

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

•

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

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

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

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

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

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)/(Dm X 2

n~ 3)d m

Here D is the value of the mantissa of the 16 bit computerm c

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 = Af/{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

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

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

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

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

center line 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

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

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

sufficiently fine to narrow the band in the frequency range

54

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

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

If a particularly long experiment was spread over more than

one disk, the operator reinitialized the process in order to

change to the new one

.

The purpose of the intermediate reduction program on the

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

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

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

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 OF 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

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

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

-1/3variation 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

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

entrainment coefficient can not increase with distance, as

buoyancy forces are decreasing in that direction, data from

these experiments can be seen to be at variance with the

model of Hirst.

E. THE JET OVERALL VELOCITY DISTRIBUTION

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 and3 m

the Gaussian velocity profile. It is representative of the

data obtained in all four experiments. On this plot the

variation of halfwidth and centerline velocity and the

Gaussian distribution of velocity with radial distance can

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

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

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

equation. 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

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 jets. 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

LIST OF REFERENCES

1. Yeh, Y. and Cummins, H.Z., "Localized Fluid FlowMeasurements With an He-Ne Laser Spectrometer", Appl

.

Phys. Lett. , pp. 176-178, 1964.

2. Cummins, H.Z., and Yeh, Y. , "Observation of Broadeningof 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. "TheDiffusion of Turbulent Buoyant Jets", to be published inAdvances in Heat Transfer , v. 16, 1983.

7. Morton, B.R., Taylor, G.I., and Turner, J.S., "TurbulentGravitational Convection from Maintained andInstantaneous Sources", Proceedings of the Royal Societyof 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 OtherDensity", Proceedings ASCE, Journal Hydraulics Division ,

v. 91(4), pp. 139-154, 1965.

10. List, E.J., and Imberger, J., "Turbulent Entrainment inBuoyant Jets and Plumes", Proceedings ASCE, JournalHydraulics Division , v. 99(9), pp. 1461-1474, 1973.

11. Fan, L.H., and Brooks, N.H., "Numerical Solutions toTurbulent Buoyant Jet Problems", California Institute ofTechnology, W. M. Keck Laboratory, Report KH-R-18, 1969.

12. Hirst, E.A., "Buoyant Jets Discharged to QuiescentStratified Ambients", Journal of Geophysical Research ,

v. 76(30), pp. 7375-7384, 1971.

68

13. Davis, L.R., Shirazi, M.A., and Slegel, D.L.,"Measurement of Buoyant Jet Entrainment from Single andMultiple 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 1990Counter Type Signal Processor for Laser Velocimeter .

16. Holman, J. P., Experimental Methods for Engineers , 3 ed

,

pp. 44-51, McGraw-Hill, 1978

69

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)

-54. Spatial location, 0.001 inches (2.54 X 10 meters)

5. Beam separation at the transmittinq lens, 0.1 mm.

6. Focal lenqth of the transmittinq lens, 0.05 mm.

-127. Laser liqht wavelenqth, 5.0 X 10 m.

For the second level of analysis, the uncertainties of

the variables which were computed from formulas involvinq

70

the basic quantities were estimated using the method of

Kline and McClintock [16]. The uncertainties are:

1. Radial position in the jet (left to right), 0.110 mm.

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 3, both at the trace to trace levelm

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

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

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.

73

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

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 7836Nozzle Exit Centerline Velocity 2.54 m/sec

S (mm) U (m/sec) B(mm),_5}___1 ,_ 1

25.4 .806 3.9750.8 .725 5.7976.2 .415 9.55

101.6 .457 8.74127.0 .333 12.88

Power curve fit equation Coefficient of Determination

U = .116S* 3**

.852m

. 699B = .0505S .934

Mean entrainment coefficient .049Standard Deviation .012

74

Experiment 8

Exit Froude Number 365 Exit Reynolds Number 7004Nozzle Exit Centerline Velocity 2.22 m/sec

S (mm) U (m/sec) B(mm)_m____ __

25.4 .983 3.0550.8 .543 6.5976.2 .376 9.45

101.6 .457 12.02127.0 .236 16.70

Power curve fit equation Coefficient of Determination

U = .0408S"*867

.996m

B = .1327S1 ' 023

.996

Mean entrainment coefficient .073Standard Deviation .007

Experiment 9

Exit Froude Number 317 Exit Reynolds Number 5954Nozzle Exit Centerline Velocity 1.91 m/sec

S (mm) U (m/sec) B(mra)_m__ _ _

25.4 .680 3.9250.8 .534 5.8076.2 .327 9.24

101.6 .260 12.94127.0 .196 17.82

Power curve fit equation Coefficient of Determination

U = .0429S*

.944m.940

B = .HIS .965

Mean entrainment coefficient .072Standard Deviation .008

75

Experiment 10

Exit Froude Number 239 Exit Reynolds Number 5"123

Nozzle Exit Centerline Velocity 1.59 m/sec

S (mm) U (m/sec) B(ram)_ m

25.4 .527 3.7850.8 .427 6.1776.2 .275 9.24

101.6 .203 13.90127.0 .173 14.93

Power curve fit equation Coefficient of Determination

U = .0409S"*726

.940m

B = .0974S .983

Mean entrainment coefficient .069Standard Deviation .009

76

SOURCE

APPENDIX C

FIGURES

PARTICLE

SCATTERING VECTOR OBSERVER

VELOCITY VECTOR

Figure 1. Geometry of Doppler Shift Model

77

BEAMSPLITTER

/-

LASER

FILTER

Figure 2. Typical Reference Beam LDV Arrangement

78

Figure 3. Fringe Model Interference

DETECTOR

FLOW

Figure 4. Typical Differential Doppler LDV Arrangement

80

BEAM PATH OUTBOUND

BEAM PATH INBOUND

LASER r/

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

o

q :

co~

o :

r4l

¥-» O .

>O -I

O A

i

oCO

I

o

0.0

o<fr

qCO

q

±f oO d>

o

q

q :

COi

o H

i

Fig 6. Doppier Bursts

With Pedestal

1.0 2.0 3.0

Time

Without Pedestal

i i1 r i i i r i i i ~

o.o 1.0 2.0 3.0

Time

— i—i—i—i—.—

i

4.0 5.0

t 1 1 r

4.0 5.0

82

(V)r

FILTERS

INPUT CONDITIONER

SCHMITT

TRIGGER CIRCUIT

1 J

TIMER

Figure 7. Signal Flow Path

83

DRAIN

' CONTROL VALVE

AAS ELECTRIC HEATER

PUMP

Figure 8. Experimental Apparatus Fluid Loop

84

Fig 9. Jet Velocity Profile

0.6

i—e—

i

-e-

O<DCO^»COk-

<D•»—

•

<D

Ec

ooo

0.5

0.4-

0.3-

0.2

0.1-

Least squares fit

e—

i

LEGEND° = Actual data

o.o -i—i—i—i—i—i—i—i—i—|—:—i—i—i—i—i—i—i—i—I—i—i—i—i—i—i—i—i—i—|—i—i—i—i—i—i—i—

r

-10.0 -5.0 0.0

r in mm5.0 10.0

85

Fig 10. Growth of Jet Width

5*10 10 10Dimensionless Axial Distance, S/D

86

Fig 11. Velocity Decay of Jet

Do.

E3

oo©>COCO

©coCOc

E

—

Data3

o=Fi = 456o c i <y ctrzA jfl -4 365+ f R=f 317

\ Alhprtsnn. F = CO x =F = 239N ^-^*^\

! !

i

s |

^ ii

i

—

I

c

—

I

(

)

\

—

'

1 ,

•—

I

—o

is

\o \*

cX

o I S

"^

—M

"o ———

-

'5*10u

10' 102

Dimensionless Axial Distance, S/D

87

Fig. 12 Entrainment Coefficient

od

o

O mO 9

o*-»

C

ESc dCO

cSWo

C3

CM

od .

od

ood

LEGENDn Experimentally Determined— Davis et al.

-i 1 1 r ~i 1 1 1 1 1 r t—l1 r -i 1

1 i

200i

r

250 300 350 400

Froude Number450 500

83

Fig 13. Streamwise

Jet Velocity Distribution

3 °I j n * m

89

i! I

LU

Tt

C3C'-J

"Z"

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APPENDIX D.

COMPUTER PROGRAMS

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INITIAL DISTRIBUTION LIST

No. Copies

1. Library, Code 0142Naval Postgraduate SchoolMonterey, California 93940

2. Dr. Paul J. MartoDepartment Chairman, Code 69Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

3. Dr. William Culbreth, Code 69CbDepartment of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

4. Dr. M. D. Kelleher, Code 69KhDepartment of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

5. LCDR Mark D. Wessman, USNUSS Cayuga (LST 1186)FPO San Francisco, California 96662

6. Defense Technical Information CenterCameron StationAlexandria, Virginia 22314

144

ThesisW4765cl

• 8Wessman

Measurement of ve-locity distributionsin turbulent jetsusing a laser dopplervelocimeter.

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201596Wessman

Measurement of ve-

locity distributions

in turbulent jetsusing a laser dopplervelocimeter.

thesW4765missmg

Measurement of velocity distributions in

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