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Produced by the NASA Center for Aerospace Information (CASI)
A Thesis

by

SAIED EMAMI

I

Major Subject: Mechanical Engineering

11wr <w

(NASA-CR-175359) PHASE AVERAGED N84-16134

MEASUREMENTS OF THE COHERENT STRUCTURE OF A

MACH NUMBER 0.6 JET M.S. Thesis (Texas A&A

Univ.) 107 p HC A06/MF A01 CSCL 01A Unclas

G3/02 15181

PHASE AVERAGED MEASUREMENTS OF THE COHERENT STRUCTURE

OF A MACH NUMBER 0.6 JET

Submitted to the Graduate College of

Texas A&M University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

9

DEC 1983
PHASE AVERAGED MEASUREMENT'S OF THE COHERENT STRUCTURE

OF A MACH NUMBER 0.6 JET

A Thesis

by

SAIED EMAMI

Submitted to the Graduate College of

Texas A&M University

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

DEC 1983

1

r. Major Subject: Mechanical Engineering

e:

4'.

t

r

t-;

. 

1
CG:It: r!d. !-WAL I

(I F FKX)i^ << 'AL.'TY

PHASE AVERAGED MEASUREMENTS OF THE COHERENT STRUCTURE

OF A MACH NUMBER 0.6 JET

A Thesis

by

SAIED EMAMI

Approved as to style and content by:

XVY

Dr. G.Morrison

(Cla irma of committee)

Dr. J. C. Dutton

(Member)

Dr. G. B. Tatterson

(Member)

^,7 ^'-r i b

// r. G. R. HO¢ i s

-h ead f Department)

Dec 1983

0

1
iii

1t

ABSTRACT

Phase Averaged Measurements of the Coherent Structure

of a Mach Number 0.6 Jet. (Dec 1983)

Saied Emami, B.S., Texas A&M University

Chairman of Advisory Committee: Dr.. Gerald L. Morrison

The existence of a large scale structure in a Mach

number 0.6, axisymmetric jet of c.,ld air has been proven by

previous work. In order to further characterize the

coherent structure, phase averaged measurements of the axial

mass velocity, radial velocity, and the product of the two

have been made. These measurements yield information about

the percent of the total fluctuations contained in the

coherent structure. These measured values were compared to

the total fluctuation levels for each quantity and the

result expressed as a percent of the total fluctuation level

contained in the organized structure at a given frequency.

These measurements were performed for five frequencies (St=

0.16, 0.32, 0.474, 0.95, and 1.26). All of the phase

averaged measurements required that the jet be artificially

excited.

The fluctuating p rofiles showed that the axial mass

velocity fluctuation maximized when excited at F. frequency

of St = 0.474. The radial velocity fluctuatiors had a lower

amplitude for both the full wave and phase averaged

Q!
v 

r

s

iv

fluctuations compared to the axial mass velocity

fluctuation. The Reynold's stresses tended to decay faster

in amplitude than the axial mass velocity and radial

velocity fluctuations for both the full wave and phase

averaged components.

The coherence contours showed that the radial velocity

fluctuations possessed higher levels of coherence than the

axial mass velocity fluctuation and the Reynold's stresses.

The temporal and spectral content of the phase

averaged radial velocicy fluctuations showed that when the

jet was excited at the frequency of St = 0.474, a high

amplitude component at that frequency dominated the entire

flowfield from X/D = 1 to 10. This fundamental frequency

was accompanied by several relatively high amplitude

harmonics. These harmonics were more dominant for the

radial velocity fluctuations.
I ^

i

1

i

Y

stn

n'yY

I.

i

I

lie

',e )

ACKNOWLEDGEMENTS

I wish to express my gratitude and sincere

appreciation to Dr. G. L. Morrison for his constant

assistance and encouragement during the course of this

research which without his assistance, completion of my

research objectives would have been impossible. I am also

grateful to Dr. J. C. Dutton and Dr. G. B. Tatterson for the

honor of having them on my committee. Special thanks to Mr.

Eddie Denk for his assistance at the Turbomachinery

Laboratories.

Finally, I would cc acknowledge the financial support

provided by NASA Langley through, grant number ( NAG1-112 ).

vi

PRECEDING PAGE. BLANK NOT FILMED'

x

1
vii

I

TABLE OF CONTENTS

1 RAGE

ABSTRACT ------------------------------------------ iii

DEDICATION ---------------------------------------- v

ACKNOWLEDGEMENTS -----------------•----------------- vi

1

TABLE OF CONTENTS --------------------------------- vii

LIST OF FIGURES ----------------------------------- viii

NOMENCLATURE -------------------------------------- xiv

CHAPTER I - INTRODUCTION -------------------------- 1

1.1 Introduction ---------------------------- 1

CHAPTER I1 - MEASUREMENT PROCEDURE AND EXPERIMENTAL

FACILITY ----------------------------- 7

2.1 Measurement Procedure ------------------- 7

2.2 Experimental Facility ------------------- 8

CHAPTER III - DISCUSSION OF RESULTS --------------- 12

3.1 Full Wave and Phase Averaged Flow

Quantities ------------------------------ 12

3.2 Coherence Level Contours ---------------- 26

3.3 Temporal and Spectral Content of Phase

Average Flow Fluctuations ------------ 51

CHAPTER IV - CONCLUSIONS AND RECOMMENDATIONS ------ 76

4.1 Conclusions ----------------------------- 76

4.2 Recommendations -------------------------

i

78

REFERENCES ------•---------------------------------- 80

APPENDIX A --------•--------------------------------- 83

APPENDIX B ------------------------------•---------- 85

VITA ---------------------------------------------- 92
P LIST OF FIGURES

FIGURE

1 Schematic diagram of the jet test facility --

1 2(a) Radial distribution of phase averaged mass

velocity fluctuation excited at St = 0.158 --

2(b) Radial distributiom of mass velocity

fluctuation full spectrum excited at

St = 0.158 ----------------------------------

3(a) Radial distribution of phase a %,araged mass

velocity fluctuation excited at St = 0.316 --

3(b) Radial distribution of mass velocity

fluctuation full spectrum excited at

St= 0.316 ----------------------------------

4(a) Radial distribution of phase averaged mass

- velocity fluctuation excited at St = 0.474 --

4(b) Radial distribution of mass velocity

fluctuation full spectrum excited at

St= 0.474 ---------•-------------------------

5(a) Radial distribution of phase averaged mass

velocity fluctuation excited at St = 0.948 --

5(b) Radial distribution of mass velocity

` fluctuation full spectrum excited at

k: St = 0.948 ----------------------------------

6(a) Radial distribution of phase averaged mass

velocity fluctuation excited at St = 1.263 --

6(b) Radial distribution of mass velocity

fluctuation full spectrum excited at

St= 1.263 ----------------------------------

7(a) Radial distribution of phase averaged radial

velocity fluctuation excited at St = 0.158 --

1

7(b) Radial distribution of radial velocity

fluctuation Lull spectrum excited at

St= 0.158 ----------------------------------

8(a) Radial distribution of phase averaged radial

/ velocity fluctuation excited at St = 0.316 --

viii

PAGE

9

13

13

14

14

15

15

16

16

17

17

20

20

21

0
PAGE

21

22

22

23

23

24

24

27

27

28

28

29

29

LIST OF FIGURES (Conti:iued)

FIGURE

8(b) Radial distribution of radial velocity

fluctuation full spectrum excited at

St= 0.316 -----------------------------------

9(a) Radial distribution of phase averaged radial

velocity fluctuation excited at St = 0.474 --

9(b) Radial distribution of radial velocity

fluctuation full spectrum excited at

St= 0.474 ----------------------------------

10(a) Radial distribution of phase averaged radial

velocity fluctuation excited at St = 0.474 --

10(b) Radial distribution of radial velocity

i fluctuation full spectrum excited at

St= 0.474 ----------------------- -----------

''- 11(a) Radial distribution of phase averaged radial

velocity fluctuation excited at St = 1.263 --

r 11(b) Radial distribution of radial velocity

fluctuation full spectrum excited at

St = 1.263 ----------------------------------

12(a) Radial distribution of the phase averaged

axial and radial flow fluctuation correlation

t' excited at St = 0.158 --------------•---------

12(b) Radial distribution of axial and radial flow

fluctuation correlation excited at St = 0.158

k< I 13(a) Radial distribution of the phase averaged

R'* axial and radial flow fluctuation correlation

excited at St = 0.316 -----------------------

13(b) Radial distribution of axial and radial flow

fluctuation correlation excited at St = 0.316

14(a) Radial distribution of the phase averaged

axial and radial flow fluctuation correlation

excited at St = 0.474 -----------------------

14(b) Radial distribution of axial and radial flow

fluctuation correlation excited at St = 0.474

ix
iI

x

LIST OF FIGURES (Continued)

FIGURE

15(a) Radial distribution of the phase averaged

axial and radial flow fluctuation correlation

excited at St = 0.948 -----------------------

15(b) Radial distribution ct axial and radial flow

fluctuation correlat!,un excited at St = 0.948

16(a) Radial distribution of the phase averaged

axial and radial flow fluctuation correlation

excited at St = 1.263 -----------------------

16(b) Radial distribution of axial and radial flow

fluctuation correlation excited at St =1.263

1

PAGE

30

30

31

31

33

34

35

36

37

1

Contours of coherence levels of phase

averaged mass velocity fluctuation excited at

St = 0.158 ----------------------------------

Contours of coherence levels of phase

averaged mass velocity fluctuation excited at

St = 0.316 ----------------------------------

Contours of coherence levels of phase

averaged mass velocity fluctuation excited at

St = 0.474 ----------------------------------

Contours of coherence levels of phase

averaged mass velocity fluctuation excited at

St = 0.948 ----------------------------------

Contours of coherence levels of phase

averaged mass velocity fluctuation excited at

St = 1.263 ----- ---------- -------------------

1 Contours of coherence levels of phase

averaged radial velocity fluctuation excited

at St = 0.159 -------------------------------- 41

Contours of coherence levels of phase

averaged radial velocity fluctuation excited

at St = 0.316 -------------------------------- 42

Contours of coherence levels of phase

averaged radial velocity fluctuation excited

at St = 0.474 •-------------------------------- 43

Contours of coherence levels of phase

averaged radial velocity fluctuation excited

at St = 0.948 -------------------------------- 44

17

18

19

20

21

22

23

24

25

f 1C
xi

►

r

r

r

:t

LIST OF FIGURES (Continued)

FIGURE PAGE

26 Contours of coherence levels of phase

averaged radial velocity fluctuation excited

at St = 1.263 -----------••---•----------------- 45

27 Contours of coherence levels of phase

averaged axial and radial flow fluctuation

correlation excited at St = 0.158 ------------ 47

28 Contours of coherence levels of phase

averaged axial and radial flow fluctuation

correlation excited at St = 0.316 ------------ 48

29 Contours of coherence levels of phase

averaged axial and radial flow fluctuation

correlation excited at St = 0.474 -•----------- 49

30 Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 1 , Z/D U -0.56, excited at St = 0.474 - 52

31 Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 3 , Z/D = 0.55, excited at St = 0.474 -- 53

32 Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 3 , Z/D = -0.2, excited at St = 0.474 -- 54

33 Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 7 , Z/D = 1.0, excited at St = 0.474 --- 55

34 Tempral and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 7 , Z/D = -0.04 , excited at St = 0.474 56

35 Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 10 , Z/D = 0.862 , excited at

St = 0.474 ------------------------------------ 57

36 Temporal and Spectral representation of the

phase averaged mass velocit- fluctuation,

X/D = 10 , Z/D = -0.06 , excited at St = 0.474 58

37 Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

X/D = 1 , Z/D = - 0.56 , excited at St = 0.474 60

^tT
xii

f

LIST OF FIGURES (Continued)

FIGURE PAGE

38 Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

I

X/D = 3 , Z/D = 0.55 , excited at St = 0.474 61

39 Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

X/D =3 , Z/D - - 0.2 , excited at St = 0.474 -- 62

1

40 Temporal and Spectral

phase averaged radial

.X/D = 7 , Z/D = 1.0 ,

41 Temporal and Spectral

phase averaged radial

X/D = 7 , Z/D = - 0.04

representation of the

velocity fluctuation,

excited at St = 0.474 -- 63

representation of the

velocity fluctuation,

excited at St = 0.474 64

1

1

1

5

42 Temporal and Spectral r epresentation of the

phase averaged radial velocity fluctuation,

X/D = 10 , Z/D = 0.862 , excited at

St = 0.474 -------------------------•---------- 65

43 Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

X/D = 10 , 7./D = -0.06 , excited at St = 0.474 66

44 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 1 ,

Z/D = - 0.56 , excited at St = 0.474 ---------- 67

45 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 3 ,

Z/D = 0.55 , excited at St = 0.474 ----------- 68

46 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 3 ,

Z/D = -0.2 , excited at St = 0.474 ----------- 69

47 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 7 ,

Z/D = 1.0 , excited at St = 0.474 ------------ 70

1

6/
i

xiii

i

i

1

LIST OF FIGURES (Continued)

FIGURE PAGE

48 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 7 ,

Z/D = -0.04 , excited at St 0.474 ---------- 71

49 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 10 ,

Z/D = 0.862 , excited at St = 0.474 ---------- 74

50 Temporal and Spectral representation of the

phase averaged axial and radial flow

fluctuation correlation, X/D = 10 ,

Z/D = -0.06 , excited at St 0.474 ---------- 75

L

F

c ^

i

1

i

y

5

1
xiv

NOMENCLATURE

ALS - arbitrary linear scale

A" - mass velocity fluctuation sensitivity coefficient

A.r - stagnation temperature fluctuatuation sensitivity

coefficient

AV - radial velocity fluctuation sensitivity coefficient

i, D - diameter of the jet

e - fluctuating hot-wire voltage

c.

F

e - fluctuating hot wire voltage

E - mean hot-wire voltage

E b - hot-wine bridge

f - frequency (Hz)

G - amplitude

m - mass velocity

M - mass velocity fluctuation ((Yu)) nondimensionalized

by the mean value of the mass velocity ( -FU)Q at

the jet exit

RW - hot wire resistance

St - strouhal number (fD/U )

T - stagnation temperature

i

T

- mean stagnation temperature

Tic - mean centerline jet velocity at the exit.

(fuv) - the Reynold stress was nondimensionalized by the

mean mass velocity (pU)e and mean axial velocity

(U)e at the jet Fait

v - radial velocity fluctuation ((v)) nondimensionalized

by the mean value of the axial velocity (U)

at the jet exit

X - downstream distance from the nozzle exit

QI
Z - radial distance from the jet centerline

t

- yaw angle of crossed hot-wire probe relative to the

local flow angle

- density

0

X v

T ^

y:

r.

f ^

0
1

CHAPTER I

u

INTRODUCTION

1.1 introduction

At the present time, jet exhaust noise is one of the

major noise problems challenging scientists and engineers.

With the development of large jet engines for use in high

r

speed commercial and military aircraft, high exhaust

velocities have made the jet noise problem very critical due

to environmental noise pollution, especially during the

aircraft's take off from metropolitan airports. Many

investigations have been performed in order to determine

ways to reduce this noise. In order to effectively reduce

noise from a jet of air., sufficient knowledge about noise

production mechanisms and noise source locations inside the

jet is desirable.

During the last three decades, there have been many

theories presented that mathematically describe the noise

generation of a jet of air. The works of Lighthill [1,2],

Ffowcs William (3], Ribner (4], Phillips [5], Pao (6),

Liiley (7], and Doak [8] ,re all capable of predicting the

noise radiated from a jet of air with some degree of

accuracy. However, in order to calculate the noise, all

i The format and style of this thesis follows that of the ASME

;' 1C Journal of Fluids Engineering.

4 

N 

1
of these works must use empirical information about flow

fluctuations in the jet. Therefore, the only way to

determine the source functions is to experimentally measure

1 the flow fluctuations required to calculate them. In jet

flows, this is an almost insurmountable task due to the

complexity of the source terms and direct measurement of the

► noise is much easier. However, by using dimensional

analysis with the theories (1-81, it is possible to

approximate the directivity of the acoustic field and the

dependence of the sound intensity upon the velocity of the

jet.

' During the past several years, a new class of jet

noise theories has been developed [9-171. TheFe theories

are based upon the experimental evidence that there is a

large scale organized structure in turbulent free shear

► flows (18-201. This organized structure starts as an

instability wave on the shear layer, is amplified and

finally decays.

According to the theories, this organized structure in

the jet is of prime importance in the noise production

mechanism in both subsonic and supersonic flows. Because of

++x these theories, a new range of noise reduction and

suppression techniques might become available. The

i

6

important inference is that the development of the large

scale coherent structure (organized structure) might be

{ controlled through the modification of initial conditions

K „

t•

x.:

^' 
and hence the noise which is generated by this organized

structure might be reduced.

For low Reynolds number, transonic and supersonic jets

[21-2' , a large scale organized structure which causes a

major portion of the noise radiation has been experimentally

!r

confirmed. In sub=onio jets, many experiments have been

performed in order to determine the noise production

mechanism. Mollo-Christensen [28] first discovered the

h coherent structure in subsonic jets for Mach numbers greater

'.t

' 27 than 0.15 and .less than 0.9 by using space-time correlations

of the near pressure field. He also measured far field

noise spectra and directivity patterns. It was believed

that the coherent structure radiated acoustic energy more

efficiently than a random structure.

Crow and Champagne [19] examined the organized

( structure in very low speed jets of air (Mach numbers less

than 0.1) by using a speaker to excite the jets in the

C

axisymmetric mode (n=o mode number). They used both

^j hot-wire anemometry and flow visualization to identify the

Cflowfield. It was concluded that there was an orderly

kstructure in the jets and this structure could be

r

approximately characterized by a linear stability theory.

They observed an instability wave in the shear layer leaving

the nozzle exit. Further downstream there was a puff

formation involving the whole jet column which scaled on the

jet's diameter.

r
1

P

1

0

0

1

1'

f 4

Chan (141, Lau, Fisher and Fuchs [201, and Moore (291

furthered the investigation of the orderly structure in

subsonic jets. Chan (14) artificially excited a subsonic

jet and measured the wave properties of three different

modes having azimuthal mode numbers of n = 0, 1, and 2. The

structure was modeled by a wave theory, and a linear

stability solution of a divergent shear flow was found to

adequately describe the local properties of the waves.

Thus, in subsonic jets, an orderly structure has been

observed and measured.

Experiments (21-251 have shown that for low Reynolds

number transitional supersonic jets there are instability

waves present which can be characterized by a linear

stability theory for the first several diameters of flow.

It was also shown that this instability produces a major

portion of the noise radiated by the jet. The instability

waves generate sound pressure level contours which are very

close in shape and amplitude to those generated by the high

Reynolds number jet. It was shown that it was highly

probable that the noise production mechanism in the low

Reynolds number jets and other high Reynolds number jets was

the same. If so, the theoretical approach taken by Tam

[9-121, Liu [151, Morris (171, and Chan [141 was

appropriate.

Morrison and Whitaker [301 measured the axial wave

'a number of the coherent structure in a Mach number 0.6 jet

L-1
P for several frequencies. It was found that the axial wave

number frequency relationship for their jet and those of

several other investigators for both natural and excited

jets with Mach number greater than 0.3 remained the same.

For these jets, the Reynolds numbers ranged from 3,700 to

over 500,000, the Mach number ranged from 0.3 to 2.5, and

some of the shear layers were laminar and others were

turbulent with various thickness. Therefore, in these

compressible jets, the importance of initial shear layer

thickness, whether the shear layer was initially laminar or

turbulent, Mach number, or Reynolds number did not matter.

3

These measurements were only for the axial fluctuations.

The overall noise level radiated by a Mach number 0.6

jet studied by Whitaker and Morrison [351 was observed to

reach a maximum value around 30 degrees from the jet axis,

It was found that the frequency content of this radiated

noise was dependent upon the angle from the jet axis. As

f the angle from the jet axis increased, the spectra of the

noise shifted to higher frequencies. When the jet was

F'.

artificially excited, the noise production mechanism in the

jet was found to be more responsive to mid-band excitation

} Q. frequencies (0.474,< St \< 0.632).

This work will further identify the coherent structure

h, in this Mach number 0.6 jet by determining the percent of

s

the total flow fluctuations that are contained in the ^;

coherent structure at the various frequencies studied for

5
r

6

the axial mass flux (pu), thn radial velocity (v), and the

product of the two(puv).

a

V

'S
C

f

^F

4

CHAPTER II

MEASUREMEMENT PROCEDURE AND EXPERIMEN':AL FACILITY

2.1 Measurement Precedure

x

The phase averaged flow quantities were recorded by a

computer based data acqusition system. This system recorded

the artificial exciter signal input and the two hot-wire

signals from the crossed hot-wires. The artificial exciter

signal was used as a phase reference for phase averaging the

hot-wire signals. The resulting wave form was spectrum

analyzed. The spectral analysis indicated the presence of

any harmonic components in the signal. The production of

subharmonics, either half or two-thirds may indicate vortex

pairing as shown by Browand and Laufer (31). By monitoring

these spectra at different axial locations, the possibility

of vortex pairing and nonlinear interaction was

investigated.

The crossed hot-wire measurements were performed using

matched crossed hot-wires. The matching of the hot-wires

was essential since it allowed instantaneous addition and

subtraction of the voltages from the hot-wires using analog

techniques. In this manner, two signals, one proportional

N

The phase average signal is q(t) = N im 1/N q(t + nT)

f 4 CO n=o

where rr is the period of the coherent structure in the jet.

4;
 r 8

to the axial mass velocity fluctuation and the other

proportional to the radial velocity fluctuations were

obtained. In addition, these two signals were multiplied

together after being digitally recorded by a computer system

in order to obtain a voltage that was proportional to the

product of axial mass velocity fluctuations and radial

velocity fluctuations.

All of the hot-wire data were decomposed into axial

mass velocity, radial velocity and total temperature

fluctuations using techiques outlined by Horstman and Rose

[33] and Johnson and Rose (341 (see appendix A). in

addition, a conditional sampling technique (phase averaging

) was used to measure the phase averaged axial mass

velocity, radial velocity and correlation of axial mass

velority and radial velocity. By ol^taining phase averaged

quantities, a comparison between full and phase averages of

fluctuating components was made. It was experimentally

determined that four hundred averages were required to

accuratly evaluate the phase averaged quantities. The

programs for the data acquisition and analysi^ ara in

Appendix B.

2.2 Experimental Facility

The experiments were performed in a free jet test

facility shown schematically in Figure 1. A round

C
9

ORIG1Pd,J. '=^rAL1TY

OF 1,00R Q

r 0^

I- q

f4 Vi

C

c. U0VLN

id WCNuLONNda0

:J

I F'

a N i y H

;n f. C U L

'rN

7 O

^

NQ

LNE

N ro L

C V

(pNN

L C

L

N •^+

W •.y

7 L ^' E i OU C.G U J n CU

C7

ZC .yU

U_ ro

O w U '^ J NN

a.i NwUE

roLa

roU

.y

roENrU

V^ ra

.y

4.

LUV

.yLOu

40. hLUu

k\ 9

3

C
" 10

axisymmetric jet of air with exit diameter of 1.25 cm. was

exhausted at atmospheric pressure into an ,o nechoic chamber

which had a free interior with dimensions of 2m * 2m * 2m.

The walls of the anechoic chamber were lined with 23 cm

thick fiberglass wedges. The air was supplied by a

reciprocating compressor by way of a storage tank, water

aftercooler, water separator/filters, an electronic pressure

requlator, an acoustic: muffler, and a 15 cm. diameter

stilling chamber. The stilling chamber consisted cf a

section of foam rubber followed by several perforated

plates, a section of honeycomb and several fine sere-vns.

The flow was then accelerated through ^ noz7,le whose conLour

is described by a third order polynomial. The contraction

ratio for the nozzle was over 100:1. Previous measurements

have shown thet this flow facility produces a jet with a

uniform exit velocity profile and a very low level of

turbulence on _he centerline of the jet.

Spectra of fluctuating quantities were obtained by

a

using a Fast Fourier Transform algorithm on the data

acquisition system. This system consists of a graphic video

terminal, a digit.l plotter and a dot matrix printer

' connected to a 280 based S100 microprocessor system. Analog

1

r data was recorded two ways. DC voltages were digitally

recorded using a 12 bit analog to digital computer and AC

voltages were digitally recorded by a high speed digital

a•

{ recorder interfaced to the computer.

t
if

r)

{` F V

11

A The hot-wire probes which were custom manufactured wort

operated by a four channel TSI model 1050 anemometer system.

A four degree of freedom (three linear and one rotation)

probe drive system was used to traverse a hot-wire probe.

The rotational degree of freedom was used for yawing the

crossed hot-wire probes for calibration.

The method of excitation in this study was the same as

the method used by Morrison and Wattanachayakul (36). A

function generator was used to provide square wave signals

as input for the artificial excitation electronics. The

device operated by generating sufficient voltage to create a

spark across a 1.5 mm gap between two electrodes. This

spark effectively put a small controlled disturbance in the

jet. Electrodes for the excitation device consisted of 1/16

inch diameter., two percent thoriated tungsten rods. In order

to stablize the spark at one location, the tips of the

electrodes were ground into sharp points. These electrodes

c

were mounted on the bottom of the jet nozzle (0=180 )

V, .

placing them right at the exit of the jet (X/D=0). The

electrode points were put into the shear layer with one

electrode further into the jet than the other so that the

spark would jump across the shear layer.
c I^

CHAPTER III

DISCUSSION OF RESULTS

3.1 Full Wave and Phase Averaged Flow Quantities

Radial distributions of the root mean square value of

the axial mass velocity fluctuation, the radial velocity

fluctuation and one component of the Reynold stress tensor

were measured. These measurements were performed at axial

locations of X/D = 1, 2, 3, 5, 7 and 10. Full wave and

phase averaged fluctuation levels were measured for five

excitation frequencies. The distribution of axial mass

velocity for full wave and phase averaged fluctuations are

presented in Figures 2 through 6. Note that in these

figures, the mass velocity fluctuation (Fu) has been

nondimensionlized by the exit value of the mean mass

velocity (YUU) , thus allowing comparisons between Figures

2-6 to be made.

These figures show that Lhe maximum fluctuation levels

initially occurred in the center of the shear layers where

there was an inflection in the mean velocity profile.

Morrison and Wattanachayakul [36) showed that the mean mass

velocity profiles did not change when the jet was excited.

However, the fluctuation profiles varied when the jet was

excited at dif.ferenL frequencies. For the lower frequency

of excitation, the radial .location of the maximum amplitude

fluctuation at X/D = 1 occurred at a radial position of 0.4.

This radial position of maximum fluctuation level shitt-:d

x

r

k

,

i

k

e

Y

C^

k^
( a ) Radial distribution of phase averaged mass velocity

fluctuation

Al

0

^^ry

i

St = 0.158

2 M = 0.6

a o °

°

) o ' 0 0

° a 3 ' ° o ° a

a 0

0 0

°

°

0

a

°V ^ e

o a

o a

o ^ °

a o

0

0

Z^C

NI,- '= t, 4J

OF POOR QUALITY

13

e

X/

ID

Z/D

2- St = 0.158

M = 6.6 .

• o

0 o e • 0

o+°

0 0

e s

n

q o • a °

' °^ ° i e a • • o

° o o °

0 .

a

a,.

a

k9:

r

Ci

1

0

Fig. 2(b• ). Radial distribution of mass velocity fluctuation full spectrum
14

ORIGINAL PAGL IS

OF POOR QUALITY

%o I

S t

0.316

M 0.6

ZL

2

^^. (a) Radial distribution of phase averaged mass velocity

fluctuation

XY 4 6

Ic S t

0.316

M 0.6

IC

7/6

C

n C) n 0 0 0

C

Fig. 3(b)• Radial distribution of mass velocity fluctuation full spectrum

C,

1 4'

i t

I I

C
r

I ^'

P

OFIGIfe L i AU18' twi

OF POOR QUALIV

15

4

=1 L 6 5

St = 0.474

2 M = 0.6

a

O

0

•

2

(a) Radial distribution of phase averaged mass velocity

fluctuation

'L 3 v

St = 0.474 0

M =0.6

°

°

0

b ^ o

o

a

SIP a•

° ,

o °

° •

0 0 0 0 0

Fig. 4(b)• Radial distribution of mass velocity fluctuation full spectrum

X/

/D

'I/,D

i

X

2

,/,0

_2
16

ORIGINAL pAt3k I,9

OF POOR QUALITY

?YD =1 2 3 5 7 10

St = 0.948

2

M = 0.6 i

9

i

I • •

a

o

a s

mi° md' d

o a

Z p a

• + m p

/D 0 m m a

oP ^ $ ° a o

• ^

a

a

^ p

• p

o

—'Z p

m (1 division = 0.004 )

(a) Radial distribution of phase averaged mass velocity

fluctuation

^p =1 2 3 5 7 0

St = 0.948

2 M = 0.6 m

m

a

m

a m

0 0 I

m

p am

m

o

G

O O"J maa a O p

0

m O

a m m °

m o

0

^a o

mo o m 3 p

m ^ m

I p om m

o

0 0

0

m

p

a

7 m

Fig. 5(b1• Radial distribution of mass velocity fluctuation full spectrum
• • o

^ • s

X/0-

St = 1.263

f M = 0.6

•O op

5

Z^ C

J °p s

o a°

V

17

ORIGINAL i-IAGE la

OF POOR QUALITY

1

0

m (1 division = 0.003 )

(a) Radial distribution of phase averaged mass velocity

fluctuation

r

Z/C) C

r

St = 1.263

M = 0.6

•

ae° 3^, g •

o ° e •

• ° e

o •

m (1 division = 0.050 )

Fig. 6(b)• Radial distribution of mass velocity fluctLation full spectrum
I tt

18

from Z/D = 0.4 to 0.6 for axial locations from X/D = 2 to

X/D = 5 for both the full wave and the phase averaged

fluctuations. Past X/D = 5, where the potential core of the

I jet ends and the mean velocity profiles become fully

developed and self similar, the maximum amplitude of tha

flow fluctuations shift toward the centerline as the flow

^C progressed downstream for both the full wave and the phase

averaged components.

Figures 2 and 3 illustrate that for the low excitation

frequencies, the full wave fluctuations of the mass velocity

profile did not develop into self similar profiles,(become

fully developed) by X/D = 10. However, tha phase averaged

IC, component of the axial mass velocity had developed into a

self similar profile at X/D = 7. Profiles with the maximum

fluctuation level on the jet centerline and a Gaussian

't distribution were defined to be a fully developed profile.

Figure 4 shows that as the excitation frequency

increased from St = 0.158 to St = 0,474, the amplitude of

the fluctuation level increased for the phase averaged and

the full wave components. The location of maximum

fluctuation level was similar to the lower excitation

frequency case. However, the higher the excitation

frequency was, the sooner the profiles become self similar

(fully developed). Figure 4 shows that the full wave and

f,

phase averaged mass velocity fluctuation profiles were

similar to each other at an excitation frequency of St =
19

0.474, and was a fully developed fluctuation profile at

X/D=6.

As the excitation frequency increased (Figure 5-6)

from St = 0.948 to 1.263, the amplitude of the maximum

fluctuation level decreased and the mass velocity profiles

developed in a shorter axial space than the low excitation

frequency case. Since the power input into the exciter

remained constant for all excitation frequencies and ( u)

maximized at St = 0.474, the jet was more responsive to

excitation at this frequency. This explains why Morrison and

Whitaker (351 observed that more noise was radiated by this

jet when excited at this frequency. Therefore, the Mach 0.6

jet is more responsive to mid-range frequency excitation of

St= 0.316 t0 0.632 for both full wave and phase averaged

components.

Figures 7 and 8 show the radial velocity profiles for

the radial velocity fluctuations at excitation frequencies

of St = 0.158 and 0.316. These figuresillustrate that the

radial velocity fluctuations wore fully developed at X/D=5.

However, as the frequency of excitation was increased above

^L St = 0.316 (Figures 9-11), the radial velocity profile did

not become fully developed until X/D=7 for both full wave

and phase averaged fluctuations. The radial velocity

fluctuation (V) was nondimensionlized using the exit value

of axial velocity (U)Q .

M1

Figures 4 and 9 show that the radial profiles for the

-E
zn

t

S.

Xp:

.7

f 4

Z^

T C

OF POOR Q!1ALI7Y

I '

St 0.158

M = 0.6

° o .

a °

•

°^ 3 c

° o

.

.

° •

) ° m

° m °

o

0

4 . (a) Radial distribution of phase averaged radial velocity fluctuation

X/

D

s = 0.158

M = 0.6 °

m .

e

° a

0 ° e

° °

°6a 9 a° o °

a d • o ° a o

°

a ° a

m e

^ I I I I

0 0 0 0 0 0

Fig. 7(b)• Radial distribution of radial velocity Fluctuation full spectrum

Z^D

L, 4

14'

!4.

G

E: 
n

u

^s=

2

1

'/0

 C

_^

_i

21

ORIGINAL PAGE_ iS

OF POOR QUALI f5'

2 3/

St = 0.316

M = 0.6

• • o

e m

e m ° 9 a ° °

eg a a i • a

a

e °

e o

m

yo

9 ° ° • m o e e

m e •

g °

° m

e m

0

^n

• 4

a,

(a) Radial distribution of phase averaged radial velocity fluctuation

= I ^_ 7

2

St = 0.316 a

M = 0.6

a

m

° m

° m8

°•m o a

.L

— i

Fig. 8(b) •

Radial distribution of radial velocity fluctuation full spectrum

i

i^

9

i
t

x, =

ro

2

ZL 0

'D -I

F

22

kjmuatill. ioAGI: Ifi

OF POOR QUALITY

St = 0.474

M 0.6

P

V (1 division = 0.015 )

(a) Radial distribution of phase averaged radial velocity fluctuation

X/

St = 0.474

M = 0.6

C

. ^ s

-C

° i e

°

J (1 division = 0.20 )

Fig. 9(b)• Radial distribution of radial velocity fluctuation full spectrum
23

11C

t t'.

C

ORIGIrwl PACC IS

OF POOR QUALITY

X6=

St = 0.948

M = 0.6

°

°• e • o

e16 m

c

® 0 °

• • °

• a •

•

o °

m

m °

0

11

V (1 division = 0.006 )

Ir (a) Radial distribution of phase averaged radial velocity fluctuation

X,6= ? 3 5 7

Y=

FSt = 0.948

M = 0.6

°

e

e •

e • a a

0m

.0441

°

a 0eo

m8

e

0 • m

Z/D

m m

°

p eo o m o

°

o

° •

o

m o

g°

° o e

° ° I

V (1 division = 0.035 )

Fig. 10(b)• Radial distribution of radial velocity fluct--

ation full spectrum

R

V
i'

ORIGNAt.:-

OF POOR QUALITY

24

Xi -

'D

2

1

C

2 J 5 I IV

St = 1.263

M = 0.6

• d

o d • .

8 mm

0

o ,

q. I

(a) Radial distribution of phase averaged radial velocity fluctuation

Xi

/D

I(

'I L J 5 / IV

St = 1.263

M = 0.6

m

a m

°

o °

m ° m

°° m

0

o m a m

m

a .

m

m . m

°

. m

m

Fig. 11(b)• Radial distribution of radial velocity fluctuation full spectrum

l

Z^D C
Ilf 25

axial and radial flow fluctuations at an excitation

frequency of St - 0.474 became fully developed between X/D =

6 and 7.

Figure 9 shows that at the excitation frequency of St

= 0.474, the jet attained its overall maximum amplitude for

the radial fluctuation for both the full wave and the phase

averaged components. Figures 10 and 11 illustrate that as

the excitation frequency increased above St - 0.474, the

maximum overall radial fluctuation amplitude decreased. in

i! general, the radial velocity fluctuation's radial dependence

compared to the axial mass velocity fluctuations had a lower

amplitude for the full wave arl phase averaged fluctuations

Rt and attained a fully developed radial profile sooner.

This difference in amplitude was expected since the

axial fluctuations include not only the axial velocity

1, 1 fluctuations, but the density fluctuation as well. Figures

7-11 also exhibit that the maximum fluctuation levels of the

radial velocity fluctuation tend toward the centerline of

fl the jet more rapidly than the maximum mass velocity

fluctuation. The radial location of maximum radial velocity

amplitude was at a radial location of 0.4 for the first

1;4

diameter of the flow and then moved outward to 2/D = 0.7 for

the second and third diameters and then moved toward the

centerline at X/D = 5 for both the phase averaged and full

I:(

wave components.

The corresponding Reynolds stress profiles are shown

s 4:

^ti
^r

26

in Figure 12-16. The Reynolds stress profiles possess the

4

same general radial dependence as the radial velocity

fluctuations profiles for X/D < 5 at all excitation

r frequencies. The Reynolds stresses tended to decay faster

i in amplitude than the (fu) and (v) fluctuations for both the

4

jff

full wave and phase averaged fluctuation. This indicates

p' r that the coherence of turbulence is decaying as the flow .P

w; moves downstream since the correlation between the axial

and radial fluctuations was decaying. The Reynold stress

'r (?uv) was nondimensionlized by the mean mass velocity (P(J)e

and mean axial velocity (U)e evaluated at the nozzle exit.

In summary, the velocity profiles of the axial mass

velocity fluctuations were different from ( 'v) and (fuv) for

both full wave and phase averaged fluctuations. (v) and (^

uv) fluctuations attained fully developed profiles by the

end of the potential core while the axial mass velocity

profiles were still developing at X/D = 7 to 10 depending

upon the excitation frequcicy. The axial mass velocity

r: profiles possessed larger amplitude fluctuations than the

(v) and (puv) fluctuations for both full wave and phase

J averaged fluctuations.

r.

3.2 Coherence Level Contours

8:

Characterization of the coherent structures is

valuable since it expands our basic understanding of jet

4
x/p :

`VD (

^l

ORIGINAL PAGE ICJ

27

OF POOR QUALITY

St = 0.158

' M = 0,6

• o

40 ••• •• °

•.

0

0

e• ° ^g • e o a °

o

• °

1

0

( y vu ) (1 division = 0.00025 )

(a) Radial distribution of the phase averaged axial and

radial flow fluctuation correlation

x^J — ` — 2^

St = 0.158

2 M = 0.6 °

e ° a

( o

m °

ip 0 ° o

°

°

°

^^ e

o

o m a

G 7' m

` a

^' ( Puv ) (1 division = 0.0040 1

Fig. 12(b) • Radial di stribution of axial and radial flow

r. fluctuation correlation

Fr 
z s 5 ^ ^^

St = 0.316

M = 0.6 • °

• o

• • % e

a

° • s

°

° ° °

e e

oe

a o

s • e

s

a

o

°

°

°

s

0 0 0 0 0

X/=

'D

U 2

Z/D 0

C

28

ORIGINAL PAGE IS

OF POOR QUALITY

C

( puv ) (1 division = 0.0010 )

(a) Radial distribution of the phase averaged axial and

{ radial flow fluctuation correlation

x^

D

'4

zID

Fig. 13(b)• Radial distribution of axial and radial flow

fluctuation correlation

i

I

i

i 4•'

s = 0.316

Z M = 0.6

• i

I

• e

u e

3

°e

°o ° e

a

D

° • °

°

e ° °

0

°

0 0 0 0 0 0
D

C Z/

/D

C

ORIGINAL PAGE 13

OF POOR QUALITY

St = 0.474

M = 0.6

• e a

• - a ^ a—ea ° o

a^a •^ °0 ° a

e

° e° e °

0

o °

°

( 7uv ) (1 division = 0.0024 )

(a) Radial distribution of the phase averaged axial and

rr radial flow fluctuation correlation

4 1 IV

St = 0.474

2

M = 0.6

°

°

o

° a °0 0

° 8°

as e

° ^ o ° a

°

° ° e

hB g ^ a a

a

0 °

a e

° e

o °

2

0

f ( f uv ) (1 division = 0.030 )

Fig. 14(b)• Radial distribution of axial and radial flow

fluctuation correlation

29

to

2

i

r^ Z^D C

G

—L

a
Y,6=

30

St = 0.948

M = 0.6

0

° •

^ 8aa me •a o m

° ° a m m °

1 ° a•

a

e• m c

°

a

o

• d • e

e •

m °

0

m

a

( Y ) (1 division = 0.0001 )

(a) Radial distribution of the phase averaged axial and

radial flow fluctuation correlation

X

,6 2 3 5 7 10

St = 0.948

M = 5 °

0

a

o

a o

° S °'' Bae °S 0 ° o

. o m a

a

° ° a

oo° Q o ° m °

m

0 0

o

a

0 °

2 °

0 0 0 0 0 0

^' (vu ) (1 division = 0.0025 )

Fig. 15(b)• Radial distribution of axial and radial flow

fluctuation correlation

zL (

Z^

1
II

31

ORIGINAL PAGE 19

OF POOR QUALITY

L J / IV

St = 1.263

2 M = 0.6

°

a , ,

° o

a , o m

a

a m

8 m • a

I ° a o e

m

, a

a ^

X6:

?/D

distribution of the phase averaged axial and

flow fluctuation correlation

1/6=

2

Radial distribution of axial and radial flow

fluctuation correlation

zJ^„T_i i

St = 1.263

M = 0.6

m

0 0

e

o e

m • a

m

y e a

, ° o

a

o m

a o° • e

m m

° o o ° o

0

m °

o y
32

n

Y

?'

e'

V

flowfields. In addition, several theoretical models ([6),

[8), [11) and [17)) suggested that these coherent structures

are of prime importance in the generation of noise. Some of

these theoretical models predicted the development of the

coherent structures present in the flowfield and then use

those results to predict the noise radiated by the jet. One

major problem facing these models is that no extensive

experimental information is available to confirm their

predictions.

Since the coherent structures play an important role

in the generation of noise, the exact percentage of the

overall fluctuations contained in the organized structure at

any location was measured for the Mach number 0.6 jet

exhausting at atmospheric pressure. The fraction of the

axial mass velocity, radial velocity and the correlation of

mass velocity and radial velocity due to organized structure

at excitation frequencies of St = 0.158, 0.316, 0.474, 0.948

and 1.263 (the percent of coherent structure) were obtained

by determining the ratio of the RMS value of the phase

averaged signal to the RMS value of the full wave hot-wire

fluctuation. These measurements were performed at axial

locations of X/D = 1, 2, 3, 5, 7 and 10, and many radial

locations thereby; generating spatial contours of coherence

level for each of the excitation frequencies.

Figures 17-21 show contours of axial mass velocity

fluctuation coherence levels. Figure 17 shows that the

F
33

ORIGINAL PAGE 19

OF POOR QUALITY

N — T CV M

(V^

U)

m

E

L

y

v

^ Nm

_CL

00

>

X\

^oa)

v^

r4,)°

W .^

0 +

N

rn T

°o

c ^+

o a

O >

v.

^o I

I

I

I ^{^

I /I

l l 1

/ I

CO

I C I I I / I ^ l

I^ I I /

I

I / I

^ j I

I I I; / r

I^ I I '/ r

l' 1 I I '^ '

I I I.

,; r

''

J C \

\I

I I

I

n n I I

I

1

p

i

I;r
S

E

N

a

m

L

N

Q^ rip

N

N

1 N

t

1

w

O

N

N

7

N 

^XP

U C

C O

^r

V SJ L

N N

r.

OU u

0 w

],(D

N ?,

L :.

7 ^.a

0 U

O

C

O N

U >

CC

m

u^ l0 I.

00 M

I

i

1 II. • !

I

I

!

I

I

/.

r

I I

!

I

I

!

1 I

I ^, I I / r

I r

I

I I

I I

I I

I: ! I

I

'I

IIIf

I I^'

II I

I'

I 1

I I

I

•^ 1.

I I

1I

I

I

I

_ O

N^

^ N

If 1

1

sa

t
35

^L

ORIG NAL PAGE US

OF POOR QUA:.ITY

fit

r

w

r

IIl i ' / /i I "

^^^

I

^• 1 II I I R

I I^'LnU

U C

C O

I to I ^i L L

:^

I ro 0 U

v 1 a ° 7

r

\. ? ° ^ W rl

V' ^G I ^ \ \\ I O W

•.

it u I111^^— o•u

^O

n c w

^' I u >

M N __ T ti rn

N
36

ORI( NLR4, I AGIi ('a

OF POOR QUALITY

C

N

N

m

e

ipc u r-co `

^

I/ II I >

I ^ I / I N I i

rtl

rn

I C

L

CL

I r O

I ^

i

I —^

N

^

II I ^ I ' ^ I / l I I >

I II (

j(

-Ln

I I;I /

I 1 I^ I (I

c o

I

/

u

I ^\I ( N N /

v

I

I M p ,^

O C I

I

N

W y

oW

II II I/ N>1

L ^ 1

\ 1 :I I I

I / L L

0 •u

O U

+ 0

c

O 0

o>

>

M N — O ^ N I'7

NAP

v+

•M

L

C

C

C

Ic

C

E

f 1^ 
37

ORIGINAL PAO`I? 14;

OF POOR QUALI7Y

I ^

4

I

I I

I 1/ 1 ` \

1 1 I

1 ^

l I

1 ^

1 I j

I 1 n

I I

^ II ^ I I I

^ `I I X11

N ^O Iyl I I ^

.-,c I I^

II II I I I' I

I I: V

I I I I I i

ro N — OQ N

N^

N

N

m

e

v

a

L

N

N

v

N

L

CL

w

O

NH

v

is v

u c

c o

v ..

S4 a

Q) m

L

O +

u u

7

W .-I

O W

N >1

L L

7 ..a

O O

c r+

O v

N

OI

y
1

38

percent of coherent structure varied between 4 and 8 percent

for the very low excitation frequency of St = 0.158. The

figure also reveals that the coherence level reached a

minimum at the edge of the jet as the flow diverged

downstream. However, traversing radially across the jet, the

percent coherent structure gradually increased through the

shear layers and reached the maximum coherency in the center

of jet. This trend occurred up to the fifth diameter of the

jet, which corresponds to the end of the potential core.

ti After the fifth diameter, the coherency level at the jet

centerline gradually decreased as the flow progressed

downstream.

Figure 18 illustrates that as the frequency of

excitation increased to St = 0.316, the coherency level

increased to 13 % at radial locations 2/D = 0.4 through -0.4

F,

1.

and axial location of 1-10 diameters As the edge of jet

L diverged downstream, the coherency level of the edge of the

jet increased 1 % at X/D = 7. Lines of constant coherency

level converged toward the jet center line up to X/D = 7 and

then spread out as the jet moves downstream.

As was explained previously, the jet was more

^. responsive and quite unstable at the excitation frequency of

St = 0.474. Figure 19 shows that the coherency levels range

from 4 to 9 percent. However, the coherency contour levels

do not follow a regular trend. At this excitation

frequency, the edge of the jet attains a high coherency
39

level compared to the coherency level in the shear layers.

This was observed from X/D = 1 to the end of the potential

core. Moving radially inward from the edge of the jet, the

coherency levels decreased and reached a minimum in the

shear layers. Continuing on toward the centerline, the

coherency increased. Beyond the end of the potential core,

the coherency at the edge of the jet increased and the

coherency at the ce erline decreased as the flow progressed

downstream. When the jet was excited at St = 0.474, the

highest coherence levels of phasi averaged mass velocity

fluctuations were attained.

As the frequency increased to St = 0.948, the jet

coherency started to follow a more regular and organized

pattern and behaved similar to when the jet was excited at

St = 0.158 and 0.316. Figure 20 shows that in this case,

the centerline from X/D = 1 to X/D = 3 has the highest .

coherency of 8 %, but the edge of the jet contains the

lowest coherency. It should be noted that the mass velocity

fluctuations had fully developed velocity profiles at X/D =

3. After X/D = 3, the coherency on the centerline drops 2 %

and stays the same all through the jet.

Figure 21 illustrates that the phase averaged mass

velocity fluctuation coherence levels for a very high

excitation frequency of St = 1.263 possessed more organized

contour lines than the jet excited at St = 0.948. The edge

of the jet contains the lowest coherency level until X/D =
/

40

7.5. Moving inward through the shear layers the coherency

levels increase up to a maximum of 6 % at the centerline.

This high coherency at the centerline continues through X/D

r = 7.5. After X/D = 7.5 the coherency level of 5 % which

was dominate in the shear layers starts to move toward the

centerline. Therefore this jet, excited at a very high

frequency, has the lowest phase averaged mass ve!.oci.ty

fluctuation coherence level.

Morrison and Whitaker [35] observed that this jet

Y produced its maximum noise level when excited at St = 0.474.

This corresponds to the case where the coherency level of

the axial flow fluctuations is a maximum on the edge of the

y jet as opposed to on the centerline which was the case for

all other excitation frequencies. This tei..' ,t +_o reinforce

Mollo-Christensen's [28) hypothesis that the organized

^• structures will emitt mor, noise since the jet with more

coherence on the edge of the jet produced more noise!

Figures 22-26 show that the radial velocity

3

fluctuations possessed higner levels of coherency compared

to the axial mass velocity fluctuations. in general, the

tM radial velocity fluctuation coherence contour lines have a

,

Q:

more organized pattern than those obtained for the axial

mass velocity fluctuations at all excitation frequencies.

Figure 22 shows that at a excitation frequency of St =

I

t

 ^. 0.158, the edge of the jet contains a high level of

_ ,.

coherency of 14 percent at all axial locations. At X/D = 1

Y 
41

ORIGINAL PAGE 121

OF POOR QUALITY

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43
L.HI:i1C.'AL PAGE i i

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46

and 2, the jet contains maximum coherency levels of 28 and

22 percent respectivley at the centerline. As the shear

layers grow together at the end of the potential core, the

centerline coherency decreases sharply from 22 to 10

percent. Moving radially inward at X/D = 5, the edge of the

jet has high coherency levels and decreases to a minmum of

10 percent.

Figure 23 shows that for St = 0.316, the jet has a

high coherency of 18 percent at the centerline through X/D =

7.5. Moving radially from the edge of the jet toward the

centerline the coherency level decreases at the shear layers

and increases from the shear layers to the centerline for

X/D = 2 to 7.5. After X/D = 7.5 , the coherency at the edge

of the jet and the centerline start to converge.

Figure 24 shows that the jet excited at St = 0.474

almost exhibits the sane radial dependence as the jet

excited at St = 0.316. Figures 25-26 reveal that as

frequency of excitation increased to St = 0.948 and 1.263

the jet has higher overall radial coherency levels than

those obtained at the other excitation fregencies. Figure

26 shows that moving radially in from the edge of the

jet,the coherency level increased at the shear layers and

then decreased to a minimum at the center line.

Figures 27- 29 show the corresponding Reynold's stress

coherency levels. The Reynold's stress components measured

possesed lower coherencies than those obtained for axial

i

t

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4.
47

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OK!G;'; Al . r .' i 4J

OF POOR QUALITY

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OF POOR QUALITY

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h mass velocity and radial mass velocity fluctuation. Figure

27 shows that the jet contains a high level of coherency at

I: the edge of jet at all axial locations. Moving radially

inward through the shear layers, the coherency level

F,

decreased and then slightly increased toward the centerline

j for the very low excitation frequency of St = 0.158.

k, r Figure 28 shows that as the excitation frequency was

increased to St = 0.316, the coherency level of the

Reynold's stresses did not change significantly and

possessed the same general dependence as the lower

frequency. Figure 29 illustrates that for a mid-range

excitation frequency of St = 0.474, the jet had a high

P coherency level at the centerline. But as flow moved

downstream, the edge of the jet possessed the lowest

coherency for X/D greater than 3. As the excitation

Q' frequency increased to St = 0.948 and 1.263 the coherency

level data were so dispersed that fitting contour lines

between them was impossible.

r^ In summary, the radial velocity fluctuations possessed

higher levels of coherence compared to the axial mass

1

velocity and Reynold's stress. The contours showed that the

^. overall coherence of axial mass velocity, radial velocity

and Reynold's stresses are very high in the potential core

for excitation frequencies of 0.316,< St <,0.632.

G;

C

MOV --
51

3.3 Temporal and Spectral Content o: Phase Averaged Flow

Fluctuations

' 2 Figures 30-36 show the temporal and spectral content

of the phase averaged mass velocity fluctuations for an

excitation frequency of St = 0.474. The spectrum in Figure

30 shows two discrete peaks centered at St = 0.474 and 1.14

dominating the initial fluctuations at X/D = 1 and Z/D =

-0.65. It should be noted that the excitation mechanism

6 input a pulse into the flow and hence contained harmonics.

Therefore the presence of this harmonic is not unexpected

and may not in -ate non-linear interactions. The harmonic

ea peak is wider in breadth and lower in amplitude. This

broadening maybe be due to the fundamental frequency (St =

0.474) varying slightly hence causing a larger variation in

`;y the harmonic.

As the flow progressed downstream to X/D = 3 and Z/D =

0.55 (Figure 31), the coherent structure contained several

discrete peaks. These peaks can all be expressed by nfi +

1

p mfz where f,= 0.318 and f2 = 0.474 which n , m = .....-2, -1,

Ah 0, 1, 2,.,.... This type of frequency interaction was

observed by Miksad [37] in wakes and was indicative of

non-linear interaction.

2 Time traces recorded at the maximum mass velocity

Q, fluctuation level were not quite as periodic as the time

traces obtained at the centerline since the jet attained a

E9
52

^r

OF POOR Qua[ IV

{1

1, B

'Q

e .000E.01

(ALS)

CC.^

i

I I

CE—C3

t (sec)

1r

4

^` d

't

G

(ALS)

2

St

Fig. 30, Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 1 , Z/D = -0.56 , St. xcite = 0.474.
-u3

e .dd^E Cl

(ALS)

,.,3L,

^ I

't

,Y

53

4

ORIGINAL PAGE I15

OF POOR QUALITY

t (sec)

G

(ALS)

I

I

n 1 e

- -

_.2 I

5 t

Fig. 31. Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 3 , Z/D = 0.55 , St excite = 0.474.
4

l:i:.: I:a ^F POOR QUALITY

54

G

(ALS1

Y

'.:CE .IEE^'—C3 .313E-03 

C3

t (sec)

St

Fig . 32• Temporal and Spectral rr_p resentation of the phase averaged mass velocity 

t/X/D = 3 f luctuarion,

Z D = -0.2 S`excite - 0.474.

^C

r 1./

F
ORIGINAL PAGE 19

OF POOR QUALITY

IT

7

:s

e

(AL S)

i a

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.':—*E, . . I ^c -w

. .75E-:3 .53,E-"u3

t (sec)

t-^ a

f4 J

G

(ALS)

u.a 1.5 2.4 3.2

St

Fig. 33• Temporal and Spectral r epresentation of the

phase averaged mass velocity fluctuation,

X/D = 7 , Z/D = 1.0 , St excite= 0.474•

i.

E 

jj ¢'

55
G

(ALS)

56

ORIGINAL PAGE 19

OF POOR QUALITY

e

ccC .Cl (ALS)'

I I I

.C:E^O1 .:5?'c-C3 .315c-03 .a'?..-^; .53CE-03

t (sec)

0 0.8 1.6 2.4 3.2

St

Fig. 34 • Temporal and Spectral representation of the

phase averaged mass velocity fluctuation,

X/D = 7 , Z/D = -0.04 , Stp xcite = 0.474.
lit I'

A 7

CE-C3

k r

e "OE,

(ALS)

57

t

URIGINAL PAGE 19

OF POOR QUALITY

t (sec)

N' F

G

(4LS)

iy

V V3

2

St

Fig. 35. Temporal and Spectral representation of the

phase average mass velocity fluctuation,

. X/D = 10 ,2/D = 0.862 , St excite = 0.474•

I 
ORIGINAL PAGE 19

OF POOR QUALITY

58

e cCCE *o^

(ALS)

C

0„CE- i-E-'3

t (sec)

0.8 1.6 2. 2

St

iporal and Spectral representat i o n of the

se averaged mass velocity fluctuation,

i = 10 , Z/D = -0.06 , Srexcite =0.474.
59

higher coherency level (Figure 19) at the centerline.

Figure 32 shows that at the centerline of the jet for the

same X/D = 3, the coherent structure was periodic with a

fundamental frequency of St = 0.474 with several harmonics

through St = 2.22. As shown in Figure 19, this also was the

location wit,i the highest coherency level. It is important

to note that as the flow progressed downstream, the

fundamental frequency increased in amplitude. Figures 33-34

show that at X/D = 7 the jet contained a periodic time trace

but the large discrete amplitude peaks, except the

fundamental frequency, disappear in the shear layer and at

the centerline of the jet. These fundamental frequencies

centered at 0.474 were followed by several low amplitude

harmonics. At X/D = 10 (Figure 35-36) the jet lost its

periodic time trace and the fundamental frequency sharply

decreased in amplitude. The production of several discrete

frequencies and spectra broadening downstream at X/D = 10

may i .ndicate stages of non-linear spectral interaction.

Figures 37-43 show the temporal and spectral content

of the phase averaged radial velocity fluctuations for the

excitation frequency of St = 0.474 at the same locations as

the previous phase averaged mass velocity fluctuation

measurements. All spectral analyses of phase averaged

radial velocity fluctuations (Figures 37-48) showed that the

fundamental frequency of St = 0.474 with a high amplitude

dominated the entire flowfield from X/D = 1 to 10. This

J

I 
Ir

I I I

v

e .aoce.a1

(AL5)

i

G

(ALS)

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60

L t

URIGINAL PAGE 19

OF POOR QUALfTY

,_2:6Z-"3 .d'?6^_C3 .63C?-_3

t (sec)

Q

+8

;F

Ni

St

Fig. 37. Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

X/D = 1 , Z/D = -0.56 , St 

excite= 

0'474'
I 7

)

^

I:

t

I I

U. e

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(ALS)

If , a

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(ALS)

C

ORIGINAL PAGE 19

OF POOR QUALITY

Id t

61

tlC_E•31 .158E-v3 .3!5E-^3 5---:3 .53"E-:3

t (sec)

r

St

Fig. 38 • Temporal and Spectral representation of the

d = phase averaged radial velocity fluctuation,

X/D = 3 , Z/D = 0.55 , 

St ekcite = 0.474,
G

(ALS)

62

ORIGINAL PAGE 19

OF POOR QUALITY

e JJ^E+v1

(ALS)

I I I

. ZZ ZE+

t (sec)

0 0.8 1.5 2.4 3.2

St

Fig. 39• Temporal and Spectral representation of the

phase averaged radial .elocity fluctuation,

X/D = 3 , Z/D = -0.2 Stexcite = 0.474.
1

r

63

ORIGINAL PAGE 19

OF POOR QUALITY

i

Y

G

(ALS)

^Y

f

^A ti

fr

14

Sr

F:

'A

h.

e

t (sec)

e 7 3E,^1

(ALS)

E. -E-C3

g

i

0 0.8 1.6 2.4 3.2

St

Fig, 40. Temporal and Spectral representation of the

phase averaged 'cadial velocity fluctuation,

X/D = 7 , Z/D = 1.0 , Stexcite = 0.474.
G

(ALS)

64 ORIGINAL PAGE 1

OF POOR QUALITY

.i53E-:3 .31bE-C3 ""5^-':3 63;.-53

t (sec)

u

0 0.8 2.4 3.2

St

Fig. 41. Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

x/n = 7- Z/p -0,04 , —excite = 0.474.
^' Y

y G

^• ( ALS )

A" Y

It C

65

T

I 3

ORIGINAL PAG 1$

OF POOR QUALITY

e .00aEcl

(ALS)

N

Fr !.

kry Y

-, .!SPE-L'3 .3!5E-C3 '26E-C3 .63E-03

t (sec)

L }'

..1 4.4 3.2

St

Fig, 42. Tempor l and Spectral representation of the

phase averaged radial velocity fluctuation,

X/D = 10 , 2/D = 0.862 , St excite = 0.474•
e .0CCE*C1

(ALS)

n1 C

n Q

IC

E-'3

t (sec)

r

G

(ALS)

O!1IGINAL PA GE

19 OF POOR QUALITY

Mr

66

0 0.8 1. .4 3.2

St

Fig. 43. Temporal and Spectral representation of the

phase averaged radial velocity fluctuation,

X/D = 10 , Z/D = -0.06 , St excite = 0.474•

ice— -

- --- --.
ORIGINAL PAGEis Of pOOR QUALITY

e .06CE+01

(ALS)

SBE-:3 .3: 5:-C3 , 47:BE-C3 63,Ed3 .

t (SeL)

G

(ALS)

0 U.8 1.5 .2

St

Fig 44. Tem p oral and Spectral representation of the

phase averaged axial and radial flow Eluccuation correlation, X/D = 1 Z/D = -4•So ,

Stexcite = 0.474.

S

i

67
"5

(

AL S).50;

.:5

r,

r,

r

E

(AL')

2'

CF.-C3

t (sec)

r

r

ORIGINAL PAGE 19

OF POOR QUALITY

68

::,t

Fig. 45• Temporal and Spectral representation of the

phase averaged axial and radial flow fluctuation correlation, X/D = 3 , Z/D = 0.55

St excite = 0.474.

,r
e

( ALS )

I; T

I d

y.

C^

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E-03

It t'

O(tl{,tt, AL PAGE i.,s

OF POOR QUALITY 69

r

t (sec)

c^

t,

` G

Q' ( ALS )

t

S 0 0.8 1.6 2.4 3.2

St

!F Fig. 46 • Temporal and Spectral repr esentation of the phase av eraged axial and radial flow fluc t- uation cor relation, X/D = 3 , Z/D = -0.2

St excite= 0.474•

I^
CCJE.. °_-:3

t (sec)

0 0.8 1.6 2.4 3.2

St

Fig. 47• Temporal and Spectral representation of the

phase averaged exial and radial flow fluct•-

ion correlation, X/D = 7 , Z/D = 1.0

xcite = 0.474.

I( Y

70 ORIGINAL PAGE IS

OF POOR QUALITY

e cce.c:

BLS)

c

G

a

(ALS)

K.
I' 4'

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( ALS )

Q;

11 r

I` t

ORIGINAL PAGE 19 71

OF POOR QUALITY

4'

0 0.8

3.2

St

^o Fig, 48 Temporal and Spectral re presentation of the

phase averaged axial and radial Clow fluctuation correlation, x/D = 7 , Z/D = -0.04

St excite = 0.474.
1

c;

}

p qi

72

fundamental frequency of St = 0.474 was followed by several

relatively high amplitude harmonics with frequencies up to

St = 2.35 all through the jet. The spectral content of the

mass velocity fluctuations followed the same trend but had a

fundamental frequency amplitude peak and this fundamental

frequency was followed by a few relatively low amplitude

harmonics up to X/D = 7. The temporal representations of

radial velocity showed that the radial velocity fluctuations

had very periodic time traces all through the jet compared

to the mass velocity fluctuation time traces. Comparing the

time traces of mass velocity and radial velocity

fluctuations, it was evident that the time traces were not

in phase with each other. This difference in phase could

cause the relatively high amplitude harmonics in Reynolds

stress fluctuations; this may explain why there was a high

coherency level in the radial velocity fluctuations and

Reynold's stresses.

Figure 37 show that at the maximum radial velocity

fluctuation amplitude,the jet had three discrete peaks with

a relativly low amplitude subharmonic. As the flow

progressed downstream (Figure 38-41) to X/D = 3, the

subharmonic increased in amplitude for maximum radial

velocity fluctuation amplitude and the discrete peaks

reduced in amplitude. However, the fundamental frequency

amplitude was still higher in amplitude than the other

discrete peaks. Moving radially towards the centerline at

tt

^s
I

73

I

I

/

/

/

X/D = 3, the subharmonic frequency reduced and completely

disappeared at the centerline of the jet. In the same

region, the fundamental frequency was followed by harmonics.

Figures 42-43 exhibit that at X/D = 10 the jet lost its

periodicity as compared to the axial locations upstream. At

this location, the centerline of the jet had the same high

amplitude discrete peak component followed by harmonics for

both the Z/D = 0.862 and centerline locations.

Figures 44-50 illustrate the corresponding temporal

and spectral content of the phase averaged axial and radial

flow fluctuation correlation. Figures 44-45 show that the

jet did not have a periodic time trace at the maximum

amplitude fluctuation at X/D = 1 and 3, but the spectral

content had five discrete peaks. These discrete peaks

reduced in amplitude as frequency inceased. Figure 46 shows

that at X/D = 3 on the centerline the jet almost had a

periodic time trace with a 2/3 subharmonic and a fundamental

frequency centered at St = 0.474 and 1.01 respectively.

Figures 47-48 show that as the flow moved downstream to X/D

= 7 the time trace and spectral content behaved like those

obtained at X/D = 3. Figures 49-50 illustrate that at X/D =

10 and a radial location of Z/D = 0.862 and the centerline

the jet had a discrete peak centered at St = 0.159 followed

by harmonics ranging from St = 0.32 to 2.99.

I;

Yrr

C-°
. UCCr.. ^^-;3

ORIGINAL PAGE IS

OF POOR QUALITY

74

e .000E*CI

( ALS )

t (sec)

G

(ALS)

0 0.8 1.6 2 .4 3.2

St

Fig. 49 Temporal and Spectral representation of the

phase averaged axial and radial flow fluctuation correlation, X/D = 10 , Z/D = 0.862

St excite = 0.474.
e .OGLE-01

(ALS)

ORIGINAL PAGE q01 POOR QUALITY

75

C1 58°- '2 .3; 5E-C3 ,4735E-"3 .537E-C3

t (sec)

i I 1

G

(ALS)

)0

0 0.8 1.6 2.4 3.7-

St

Fig. 50• Temporal and spectral representation of the

phase averaged axial and radial flow fluctuation correlation, Y/D = 10 , Z/D = -0.06,

Stexcite = 0.474.

' 6 
R

76

P CHAPTER IV

CONCLUSIONS AND RECOMMENDATIONS

4.1 Conclusions

The following conclusions may be drawn from the

experimental investigation reported herein.

(1) Mass velocity fluctuation profiles showed that as

the excitation frequency increased from St

the maximum fluctuation amplitude increased

..he excitation frequency increased from St

the maximum fluctuation amplitude gradually

the mass velocity profiles developed sooner

excitation frequency case.

0.156 to 0.474,

. However, as

0.474 to 1.263,

decreased and

than the low

(2) The overall axial mass velocity fluctuation

levels maximized for an excitation frequency of St = 0.474.

Therefore, the jet was more responsive to excitation at this

frequency since the power input to the exciter was held

constant.

(3) The axial mass velocity fluctuations had a higher

amplitude than the radial velocity fluctuations and the

Reynold's stresses because the axial mass velocity

fluctuations include not only the axial velocity

fluctuations, but the density fluctuation as well. The

Reynold's stresses had the lowest amplitude fluctuation

because the correlation between the axial and radial

fluctuations decayed faster in amplitude.
a

77

( 4 ) The radial velocity fluctuations' radial

dependence compared to the axial mass velocity fluctuations

had a lower amplitude for the full wave and phase averaged

fluctuations and attained a fully developed profile sooner.

(5) The maximum fluctuation levels of the radial

velocity fluctuation tend toward the centerline of the jet

more rapidly than the maximum mass velocity fluctuations.

(6) The Reynolds stress profiles possess the same

general radial dependence as the radial velocity

fluctuations profiles for X/D < 5 at all excitation

frequencies.

(7) The Reynolds stresses tended to decay faster in

amplitude than Vu) and (v) fluctuations for both the full

wave and phased average fluctuations.

(8) The radial velocity fluctuations possessed higher

levels of coherence compared to the axial mass velocity and

Reynold's stress. The overall coherence of the axial mass

velocity, radial velocity, and Reynold's stresses are very

^• high in the potential core for excitation frequencies of

0.316 ^<,St ,^ 0.632. This would suggest that these coherent

K^

r

structures are important in the generation of noise since

( the jet produced its maximum noise level when excited at

these frequencies.

(9) The maximum mass velocity fluctuation levels were

not quite as periodic as the time traces obtained at the

centerline since the jet attained a higher coherency level

:^
78

r

1

^, r

i'

r

u

i

1

4.♦m

I^r `

f'

at the centerline.

(10) The production of several discrete frequencies and

spectra broadening as the flow progress = d downstream for the

axial mass velocity fluctuations at X/D = 10 may indicate

stages of non-linear spectral interaction.

(11) Comparing the time traces of miss velocity and

radial velocity fluctuations, it was evident that the time

traces were not in phase with each other. This difference

in phase could cause the relatively high amplitude harmonics

in the Reynold's stress fluctuations; this may explain why

there was a high coherency level in the radial velocity

fluctuation and Reynold's stresses.

(12) The corresponding temporal and spectral content of

the phase averaged axial and radial flow fluctuation

correlation show that the jet did not have a periodic time

trace at the maximum amplitude fluctuation at X/D = 1 and 3.

4.2 Recommendations

To futher enhance the state of knowledge in this area,

the following studies are recommended:

(1) Sound pressure level contours of noise that is

directly emitted by the coherent structure in the jet should

be measured. This set of measurements can provide valuable

information about the location and directivity of the

coherent noise produced by the jet.
I 79

I e' (2) The Reynolds stress components of the coherent

structure should be measured when the jet is not excited.

Therefore, two crossed hot wire probes should be used to

I measure the axial wavelength of the different frequency

components being studied. This will help to determine if

the artificial exciter is altering these components from the

If naturally ocurring state.

(3) The phase relationship between the three different

quantities measured by the crossed hot-wire probes (?U, v,f

uv) should be studied.

(4) The percentages of the turbulent kinetic energy

and turbulence dissipation rate contained in the coherent

structure should be measured for the Mach number 0.6 jet.

D
80

r REFERENCES

1. Lighthill, M. J., " On Sound Generated

Aerodynamically, I General Theory'', Proc. Roy. Soc., A211

(1952), PP. 546-587.

2. Lighthill, M. J., ''On Sound Generated

Aerodynamically, II Turbulence as a Source of sound'', Proc.

Roy. Soc., A222 (1954), PP. 1-32,

3. Ffowcs Williams, J. E., " The Noise From Turbulence

Convected at High Speed'', Phil. Trans. Roy. Soc., A255

9 (1963), PP. 459.

4. Ribner, H. S., ''The Generation of Sound by

Turbulent Jets'', Advances in Applied Mechanics, Vol. 8

(1964), PP. 103-182.

5. Phillips, 0. M., ''on the Generation of Sound by

Supersonic Turbulent Shear Layers" , J. Fluid Mech., Vol. 9

(1960), PP. 1-28.

6. Pao, S. P., and M. V. Lowson., ''Some Applications

of Jet Noise Theory'', AIAA Paper No. 70-233, 1970.

7. Lilley, G. M., P. Morris, and B. J. Tester., " On

the Theory of Jet Noise and its Applications'', AIAA Paper

No. 73-987, 1973.

B. Doak, P. E., ''Analysis of Internally Generated

Sound in Continuous Materials: 2. A Critical Review of the

Conceptual Adequacy and Physical Scope of Existing Theories

of Aerodynamic Noise, with Special Reference to Jet Noise " ,

Journal of Sound and Vibration., Vol. 25 (1972), PP.

` 263-335.

i

9. Tam, C. K. W., " On the Noise of Nearly Ideally

r

Expanded Supersonic Jets" , J. Fluid Mech., Vol. 51 (1972),

PP. 69-95.

ti.

0. 10. Tam, C. K. W., ''Directional Acoustic Radiation

from a Supersonic Jet Generated by Shear Layer

Instability " , J. Fluid Mach., Vol. 46 (1971), PP. 757-768.

11. Tam, C. K. W., ''Supersonic Jet Noise Generated by

I Large Scale Distubances " , AIAA Paper 73-992, 1973.

12. Tam, C. K. W., "Supersonic Jet Noise Generated by

Large Scale Disturbances " , J. Sound and Vibration, Vol. 38

(1975), PP. 51-79.

r

r_
I

13. Chan, Y. Y., " Discrete Acoustic Radiation from a

High Speed Jet as a Singular Perturbation Problem'',

Canadian Aeronautics and Space Journal, Vol. 21 (1975), PP.

221-7.27.

14. Chan, Y. Y., " Noise Generated Wavelike Eddies in a

Turbulent Jet" , ICAS Paper No. 76-42, 1976

15. Liu, J. T. C., ''Developing Large-Scale Wavelike

Eddies and the Near Jet Noise Field " , J. Fluid Mech ., Vol.

62 (1974), PP. 437-464.

16. Morris, P. J., ''The Spatial Viscous Instability of

Axisymmetric Jets " , J. Fluid Mech., Vol. 77, Part (1976),

PP. 511-529.

17. Morris, P. J., " Flow Characteristics of a

Large-Scale Wavelike Structure of a Supersonic Round Jet" ,

J. Sound and Vibration, Vol. 53 (1977), PP. 223-244.

18. Winant, C. D. and Browand, F, K., " Vortex Pairing,

the Mechanism of Turbulence Mixing Layer Growth at Moderate

Reynolds Numbers'', J. Fluid Mech., Vol. 63 (1974), PP.

237-256.

19. Crow, S. C. and Champagne, F. H., ''Orderly

Structure in Jet Turbulence " , J. Fluid Mech., Vol. 48

(1974), PP. 237-256.

20. Lau, J. C., Fisher, M. J. and Fuchs, H. V., " The

Intrinsic Structure of Turbulent Jets" , J. Sound and

Vibration, Vol. 22 (1972), PP. 379-406.

21. McLaughlin, D. K., Morrison, G. L. and Troutt, T.

R., ''Experiment on the instability Waves in a Supersonic

Jet and Their Acoustic Radiation " , J. Fluid Mech., Vol. 69

(1976), PP. 73-95.

22. McLaughlin, D. K., Morrison, G. L. and Troutt, T.

R., ''Reynolds Number Dependence in Supersonic Jet Noise" ,

AIAA J., Vol.. 15 (1977), PP. 526-532.

' K ` 23. McLaughlin, D. K., Morrison, G. L. and Troutt, T.

R., ''Experiments on the Instability Waves in a Supersonic

Jet and Their Acoustic Radiation" , In Proceedings of the

u M Sound Interagency Symposium on University Research in

Transportation Noise, Raleigh, North Carolina, June 1974.

i 24. Morrison, G. L. and McLaughlin, D. K., " The

Instability Process in Low Reynolds Number Supersonic 

Jets" , AIAA J., Vol. 18 (1980), PP. 793-800.

25. Morrison, G. L. and McLaughlin, D. K., " The Noise

k

Y
Generated by Instabilities in Low Reynolds Number Supersonic

Jets" , J. Sound and Vibration. Vol. 65 (1979), PP. 177-191.

26. Morrison, G. L., " E'low Instability and Acoustic

Measurements on Low Reynolds Number Supersonic Jets " , Ph.D.

Dissertation, Oklahoma State University, 1977.

27. Stromberg, J. L., " Flowfield and Acoustic

Measurements of Low Reynolds Number Jets in a Transonic

Range'', M.S. Thesis, Oklahoma State University, 1978.

28. Mollo-Christensen, E., ''Jet Noise and Shear Flow

Instability Seen From an Experiment's Viewpoint" , J. Appl.

Mech., Vol. 34 (1967), PP. 1-7.

r

29. Moore, C. J., ''The Role of Shear Layar Instability

Waves in Jet Exhaust Noise" , J. Fluid Mach., Vol 80, Part 2

(1977), PP. 321-367.

30. Morrison, G. L. and Whitaker, K. W., " Mach Number

x' Dependence of the Coherent Structure in High Speed Subsonic

Jets " , AIAA. Paper No. 82-49.

31. Browand, F. K. and Laufer, J., ''The Role of Large

Scale Structures in the Initial Development of Circular

Jets " , Proceeding of the Fourth Biennial Symposium on

^• Turbulence in Liquids, University of Missouri at Rolla.

September, 1975.

32. Hussain, A. K., Kleis, S. J., and Sokolov, M., " A

'Turbulent Spot' in an Axisymmetric Free Shear Layer. Part

2 " , J. Fluid Mech., Vol. 98, Part 1 (1980), PP. 97-135.

33.• Horstman, C. C. and Rose, W. C., ''Hot-Wire 

Anemometry in Transonic Flow " , AIAA J., Vol. 15 (1977), PP.

395-401.

34. Johnson, D. A., and Roso, lJ. i., " ,user Velocimeter

and Hot-wire Anemometr y Ci , jmparison in a Supersonic Boundary

Layer" , AIAA J., Vol.. 13, No. 4 (1975), PP. 512-515.

35. Whitaker, K. W., and Morrison, G. L., "Near Field

Acoustic Measurements in Natural .nd Artificially Excited

High Speed Subsonic Jets" , AIAA. Paper No. 83-725.

36. Morrison, G. L., and Wattanachayakul, M., ''Large

Scale Structure in a Mach Number 0.7 Jet" , AIAA. Paper No.

81-59.

37. Miksad, R. W., ''Experiments on Non-Linear

Interactions in the Transition of a Free Shear Layer", J.

S> Fluid Mech., Vol. 59 (1973), PP. 1-21.

m:

i
ORIGINAL FACE f£;

OF POOR QUALnY

APPENDIX A

sot-Wire Data seduction Technique

I^ A hot-wire data reduction technique similar to that

outlined by Horsman and Rose [331 and Johnson and Rose [341

i

was used in this study. This method let us directly

i calibrate the sensitivity of the hot-wire to the axial mass

velocity and radial velocity for each hot-wire probe used.

Ir' In this manner, the substantial conduction end losses are

accounted for. The sensitivity of the hot-wire to

stagnation temperature fluctuations (AT+) is calculated

using hot-wire voltage and resistance data recorded at

constant flow conditions.

The bridge voltage, E b , of the hot-wire is comprised

t of two parts, a fluctuating component, e , and a time

averaged mean value, E. An oblique hot-wire responds to

axial mass velocity (fu), stagnation temperature (To), and

+J radial velocity (v) fluctuation according to:

e

ll M`

_Z

- Am t AVE m - AT T u 0

The sensitivity coefficients A m

AT

and Ay can be

evaluated as follows: A

aIn E

m

alnu) -I(p To R w , ,X constant

din E

4

---)

d a u, f TO, RW constant

F _)In E i

!^

A 

T - aln-T-01 Yu, RW, a< constant
r

84

both A.m and Ay were evaluated by direct calibration of each

wire in the flow using the relations above. Following the

G' method of Horsman and Rose (33] and Johnson and Rose (341

the stagnation temperature sensitivity was evaluated as

follows:

In Tw In E + 1 _ RW ] +0.765 Am - 0.9425

y AT = --rn Rw ( In RW 2 RSV + Rs

The crossed hot-wires were matched so that A l

and Ay

were approximately the same for each wire. The output of

the two wires were then instantaneously added and subtracted

so that the two resulting voltages would be proportional to

m / m and v/ U Hence, neglecting stagnation temperature

fluctuations: v

( el e2ems (E l A vl + E 2 A v2 ) ( )rms

^P ( e l + e2) = (ElAMI+ E2Am2) m

rms

Q; where ( e l - e2) corresponds to radial velocity fluctuations

rms

and( el+ e2)rmsto axial mass velocity fluctuations.

IC,

C
85

Q^

4

i

6.

c

1:

, 

^ F.

C

APPENDIX B

C--------> THIS PROGRAM IS WRITTEN FOR EXCITED JET MACH#= .6

DIMENSION

NAME(6),RIDATA(100),R2DATA(100),R3DATA(100),X(100)

*,DATA(2,100),XMULT(100)

WRITE(2,43)

43

FORMAT(1X,3X,'Z',4X,'E1',4X,'E2',5X,'SUM',5X,'DIFF',$X,

*'UVRMS',5X,'AM1',5X,'AM2',5X,'MBAR',6X,'M/MBAR',4X,'V/

VBAR',

*3X,'RHO*UV',4X,'FM/MBAR',4X,'FV/VBAR',3X,'FRHO*UV')

WRITE(3,66)

66 FORMAT(' WHAT IS BIO S.RATE,SEC(F10.4),AND EXCITED

FREQUNCY,I6f/)

READ(3,67)BSR,IFRQ

67 FORMAT(F10.4,I6)

111 FORMAT(' BIO SAMPLING RATE=',F10.7)

112 FORMAT(' EXCITED FREQUNCY=',I6)

WRITE(3,4)

4 FORMAT(1X,'WHAT IS THE NAME OF THE FILE TO WRITE

IN?',/)

READ(3,5)(NAME(I),I=1,6,1)

5 FORMAT(6A2)

CALL CiPEN(6,NAME,2)

WRITE(6,111)BSR

C--------> READING SAMPLING RATE

WRITE(6,112)IFRQ

C--------> READING EXCITATATION FREQUENCY

DO 900 I=1,100

X(I)=I

900 CONTINUE

DO 333 I=1,100

RIDATA(I)=0.0

R2DATA(I)=0.0

R3DATA(I)=0.0

333 CONTINUE

WRITE(3,6)

6 FORMAT(' WHAT IS TH! BIO SENSITIVITY = ? (F4.1)',/)

READ(3,7)BS

7 FORMAT(F4.1)

WRITE(6,113)BS

113 FORMAT(' BIO SENSITIVITY=',F4.1)

WRITE(3,21)

21 FORMAT(' HOW MANY TIMEfj DO YOU WANT TO TRIGGER BIO',/)

----------> NUMBER OF TRIGGERING OF TIMES BIOMATION

READ(3,22)NN

22 FORMAT(I3)

CALL DC(1.,1000,DC1)

CALL DC(2.,1000,DC2)

----------> READING DC VALUE
r.

t,

r

G

r

i

7

P

c.'p

a:

86

DO 334 KK=1,NN

WRITE(3,888)KK

888 FORMAT(' SAMPLE NUMBER ',I3)

CALL SUBBI2(DATA)

DO 23 I=1,100

RIDATA(I)=DATA(1,I)+RIDATA(I)

R2DATA(I)=DATA(2,I)+R2DATA(I)

23 CONTINUE

SUMI=0,

SUM2=0.

DO 24 I=1,100

SUMI=SUMI+DATA(1,I)

SUM2=SUM2+DATA(2,I)

24 CONTINUE

SUMI=SUMI/100.

SUM2=SUM2/100.

DO 25 I=1,100

XMULT(I)=(DATA(1,I)—SUM1)*(DATA(2,I)—SUM2)*(BS/256.)**

2

25 R3DATA(I)=XMULT(I)+R3DATA(I)

IF(KK.GT .10)GO TO 26

— — --> FINDING RMS VALUE

CALL RMSV(ANS,XMULT,100)

XSUM=ANS+XSUM

26 CONTINUE

334 CONTINUE

SUMI=0.0

SUM2=0.0

DO 10 I=1,100

SUMI=SUMI+RIDATA(I)

SUM2=SUM2+R2DATA(I)

10 CONTINUE

AVEI=SUMI/100.

AVE2=SUM2/100.

WRITE(3,392)AVEI,AVE2

392 FORMAT(' AVE1 = ',Ell.4,' AVE2=',Ell.4)

DO 20 I=1,100

RIDATA(I)=(RIDATA(I)—AVE1)*BS/256.

R2DATA(I)=(R2DATA(I)—AVE2)*BS/256.

20 CONTINUE

E2=CC2

E1=DC1

WRITE(3,18)E1,E2

18 FORMAT(' E1=',F4.2,' E2=',F4.2)

IF(E2.GT.5.0)GO TO 1000

IF(E2.GT.4.5)GO TO 1002

A20=2.61437

A21=0.31366

A22=-0.012717

GO TO 1001

1000 A20=4.2398

A21=0.03529

r
87

1'1

A22=-0 000185

GO TO 1001

1002 A20=3.7868

A21=0.071825

A22=-.0009514

1001 CONTINUE

IF(E1.GT.5.)GO TO 1003

IF(E1.GT.4.5)GO TO 1004

A10=2.61437

A11=0.31366

Al2=-0.012717

GO TO 1005

1003 A10=4.2398

A11=0.0_'529

Al2=-0.000185

GO TO 1005

1004 A10=3.7868

A11=0.071825

Al2=-0.0009514

1005 CONTINUE

--------> FINDING HOT-WIRE COEFFICIENT

DISC=All*All-4.*Al2*(A10-E1)

RM1=(-1.*All+SQRT(DISC))/(2.*Al2)

DISC=A21*A21-4.*A22*(A20-E2)

RM2=(-1.*A21+SQRT(DISC))/(2.*A22)

AM1=(RM1*(All+2.*Al2*RM1)/(A10+All*RM1-FAl2*RM1*RM1))

AM2=((RM2*(A2].+2.*A22*RM2))/(A20+A21*RM2+A22*RM2*RM2)

AV1=-0.077114

AV2=0.0727741

RIXMAX=0.0

RIXMIN=0.0

R2XMAX=0.0

RIXMIN=0.0

R3XMAX=0.0

R3XMIN=0.0

DO 222 I=1,100

RIDATA(I)=RIDATA(I)/KK

IF(RIDATA(I).GT.RIXMAX)RIXMAX=RIDATA(I)

IF(RIDATA(I).LT.RIXMIN)R],XMIN=RIDATA(I)

R2DATA(I)=R2DATA(I)/KK

IF(R2DATA(I).GT.R2XMAX)R2XMAX=R2DATA(I)

IF(RIDATA(I).LT.R2XMI[4)R2XMIN=R2DATA(I)

R3DATA(I)=R3DATA(I)/KK

IF(R3DATA(I).GT.R3XMAX)R3XMAX=R3DATA(I)

IF(RIDATA(I).LT.R3XMIN)R3XMIN=R3DATA(I)

222 CONTINUE

----------- > PLOT ON CRT

CALL CRT(X,RIDATA,RIXMAX,RIXMIN,100.,1.,100)

PAUSE

CALL CRT(X,R2DATA,R2XMAX,R2XMIN,100.,1.,100)

PAUSE

IH

L

.-

_..
CALL CF<T(X,R3DATA,R3XMAX,R3XMIN,100.,1.,100)

Q' PAUSE

CALL RMSV(SUMRMS,RIDATA,100)

CALL RMSV(DIFRMS,R2DATA,100)

CALL RMSV(UVRMS,R3DATA,100)

RHOU= (RM1+Rt12) / 2 .

TWIM=SUMRMS/(E1*AM1+E2*AM2)

Q VPRIMU=DIFRMS/(E2*AV2-E1*AV1)

RUOUV=UVRMS/((E1*AM1+E2*AM2)*(E2*AV2-E1*AV1))

WRITE(3,527)

527 FORMAT(' WHAT IS VALUE OF (SUMFRU,SUMFV,F8.4,)'

{ READ(3,528)SUMFRU,SUMFV

526 FORMAT(2F8.5)

SUMFUV=XSUM110.

FVPRIM=SUMFV/(E2*AV2-E1*AV1)

FTWIM=SUMFRU/(E1*AMI+E2*AM2)

FRUOUV=SUMFUV/((E1*AM1+E2*AM2)*(E2*AV2-E1*AV1))

WRITE(3,288)

288 FORMAT(' WHAT IS THE LOCATION OF (X),(Y),(Z),6.

"' READ(3,289)X1,Y,Z

289 FORMAT(3F7.3)

! WRITE(6,290)X1,Y,Z

290 FORMAT(' X= ',F7.3,' Y = ',F7.3,' Z=',F7.3)

WRITE(3,28)

28 FORMAT(' WHAT. IS THE STAG PO ("HG,F4.2),AND TO

(I2)', /)

READ(3,29)PO,ITO

29 FORMAT(F6.3,I2)

WRITE(6,45)PO,ITO

45 FORMAT(' PO=',F6.3,' TEMP=',I2)

WRITE(6,30)E1,E2

30 FORMAT(' DC1=',E11.4,' DC2=',E11.4)

t WRITE(6,32)AM1,AM2

32 FORNIAT(' AM1= 1 ,E11.4,' AM2=',E11.4)

WRIIE(6,34)RHOU

34 FORMAT(' RHOU AVE=',E11.4)

WRITE (6 , 42) RiIOUV

42 FORMAT(' RUOUV=',E11.4)

WRITE(6,35)TWIM,VPRIMU

3'r/)

1

88

X

35 FORMAT(' RHOU PRIME(RMS)/RHOU AVE = ',E11.4,' VPRIME RMS

*/VAVE=',E11.4)

WRITE(6,39)FTWIM,FVPRIM,FRUOUV

39 FORMAT(' FRHOU PRIME/RHOU AVE=',E11.4,'

FVPRIME /VAVE',E11.4

*,' FRUOUV=',E11.4)

WRITE (2r44)ZrEI E2,SUMRMS,,DIFRMSrUVRMS,AM1 AM2r RHOU rTW

IM,

*VPRIMU,R000V,FTWIM,FVPRIM,FRUOUV

44

FORMAT(1X,F6.3,1X,F5.3,1X,F5.3,1X,F6.4,3X,F6.4,2X,F7.4,2X,

*F7.5,1X,F7.5,2X,F8.3,4X,F7.5,1X,F7.5,F10.5,4X,F7.5,4'C,

F7.5,

vF

Fyo...
M

r.

f'

t

89

*2X,F8.5)

WRITE(3,8888)

8888 FORMAT(' READY TO WRITE DATA ON DISK')

WRITE(6,37)(RIDATA(I),R2DATA(I),R3DATA(I),I=1,100,1)

37 FORMAT(1X,6E1.1.4)

ENDFILE 6

STOP

END

i^

h.

up.

s^

^_,

`w

n;

C**********************************t***********r***********

C THIS PROGRAM USES THE FAST FOURIER TRANSFORM ALGORC ITTHM AND IT MUST BE CALLED FROM MAIN PROGRAM.

C**********************************************************

SUBROUTINE FFT(XREAL,XIMAG,N,NU)

DIMENSION XREAL(N),XIMAG(N)

N2=N/2

NU1=NU-1

K=0

DO 100 L=1,NU

102 DO 101 I=1,N2

P=IBITR(K/2**NU1,NU)

ARG=6.283185*P/FLOAT(N)

C=COS(ARG)

S=SIN(ARG)

K1=K+l

K1N2 =K1+N2

TREAL=XREAL(K1N2)*C+XIMAG(K1N2)*S

TIMAG=XIMAG(K1M2)*C—XREAL(K1N2)*S

XREAL(K1N2)= 2:F.EAL(Kl)—TREAL

XIMAG(K1N2)=XIMAG(Kl)—TIMAG

XREAL(K1)=XREAL(K1)+TREAL

XIMAG(K1)=XIMAG(K1)+TIMAG

101 K=K+1

K=K+N2

IF(K.LT.N)GO TO 102

K=0

NU1=NU1-1

100 N2=N2/2

DO 103 K=1,N

I=IBITR(K- 1,NU)+1

IF(I.LE.K)GO TO 103

TREAL=XREAL(K)

TIMAG=XIMAG(K)

XREAL(K)=XREAL(I)

XIMAG(K)=XIMAG(I)

XREAL(I)=TREAL

XIMAG(I)=TIMAG

103 CONTINUE

RETURN

END

FUNCTION IBITR(J,NU)

J1=J
t

90

IBITR=O

DO 200 I=1,NU

J2=J1/2

IBITR=IBITR*2+(J1-2*J2)

J1=J2

RETURN

END

a SUBROUTINE DC(CH,NUM,DATA)

DATA=0.0

DO 1 I=1,NUM,1

CALL ATOD(CH,X)

DATA 'DATA+X

a^

1 CONTINUE

DATA=DATA/NUM

RETURN

END

SUBROUTINE SUBBI2(DATA)

C DATA IS AN ARRAY (2,2048) WHICH CONTAINS THE SAMPLED DATA

FROM THE

C TWO (1 AND 2) DIFFERENT CHANNELS. IT IS AN INTEGER ARRAY

IN ORDER TO MINIMIZE

C STORAGE USAGE.

C IJ = NUMBER OF CHANNELS TO BE RECORDED

C NUM = NUMBER OF DATA POINTS PER CHANNEL

C THIS PROGRAM MUST HAVE THE SAMPLE RATE SET ON THE

BIOMATION.

C THIS PROGRAM IS TO CONTROL THE BIOMATION 2805 WAVE FORM

DIGITIZER

DIMENSION DATA(2,100)

C SET ARM, OPT AND WDC HIGH AND CBEN LOW

CALL OUT(32,56)

C ARM THE DIGITIZER TO TAKE DATA

CALL OUT(32,118)

CALL OUT(32,56)

WRITE(3,100)

100 FORMAT(' BIOMATION HAS BEEN ARMED')

C SEE WHEN RECORD AND FLAG GO LOW SAYING DATA IS READY

10 J=INP(32)

IF(J-4)10,11,10

11 CONTINUE

C DATA HAS BEEN RECORDED NOW SELECT A CHANNEL AND TRANSFER

ITS DATA

WRITE(3,101)

101 FORMAT(' DATA HAS BEEN RECORDED')

IJ=2

DO 13 K=1,IJ,1

KK=K-1+56

CALL OUT(32,KK)

WP.ITE (3 , 989) KK

989 FORMAT(I5)

T

200

W,

e

y

v

# Yc
91

C SET OPT LOW SO THE BIOMATION WILL START TO TRANSMIT DATA

KKK=.<K-16

CALL OUT(32,KKK)

DO 14 JK=1,200,1

15 J=INP(32)

IF(J.EQ.14)GO TO 16

GO TO 15

16 CONTINUE

LMN=INP(40)

IF(LMN.LT .0)LMN=LMN+255

DAfA(K,JK)=FLOAT(LMN)

C REQUEST A NEW WORD BY PULSING WDC

KKK=KKK-32

CALL OUT(32,KKK)

' KKK=KKK+32

CALL OUT(32,KKK)

14 CONTINUE

C SET OPT HIGH SO NEW CHANNEL CAN BE SELECTED

KKK=KKK+16

CALL OUT(32,KKK)

13 CONTINUE

RETURN

END

SUBROUTINE RMSV(RMS,DATA,N) C*********** (N) IS NUMBER OF DATA POINT

DIMENSION DATA(100)

SUM=0.0

DO 1 I=1,N

SUM=SUM+DATA(I)

1 CONTINUE

DC=SUM/N

R=0.0

DO 2 I=1,N

R=R+((DATA(I)-DC)**2)

2 CONTINUE

R=R**0.5

RMS=R/(N**0.5)

RETURN

END

W,
92

i

y VITA

Saied Smamai the son of Mr&Mrs Hassan Agha Eatami was

born on in . He received his

i' high school education at Khamenee l poor School, Tehran, Iran.

He received a AA degree in elementry Engineering from

„ Weaterford college in May 1977. He received also a Bachelor

i' degree in Mechnical Engineering from Texas A&M University in

May 198 1 . He intends to remain at Teaxas A&M University

after earning his degree of Master of Science to work

i- towards his degree of Doctor of Philosophy in Mechanical

Engineering. His permanent address is:

Saied Emami

i; c/o Wanda Ballow

1300 Brierwood

Weatherford, Texas 76086

Ph: 817 - 594 - 6667

s

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w