The development of a high performance laser doppler velocimeter for fluid mechanics and acoustics research applications

THE DEVELOPIì,IENT OF A HIGH PERFORMANCE

I,ASER ^DOPPLER VELOCII4ETER FOR FLUID MECHANICS AND ACOUSTICS RESEARCH APPLICATIONS

by

Neil Mclay WILSON. B.Tech., ^B.Sc.

A thesis submitted for examination for the degree of

Master of Applied ^Science

University of ^Adelaide

Mechanical Engineering ^Department

JuIy ^1977.

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TABLI] OF CONTENTS

SUMMARY

ÀCKNOWI,EDGEMENTS NOMENCLATURE

CHAPTER ¹ VEI,OCITY ^MEASUREMENTS IN FLUID

MECHANICS AND ^ACOUSTICS ^{RES EARCII} Conventional ^Techniques

Laser Doppler VelocimetrY

CHAPTER ² L.D.V. ^METHODS, LIMITATIONS ^AND

ffi

1.1L.2

Page

iii i iv

10 11 14 15 18 19

I I

4

2.L

2.2 Optical HeterodYning Mode Geometries

2.2.r

2.2.2 2.2.3

Reference l4ode ^GeometrY

Fringe ^{Mode GeometrY} Doppler ^{Mode GeometrY}

Dístribution of Light in the ^{Focal Volume} Further Optical Considerations

2.4.L Focal Volume Size

2.4.2 ^Optimum Particle Specifications

2 .4 .3 SPectral Broad'ening

Directional Aliasing with Fringe Anemometers ⁴⁰

2 2

3 4

2L 25

67

2.5

CHAPTER ³

CHAPTER ⁴

OPTICAL ^METHODS OF ^{FREQUENCY BTASING}

25 31 36

49 50 53 59 60 62

3.13.2 3.33.4

Mechanical ^SYstems

Magneto-optic ^Techniques Electro-optic ^Devices Acousto-optic ^Devices

4.14.1

4.r 3.4.1

3.4.2 Debye-Sear s Scattering

Bragg Diffraction

IREMENTS OF AND ^{DESIGN PROACH}

FOR A GH RES ION L.D. ⁷⁷

82 86

4.I Requirements of a Laser Doppler ^System Optical ^{FrequencY Biasing}

Samp1e Biasing

Spectral ^Broadening 4.2 ^Frequency DemodulaÈion ^Methods

Frequency ^Domain AnaIYsis Time Domain AnalYsis

.1.2 .3

4.2.L 4.2.2

77 77 78 81 82

TABLE OF CONTENTS (CONIId)

CTIAPTER 5 OPERATION OF THE L.D.V.

Introduction

Block Diagram DÈscripti.on

Detailed ^Sy=tern Lìperation - Signal ^Processor

Analogue Unit - ^Ul Main Control Unit ^U2 Main Counter Unit ^U3 Buffer Storage Unit - ^U4

D to A Converter Unit - ^U5

System Specifications Applications

SUMMARY OF CONCLUSIONS

Page

89

5.r5.2 5.3

90 90 94 94 99 105 110

r14 I16

119 L24

5.3.1 s.3.2 5.3.3 s.3.4 5.3.s

5.45.5

APPENDICES

REFERENCE LIST

Logic Mnemonics

Block Diagram

Ul - ^Analogue Unit

U2 - ^Main Control Unit U3 - Main Counter Unit

V4 - Buffer ^Storage Unit U5 ^DAC Unit

Driver Circuit Acousto-optic CelI

Photographs

A1 A2 A3 A4 A5 A6 A7 B1 B2 B3

a SUMI'IARY

It is the ^purpose of this present study to delineate the design criteria ^and operating principles of a high ^speed, digitat laser ^Doppler velocimeter that is suitable for ^a

large ^nun¡ber of applications in fluid mechanics and acoustícs research.

The shortcomings of existing techniques for the ^measure-

ment of fLuid ^and surface velocities are ^{discussed and the}

advantages of laser Doppler ^systems are investigated'' ^Relevant theoretical considerations are presented, with particular

reference to the capabilities ^and limitations of light scatter- ing techniques. A comprehensive review cf the currently

available ^methods for optical frequency biasing forms the basis for the development of a high diffraction efficiency acousto-optic ceIl. ^The essential ^and desirable characteris- tics of a high performance LDV are established ^and incorporated into the design and construction of a digital signal ^processing

system that uses Èime domain analysis for the demodulation

of velocity ^and real time information. The system is shown

to offer solutions to the serious ^problems of directional aliasing; signal biasing; spectral broadening and signal dropout ^and is used with a modified ^Michelson interferometer to detect the surface velocity of a mechanically driven mirror.

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STATEMENT

This thesis contains ^no material which has been accepted for the award of

any other degree or diploma in any university and, to the best of ^my knowledge and belief' contains no material previously ^published or written by another person, except ^where due reference is made in the text.

l-l-1.

ACKNOWLEDGEME¡lTS

There are many people whom I wish to thank for their assistance and guidance during the course of this project.

In particularr ^mY supervisors' Drs. G.L. ^{Brown and}

D.A. Bies, vrere a continual ^source of inspiration ^and enthusi- astic encouragement. Their assistance, on ^{So many occasions,}

was readily forthcoming and always in a sense of helpful criticism ^and direction. Professor H.H. Davis initially provided the opportunity for ^me to do this research ^and

professor S.E. Luxtonr or appointment as Head of the Department' continued to provide the departmental assistance that' ^{was so} necessary for the successful completion of the work.

f{ithout the expertise and generous support of ^the

electronics workshop, the project would have required a signi- ficantly longer time for completion ^and would have ^produced an instrument well below the standard achieved. ^My particular thanks are therefore directed to ^Messrs. H. Bode, P. ^Walker

and G. Osborne of the Mechanicat Engineering ^Department Electronics lr7orkshop .

I ^am also grateful to Mr. A. Davis for the development and construction of the acousto-optic cell driver ^and for the assistance ^and advice that he willingly offered during ^the construction ^phase of the ^LDV.

In the latter ^stages of the project, Dr. c.J. Abell

gave me invaluable assistance ^through helpful cliscussion ^and suggestion ^and companionship through those times ^when all

seemed tost. For this I will ^always be indebted'

To Helen ^{and my f amily} r ^{Ets always} , I ^owe the greatest debt.

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NOMENCLATURE

constant

receiver ^{apert,ure radius}

speed of light

fringe spacing; grat.ing ^sPacing particle diameter

incident, scattered light ^beam unit vectors

,rth otd"t scattered light ^beam unit vector ^(Fig'13) frequency; focal length of a ^lens

acoustic ^frequencY bias frequency Doppler ^frequencY

frequency of incident, scattered light ^beam modulating ^frequencY

frequency of ,rth otd"r diffracted ^beam laser ^frequency

Landé g factor

height of acoustic beam; Planckrs ^constant intensity functions

quantum number

incident., scattered ^wave vectors; incident, scattered ^{photon momentum vectors}

length of focal r,'olume; Iength of laser cavity;

solenoid length.

focat volume dimension ^(Fig.L2) ¡ ^{quantum number.}

effective probe length molecular ^mean free _Path

minimum probe length

total angular ^{momentum quantum number}

diffracted order; no. of particles; ^percentage error; no. of turns.

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NOMENCLATURE (Cont'd)

P

Pti ^P>t

phase retardation; elasto-optic coefficient' ^(79') probabilities

r pinhole radius; disc ^radius s Laplacian oPerator

srs'ts'rts'rts', dimensions (Fig.8) t time; focal ^{volume thickness}

v velocitY

r" acoustic velocitY

v- particle velocitY vector

;p

vf. fluid velocitY; fringe velocitY r{ ^{beam width}

*r r*r- dimensions (Fig.8)

A

D

E¡ rEz- E. l' ,Es

EP E ,

o

(a) -

F H

I ro re n

receiving optics ^aPerture

e-1 diameter of unfocused laser ^beam intensities of the two incident ^beams incident, scattered ^beam intensities

intensity at the centre, ^âE a point p in the focal

volume.

Gaussian F number

magnetic field intensitY coil current

unattenuated laser intensitY

scattered ^beam intensity at an angle 0

Bessel ftn.

propogation constant of ^sound waves; Cunningham const.

incident ^{phonon \^lave} vector.

scattering ^{coef f} icient

J

K ruêK

Ks

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NOÌ\îENCLATURE (Cont ^I d)

P

orbital angular ^momentum vector.

figure of meriti constant.

no. of wavefronts; Avogadrors no. i no. of no. of scattering Part.icles.

hydrostatic ^pressure acoustic ^power

gas constant

receiver distance from scattering ^volume spin angular ^momentum vector.

absolute temperature; measurement interval.

mean velocity

size of the focal ^volume acoustic ^beam width

const

t-

orßr'Y-

ß- ô-

angular notation modulation ^index

radius of ^beam waist

radius of scattered ^beam waist error ^due to Particle inertia refractive index; viscositY constant

angle of incidence Bragg angle

,rth otd.r diffracÈion ^angle.

optical ^wavelength

incident, scattered wavelengths.

nett magnetic ^moment vector Bohr magneton.

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vf..

cycles.

Np

P

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NOMENCLATURtr (Contrd)

kinematic viscosity laser frequency density

particle, f1uid. densitY minimum time of flight

angle of inclination of Yp; phase angle

incident, scattered ^wave functions.

angular ^frequencY.

angular Doppler ^frequencY

incident, scattered ^beam angular frequencies

maximum angular turbulence ^frequency.

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dimension (Fig. 8)

induced change in atomic energy leve1s.

Iaser cavity half width

Doppler spectral broadenitg; ^{Doppler frequency}

He-Ne laser half line ^width

half the length of the focal volume (Fi9.8) _' particle Brownian motion

fringe ^separation

Zeeman frequencY shift

solid angle ^subtended by receiving aperture' geometric constant

acoustic wavelength.

solid angle of accePtance.

var.

deviation.

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