NASA Contractor Report 3371

Refraction and Scattering

of Sound by a Shear Layer

Robert H. Schlinker and Roy K. Amiet

United Technologies Research Center

East Hartford, Connecticut

Prepared for

Langley Research Center

under Contract NAS1-15339

N/ /X

National Aeronautics

and Space Administration

Scientific and Technical

Information Branch

1980

TABLE OF CONTENTS

SUMMARY .................................

INTRODUCTION'. ..............................

Previous Theoretical Investigations ...............

Previous Experimental Investigations ................

Method of Approach .........................

LIST OF SYMBOLS .............................

DESCRIPTION OF THE EXPERIMENT ....................

Page

1

3

4

5

6

7

12

Acoustic Research Tunnel ...................... 12

Experimental Arrangement ...................... 16

Instrumentation ........................... 20

Test Program ............................ 21

DEFINITION OF THE OPEN JET SHEAR LAYER .................. 2_

Mean Velocity Profiles ....................... 24

Shear Layer Thickness ........................ 25

Similarity of Mean Velocity Profiles ................ 26

Turbulence Intensity ........................ 26

THEORETICAL FORMULATION OF THE REFRACTION PROBLEM ............ 28

Review ............................... 28

Shear Layer Correction For an Off-Axis Acoustic Source ....... 29

Theoretical Refraction Predictions for Comparison With Experiment • 30

EXPERIMENTAL ASSESSMENT OF REFRACTION ANGLE CORRECTION THEORY ...... 34

Experimental Approach ........................ 34

Measured Phase Difference and Calculated Angle Change ........ 34

Background Noise and Non-Anechoic Effects .............. 36

Plane Wave Propagation Assumptions ................ 38

Comparison of Measured and Theoretical Refraction Angle

Correction .......................... _0

Summary and Evaluation ....................... $1

iii
TABLEOF CONTENTS(Cont'd)

EXPERIMENTALSSESSMENTOFREFRACTIONAMPLITUDECORRECTIONTHEORY....

Experimental Approach ........................

Calculating the Refraction Amplitude Correction from MeasuredSound

Pressure Levels ........................

Nose ConeDirectional Sensitivity Effects ..............

Comparisonof Measuredand Theoretical Refraction Amplitude

Correction ...........................

ComparisonsWith Other Investigators . . . .............

Summaryand Evaluation .......................

TURBULENCESCATTERINGOFSOUNDEXPERIMENTS................

Formulation of the Problem .....................

ParametersControl!ing Scattering ..................

Discussion of Experimental Results .................

Prediction of Turbulent Scattering Effects ...........

CONCLUSIONS

APPENDIXA - DERIVATIONOFSHEARLAYERCORRECTIONFORAN 0FF-AXIS

ACOUSTICSOURCE......................

APPENDIXB - WAVEFRONTANGLECHANGECALCULATION.............

APPENDIXC - SHEARLAYERANGLECORRECTIONCALCULATION..........

APPENDIXD - MICROPHONE-ACOUSTIC DRVERCROSS-CORRELATION

TECHNIQUE..........................

APPENDIXE - CROSS-CORRELATION TECHNIQUEIN PRESENCEOF REFLECTED

SOUNDWAVES.........................

APPENDIXF - ERRORANALYSISFORSHEARLAYERANGLECORRECTION

EXPERIMENT.........................

Page

43

43

44

4?

48

53

55

56

56

57

59

63

6?

69

84

85

86

89

92

REFERENCES .................. . .............

TABLES ..... , ......................... _ •

FIGURES .................................

93

95

97

iv
SUNMARY

A theoretical and experimental investigation was conducted to determine the

effect of refraction and turbulence scattering on sound transmission through a

circular, open-jet shear layer. Experiments were performed using a 0.91 m diameter

open jet in the United Technologies Research Center (UTRC) Acoustic Research

Tunnel. Free stream Mach number was varied from 0.i to 0.4.

For measurements directed toward assessment of the refraction angle and

amplitude change, a discrete tone acoustic source with a frequency range of

i kHz to iO kHz, was situated in the airstream. Sound wavefront angle and

amplitude changes across the shear layer were measured for several axial source

locations and two off-axis source positions. Far-field noise directivity

patterns were significantly altered at test Mach numbers of 0.i and greater due

to refraction by the open-jet shear layer. Experimental results were compared

with an existing refraction theory which was extended in the present study to

account for off-axis source positions.

Good agreement between refraction theory and experiment was obtained over

the test Mach number, frequency, and angle measurement range for all on-axis

acoustic source locations. For the range of open-jet shear layer thicknesses

investigated by changing the source location, the refraction angle_nd amplitude

changes were independent of shear layer thickness. This independence of shear

layer thickness and divergence confirms the zero thickness shear layer model used

in the theoretical prediction.

The refraction angle and amplitude changes were independent of frequency over

the frequency range considered in the present experiment. This independence

confirms the theoretical prediction. Angle and amplitude changes across the

shear layer can, therefore, be corrected for using the experimentally verified

refraction theory. A general correction procedure is, thus, available for

reducing far-field noise data acquired in open-jet test facilities.

The generalized refraction theory predicted large differences between

on-axis and off-axis corrections. Good agreement between theory and experiment

was obtained at a source-to-shear layer separation distance greater than the jet

radius. Mach number dependence and frequency independence were confirmed.

Measurable differences between theory and experiment occurred at a source-toshear layer separation distance less than one jet radius. This disagreement is

at present not understood.
An experiment was also conducted to evaluate the effect of open-jet shear

layer turbulence scattering on discrete tone propagation. Frequencies varying

over the range of 5 kHz to 15 kHz were investigated as the Machnumbervaried

from O.1 to 0.3. Attenuation of the discrete tone amplitude and the resulting

tone broadening were measured. These features were found to be stronger at angles

close to the open-jet axis than at 90° . More severe scattering was also observed

for downstreamsource locations where the ratio of shear layer propagation path

length to acoustic wave length approacheda value of iO.

In addition to the experimental effort, an existing single-scattering analysis

was modified to provide an estimate for the operating conditions at which the onset

of scattering occurs and the resulting discrete tone amplitude attenuation.

Experimental results showedreasonable agreement.
INTRODUCTION

i

A

Openjet acoustic test facilities are currently used to investigate

the effect of forward flight on aeroacoustic noise mechanisms. The technique

permits studying a wide variety of problems such as airframe noise, model

propeller and rotor noise, isolated airfoil and blown flap noise, and jet

noise forward flight effects. For tests conducted at free stream Mach

numbersless than 0.i, measurementsoutside the airstream can be used to

directly infer the source noise characteristics. However, at higher Mach

numbers, the open jet technique is influenced by the presence of the shear

layer through which the sound is transmitted. The shear layer serves to

refract, reflect, and scatter the sound radiated from the model. These

effects significantly alter the acoustic source directivity pattern and

hence alter the conclusions drawn from a particular experiment.

The lack of a firm understanding of these effects created a clear need

for a validated shear layer correction procedure. The present study was

undertaken to experimentally assess the refraction angle and amplitude

changes due to propagation through a finite thickness shear layer. Both

on-axis and off-axis acoustic source locations were tested for a circular

jet geometry. Acoustic source frequency and jet Machnumberwere also

varied to evaluate the dependenceon these parameters. In addition to the

experimental effort, an existing refraction theory was extended to treat

the case of a general off-axis source location. If the experiment verified

the theory, a general correction procedure would be available for reducing

the far-field noise data acquired in open jet test facilities.

These objectives were pursued in two separate but sequential research

programs. The first program (ref. i) investigated the refraction angle

change and found good agreement between theory and experiment. A small

effort was also devoted to the refraction amplitude change but the theory

could not be verified due to limitations of the experimental technique.

A second research program was therefore conducted to provide a definitive

experimental assessment of the refraction amplitude correction theory.

Results of this study are presented in this report.

Since the refraction angle change across the shear layer was needed

to determine the far-field microphone location in the amplitude correction

experiment, the results of the first research program were critical to conducting the second study. For this reason, the refraction angle correction

experimental results are also included in this report. Refraction

theory for the general off-axis source position is also included. Thus,

this report provides a complete theoretical solution to the refraction problem in addition to the experimental verification of the theory.

This theoretical correction procedure can now be used to analyze far-field

noise data acquired in open-jet acoustic wind tunnels. A listing of the
computer program for predicting the refraction angle and amplitude

corrections is given in the appendix.

An experiment was also conducted to evaluate the effect of open jet

shear layer turbulence scattering on discrete tone propagation. While this

scattering phenomenon has been found to be unimportant for acoustic wind

tunnel tests of broadband noise sources, it may be important for studies

in which discrete tones are generated. Examples of such studies include model

propeller and helicopter rotor noise, turbofan noise, and supersonic jetscreech noise. The magnitude of turbulence scattering in each case is a

function of the discrete tone frequency, the open jet Mach number, and the

acoustic source position. In such model studies, a scattering correction

may be needed to calculate absolute sound pressure levels and directivity

patterns from the far-field microphone data. For these reasons, an experiment was conducted to measure the reduction in the discrete tone amplitude

and the resulting tone broadening due to turbulence scattering.

A range of frequencies and Mach numbers were employed to determine

when scattering becomes significant. The importance of propagation path

length through the turbulent shear layer and the turbulence length scale

were investigated by locating the acoustic source at various axial stations.

These parameters were also evaluated as a function of acoustic radiation

angle relative to the open jet axis.

in addition to the experimental effort an existing single scattering

analysis was modified to provide an estimate of the discrete tone amplitude

attenuation. The modified analysis was also used to derive an expression

for predicting the onset of turbulence scattering. Experimental results

were compared with calculations from the modified analysis. Predictions

from an existing multiple scattering analysis were also compared with the

experimental data.

Previous Theoretical Investigations

Because the use of open jet wind tunnels for determining the acoustic

radiation properties of test models is a relatively new technique, methods

have only recently become available for correcting the acoustic data obtained

in such a facility for the effects of refraction. However, the refraction

problem had received previous attention because of its importance in the

jet noise problem. The case of refraction of a plane sound wave by a plane,

zero thickness shear layer, was first correctly treated by Ribner (ref. 2)

and Miles (ref. 3). Gottlieb (ref. 4) extended the analysis to the case of

a point source beneath a plane shear layer. Graham and Graham (ref. 5)

considered the problem of a plane wave interacting with a finite thickness

shear layer and subsequent publications of theirs consider the field of

specific singularities near a shear layer. Amiet (ref. 6) and others also

considered the sound field of specific source types near a shear layer.
The abovestudies were not concernedwith correcting acoustic wind

tunnel data, however, and further analysis of the problemwasneeded. In

particular, a methodwas required which madeno assumptionsregarding

the nature of the sources (e.g., monopole,dipole, etc.), since, in general,

the nature and distribution of sources in a given test was unknown. Subsequently, Amiet (ref. 7) derived a correction procedure which applied both

an angle changeand an amplitude changeto the data. This assumeda plane

zero thickness shear layer. It wasonly by this separation of angle and

amplitude effects that it waspossible to arrive at a correction independent

of source type. The problemwas also analyzed by Jacques (ref. 8) who

arrived at the sameresult for refraction by a plane shear layer, and also

considered the case of a source on the centerline of a cylindrical shear

layer of zero thickness. The solution for refraction by a thick cylindrical

shear layer with a source on the centerline wasgiven by Tester and Morfey

(ref. 9) and for a thick plane shear layer by Amiet (ref. I0). This work of

Amiet also gives a thorough review of the several correction procedures.

The abovecorrections are in algebraic closed form. Candell (ref. ii)

recently developeda numerical ray tracing procedure which appears to give

results very close to the closed form solutions. Recent studies by Tester

and Burrin (ref. 12) indicate that the axial variation of the shear layer

has little effect on the refraction corrections. Thus, it is possible to

model the open jet shear layer without axial variations.

References 7-12 rely on the technique of correcting both angle

and amplitude. Mani (ref. 13) employeda different approachto the problem,

but this appears to be less well established than the abovementioned techniques of correcting angle and amplitude.

Previous Experimental Investigations

Fewexperimental studies exist documentingthe shear layer refraction

and scattering characteristics. Amiet (ref. 7) reported the results of an

exploratory experiment for the angle correction using a plane shear layer.

The results tended to support the theoretical predictions presented in the

samestudy. Candell et al. (ref. 14) provided an experimental assessment

of a refraction theory for a circular jet. In addition they presented

preliminary results for turbulence scattering by the jet shear layer.

Similarly, Ahuja et al. (ref. 15) recently reported an assessmentof the

refraction theory of reference 12 for a circular jet. Also included was

an exploratory study of turbulence scattering at low jet Machnumbersand

low acoustic source frequencies. Ozkul andYu (ref. 16)investigated the

angle and amplitude changesin a Circular jet and comparedthe results to

the refraction theory given by Amiet in reference 7. All of the above

experimental investigations were limited to on-axis source locations.

5
Methodof Approach

In the present study, the refraction angle changewas assessedby

cross-correlating far-field microphonesto measurethe local acoustic wavefront propagation angle outside the openjet. Knowingthe propagation angle,

the acoustic ray normal to the wavefront was traced back to the shear layer

crossing point. In determining this point, the shear layer was assumedto be

cylindrical with a radius equal to the inlet nozzle radius and to have zero

thickness. Fromthe acoustic ray crossing point, the original propagation

angle inside the shear layer wasdetermined for comparisonwith the general

refraction angle correction theory developedas part of this study.

The refraction amplitude changeacross the shear layer was assessedby

comparingacoustic source soundpressure level measurementsinside and outside the openjet test section. Themicrophonelocation inside the potential

core coincided with a ray propagating at a selected radiation angle. The

out-of-flow or far-field microphonewas situated on the sameacoustic ray

except that the ray was not refracted by the jet shear layer. The intersection of the refracted ray with the microphonesideline determined the

far field measurementstation. This intersection point was predicted

analytically by the refraction angle changetheory. Verification of the

refraction angle changewas, therefore, a prerequisite to conducting the

refraction amplitude correction experiment.

The ratio of the measuredin-flow to far-field microphonesoundpressure

level represented the amplitude changealong the refracted path. This

amplitude changewas comparedwith the calculated inverse square-law

amplitude changealong a non-refracted ray path which intersected the same

microphonesideline. The inverse square-law changecorrespondedto the

soundpressure level changein the absenceof a refracting shear layer.

The decibel difference betweenthe amplitude changeon the refracted and

non-refracted path represented the refraction amplitude correction. The

experimentally determined amplitude correction was then comparedwith the

theory. It should be emphasizedthat the refraction amplitude correction

converts a soundpressure level measurementoutside the openjet to a level

that would be measuredin the flow but in the absenceof the shear layer.

The discrete tone turbulence scattering experiment was conductedusing

the samein-flow and far-field microphonegeometryemployedin the refraction

amplitude correction experiment. In-flow spectra were comparedwith far

field spectra after correcting for the refraction amplitude changeand inverse square-law decay betweenthe two microphonestations. Differences

betweenthe discrete tone amplitudes in the two spectra provided a direct

calibration of signal attenuation due to scattering of sound into other

propagation directions and frequencies. The significance of tone broadening

was determined from the spectrumshape. Experimental results were compared

with predictions from two separate scattering analyses.
A

AMP

BI, B2, B3, B4

B2,R

C

O

C F

m

D/Dt

dB

d_

f

GI, G 2

GA, C GA, B

g

LIST OF SYMBOLS

Cross-sectional area of ray tube

Radius of tunnel

Amplitude correction function

Discrete tone pressure wave amplitude measured at microphones,

m I , m 2 , m 3 , m 4

Reflected wave amplitude measured at microphone m 2

Sound speed

Amplitude correction function

_l_t + U _l_x

Decibel

Vector defining side of ray tube

Energy scattered in new directions from a unit volume of

turbulence per unit time

Acoustic source frequncy, Hz

Microphone sensitivity

Cross-power spectral density functions

i- h/a or l-h/R o

Cross-correlation amplitude

Source-to-shear layer distance. Also corresponds to sourceto-lip-line distance.

Intensity of incident sound
LIST OFSYMBOLS(Cont'd)

^

i, j, k

k, k , k

x y z

L

L 1

M

m1 , m2 , m3 , m4

n

^

n

e

^ ^

n 1, n 2

P

P1 '' P2'

R

R

O

R, R1/2

Rra, Rro

r

r 1

Unit vectors in x, y, z directions

Wave number vector

x, y or z wavenumber

Propagation path length in turbulent shear layer

_cro scale of turbulence in the direction of the incident

sound

Microphone separation distance

Streamwise turbulence length scale

Mach number of stream

Denote far-field microphones

Integer

Unit vector from retarded source position to shear layer

crossing point

Unit vector along ray path beneath shear layer and above

shear layer, respectively

Pressure

Random noise measured at microphones ml, m 2

Reflection coefficient

Radius of tunnel, 0.455 m

Local radius and radius of half velocity line (U/U ° = 0.5)

in shear layer

Apparent source to microphone distances

Source-to-microphone distance

Distance from source-to-shear layer crossing point
r 2

r 3, r 4

S

T

t

U, UO

V

(vI ) 2

W

X

0

X, Y

x, y, z

x, y'

C_

B2

Y

A

P

A

r

A, A'

Z v

LIST OF SYMBOLS (Cont'd)

Distance from shear layer crossing point to far-field

microphone

Distance from source to in-flow and far-field microphone

on non-refracted path ray path

Cross-correlation function

Transmission coefficient

Time

Local stream velocity in shear layer and potential core

velocity

Voltage signal

Mean-square velocity of turbulence

z component of perturbation velocity

Acoustic ray shear layer crossing-point

Axial and transverse coordinates in the horizontal plane

coinciding with open jet axis

Cartesian coordinates rotated by _ from x, y', z'

Cartesian coordinates fixed to laboratory frame

Angle made by tangent plane

i- M 2

_+a

Phase lag between speaker output and acoustic signal arriving

at microphone

Difference in distances between source and individual microphones

Phase difference between microphones due to propagation path

length differences at M = 0 and M # 0

9
AR

AT, AT '

AT

A*

6

!

_2

HI ' _2

@

_o' _i

_D

_R

LIST OF SYMBOLS (Cont'd)

Phase lag between individual microphone input and output

Signal phase lag between input and output of amplifier and

speaker

Phase difference between direct and reflected sound waves

Total phase difference between microphone output signals

at M = 0 and M # 0

Incremental delay time

Difference defined by A* ' '

= nl-_2- T

Shear layer thickness

Angle between in-flow traverse line and jet centerline

(i- M cos 0) 2 - cos 20

Phase difference between individual microphones

kxx+_y-mt

Polar angle

Total phase lag between signal generator and acoustic signal

arriving at microphone

Acoustic wavelength

Angle between microphone array and wavefront at M = 0 and

M#0

Density

Cross-correlation function or signal enhancement function

delay time

Time difference between acoustic driver signal and the

direct propagating sound wave

Time difference between acoustic driver signal and the

combined direct and reflected sound waves

i0
@

W

<>

Subscripts

i

V

t

C

m

LIST OF SYMBOLS (Cont'd)

Velocity potential

Polar angle

Radian frequency

Time average of fluctuating signal

Incident

Reflected

Transmitted

Corrected

Measured

ii
DESCRIPTIONOFTHEEXPERIMENT

Acoustic ResearchTunnel

Operating Characteristics - The experimental study was conducted in the

UTRC Acoustic Research Tunnel. A detailed description of the facility is

given in reference 17. The tunnel, shown schematically in figure 1 is an

open-circuit, open-jet design. The inlet is provided with a high lengthto-diameter ratio honeycomb section and a series of turbulence suppression

screens. These features, in conjunction with a large tunnel contraction,

.provide a spatially uniform, temporally steady flow with a controlled test

section turbulence level of approximately 0.2 percent. Turbulence generators and grids can be inserted upstream of the nozzle to generate wake profiles (ref. 18) and a range of turbulence levels (ref. 19) in the test section.

The open jet test section is surrounded by a sealed anechoic chamber

4.9 m high, 5.5 m long (axial direction), and 6.7 m wide. Downstream of

the test section the airflow enters a diffuser by way of a collector that

has anechoic treatment on its flow impingement surface.

The diffuser operates unstalled and is thus not a major source of

background noise. To avoid tunnel fan noise from propagating upstream into

the anechoic chamber a Z-shaped muffling section with two right angle bends

and parallel treated baffles is located between the diffuser and the fan.

The ii00 kW centrifugal fan exhausts to the atmosphere through an exhaust

tower.

Tunnel speed is determined from total pressure measurements at the

contraction inlet and static pressure measurements within the sealed anechoic chamber. Since losses are confined to the boundary layer, total pressure

upstream and downstream of the contraction are predicted and have been

verified, to be equal. The test section velocity has been shown to be

temporally steady.

Open Jet Geometr_ - A circular inlet nozzle with a radius, R° = 0.455 m,

was employed in all tests. Initial facility tests reported in reference 17

identified an acoustic coupling between the inlet nozzle and the collector

lip resulting in edge tones at high tunnel speeds. To suppress this noise

mechanism, triangular tabs (see figure 2) were distributed around the nozzle

periphery during the refraction angle correction experiment to disturb the

azimuthal symmetry of the shear layer and prevent the generation of feedback tones. On the other hand, the shear layer thickness was increased by

the tabs. Despite this alteration of shear layer thickness, the measured

angle change associated with the wavefront propagation showed good agreement

with the change calculated using the zero thickness shear layer theory of

Amiet.

12
After completion of the refraction angle correction study, a major

anechoic chambermodification wasperformed. The facility changesincluded

replacement of the acoustic treatment on the walls and on the surface of

the downstreamcollector. Thesecombinedchangeseliminated the nozzle

lip to collector feedbackproblem permitting the nozzle to be usedwithout

tabs. The impact of the separate facility modifications on the feedback

mechanismis not currently understood.

Operation of the openjet without tabs was advantageousto the refraction amplitude correction study which was conductedafter the facility

modification. Therefraction amplitude correction experiment required

measuringthe acoustic field strength within the openjet potential core.

To avoid measuring the source near-field characteristics it wasnecessary

to maximizethe separation distance betweenthe source and the in-flow

microphone. Without tabs the shear layer was thinner resulting in a larger

distance betweenthe jet centerline and the inner edgeof the shear layer.

Themicrophonecould, therefore, be movedto a larger radius before it

penetrated the turbulent shear layer velocity field.

Shearlayer thickness in the presence or absenceof the tabs is

documentedin the section titled Definition of the OpenJet ShearLayer.

The importance of shear layer thickness on the refraction angle and amplitude correction experiments is discussed in the corresponding sections.

Anechoic Characteristics and Acoustic Source Selection - Figure 2 shows the

interior of the anechoic chamber during the refraction angle correction experiments. The chamber walls, lined with 0.3 m fiberglass wedges, were

found to be anechoic (ref. 17) for broadband noise over a 200 Hz to 20 kHz

range of calibration frequencies. In other words, the sound pressure level

followed a 6 dB decay rate per doubling of source-to-observer separation

distance. This decay rate was maintained within approximately ±0.25 dB

over the 200 Hz to 20 kHz frequency range.

Since discrete tone source frequencies were used in the refraction

angle correction experiment, it was necessary to conduct intensity versus

distance calibration measurements to verify the free field behavior for a

discrete tone. For these tests a speaker wag located on the centerline of

the open jet test section. A microphone was traversed radially outwards

from the acoustic source at different angles to the jet axis. Figure 3

shows a typical result at 90 ° to the jet centerline.

A close examination of the decay curves in figure 3 indicates

approximately a ±0.5 dB variation about the inverse square law line for

frequencies below 5 kHz. Such fluctuations suggest the presence of weak

reflected waves in the anechoic chamber. These reflected waves combine

with direct waves radiating from the acoustic source to the microphone

resulting in nodes and antinodes distributed throughout the anechoic

13
chamber. For example, a +0.5 dB variation represents a reflected-to-direct

waveamplitude ratio of 0.06 if the two wavefronts are in phase. The refraction angle correction experiment could tolerate reflected wavesof such

amplitudes since the measurementsemphasizedphasedifference and not

absolute amplitude at the far field measurementstation. This was verified

analytically and is discussed in the section describing the angle correction

experiment. Thus, the anechoic chamberwas considered adequatefor the discrete tone source signalsused in the angle correction experiment.

Thesource of the reflected waveswas found to be the openjet

face. This was determinedwhile conducting pure tone free-field decay

measurementsprior to the refraction amplitude correction investigation.

Thepurposeof these measurementswas to check the acoustic characteristics

of the anechoic chamberafter it was lined with new fiberglass wedges.

Theexperimental set-up, with the newanechoic wedgesis shownin the

photo of figure 4. A suspendedmicrophonetraverse systemwas employedto

facilitate changing the traverse line orientation relative to the openjet

axis. Theacoustic source used in the casewas different from that used in

the angle connection experiment. Theprevious source was replaced by a

secondunit which was smaller in size (fig. 4). Details of the source are

given in the section titled Experimental Arrangement.

Thenew directional acoustic source was first pointed toward the downstream collector. The intensity versus distance plots showednumerous

fluctuations about the inverse square-law curve with the microphonetraversing

at 90° to the openjet axis. Figure 5 showsa typical trace for a 1.25 kHz

discrete tone. Both the inflow and far-field microphonestations used in the

amplitude correction experiment are also shownso as to identify the spatial

regions in which the free-field condition must be satisfied. Note that these

positions correspond to M = 0 operating conditions. The far-field microphone

station changedslightly for non-zero Machnumbers.

With the source facing the microphonetraversing at 90° to the flow,

the deviations from the inverse square-law line were reduced. It was concluded that whenthe highly directional source faced the downstreamcollector, the reflected soundwaveamplitude arriving at the 90° microphonewas

comparableto the direct source-to-microphone radiation. Thusthe collector

could alter the measureddirectivity pattern of discrete tone aeroacoustic

noise mechanismswith a maximumdirectivity in the rear arc. This observation was, however, limited to low frequencies since the deviations from

the inverse square-law were muchsmaller at high frequencies.

It should be noted that the deviations in the intensity versus distance

curves in figures 3 and 5 differ becausethe acoustic source locations are

different. In addition, the acoustic treatment on the collector surface

was changedbetweenthe refraction angle and amplitude correction experiments described by figures 3 and 5.

14
Since the refraction amplitude changewas expected to be approximately

zero at 90° to the openjet, it wasnecessary to minimize any potential

errors in the soundpressure level measurements. A criterion limiting the

non-anechoic characteristics of the facility to ±0.2 dB was, therefore,

established. Oneof the methodsconsidered for achieving this criterion

used a randomnoise source to provide uncorrelated signals for the direct

and reflected soundwaves. Themajor disadvantage of this approachwas

the distribution of acoustic source output powerover a large portion of

the spectrumresulting in low acoustic energy levels per unit Hertz. These

low levels would be maskedby the microphoneself-noise at the in-flow

measurementstation and the openjet backgroundnoise at the far-field

station. In general, the signal-to-noise ratio could be expected to be

low.

The abovesignal-to-noise problemswere encounteredby Ahuja et al

in a shear layer refraction study reported in reference 15. Their technique

for overcoming the signal-to-noise limitation employeda cross-spectrum

analysis which required two in-flow microphonesand one far-field microphone. Themeasurementerrors associated with this approach, however, precluded using theconcept. In addition, the ability of the technique to

recover the source signals wasquestionable at the highest Machnumberof

M = 0.4 used in the present study. Theselimitations will be discussed

further in the section titled Experimental Assessmentof the Refraction

Amplitude Correction Theory.

Due to the non-ideal anechoic characteristics obtained with the continuous

discrete tone signal and the signal-to-noise limitation of the randomnoise

signal, an alternate approachwasdeveloped. Themethodemployeda discrete tone burst generated at the acoustic source. Theburst duration time

and repetition rate were selected to avoid interference betweenthe direct

radiated soundarriving at the microphoneand the reflected sound from the

collector. Using a discrete tone wasalso advantageousbecauseit provided

a large signal-to-noise ratio at both the in-flow and far field microphone

stations. This wasnowpossible becausethe total acoustic powerwas concentrated in the discrete tone signal rather than being distributed in a

broadbandrandomnoise signal. The tone burst free-field decay measurement

is comparedwith the continuous discrete tone measurementin figure 5. The

resulting radial traverse curve for the tone burst has few discernable deviations from the expected free field decay characteristics.

Measurementsmadeover the complete angular range of 30° to 140°

from the openjet axis showedsimilar free-field behavior. For example,

figure 6 showsthe intensity versus distance curve at 30° from the open

jet axis with the source facing the collector. Note that two separate

traverses were neededto cover the source-to-far-field microphonedistance.

Figure 6 showslittle evidence of interference betweenthe direct radiated

15
soundarriving at the microphoneand the reflected soundfrom the collector

surface. This was true for all source frequencies of f = 1.25, 2.5, 5 and

i0 kHz used in the refraction amplitude correction experiment. Basedon

the success of the discrete tone burst technique, this acoustic source

signal was selected for the refraction amplitude correction experiment.

Additional calibrations demonstrating the accuracy of the methodwill be

presented later.

It is probable that all openjet acoustic wind tunnel facilities with

collectors suffer from the samenon-anechoic environment for continuous

discrete tones. Randomnoise calibrations have in the past maskedthis problem. Thediscrete tone provides a moresevere test for evaluating freefield characteristics. Furthermore, by using a continuous traverse, in

conjunction with the discrete tone the spatial distribution of nodesand

anti-nodes can be used to identify the occurrence of wavefront interference.

In comparison,measurementsmadeat incremental distances from the acoustic

source cannot be expected to coincide with the node and anti-anode locations.

In this case, deviations from the free-field decay characteristics can be

erroneously interpreted as scatter in the experimental data.

Experimental Arrangement

Refraction An$1e Correction Experiment - Figures 2 and 7 show the

anechoic chamber test arrangement employed for the angle correction measurements. The nozzle inlet and collector described earlier are evident in the

photos.

An acoustic source, consisting of a speaker enclosed by an aerodynamic

fairing (see fig. 7), was located in the open jet airstream. The fairing

measurements were: 17 cm long (axial direction), i0 cm high, and 5 cm deep.

Leading and trailing edges of the fairing were rounded. The wake shed by

the body produced no significant discrete vortex shedding tones in the farfield acoustic spectrum.

The speaker fairing was held in place by a support arm which extended

through the open jet to a rigid stand outside the flow. The support arm

consisted of a short section of cylindrical tubing and an aerodynamically

shaped fairing. Although the cylinder generated an aeolian tone, the

dominant dipole radiation pattern was in a vertical direction perpendicular

to the horizontal plane containing the speaker and the far-field microphones.

Therefore this extraneous noise mechanism was not sensed. Similarly, noise

generated by impingement of the highly turbulent shear layer on the aerodynamic fairing radiated in a vertical direction and was not sensed by the

far-field microphones. Acoustic insulation was applied to the support stand

and the exterior of the inlet nozzle.

16
Thespeaker face, with its 2.5 cmdiameter aperture, was covered with

a plastic grid of the sameaperture size. Thegrid prevented flow separation

and distortion of the meanvelocity field at the speaker-flow interface.

Thecenter of the grid aperture marked the acoustic source position. All

far-field microphonelocations were referenced to this station.

The acoustic wavefront angle outside the openjet wasmeasuredby a

pair of far-field microphones. Themicrophones, designated as ml, and m2

in figures 7 and 8, were mountedat grazing incidence on a rotating boom.

Theboompivot point, located beneath the openjet, was aligned with the

acoustic source position. Although figure 8 showsthe source situated on

the tunnel centerline, off-centerline stations were also investigated. The

microphonesscanneda horizontal plane at the sameheight as the tunnel

centerline and the acoustic source. Different microphoneseparation distances, _, were used dependingon the acoustic source frequency. The fixed

microphoneradius, r = 1.83 m, wasmeasuredto the midpoint of the microphonearray. The radius was selected to permit scanning the boomclose to

the jet axis while still maintaining a large separation distance betweenthe

microphonesand the downstreamcollector. This minimized the ratio of

direct-to-reflected soundwavepressure amplitudes for acoustic rays propagating in the direction of the collector. Themicrophoneswere mounted

rigidly using guy wires and braces to minimize any vibration or deflection

whenthe openjet wasoperated.

Theboomangular position was defined by the angle, em, measuredfrom

the downstreamjet axis. The angle was referenced to the midpoint between

the two microphones. A line connecting the microphonesformed approximately

a 90° angle with the radius, r. A potentiometer, attached to the boompivot

shaft, provided a voltage output corresponding to the boomangular position.

Thevoltage was amplified and displayed on a digital voltage readout providing a resolution of 0.016 deg. The systemwas calibrated daily using

the open jet centerline and a line perpendicular to the centerline as

references. Theaccuracy of the calibration was approximately 0.3 degrees.

The intensity versus distance curves shownin figure 3 were obtained

using the acoustic source described above. All refraction angle correction

measurementwere conductedat r = 1.83 m, where the free field behavior was

well established.

Deviations from the inverse square law at distances less than i mwere

possibly due to the near-field characteristics. At small distances from the

source, the aerodynamicfairing surrounding the speakerwould appear as a

baffle over which acoustic pressure fluctuations act. Themicrophonewould

then sense the geometric near field and possibly the acoustic near field of

the distributed source region. Since the refraction amplitude correction and

turbulence scattering experiments required in-flow microphonemeasurementsat

distances less than I m the abovedescribed source could not be used. Instead,

a secondsource was developedfor these studies. The"characteristics of

17
the source were described earlier in the subsection titled AnechoicCharacteristics andAcoustic SourceSelection. Additional details are given below.

Refraction Amplitude Correction Experiment - Figure 9 shows the anechoic

chamber test arrangement employed in the amplitude correction experiment.

Both in-flow and far-field traversing microphones are shown.

In-flow microphone measurements were required as part of this study,

with the source-to-microphone separation distance being less than 0.455 m.

As noted earlier, deviations from the inverse square law decay curve occurred

for separation distances less than 1 m when using the acoustic source developed

for the angle correction experiment (fig. 3). For this reason a second

acoustic source was developed.

The second source consisted of a commercially available ii0 watt acoustic

driver coupled to a tube using an inverse cone section. The 2.54 cm constant

diameter tube terminated inside the open jet section. Locating the acoustic

driver outside the test section with the tube crossing the open jet shear

layer provided an additional advantage. The size of the acoustic driver was

not limited thereby permitting a large and acoustically powerful driver to be

used. This provided a significant improvement in signal-to-noise ratio compared to the acoustic source employed in the refraction angle correction equipment. In the latter case, the speaker size was limited by the aerodynamic

fairing dimensions.

Microphone traverses in radial directions from the acoustic source

were presented earlier in the discussion of the anechoic chamber characteristics. Measurements conducted at 90 ° and 30 ° from the downstream jet

axis were shown in figures 5 and 6. In addition to satisfying free-field

conditions at the far-field microphone station, these figures demonstrate

that free-field conditions are satisfied at the in-flow microphone station.

Both figures indicate a free-field condition beyond 15 cm from the source.

This ensured that the traverse line selected for the in-flow microphone was

situated in the acoustic source free-field for all measurements.

The acoustic source orientation relative to the open jet centerline

shows a 90 ° bend at the tube termination in figure 4. This orientation

was used only in the static free field decay measurements. The angle was

changed to a 45 ° orientation in the amplitude correction experiment to

provide a maximum source directivity pattern in the downstream arc where

the open-jet background noise was expected to be large. The final

orientation is shown by the insert in figure 9.

Vortex shedding noise from the tube in figure 9 was suppressed by a splitter

plate attached to the rear stagnation point. The objective was to suppress

potential field fluctuations which the in-flow microphone would sense. While

this suppression technique generated random noise, the radiation pattern was in

a vertical direction perpendicular to the horizontal plane containing the source

18
and the in-flow and far-field microphones. Therefore, this extraneous noise

wasnot sensed. Similarly, noise generated by the impingementof the highly

turbulent shear layer on the support tube radiated in a vertical direction

and wasnot sensedby the microphones. Acoustic insulation wasapplied to

the support stand and the exterior of the inlet nozzle.

The acoustic source signal wasmeasuredby the in-flow and far-field

microphonesdesignated as m3 and m4 in figure i0. Microphonem3 was traversed in straight line parallel to the intermittency line used to define

the inner edge of the shear layer. A separation distance of 5 cmbetween

the traverse line and the intermittency line avoided penetrating the

turbulent shear layer with the in-flow microphone. Locating the in-flow

microphoneclose to the edgeof the shear layer maximizedthe source-tomicrophoneseparation distance thereby providing additional assuranceof

achieving a free-field condition at the microphone.

A nose conewas used for all in-flow microphonemeasurements. The

microphonewas always aligned parallel to the flow direction with the nose

cone pointing upstream.

Far-field microphone, m4, was traversed on a straight line parallel

to the openjet at a sideline distance of y = 1.83 m. This distance was

selected to maximize the refraction amplitude correction measurementswhich

increase with sideline distance. The only limitation of this distance was

the proximity of the anechoic chamberwalls at angles close to the openjet

axis. Like the in-flow microphone, a nose cone wasused on the far field

microphonewith the microphonealigned parallel to the flow and pointing

upstream. Thereasons for using a nose cone outside the flow field are

discussed in section titled Experimental Assessmentof Refraction Amplitude

Correction Theory.

The separate traverse units permitted locating the in-flow microphone

at a specified radiation angle, ec, with the far field microphoneshifted

to the refracted angle, em, determined from refraction theory.

Although figure i0 showsthe source situated on the tunnel centerline,

off-centerline source positions were also investigated. As in the refraction angle correction experiment, the microphonesscanneda horizontal

plane at the sameheight as the tunnel centerline.

The in-flow and far-field microphonepositions were measuredfrom the

openjet exit plane. Linear cable transducers were used to provide a

voltage output corresponding to the microphoneposition. Voltage was

amplified and displayed on a digital readout. The resolution of the linear

position provided approximately a 0.5° angular resolution at the in-flow

microphonestation and a 0.i ° resolution at the far-field microphone.

19
The systemwas calibrated daily with the accuracy of the calibration at

either microphonestation being the sameas the resolution capability.

Discrete Tone Scattering Experiment - The acoustic source and

microphone arrangement were similar to the experimental set-up used in the

refraction amplitude correction experiment, but a continuous discrete tone

signal was used in place of the tone burst. Free-field decay measurements

described earlier indicated a non-anechoic behavior of the chamber for continuous discrete tone sources. To avoid contamination of the far-field

microphone signal by sound reflected from the collector, the sideline distance was decreased to y _ 0.91 m so that the direct radiation arriving at

the microphone dominated the reflected sound. It should be noted that this

approach was not feasible in the refraction amplitude correction experiment

because the amplitude change approaches zero as the sideline distance

approaches the open jet radius. This is explained further in the section

on theoretical formulation of the refraction problem.

Acoustic source near field effects were not expected to be a problem at

the in-flow microphone station since the experiment employed the second

acoustic source developed specifically to permit such measurements. Decay

characteristics in figure 6 show few discernible deviations from the inverse

square law line at the in-flow microphone station when using a discrete tone

burst. Assuming the near field characteristics are the same for the continuous tone, the near field effects would be minimal. This is verified by

the continuous tone decay curves in figure 5 which follow the inverse square

law for distances less than .4 m.

Instrumentation

The various speakers and acoustic drivers used in the refraction and

scattering experiments were powered by a 150 watt single channel amplifier.

A sine wave generator with a tone burst output capability provided the

amplifier input. The generator frequency was held to within 2 Hz of each

source frequency evaluated in the test program.

Far field sound pressure levels were measured with commercially

available 0.635 cm diameter condenser microphones. Protective grids were

used in the angle correction experiment while nose cones were used in the

amplitude correction and scattering study. Admittedly, the microphone

frequency response was not flat due to the protective grid or nose, but

comparisons of absolute sound pressure levels at different frequencies

were not needed. For example, the angle correction experiment measured

the acoustic wavefront propagation angle which was independent of radiated

sound pressure level. The amplitude correction experiment used only the

2O
difference betweenthe in-flow and far-field microphonesoundpressure level

at the samefrequency. Since nose coneswere used on both microphones,

the frequency responsecharacteristics were expected to be identical.

Finally, the scattering experiment used the samesoundpressure level

measurementschemeas in the refraction amplitude correction experiment.

As before, frequency dependentnose cone responsecharacteristic were not

needed. All microphoneswere calibrated daily with a 250 Hz pistonphone

signal.

Microphonesignals and the sine wavegenerator signal were recorded

on magnetic tape during certain portions of the test. The frequency responseof the FMtape systemwas flat over the frequency range investigated

here.

Spectrumanalysis during the angle and amplitude correction study was

conductedwith a narrow band, 500 line, real time spectrumanalyzer - ensemble

averager and a 1/3 octave band analyzer. The 50 Hz effective bandwidth of

the narrowbandanalyzer was found to be inadequate for the discrete tone

scattering experiment. For this reason a secondnarrowbandanalyzer with

a 0.25 Hz resolution wasemployed.

Cross-correlations and signal enhancementwere performed using a 400 point,

real time correlation and probability analyzer with the smallest available

increment of resolution in the time domainbeing 0.2 _sec. Input signals

were not filtered in the refraction angle correction experiment. Filtering

was used in the amplitude correction experiment.

Meanvelocity measurementsof the openjet shear layer were acquired

with a 0.025 mmdiameter hot film operating in conjunction with a constant

temperature anemometersystem. The probe was calibrated in the tunnel test

section.

Test Program

Refraction Angle Correction Measurements - Measurements were performed

at various acoustic source locations, open jet Mach numbers, and source

frequencies to assess these parameters in the refraction angle correction

theory. Two coordinates defined the source location: the axial station,

X, and the source-to-open jet-lip line separation distance, h. Both coordinates are shown in figure 8. Table I lists the test conditions evaluated in the present study with the source position coordinate normalized

by the open jet radius. Included in the table is the ratio, h/r, which

defines the far-field microphone position relative to the source-to-lip

line distance. This parameter is an input to the experimental and theoretical angle and amplitude correction calculations. The lip line also defines

21
the location of the zero thickness shear layer used in the refraction theory

described in the section titled Theoretical Formulation of the Refraction

Problem . Therefore, h is at times referred to as the source-to-shear

layer separation distance. It should be noted that since the source-tomicrophonedistance, r, was fixed, changesin h resulted in both h/Ro and

h/r changing.

With the acoustic source situated at X/Ro = 1.33 and h/Ro = i, the

measurementangle, 8m,was varied from 22.5° to 105° in 7.5° increments.

Angles less than 22.5° were not investigated since microphonem2 in figure

8 would then penetrate the open jet shear layer. Onthe other hand, angles

greater than 105° were not investigated since an adequateseparation distance betweenmI and the upstreamanechoic chamberwall must be maintained.

Line-of-sight interference by the tunnel inlet betweenthe source and microphonem2 did not occur until em exceeded136° . Moving the source to

X/Ro = 2.66 and 4.0 permitted increasing the upstreammeasurementangle

to 127.5° . However,downstreammeasurementangles less than 30° could not

be attained due to shear layer spreading.

The samemeasurementangle range wasused for the off-centerline

source positions listed in Table I. For h/r = 0.36, measurementangles

less than 30° could not be investigated since m2 penetrated the flow. As

in the on-centerline test geometries, line-of-sight interference was not

a problem.

Refraction Amplitude Correction Measurements - Measurements were

performed using the same open jet Mach numbers and acoustic source frequencies investigated in the refraction angle correction experiment.

Similar test conditions were investigated because the angle correction

was needed to define the refracted ray path outside the open jet. The

intersection of the refracted ray with the sideline determined the location

of the far-field microphone in the amplitude correction experiment.

Far-field microphone measurements were conducted at a constant sideline

distance instead of a constant radius location as in the angle correction experiment.

The constant sideline geometry was selected because the refraction amplitude

difference between the in-flow and far-field microphone was larger'than in

the constant radius geometry for angles close to the open jet axis. This

point is illustrated by figure 44 and is discussed in the section titled

Experimental Assessment of Refraction Amplitude Correction Theory. The

larger amplitude change improved the accuracy of the experiment relative to

the -+0.2 dB error band established from calibration measurements at static

operating conditions.

22
As shownin figure i0, angle 0c inside the openjet determined the

far-field microphonemeasurementangle Om. Theseangles are related by

the refraction angle correction discussed later. Angle ec was selected

as the principal variable permitting the in-flow microphonestation to be

held fixed as the open jet Machnumberincreased. This facilitated the

measurementprocedure. All comparisonsbetweenamplitude correction theory

and experiment are, therefore, plotted as a function of ec.

Test conditions for the amplitude correction experiment are listed

in Table If. The parameter, h/r, which described the far-field microphone

position in the angle correction experiment, has been replaced by the

parameter, h/y. The theory predicts the amplitude changefor an arbitrary

value of h/y. Since the sideline distance, y, was fixed, changesin h

resulted in h/Ro and h/y changing.

With the acoustic source at x/Ro = 0.66 and h/Ro = i, angle ec

varied from 25° to 90° . Thesameangular measurementrange was used for

the off-axis source position. Angles greater than 90° were not investigated

to avoid interference betweenthe acoustic ray and the nozzle lip. Tests

at a seconddownstreamstation, corresponding to X/Ro = 2.66, permitted

makingrefraction amplitude correction measurementsfor the upstream

directivity quadrant.

Discrete Tone Scatterin$ Experiment - Measurements of the discrete

tone scattering phenomenon were obtained at ec = 90 ° and several angles

in the upstream and downstream quadrant. Tests were conducted over the

same Mach number range as investigated in the refraction experiments. Two

of the source frequencies corresponded to the f = 5 and i0 kHz signals used

in the refraction experiment. The motivation for selecting these frequencies

was to verify the presence of discrete tone scattering observed in the refraction amplitude correction experiment. A third frequency of f = 15 kHz

was expected to encounter strong turbulence scattering effects. The axial

source positions covered the same measurement range as used in the refraction experiment. A listing of the test conditions is given in Table III.

23
DEFINITIONOFTHEOPENJETSHEARLAYER

Theobjective of the meanvelocity measurementsdescribed here was to

documentthe shear layer characteristics of the UTRCAcoustic ResearchTunnel

as a function of axial position and Machnumber. Measurementswere obtained

for the open jet operating with and without tabs attached to the periphery

of the inlet nozzle. In the latter case, the velocity profile characteristics

apply to the refraction amplitude and turbulence scattering experiments.

Hot film anemometrywasused for all measurements.

Radial distributions of the meanvelocity will be presented first to

illustrate how the shear layer features changewith axial distance. Using

these results, the shear layer growth rate will be presented as a function

of axial location. Finally, to isolate changesin the velocity distribution

with axial location, the velocity profiles are plotted in a dimensionless

form using a similarity parameterbased on the shear layer growth rate. The

resulting curves from various axial stations collapse onto a single curve

demonstrating similarity of the velocity profiles. This similarity, which

has beenwell substantiated by other investigators, permits comparisonsof

the UTRCopenjet test facility with other facilities.

In addition to meanvelocity profile measurements,shear layer turbulence intensity wasmeasuredfor the open jet operating without tabs.

Measurementswere obtained at each axial station to provide the necessary

input to an existing theoretical scattering analysis.

MeanVelocity Profiles

Meanvelocity profile measurements,with tabs attached to the nozzle

periphery, were conductedat an azimuthal station coinciding with one of the

tabs. Figure II showsthe radial distribution of the meanaxial velocity

at various stations downstreamof the nozzle exit for M = 0.2 and 0.4.

Here the local velocity, U, is normalized by the potential core velocity, UoThe axial position, X, and radial distance from the jet centerline, R, have

beennormalized by the jet radius, R . Although only two Machnumbersare o

presented, self-similar velocity profile shapeswere obtained at all velocities whenthe axial station washeld fixed.

Thepotential core andmixing zone are clearly identified in figure ii.

The distributions exhibit a familiar behavior with the velocity profiles

spreading radially with increasing axial distance. The bulge in the velocity

profiles at X/Ro = 0.66 wasdue to the severe mixing forced by the tabs

24
attached to the open jet nozzle. This feature is smoothedout with increasing

distance from the nozzle exit disappearing altogether beyondX/Ro = 1.33.

Figure 12 showsthe normalized velocity profiles without tabs attached

to the inlet nozzle. Thebulge observed at X/Ro = 0.66 in figure ii is now

absent. Here the open jet shear layer growsnaturally.

Shear Layer Thickness

Figure 13 showsa schematic representation of the coordinates needed

to describe the shear layer thickness. Since there is no universally

accepted definition of shear layer boundaries, the inner and outer edgesof

the shear layer are defined here by the 90 percent (U/Uo = 0.9) and I0 percent (U/Uo = 0.i) velocity lines, respectively. The distance from the jet

centerline to the half-velocity line (U/Uo = 0.5) is denoted by RI/2. The

local shear layer thickness, 8 , is defined as the difference betweenthe

inner and outer edgesof the openjet.

Theaverage radial position of the inner and outer edgeof the shear

layer over a range of _ch numberswasdetermined from the velocity profiles

in figures ii and 12. The results are shownin figures 14 and 15 as a

function of normalized radius. Also shownis the averagehalf-velocity

position. The shear layer thickness was calculated as a function of axial

position using these average characteristics. Theresults, shownin figure

16, describe the shear layer growth rate.

Theanalytical solution derived by Goet]er (see ref. 20, page96)

describing the growth of a two dimensional shear layer is also shownin

figure 16. The analysis wasused to calculate the inner and outer edges

of the shear layer (without tabs present) defined by the 90 percent and

i0 percent velocity points. Ilere the Goetler solution is considered adequate"

for determining the growth rate of an axisymmetric jet flow within the first

two jet diameters since the flow is nearly two-dimensional in the region.

Goodagreementbetweentheory and axisymmetric jet flows is also evident

from the measurementof Candell (ref. 21) which are shownin figure 16.

Note that tabs were not used in reference 21.

Several conclusions can nowbe drawnregarding the UTRCopen jet test

section. First, with tabs attached to the inlet nozzle, the open jet shear

layer is larger than an axisymmetric jet without tabs. This is due to the

early mixing forced by the presenceof the tabs. However,at large X/Ro,

the shear layer thickness approachesthe standard jet result. Finally

the initial shear layer growth rate, with the tabs removed,can be predicted by the Goetler analysis for a two dimensional plane jet.

25
Tabswere attached to the nozzle periphery during the refraction angle

correction measurements. The resultant thickening of the shear layer provided a more severe test for verification of the vortex sheet shear layer

modelused in the refraction theory. Despite the thickening of the shear

layer by the tabs, the refraction angle changesshowedgoodagreementwith

theory.

Similarity of MeanVelocity Profiles

To permit direct comparisonof the openjet velocity profiles at

various axial stations, the meanvelocity distributions in figures ii and 12

were plotted versus the similarity parameter, n. Here _ is defined as,

= (R - RI/2)/6. A comparisonof the normalized velocity profiles is given

in figures 17 and 18 for three different axial stations and two Machnumbers,

M= 0.2 and 0.4. Thevarious curves at the three stations collapse onto a

single curve.

Also shownin figures 17 and 18 is the standard hyperbolic tangent

analytic curve used for two-dimensional plane-jet shear layers. The good

agreementbetweenexperimental data and the hyperbolic tangent curve means

this relationship adequately describes the UTRCshear layer characteristics.

Turbulence Intensity

Shearlayer turbulence intensity profile measurementswere conducted

for the openjet with the tabs removed. Radial distributions were obtained

at the sameaxial stations for which meanvelocity profiles were measured.

Figure 19 showsthe M = 0.4 turbulence intensity profiles plotted as a

function of the similarity parameter, _.

The results indicate that the similarity parameter used for the mean

velocity profiles also collapse the different turbulence intensity profiles

onto a single curve. Peak turbulence intensity is approximately constant

betweenthe upstreamstation and the farthest downstreamstation.

To assess the effect of changingMachnumber,radial distributions are

comparedat X/Ro = 4 for two different Machnumbers. Theresults, shownin

figure 20, verify that the turbulence intensity profiles are independentof

openjet velocity.

26
Theturbulence intermittency boundary used to define the inner edgeof

the shear layer is shownin figure 15. A knowledgeof this boundarywas

necessary to avoid locating the in-flow traversing microphonein the turbulent flow. This boundarywasdetermined by monitoring, on an oscilloscope,

the fluctuating voltage signal from the hot film probe and noting whenthe

randomfluctuations disappeared. The advantageof this technique is that it

is sensitive to the occasional turbulent bursts which occur near the edge

of a shear layer.

27
THEORETICAL FORMULATION OFTHEREFRACTIONPROBLEM

Review

Thebasic approach for most of the present shear layer correction

theories was initially given by Amiet (ref. 7). This analysis treated the

case of a source beneath a plane zero-thickness shear layer. Theobserver

was assumedto be in the geometric and acoustic far field of the source.

However,the shear layer could be at any distance from the source. There

were no requirements for the source to be acoustically compactor a point

source. This analysis, basedon the previous work of Ribner (ref. 2) and

Miles (ref. 3), requires that the measurementsmadeoutside the shear layer

be corrected in both angle and amplitude. The result is a correction method

which is independent of frequency and source type (i.e., monopole,dipole,

quadrupole).

Independenceof frequency and source type and the absenceof any requirements for the source to be compactor the shear layer to be in the far field

of the source is rigorously true only for the plane shear layer case. These

points were not proved in the original derivation of Amiet (ref. 7), however,

the rigorous derivation of Amiet (ref. i0, Appendix I) for the plane shear

layer verified these statements. This has led to confusion on the part of

somereaders who continue to base their conclusions on the original derivation.

Theonly requirement for the second derivation is that the observer distance

be large comparedto the source dimensionsand the acousticwavelength.

Theanalysis for the single plane shear layer is simple becausethere

are no multiple reflections. Themorerealistic caseof a cylindrical shear

layer does require additional assumptionsto be made. Jacques(ref. 8) first

treated the cylindrical shear layer case for a source on the jet centerline.

Themultiple reflections which occur for this caseare neglected since the

reflection coefficient is generally small at tunnel Machnumbersof interest.

Also, the acoustic wavelength must be small comparedto the source-shear

layer distance. This restriction is easily satisfied since figure 4 of

reference i0 indicates a wavelength smaller than a few jet diameters is

generally small enough. For openjet diameters encounteredin practice, this

is not usually a severe limitation. Thecutoff frequency (frequency below

which the surrounding chamberbecomesnon-anechoic) of openjet acoustic

test facilities typically correspond to a wavelength to diameter ratio on the

order of i.

The high frequency case of a source on the centerline of a cylindrical

shear layer with a thickness significantly greater than a wavelength was

treated by Tester and Morfey (ref. 9). Although not explicitly derived as a

correction for open-jet wind tunnel measurements,the results of the analysis

were applied toward this end by Ahuja et al., in reference 15.

28
It is interesting to note that the shear layer corrections for the two

cases of zero thickness (as formulated by Amiet) and infinite thickness

shear layers (as formulated by Ahuja et al) differ by only a few hundredths

of a decibel over most of the angular range as shownin reference I0. This

would be expected since the basic difference betweenthe two corrections is

that the zero thickness case assumesa reflected waveexists while the infinite thickness case assumesthat all the energy is transmitted. Since the

amplitude of the reflected waveis small over most of the angular range

(see e.g., reference 7) and since the reflected energy is proportional to

the square of the amplitude, one should expect little difference betweenthe

corrections. At the extremeangles where the reflected wavecan have a significant magnitude, both the zero thickness and the infinite thickness corrections should be used with caution since neither correction accounts for

multiple reflections within the shear layer. Thus, the correction procedure

for an infinite thickness shear layer used by Ahuja et al (ref. 15) has the

sameangle correction as that of Amiet (ref. 7 and i0) and Jacques (ref. 8)

and an amplitude correction differing by a few hundredths of a dB over most

of the angular range. It is, for all practical purposes, equivalent to the

correction procedure for a zero thickness shear layer. A moredetailed comparison betweenthe various zero thickness, infinite thickness, plane shear

layer and cylindrical shear layer results is given in reference i0.

Shear Layer Correction for An Off-Axis

Acoustic Source

For the case of a source on the centerline of a cylindrical shear layer,

as was discussed in reference i0, the shear layer must be in the acoustic far

field of the source for the shear layer correction to be independent of

source type and frequency. Thus, ray acoustics principles are applicable and

the shear layer correction can be derived by ray tracing arguments. For the

case of a source off the centerline, the derivation will also be based on

ray acoustics. The samefar-field assumptionrequired for the on-axis source

solution applies here. Themain difference betweenthis case and the oncenterline case is that the algebra for the ray tracing of the off-center

case becomessignificantly morecomplex. Thebasic principles governing

the crossing of the shear layer by a ray remain the same,however.

Figures 21 and 22 showthe basic geometry and the coordinate system

used in the derivation. The zero thickness cylindrical shear layer has a

radius, a, and the source is located off the centerline by a distance a-h.

A Cartesian coordinate systemhas the origin located at the source, S, the

x axis parallel to the tunnel axis and the z axis along the normal from the

tunnel centerline to the source. A ray travels from the source along the

29
path labeled r I crossing the shear layer at point Xl, YI'' Zl'' and continues

along path r 2 to the observer 0 at x2, y ', z_'. Theplane tangent to the

shear layer at point x., YI" Zl' makesan anile _ with the x-y' plane.

Angles ec and _c describe the ray path beneath the shear layer, 0t and _t

describe the ray path above the shear layer and 8m and _mdescribe the

observer position relative to the source.

The angle 8 is the angle betweena given line and the x axis or a line

parallel to the x axis. Thus8c is the angle betweenthe ray beneath the

shear layer and the x axis, 0t is the angle betweenthe transmitted ray and

a line parallel to the x axis at the shear layer crossing point, and e is m the angle betweenthe x axis and the line joining source and observer. The

angle _ is the angle betweenthe x-y plane and a plane containing a given

line and parallel to the x axis. Thus, _c is the angle betweenthe x-y plane

and the plane defined by the x axis and the ray beneath the shear layer, _t

is the angle betweenthe x-y plane and the plane containing the transmitted

ray and parallel to the x axis, and _mis the angle betweenthe x-y plane

and the plane containing the x axis and the observer point. The unprimed

coordinate system is defined by rotating the x, y', z' coordinate system

through an angle _ about the x axis so that z is normal to the tangent plane.

The detailed derivation of the off-axis source correction is given in

AppendixA. Results of this calculation can be summarizedas follows: the

amplitude correction is different from the on-axis case for all sourceobserver positions. In the special case of an observer located in the plane

containing the source and open-jet centerline, the angle correction is identical to that obtained for an on-axis source or for the case of a plane shear

layer.

A listing of the generalized computerprogramwhich predicts the refraction effects described above is given in AppendixA. A sampleprintout is

also provided. The programis extremely short thereby simplifying the task

of generating refraction amplitude correction predictions.

Theoretical Refraction Predictions For

ComparisonWith Experiment

Theprimary objective of the experimental effect was to measurethe

refraction angle and amplitude changesassociated with acoustic wave-front

propagation through an openjet shear layer. While various combinations of

source-observer locations could be evaluated the present study was limited

to acoustic source and far-field microphonepositions situated in a plane

which coincided with the jet axis. Under these conditions, angles _c = 90o

3O
and a = 0° in figures 21 and 22. The resulting propagation path, SBOin

figure 22, was thus confined to a plane normal to the tangent plane at the

shear layer crossing point.

The three-dimensional geometry in figures 21 and 22 can therefore be

replaced by the two-dimensional geometry in figure 23. Here wavefronts

propagating in the direction, ec, inside the airstream propagate in the

direction, et, outside the openjet. Theactual path of an acoustic ray is

described by the points SBO. The changefrom ec to et is a result of

refraction by the shear layer. Without flow the soundpropagates at angles

em

Therefraction angle and amplitude corrections convert measurementsat

the observer station (0) in figure 23 to either the constant radius station

(C) or constant sideline station (D) on the non-refracted path.. Selection of

the particular conversion dependson the far-field microphonearray geometry

used to measurethe acoustic source directivity pattern. Whichevermicrophonegeometry is used, the corrected soundpressure level represents an

equivalent measurementin the absenceof the shear layer. In other words,

the shear layer is considered located at infinity with uniform flow existing

betweenthe source and the far-field microphoneat either station C or D.

Several features of the refraction theory are worth noting. First,

the transmitted angle, et, is the samewhether a constant radius or constant

sideline measurementis selected. The amplitude correction is partially

a function of the difference in path length betweenthe source and the

far-field microphoneon the refracted and non-refracted acoustic ray.

Theamplitude correction is also a function of the difference in ray

divergence on the convectedray path inside the open jet (SB) and on the

refracted ray path (BO)outside the openjet. Oncethe amplitude correction is

calculated for either station C or D on the non-refracted ray, the amplitude

at the remaining station is simply calculated using the inverse square-law.

For example, if dBCrepresents the decibel amplitude correction neededto

convert the measurementat station O to station C, then the decibel correction

for station D is dBD = dBC- i0 Log (SD/SC)2

If the sideline microphonedistance approachesthe openjet radius

the amplitude correction decreases to a finite value independent of the

open jet radius. This finite value represents the difference in acoustic

energy between the incident and reflected waves inside the open jet. It

should be noted that the effect of path length difference between the

refracted and nonrefraeted ray paths does not influence this conclusion.

This is because the path difference approaches zero as the sideline microphone

approaches the open jet radius. Furthermore, for measurement locations just

outside the open jet the ray tube has diverged only a small amount compared to

the ray tube inside the open jet. Thus, changes in the divergence rate across

31
the shear layer would not be perceptible for out-of-flow microphonestations

close to the open jet. Amplitude changesacross the shear layer would

insensitive to divergence rate changes. Consequently, the amplitude changefor

microphonestations close to the open jet radius is limited %othe difference

betweenthe acoustic energy of the incident and reflected wavesinside the open

jet. This amplitude changeis represented by equation A.21 in reference 7.

Figure 24 showsthe predicted refraction angle correction for a constant

radius microphonegeometryas a function of openjet Machnumber. Specific

coordinates for-the source and far-field microphonepositions are given by

the parametersh/Ro and h/r. The values for these parameterscorrespond to

the conditions tested in the experimental study and listed in Table I. The

significance of the angle correction is evident whencomparingthe difference

betweenangles @ and @. For exampleat M = 0.4 a microphonemeasurement m c

at @m= 60o corresponds to a measurementon an acoustic ray initially

propagating at 0c = 45° inside the open jet.

Moving the source off axis results in a significant angle changeas

shownby figure 25 for the fixed Machnumber,M = 0.3. The range of off-axis

source positions is defined by either the _arameter h/Ro or the parameter g.

The latter variable is defined as g = 1 - L, where h is measuredfrom the

shear layer closest to the observer. The§_all insert in figure 25 defines

the range of the parameter g.

Refraction amplitude correction predictions are shownin figure 26 for

two Machnumberswith the source situated on the open jet axis. The

amplitude correction is addedto the soundpressure level measuredat angle

@mto give the equivalent noise level obtained on the non-refracted ray

identified by angle @c" The curves indicate a small negative amplitude

correction for measurementangles close to the openjet axis, and a positive

correction in the upstreamquadrant. The effect of moving the source off-axis

is significant as shownin figure 27 for a fixed Machnumber,M = 0.3.

Figures 28 through 31 showa similar set of curves for the constant

sideline refraction angle and amplitude corrections. Predictions are presented for both on-axis and off-axis acoustic source positions. Here the sideline parameter, h/y = 0.25, was selected equal to the constant radius parameter, h/r = 0.25, used in figures 24 through 27. A comparisonof the

amplitude corrections at the sameangle @min figures 26 and 30a showsa

significant difference betweenthe two geometries. Figure 30b showsthe

sameamplitude correction plotted versus angle 0c. All figures presented in

the section describing the experimental assessmentof the amplitude correction

are plotted as a function of 8c.

32
It is important to recognize that the theoretical predictions in

figures 24 - 31 are a function of the source position (h/Ro) and the microphoneposition (h/r or h/y). The predicted angle and amplitude correction

curves are replaced by a different set of curves if these parameters change.

33
EXPERIMENTAL ASSESS}lENTOFREFRACTIONAGIECORRECTIONTHEORY

Experimental Approach

The experimental refraction angle correction for the geometry in

figure 23 wasobtained using the test set up shownin figure 8. Acoustic

ray angle changeswere determined from measurementsof the constant phaseor

wave-front surfaces outside the airstream. In this region, the acoustic ray

is perpendicular to the wave-front. Oncethe wave-front angle at the observer

location is known, the ray normal to the wave-front ray can be traced back to

the point, Xo, at which the soundemergedfrom the shear layer. Theoriginal

propagation angle inside the openjet is then obtained from the relationship

@c= arctan (h/Xo)

Thewave-front angle wasmeasuredin the following manner. Soundwas

generated at discrete frequencies by an acoustic source inside the openjet.

Thephasedifference, betweenthe signals arriving at microphonesmI and m2

in figure 8, was then determined by cross-correlating the signals. From

this, the wave-front angle relative to the microphonearray was calculated

permitting the ray to be traced back to the shear layer crossing point.

MeasuredPhaseDifference and Calculated Angle Change

It now remains to derive the equations linking the measuredphase

difference and the original propagation angle, ec, inside the free jet.

Themodeling problemis shownin figure 32. For M = 0, the angle between

the wave front arriving at m2 and the line connecting the array is denoted by

_o" This parameter accounts for small differences in the distance, kr,

(fig. 32) betweenthe source and the individual microphones. This difference

is due to inaccuracies in placing the two microphonesat exactly the same

radial distance from the source. The difference was consistently held to

less than 0.25 cmduring the experiment. Assumingthis value of kr results in

a maximumvalue of >o = 0.016 radians for the smallest microphoneseparation

distance, _, shownin figure 32.

If the askewmicrophonearray orientation were neglected, errors would arise

in the phaseshift measurement. For example, if gr = 0.25 cm, then at i0 kHz

a 0.07 cycle phase shift occurs betweenmI and m2. Since the present experiment required an accuracy of 0.02 cycles it wasnecessary to account for the

skewedmicrophonealignment. That is, the measuredphase shift at M= 0

was subtracted from the phase shift obtained at finite Machnumber. This

effectively calibrated the measurementof phaseshift to account for microphoneplacementerror. Themathematical details are presented below.

For M= 0, the total phasedifference (expressedin cycles) betweenconstant phasepoints arriving at mI andm2 is given by the relation

34
AT: Z_+(A I- AZ) (i)

where

f_

A : -- sin /.z 0

Co

The parameters, A I and A2, account for the phase lag between the

acoustic input signal to each microphone diaphragm and the final voltage

signal applied at the correlator. Nominally, at M = 0 this phase lag is

less than 0.i cycles for the frequency range employed in the present angle

correction experiment. The microphone cartridge phase lag characteristics

are included in this parameter.

(2)

The parameter, A_, was measured directly by cross-correlating the

T

periodic signals arriving at the adjacent microphones. Figure 33 illustrates

the correlator time delay trace. Based on the phase shift of the first

maximum, 5 T = T'f. The magnitude of T has been exaggerated to make it

perceptible in the figure. Nominally, A T is less than 0.i cycles at M = 0.

The location of the first maximum in the correlation function was defined as

the mid-point between the zero cross-over points. In figure 33 the mid-point

of the second cycle and a knowledge of the period were used to locate the midpoint of the first cycle. By using two cross-over points irregularities in

the correlation function were averaged. The term "irregularities" is used

here to describe a deviation of the measured correlation functions from a

smooth sinusoidal behavior. These deviations occurred when both microphones

sensed open jet shear layer background noise in addition to the source noise

at non-zero Mach numbers.

For M # 0, the total phase difference is given by

n_: n'+ (nj-n z) (3)

where

A J f_

- CO sin (H.o+iU-I) (4)

Here _i describes the angle between the two wavefronts in figure 32.

Solving for the difference 6' T - A T gives

(5)

Appendix B shows how this expression may be simplified for the small values

of _o < 0.016 radians used in the present experiment. Solving for Pl gives

; 35
From this

c

where

/.ll = S in- I [ _C--_'9"_( AfT - ,,%T ) ]

can be determined using the relationship

8¢ = ton-' (h / Xo)

X_r cos _m- (r sin_m-h) cot (/J'l + _m )

(6)

(7)

(8)

The expression for X o is derived in Appendix C.

Accuracy requirements of the phase measurements necessitated small

time delay increments in the cross-correlation function calculation.

Depending on the acoustic source frequency, the following time delay

resolution values, dT, were used: a) f = i0 kHz, dT = 1 usec, b) f = 5 kHz,

dr = 2 _sec, c) f = 2.5 kNz, d_ = 5 _sec, and d) f = 1.25 kHz, dr = 10_sec.

Background Noise and Non-Anechoic Effects

The above cross-correlation approach was successful only at M N 0.i

For higher open jet Mach numbers, the facility random background noise

dominated the cross-correlation function as is illustrated by the two-microphone correlation function in figure 34. Although a periodic waveform is

present in the cross-correlation function, the measured result is not suitable

for solving equation 6 for the wavefront propagation angle. To verify that

the time delay trace is dominated by facility noise, a second trace is shown

with the acoustic source turned off.

The background noise dominated the cross-correlation function despite the

12 dB signal to noise ratio shown in figure 35. This occurred because the

microphone input signals to the correlator were not filtered permitting the

complete background noise signal to contribute to the cross-correlation. It

may appear that this problem can be circumvented by narrowband filtering the

microphone spectrum shown in figure 35 to pass only the pure-tone component.

However, this still retains in the correlation function a contribution from

the cross-correlation of the filtered narrowband microphone signals. The

periodicity of this contribution corresponds to the filter cutoff frequencies.

Since these frequencies are close to the acoustic source frequency, a portion

of the narrowband random contribution would remain in the cross-correlation.

36
An alternate cross-correlation technique developed by Schlinker (ref. 23)

was therefore employed. The method involves cross-correlating the individual

microphone signals with the periodic input signal to the acoustic driver

system. The random signals due to facility noise are rejected leaving only

the periodic component. The success of the method is illustrated by the

correlation traces in figure 36. Here, SI, s and $2, s represent the individual

microphone-signal generator cross-correlation functions. To verify that

the traces are independent of the facility noise, one trace is shown with the

source turned off.

The mathematical details linkSng the correlations in figure 36 with the

microphone orientation angle _I + _o are presented in Appendix D. The final

result for the phase difference at non-zero Mach number is

A_- A T = 7,-72-AT

(9)

where ql' n2 represent the phase difference between the acoustic driver signal

and the individual microphone signals. Equation (9), when used in conjunction

with equation (6), gives (for small Po),

• "l[ - AT) ] (I0)

A brief discussion of the measured phase difference is now warranted

since the angle correction is derived from this parameter. Figure 37 Shows

the experimentally determined phase difference, A T ' - A T , for a 2.5 kHz

acoustic source frequency with the open jet nperating at M = 0.3. The source

position corresponded to Test Configuration 1 in Table I. Two different microphone spacings were used in the measurement. For angles near 90 ° , where

refraction is minimal, a large separation (Z = 0.48 m) was used to obtain a

measurable phase shift. In contrast, at angles close to the jet axis where

the phase shift is large a smaller separation (Z = 0.3 m) was used.

The measured data in figure 37 are compared to the phase difference

calculated from the refraction theory described in Appendix A. The figure

shows excellent agreement between the theory and experiment over the complete

range of measurement angle. The measured phase was then used to calculate

the angle correction associated with the transmission of sound through the

shear layer.

37
Plane WavePropagation Assumptions

The above described experimental approachassumesthat the wavefront

arriving at the far-field microphonearray is plane. Thepossible error in

this assumptionwas evaluated by calculating the time for the sound to travel

from the source to the individual far-field microphones. Thedifference between these times was then comparedto the time calculated using the plane

waveassumption.

If e = 0 at t = 0,

at time to where

For a point source in a flow, the phase,@, of the waves is

then the samewavefront will reach the point (Xo, O, h)

Co 2,o ÷ MXo:,/Xo 2 + (12)

Here X o is the shear layer crossover in figure 23.

with equation A.18 relating Qc and 8c gives

Using tan e c = h/X ° along

h (I- MCOS_I) (13)

to = C0_t

The time for the wave to travel from X to the observer at 0 (see figure 23)

is o

r sin 8m - h

t I = c o slnsl (14)

The total time for a sound wave to travel from the source to a far-field

microphone is then t2 = to + tl. The exact time difference, &te, for the

sound to reach the two separate microphones is obtained from the difference

between the value of t 2 calculated for each microphone.

On the other hand, the approximate calculation treating the wave front

as plane gives for the time difference (see figure 32).

: sin(e t = sin (15)

This expression is easily derived from equation (B.5). Note that for

this calculation the angles 9 t and em are averages calculated for an observer

midway between the two microphones,

38
Figure 38 shows the percent error between the exact (At e ) and

approximate (At a) solutions defined as

L_t¢ -/ktg

PERCENT ERROR -- [00 Ate (16)

The calculations are for the maximum microphone separation used which was

= 0.48 m. The error decreases as the square of the microphone separation

so that the next smaller separation value listed in figure 32 would give an

error approximately 1/4 as large. Even at the large separation, however,

the error was very small, on the order of a few percent. This justifies the

experimental approach described earlier.

The above error estimate assumes that the acoustic wave front arriving

at the far-field microphone array originates at the sound source. Measurements of the free-field decay characteristics, discussed earlier in the

description of the experiment, indicated the presence of waves reflected

from the downstream collector surface. For the case of a continuous discrete

tone acoustic source signal these reflected waves combined with the direct

acoustic waves arriving at the microphone. This resulted in nodes and

antinodes distributed throughout the chamber. Deviations from a free-field

anechoic environment were only + 0.5 dB which represented a reflected-todirect wave amplitude ratio of 0.06 if the two wavefronts were either

in phase or 180 ° out of phase.

The refraction angle correction experiment could tolerate reflected

waves of such amplitudes since the measurements emphasized phase difference

and not absolute sound pressure level measurements at the far-field microphone measurement station. This was verified analytically in Appendix E.

,The estimated error in the phase measurement was found to be 0.0091 cycles.

This error is comparable to the experimental accuracy of the phase measurement and is less than the 0.02 cycle accuracy required in the experiment.

It is worthwhile to perform an error analysis to determine the sensitivity of the corrected angle, 0c, to errors in the experimentally determined phase difference in the argument of equation i0. Such an error

analysis is provided in Appendix F for the case of Om = 90. Here the

magnitude of the phase difference is a minimum (see figure 37) so that

small errors in the measured phase difference become significant. Considering the case of M = 0.4, the sensitivity of 0 c to changes in the phase

difference is estimated by the differential equation d0 c = 1.6 d(&*) where

A* = n I - n 2 - A T . Assuming a 0.02 cycle error in the measurement of A*

the error in 0c is calculated to be 1.8 ° . This is considered to be small

compared to the absolute magnitude of O c = 72 ° in this case. Thus, the

accuracy of the phase measurement had a negligible effect on the experimentally determined value of 0 c.

39
Comparisonof Measuredand Theoretical

Refraction Angle Correction

Comparisonof theory and experiment is given first for the case of an

on-axis source location. Shownin figure 39 is a comparisonbetweenthe

measuredand theoretical angle correction as a function of openjet Mach

numberand acoustic source frequency. The source and far-field microphone

positions correspond to Test Configuration i. Specific coordinates for this

geometry are given in figure 39(a). Only two curves are shownin each plot

to avoid crowding the experimental data points.

The agreementbetweentheory and experiment is considered goodparticularly at frequencies above1 kHzwhere the phasedifferences are large and

measurementaccuracy is correspondingly good. At 1 kHz, the small measured

phase difference introduced somescatter into the experimental data points.

To obtain a quantitative assessmentof the refraction correction theory, the

absolute difference betweenthe theoretical curves and the data can be calculated. Considering the measurementangle, em= 37.5°, where the correction

is significant, the averagedifference was 1.25° at M= 0.i, 0.25° at M = 0.2,

0.4° at M= 0.3, and 0.6° at M = 0.4. The largest deviations occurred at

low Machnumberdue to the small measuredphasedifference.

Figures 40 and 41 showcomparisonsbetweenthe measuredand theoretical

angle correction at two additional downstreamlocations. The frequency

dependenceat M = 0.4 is shownin part (a) and (b) of each figure while the

Machnumberdependenceat a fixed frequency of 5 kHz is shownin part (c) of

each figure. This limited frequency and Machnumberstudy was conductedto

verify the trends obtained in figure 39. In all cases, the agreementbetween

theory and experiment is good. The absolute difference betweentheory and

data points was, in all cases, less than 2° at _m= 37"5o"

Considering nowoff-axis source locations, figure 42 is a comparison

betweenthe measuredand theoretical angle correction as a function of openjet Machnumberand acoustic source frequency. The test conditions are

identical to those evaluated in the on-axis geometrypresented in figure 39.

This approachpermitted assessing the capability of the theory to predict

changesin source-to-shear layer separation distances. Theresults for

f = 1 kHz are not included due to the large scatter in the data.

Comparisonsbetweenthe measuredand theoretical angle corrections in

figure 42 indicate goodagreementat angles close to the jet axis. However,

a consistent discrepancy occurred at large measurementangles for all

frequencies and MachnumbersaboveM = 0.i. A detailed error analysis of the

experimental procedure was conducted to isolate the origin of the discrepancy. First, the sensitivity to assumedchangesin h was evaluated analytically. Second, the sensitivity to errors in the measurewavefront propagation

40
angles was evaluated. Both analyses indicated that the resulting corrections to

the emversus 0c curves were smaller than the discrepancies noted in figure 42.

It should be noted that the shear layer wasnot required to be in the far field

of the acoustic source. This is discussed in the Reviewsection of the chapter

titled Theoretical Formulation of the Refraction Problem.

The zero thickness shear layer assumptionwas also questioned.

Refraction theory was used to trace an acoustic ray propagating from the

source to the outer edgeof the finite thickness shear layer. The she_r

layer wasmodeledas a series of parallel vortex sheets with the refraction

theory applied across each sheet. The shear layer crossing point, Xo, and

wavefront propagation angle outside the flo_ were determined by this detailed

analysis. The resulting measurementangle emwas then calculated and

comparedto the value predicted by the zero thickness calculation in figure

42. The difference was found to be insignificant.

Meanvelocity profiles betweenthe speaker aperture and the shear

layer were also measuredas part of the experimental procedure error analysis.

Theobjective was to check for flow-field distortion due to the finite

source size. Theresults indicated at most a 5 percent deviation from a

uniform velocity profile measuredin the absenceof the speaker. Failure to

obtain agreementat an off-axis source position having small h/Ro is not

presently understood.

To further investigate the observeddisagreementbetweentheory and

experiment for the off-axis case, additional measurementswere performed

with the source at the sameaxial location (X/Ro = 1.33) but displaced in

the opposite direction from the jet centerline (h/Ro = 1.44). Here the

source and far-field microphonepositions correspond to Test Configuration

5. Shownin figure 43 is a comparisonbetweenthe measuredand theoretical

angle correction at selected Machnumbersand acoustic source frequencies.

The agreementbetweentheory and experiment is observedto be good at all

operating conditions.

Summaryand Evaluation

A theory capable of predicting the circular openjet refraction angle

changesfor an arbitrary source type, on-axis source position, and far-field

microphoneposition was validated. Data obtained at three on-axis source

positions, four source frequencies and four MachnumbersbetweenM= 0.i

and 0.4 verified the theoretical Machnumberdependenceand the frequency

independence. Excellent agreementbetweentheory and experiment verified

41
J

that the lip-line vortex sheet model is an adequate representation of the

finite thickness shear layer. Axial variations in the mean shear layer

properties and divergence of the flow field are therefore not needed in

the theoretical formulation.

Off-axis theory was validated for a source position having a large

value of h/R o. Failure to obtain agreement at an off-axis position having

a small value of h/R o is presently not understood and will require additional

research in the future.

42
EXPERIMENTAL ASSESSMENT OFREFRACTION

AMPLITUDECORRECTIONTHEORY

I

i

!

Experimental Approach

The objective of this investigation was to measure the amplitude

change associated with an acoustic-wave propagating through an open Jet

shear layer. Measurements were conducted at the same open jet Mach

numbers and acoustic source frequencies investigated in the refraction

angle correction experiment. Similar test conditions were investigated

since the angle correction was needed to define the refracted ray path

on which the amplitude correction was measured.

The refraction amplitude change across the shear layer was assessed

using the constant sideline measurement geometry shown in figure 23.

Acoustic source sound pressure levels were measured inside and outside the

open jet. The microphone location inside the open jet coincided with a ray

propagating at a selected angle 8c. The far-field microphone was situated

on the same acoustic ray except that the ray path was now refracted by the

shear layer to the new propagation angle, et, shown in figure 23. The

intersection of the refracted ray with the sideline determined the measurement angle, em, which defined the far-field microphone coordinates.

A constant sideline geometry was selected for this experiment instead

of the constant radius geometry previously described in the angle correction experiment. This choice was based on the large refraction amplitude

correction which occurs in the sideline geometry. The magnitude of the

correction is evident in figure 44 where the theoretical refraction

amplitude corrections are compared for a constant sideline and constant

radius microphone geometry at M = 0.4. The larger corrections for the

sideline geometry were expected to improve the accuracy of the experiment

relative to the ± 0.2 dB error band expected from the signal enhancement

measurement technique described below.

All figures presented in this section show the experimentally determined

amplitude correction plotted as a function of 0c. This angle, instead of

em, was selected as the principle variable in the experiment since this

permitted the in-flow microphone station to be held fixed as the open jet

Mach number increased, thereby, facilitating the measurement procedure.

Recall that angle em can be determined from angle ec using the appropriate

refraction angle correction curves in figure 24 or 28.

43
Calculating the Refraction Amplitude Correction From

MeasuredSoundPressure Levels

The refraction amplitude correction converts soundpressure level

measurementsat the observer station (0) in figure 23 to the constant sideline station (D) on the non-refracted path. The corrected soundpressure

level represents an equivalent measurementat station D in the absenceof

the shear layer.

Therefraction amplitude correction wasexperimentally assessedusing

acoustic source soundpressure level measurementsinside and outside the

openjet test section. Themicrophonepositions were defined by m3 and m4

in figure i0 with the latter station being equivalent to the observer station

(0) in figure 23. The equation linking the measuredsoundpressure levels

and the calculated refraction amplitude correction betweenstations (0) and

(D) in figure 23 will nowbe derived.

Mean-squaresoundpressure levels measuredinside and outside the

open jet were represented by the function P32(ec,f,M) and P42(0m,f,M).

amplitude correction function, AMP(6c,f,M ) was then determined from the

logarithmic expression

The

AMP = IO lOg PS,__z IO lOg (SD _2 (17)

P4Z \ Sm j

Here the ratio, P32/P4 _, represents the measured amplitude change on the

refracted path. This change was compared with the calculated inverse squarelaw amplitude change on the non-refracted path. The non-refracted path

change is represented by the ratio of the source-to-microphone distances

in the second term on the right side of equation 17.

mean square sound pressure level ratio, P32/PA 2, could not be The

measured directly because the acoustic source signal cSnsisted of a toneburst. Instead, the acoustic pressure wave-amplitude was measured. Letting

B 3 and B 4 represent the amplitude of the periodic signal during a tone

burst, the mean square sound pressure level was then replaced by the ratio

B32/B42.

Parameters, B 3 and B4, were measured using a time delayed signal

enhancement technique which captured the tone burst waveform arriving at

either the in-flow or far-field microphone. The details of this approach

can be described using figure 45a. Recall that the repetitive discretetone burst was provided by a function generator which powered the acoustic

driver. The generator also provided a variable delay pulse signal which

triggered the signal enchancement circuit to capture the tone burst.

The delay time, T, was selected to correspond to the propagation time

between the acoustic source and the individual microphones. The delay

44
was adjusted until the tone burst appearedin the sampling time windowof

the signal enhancementcircuit.

The circuit schematic in figure 45a showshoweither the in-flow

microphone (m3) or the far-field microphone (m4) were selected for

signal enhancement. Note that by using a commonfilter and amplifier,

differences in sensitivity were restricted to differences in the cartridge

and preamplifier sensitivities of the separate microphones. Thesedifferences were calibrated daily using a pistonphone and the autocorrelation

modeon the analyzer used for signal enhancement.

Figure45b illustrates a segmentof the tone burst signal obtained from

either the in-flow or far-field microphoneafter signal enhancement. Sample

increment times for the 400 point signal enhancementanalysis were selected

to give a maximumof 5 maximaof the periodic signal with the analyzer

time windowdefined by (T,T+AT). By limiting the numberof cycles, each

cycle wasdescribed by a minimumof 80 discrete points. This was considered

sufficient to resolve the amplitude of the discrete tone signal during the

tone burst.

The time trace in figure 45bshowsa modulated sine wavewith a slowly

increasing amplitude. In contrast, the function generator output signal

(fig. 45a) showsa constant amplitude signal applied to the acoustic driver.

The difference betweenthe two signals which was found to be a function of

the acoustic driver dynamicresponse, would appear to have an impact on the

equality, _--_zp,-_ 1 4 =_3B32/B42" This expression assumesa constant discrete

tone amplitude during the tone burst. The modulation was, however, identical at the in-flow and far-field microphonessince it originated at the

acoustic driver. The acoustic pressure ratio could therefore be replaced

by the ratio of the peak pressure associated with the corresponding cycle

at the in-flow and far-field microphonestation. Hence

P5 2 B 2 B 2

3,2

p2 B4,12 B4, 2 z

: .... (18)

The second subscript in each term identifies the corresponding cycle in

either the in-flow or far-field microphone time trace. For example, if

figure45brepresented the far-field microphone, the amplitude of the fifth

To ensure sufficient accuracy, the

maximum is designated by the term B4, 5.

pressure ratio at a minimum of 4 peaks in the time signal were averaged

and a standard deviation was also calculated. Hence

P5--z I 5,1 n > 4

p4z "-fi- i= B4,i 2

(19)

45
Both positive and negative pressure peakswere used in the summationin

equation 19. Additional cycles neededfor the summationwere obtained by

applying an additional delay time at the analyzer resulting in the time

window (T+A_, T+2AT)shownin figure 45b.

At high frequencies, acoustic pressure amplitudes associated with the

first few cycles in the time trace were neglected since the amplitudes were

small. Similarly, the last few cycles, which were generated by the acoustic

driver after the termination of the tone, were also neglected. Theduration

of the tone burst wasusually limited to l0 cycles of the discrete tone at

the acoustic driver input. This provided a starting point and termination

point in the signal enhancedtime trace. With the aid of these two reference points the corresponding peaks at the in-flow and far-field microphone

stations were easily identified.

The successof the abovedescribed approachfor capturing the tone

burst is demonstratedat M = 0 in figure 46. For this static operating condition the amplitude correction in equation 17 is zero since the acoustic

rays are not refracted. The data in figure 46 indicates a ± 0.2 dB deviation from the theoretical prediction. A ± 0.2 dB error band can, thus,

be assigned to all experimental data points.

For M = 0, 0.I, and 0.2, the tone burst signal waseasily detected by

the far-field and in-flow microphones. As the open jet Machnumberwas

increased further, the facility randombackgroundnoise beganto dominate

the acoustic signal arriving at the far-field microphone. Similarly, the

in-flow microphonesignal wasdominatedbymicrophoneself noise. Toovercome

these signal-to-noise limitations, the numberof ensemblesin the signal

enhancementwas increased as the Machnumberincreased. Thelonger sampling

times at the higher Machnumbersprecluded recording on analog tape the

simultaneous in-flow and far-field microphonesignals at each angular measurement station. Consequently, the two microphonesignals were processedsequentially using the circuitry shownin figure 45a. The acoustic driver output amplitude remainedconstant during the long sampling time required to

separately analyze the in-flow and far-field microphonesignals. This was

verified by repeating the signal enhancemento obtain a secondmeasurement

of the tone burst.

The successof the signal enhancementtechnique at high Machnumbersis

illustrated in figure 47. Thecurves represents the tone burst signals

recovered from the far-field (em = 44°) and in-flow (0c = 30°) microphonesat

M = 0.3. Similar to figure 45b, the tone burst signals contain a modulated

sine wave. The corresponding peaks at the in-flow and far-field microphone

measurementstationso are numberedusing the schemedesignated in equation 19. The ratios, B_,i/B_,i, in equation 19 are obtained from the ratio of the

corresponding pressure amplitudes and the amplifier settings used during the

data acquisition.

46
NoseConeDirectional Sensitivity Effects

The abovedescribed experimental approach assumedan omni-directional

sensitivity for the in-flow microphone. Free-field correction curves provided by the microphonemanufacturer indicated that the measurednose cone

responsewasa function of the incidence angle, Oc, shownin figure 48.

Since 9c changedas the microphonemovedalong the In-flow traverse line

the in-flow microphonedirectional sensitivity varied with traverse position.

To eliminate any differences betweenthe in-flow and far-field microphone

response, a nose cone wasalso used on the far-field microphone. In addition, the far-field microphonewasaligned parallel to the flow with the

nose cone pointing upstream similar to the in-flow microphoneorientation.

Since the refraction amplitude correction was basedon the decibel difference

betweenthe in-flow and far-field microphonesound pressure levels, the nose

cone directional characteristics were, in concept, nullified.

The aboveconclusion is correct only if the incidence angle is identical

at the in-flow and far-field microphonestations. Refraction, however,

changedthe acoustic ray incidence angle to Ot outside the flow. This change

wasaccountedfor by using theexperimentally determined nose cone directional

sensitivity curves shownin figure 49. Curveswere generated for the four

tone burst frequencies used in the refraction amplitude correction experiment.

Themicrophoneresponseat different frequencies wasplotted as a function

of the acoustic ray incidence angle. All amplitudes in figure 49 were

normalized re]ative to the zero incidence angle measurement. Stationarity

of the acoustic source during the measurementwas verified by a separate

reference microphone. A typical reference microphone me_aureme_ is plotted

in figure 49 for the i0 kHz case.

Far-field microphone data Was t]ien corrected by the difference b_tween

tile amplitude response measured at incidence angles _c and 0 t. Since the

transmitted angle, 0t, changed with Mach number, the directional sensitivity

correction also varied with Mach number.

The response curves in figure 49 change rapidly for incidence angles

greater than 90 ° These features differ from the nose cone free field response curves provided by the microphone manufacturer. The discrepancy is

presently not understood. Other investigators have, however, observed similar discrepancies.

It should be noted that using a standard grid on the far field microphone

would result in a larger directional sensitivity correction. This is because

of the vastly different response for a standard microphone grid and the nose

cone used on the in-flow microphone. Ahuja, et al. (ref. 15) used a nose cone

47
and standard grid microphonecombination but did not include the Mach

numberdirectional sensitivity responsecorrections. This raises questions

about the accuracy of their measurements.

Comparisonof Measuredand Theoretical Refraction Amplitude Correction

Downstream Quadrant, On-Axis Source Location - Comparisons of refraction amplitude correction theory and experiment are first presented for the

case of an on-axis acoustic source location. The Mach number dependence of

the refraction amplitude correction is assessed in figure 50 over the range

M = 0.i to 0.4. The experimental results were obtained using a fixed acoustic source frequency of f = 1.25 kHz. Figure 50d also includes the measured

correction at a source frequency of f = 2.5 kHz. Error bars designate the

limits of the standard deviation calculated from the separate amplitude

ratios in equation 19. Error bars smaller than the symbol size were not

included.

Source and microphone positions in figure 50 correspond to Test Configuration 6 listed in Table II. Measurements at angles greater than 80 ° could

not be obtained for this source location due to line of sight interference

by the open jet nozzle lips. Moving the source downstream to X/R o = 2.66

permitted increasing the upstream quadrant measurement angle to 8c = 120 ° .

These results correspond to Test Configuration 7 and are presented in the

following subsection.

The agreement between theory and experiment in figure 50 is considered

good over the complete angle range and Mach number range. As expected from

theory the refraction amplitude correction is a minimum near 0 c = 90 ° .

At angles close to the open jet axis, the amplitude correction increases in

magnitude with increasing Mach number. This is demonstrated in figure 51

where the amplitude correction for a ray propagating at 8c = 30 ° is plotted

as a function of increasing Mach number.

Figures 50 and 51 verify the theoretically predicted Mach number dependence of the amplitude correction at a fixed source frequency. The theory

also predicts that the refraction amplitude correction is independent of

frequency. This theoretical result is assessed in figure 52, where the Mach

number is fixed at M = 0.3 and the frequency increased from f = 1.25 kHz to

i0 kHz. At f = 1.25 kHz and 2.5 kHz, the agreement between theory and experiment is shown to be good. At f = 5 kHz and i0 kHz, however, a significant

disagreement between theory and experiment occurs at angles close to the jet

axis. For example, figure 52d shows approximately a i0 dB difference between

theory and experiment at 0c = 25 ° . These results appeared to conflict with

those of Ahuja, et al. (ref. 15) who found reasonable experimental agreement

48
with a theory similar to that developed in the present study. Experimental

assessmentin the study by Ahuja employeda broadbandnoise source.

Thediscrepancy in figures 52c and 52d waspostulated to be due to

frequency and directional scattering of the discrete tone burst energy by

the turbulence in the openjet shear layer. Since the narrowbandfilter

in figure 45awascentered at the discrete tone frequency, energy scattered

into adjacent frequency bandswasnot measuredby the far field microphone.

Similarly energy scattered in directions different from the refracted propagation angle, 0t, would not be measuredby the far-field microphone. Thus,

the measuredsoundpressure level, P--_,in equation 17 would be smaller than

anticipated resulting in a larger ratio for P-_/P-_4'Thedifference term on

the right side of equation 17 would then provide a positive amplitude

correction similar to that observedat ec = 25° in figure 52d.

The importance of the scattering mechanismwas investigated in a preliminary experiment conductedduring the first research programreported in

reference i. Theresults indicated a significant loss in discrete tone

soundpressure levels at high frequencies and high Machnumbersfor sound

propagating through the openjet shear layer. Themagnitudeof the loss was

comparableto the amplitude changesin figure 52d, and increased as Mach

numberand the ratio of the shear layer thickness to acoustic wavelength

increased.

A brief discussion of the parameters controlling the scattering phenomenon will be presented here to help in the interpretation of the discrepancies

in the refraction amplitude correction data. Additional details are given

in the section on turbulence scattering. The openjet Machnumbercontrols

the absolute turbulence intensity in the shear layer. In the absenceof

turbulence, scattering would be nonexistent. The shear layer thickness

controls the local turbulent eddy size. This is an important parameter since

soundis scattered only by the componentof turbulence which possessesa wave

numbercomparableto the acoustic wavenumber. The shear layer thickness

also controls the acoustic propagation path length in the turbulent medium.

A larger path length results in moreinteractions betweenthe acoustic wavefront and the turbulent eddies which scatter the sound.

To isolate those test conditions in which scattering effects contaminated

the refraction amplitude correction data, the difference betweentheory and

experiment wasplotted as a function of L/% and Machnumber. Here L is the

propagation path length in the turbulent shear layer. Theresults are shown

in figure 53 for two different propagation directions. At angle 0c = 30° ,

where the acoustic ray propagates obliquely through the shear layer, the path

length was estimated to be 0.31 m. This calculation wasbasedon the simple

49
expression, L = 6/sin 0c, where _ corresponds to the local shear layer

thickness at the intersection of the acoustic ray and the openjet lip

line. Figure 53a showsthat for low frequencies, whereL/% is approximately

unity, scattering wasnegligible for all Machnumbers. But as L/% approached

a value of i0 scattering becamesignificant for increasing Machnumbers. In

this case the numberof scattering interactions betweenan acoustic wave

front and the turbulent eddies in the shear increased by a factor of approximately I0 resulting in dramatically stronger scattering.

Whenthe acoustic ray penetrated the shear layer at 0c = 80°, L was

approximately equal to the shear layer thickness, 6. The acoustic measurements_in this case showeda negligible difference betweenrefraction amplitude correction theory and experiment over the complete frequency and Mach

numberrange. As expected the ratio of L/%was small for all operating conditions. This provided further support to the supposition that discrepancies

betweentheory and experimentwere due to turbulence scattering of acoustic

energy.

To provide a conclusive confirmation of the presenceof discrete tone

scattering in the amplitude correction experiment, measurementswere repeated

using randomnoise. The experiment wasperformed at i0 kIIz where the

largest discrepancy betweentheory and experimentwasobserved. In-flow and

far-field soundpressure level measurementswere obtained at M = 0.2 using

a 1/3 octave band filter centered at I0 kHz. For this operating condition,

the acoustic driver output powerdominatedover the in-flow microphoneselfnoise and the openjet backgroundnoise by almost i0 dB. The experimental

amplitude correction, calculated from equation 17 is shownin figure 54.

Theresults indicate goodagreementwith theory over the complete angular

measurementrange whenusing randomnoise. In contrast, figure 54 showsa

significant discrepancy betweentheory and experiment whenusing the tone

burst noise source. Since scattering would be expected to be muchstronger

for pure tones than randombroadbandnoise, the aboveresults confirmed

the hypothesis that scattering is responsible for the observeddisagreement

betweentheory and experiment in figure 52. _hen the goodagreementfor the

randomnoise result at I0 kHz is combinedwith the goodasreementat f = 1.25

kHz and 2.5 kHz in figure 50, the frequency independenceof the refraction

amplitude correction is confirmed.

Figure 54 suggests that randomnoise should be used for all operating

conditions in the amplitude correction experiment. Randomnoise, unfortunately, creates an immediatesignal-to-noise limitation at high Machnumbers.

Themajor disadvantage of this approach is the distribution of acoustic

source output powerover a large portion of the spectrumresulting in low

acoustic levels per unit Hertz. Theselow levels are maskedby the microphoneself-noise at the in-flow measurementstation and the openjet backgroundnoise at the far field station. Consequently, the signal-to-noise

50
ratio is low. Onemethodfor circumventing this backgroundnoise limitation

employs the cross-spectrum measurementtechniques used by Ahuja, et al.

(ref. 15). Themeasurementerrors associated with this approach, however,

precluded using the concept. This will be discussed further in the subsection

titled "Comparisonwith Other Investigators" In addition, the ability of

the technique to recover the source signals was questionable at the highest

Machnumberof M = 0.4 used in the present study. Basedon scaling laws,

the facility backgroundnoise due to the openjet noise would increase by

12 dB relative to the M = 0.27 maximumopen jet velocity investigated by

Ahuja. For these reasons, the discrete tone approachwasused throughout the

present study.

Continued application of the discrete tone signal in the amplitude

correction experiment required identifying those test conditions in which

scattering contaminated the data. Thesecases were easily recognized by the

large positive amplitude correction at angles close to the open jet axis.

Comparisonsbetweentheory and experiment are not presented for these cases.

The remaining test conditions for which turbulence scattering wasnegligible

are shownin figures 55 and 56. As before, the agreementbetweentheory and

experiment is considered goodwith the exception of a few angles below 0c =

35° in figure 56. Whenthe results in figures 55 and 56 for f = 2.25 and

5 kHzare combinedwith the good agreementat 1.25 kHz (fig. 50) and i0 kHz

(fig. 54) the frequency independenceof the refraction amplitude correction

is verified.

Upstream Quadrant, On-Axis Source Location - Refraction amplitude correction tests were conducted for a second on-axis source station described by

Test Configuration 7 in Table II. The source location, which corresponded

to X/R o = 2.66, was downstream of the station described previously. This

permitted making amplitude correction measurements in both the downstream

and upstream quadrant.

Comparisons of refraction amplitude correction theory and experiment are

presented in figure 57a for f = 1.25 kHz and M = 0.3. A limited number of

measurements were made at angles _c < 90° based on the good agreement obtained

at 9 c = 30 ° and 40 ° where the amplitude correction is the largest. Figure 57a

also provided the first confirmation of the refraction amplitude correction

for measurement angles in the forward arc corresponding to 8 c > 90 ° .

As the source frequency increased, disagreement between theory and experiment became prevalent as shown by the f = 5 kHz, M = 0.3 case in figure

57b. When compared to the measurements described previously in figure 52c

the discrepancy increased as the acoustic source moved downstream. This

trend is easily explained by the increase in shear layer thickness as the

source position moves downstream. The propagation path through the turbulent

shear layer then increases resulting in stronger scattering effects.

51
To assess the Machnumberdependenceof the amplitude correction in the

absenceof shear layer scattering, the lowest acoustic source frequency was

selected. Figure 58 showsthe comparisonof theory and experiment over the

range M= 0.I to 0.4 with f = 1.25 kHz. Measurementsat M = 0.3 were made

in 5 degree increments to assess the detailed shapeof the correction curve.

Selected angles were investigated at the other Machnumbersto verify the

theory at the extrememeasurementangles. In each case, the agreement

betweentheory and experiment is considered good. The theoretical dependence of the amplitude correction on Machnumberwas, therefore, verified.

The goodagreementbetweentheory and experiment at the two different

axial source stations presented in figures 50 and 58 also verified that the

refraction amplitude changeis independent of shear layer thickness. This

independenceof thickness in addition to shear layer divergence confirms a

previous theoretical prediction reported by Amiet in reference i0. The lip

line vortex sheet model employedin the present theory is, therefore, an

adequaterepresentation of the finite thickness shear layer.

To assess the frequency independenceof the refraction amplitude correction theory in the upstream quadrant, the Machnumberwasheld fixed and the

acoustic source frequency was changed. The experimental results shownin

figure 59, indicate goodagreementat f = 1.25 kHz as well as 5 kHz. The

good agreementat 5 kHz contrasts the results in figure 52c where significant

disagreementbetweentheory and experimentoccurred for angles close to

the openjet axis. At the highest frequency of i0 kHz, figure 59c indicates

a maximumdisagreementof only 3 dB comparedto a i0 dB difference in

figure 52d. The improvedagreementfor the 5 and i0 kHz source frequencies

in the upstreamquadrant wasdue to weaker scattering of soundby shear layer

turbulence. This occurred becausethe ratio L/%was smaller. For example,

with X/Ro = 0.53 and ec = 30° , L/% = 9 at f = i0 kHz. In comparison, for

X/Ro = 2.66 and _c = 120°' L/%= 4. Scattering effects would then be weaker

at 0c = 120° resulting in the improvedagreementbetweentheory and experiment. Thesetrends are discussed further in the section titled Turbulence

Scattering of SoundExperiments.

Off-Axis Source Location - The refraction amplitude correction was also

investigated at an off-axis source location defined by Test Configuration 8

in Table II. The axial position, defined by the parameter, X/Ro, corresponded

to the source position investigated in Test Configuration 6. The off-axis

location, defined by the parameter, h/Ro, provided a source to shear layer

separation distance larger than one jet radius. Source locations with h/R o < i

were not investigated because of the failure to obtain agreement between refraction angle correction theory and experiment at this test condition.

This was discussed in detail in the section titled Experimental Assessment

of Refraction Angle Correction Theory.

52
Figure 60 showscomparisonsbetweenthe measuredand theoretical

amplitude correction at two acoustic source frequencies for M = 0.3. The

goodagreementat the lowest frequency, where scattering is the weakest,

confirms the off-axis dependenceof the amplitude correction.

ComparisonsWith Other Investigators

Fewexperimental studies exist documentingthe shear layer refraction

amplitude correction. Candel, et al. described the experimental assessment

of a refraction theory but provided little documentationto verify the dependenceon frequency, Machnumber, and acoustic source position. Ozkul

and Yu (ref. 16) also evaluated the refraction amplitude correction for an

on-axis acoustic source. Their experiment was limited to a maximumMach

numberof M = 0.i. Themeasurementshowedgoodagreementwith the theory

reported earlier by Amiet in reference 7. This sametheory also formed the

basis for the analytical extension to off-axis acoustic source geometry

derived in the present study.

Ahuja, et al. recently reported an experimental assessmentof a separate

refraction theory developedas part of the work reported in reference 15.

It is worthwhile to clarify the relationship betweenthe present refraction

theory and that presented by Ahuja, et al. before discussing any experimental

comparisons.

The refraction theory reported in reference 15 was limited to on-axis

source locations. The angle correction segmentof the analysis is exactly

that given earlier by Amiet (ref. 7) and Jacques(ref. 8) for a zero thickness shear layer. The general analysis in the section titled Theoretical

Formulation of the Refraction Problem reduces to that given in reference i0

for the special case of an on-axis acoustic source.

Thegeneral amplitude correction theory in the present study assumesa

zero thickness shear layer. In contrast, the on-axis analysis used by Ahuja

assumesa shear layer thickness which is infinite comparedto the acoustic

wavelength. The difference betweenthese two approachesfor an on-axis source

was given earlier by Amiet (eq. (14) of ref. i0) and is quite small over most

of the angular range, as shownin figure 61. At the extrememeasurement

angles (near the zone of silence and near the upstreamaxis) where the

difference betweenthe two approachesbecomessignificant, neither result

would be expected to be accurate since each approachneglects the multiple

reflections which occur in these regions. Thus, in the range of practical

use, the approachof Ahuja gives results which differ little from those previously given by Amiet (ref. 7) and generalized here to treat the case of an

off-axis source.

53
Verification of the amplitude correction theory in the present study

was considered to be moreaccurate than the experimental assessmentreported

by Ahuja, et al. in reference 15. This is becausethe errors associated with

the signal enhancementmethodwere smaller than those encounteredin the

cross-spectrum measurementtechnique. This point will nowbe discussed

further.

Recall that the cross-spectrum approachwasemployedby Ahuja et al. to

circumvent the signal-to-noise limitation encounteredwhenusing a random

noise acoustic source. The methodemployeda reference microphoneadjacent

to the acoustic source. Microphonesignals were then processedto give the

reference-to-in-flow microphoneand reference-to-far-field microphonecrossspectra. The experimentally determined amplitude correction was then obtained from equation 4-3 in reference 15,

IGAc,(f)l2 RrT 2

, : IG B(f)I2 Rro Rro C20)

Here the parameters, GAC , and GAB , represent the square of the modulus of the

pressure cross-power spectral densities. The ratio of these two spectra

is similar to the ratio of the mean-square acoustic pressures in equation 17

of the present report. The remaining terms in equation 20 represent

different source-to-microphone distance corrections.

Measuring the decibel difference between GAC and GAB , provided the experimental input to the refraction amplitude correction calculation in equation 21. The present authors fee! that the scatter in the individual crossspectrum curves makes it difficult to accurately determine the decibel

difference. Figure 62 shows the cross-spectra reported by Ahuja in figure

4.41 of reference 15. This figure was obtained by photographically enlarging

the original curve by a factor of 4 and tracing the resulting spectra.

Frequencies below 1 kHz and above 14 kHz are not included due to the poor

quality of the original curve published in the report.

As noted in reference 15, the cross-spectra curves are displayed i0 dB

apart to show the approximately constant amplitude difference as a function

of frequency. A close examination of figure 62, however, indicates that

the difference between the curves is not constant. This is because details

found in one curve are not necessarily present in the second curve. For

example, at f = 2.5 and 3 kHz, GAB(f ) has two minima which fail to appear in

the curve for GAc(F). Consequently, the amplitude difference is estimated

as 14.2 and 13.6 dB instead of i0 dB. Similar comparisons are provided

across the entire spectrum in figure 62.

54
Fluctuations of several decibels in the logarithmic difference, GAc-GAB,

makes it difficult to assign a single value to the amplitude difference

between the two cross-spectra curves. Furthermore, the fluctuations make it

difficult to conclude, as Ahuja, et al. did, that the amplitude correction

is frequency independent. These observations raise the question of uncertainty in the experimental approach. The fluctuations in figure 62

suggests a 1 dB error is reasonable and possibly the error is larger. In

comparison, the largest refraction amplitude correction measured by Ahuja,

et al. was approximately 3 dB. This occurred at 0 c = 40 ° and M = 0.27. A

comparison of the uncertainty with the largest amplitude correction measured

demonstrates that errors associated with the cross-spectrum approach were

significant. For this reason the cross-spectrum measurement technique was

not employed in the present study. Instead, the signal enhancement technique

with its ± 0.2 dB error was employed. Admittedly, this required using a

discrete tone source signal which was sensitive to turbulence scattering.

But the operating conditions in which scattering occurred were easily recognized without compromising the accuracy of the experiment.

Summary and Evaluation

Refraction of sound waves passing through an open jet circular shear

layer results in significant amplitude changes at Mach numbers greater than

M = 0.i. Acoustic source directivity patterns are therefore changed resulting in erroneous conclusions being drawn from an experiment. The measured

amplitudes at the far field microphone station can be corrected theoretically

using the refraction amplitude correction analysis verified by the present

experiment.

The experiment verified the ability of the theory to predict the circular open-jet refraction amplitude changes for an arbitrary acoustic source

position and far-field observer position. The lip line vortex sheet model

employed in the theory is, therefore, an adequate representation of the

finite thickness shear layer investigated in the present study. Axial

variations in the mean shear layer properties and divergence of the flow

field are therefore not needed in the theoretical formulation. The Mach

number dependence and frequency independence of the theory was also verified.

55
TURBULENCE SCATTERINGOFSOUNDEXPERIMENTS

Formulation of the Problem

Measurementsobtained during the refraction amplitude correction

experiment indicated the occurrence of discrete tone scattering as sound

propagated through the openjet shear layer. For example, the discrepancy betweenamplitude correction theory and experiment in figure 52 was

traced to the presenceof scattering. Theobjective of the experiment

described in this section was to quantitatively assess the magnitudeof

turbulence scattering in the open jet. This was accomplishedby monitoring the discrete tone broadening and the discrete tone amplitude reduction

as soundpropagated through the shear layer.

Theexperiment was conductedusing the sideline microphonegeometry

described in the refraction amplitude correction experiment (figure i0).

In-flow and far-field spectra were measuredon the sameacoustic ray path.

Theresulting spectra were comparedafter accounting for the refraction

amplitude change, the inverse square-law decaybetweenthe two microphone

stations, and the nose cone directional sensitivity characteristics. Differences betweenthe discrete tone amplitudes in the two spectra provided

a direct calibration of the magnitude of the discrete tone attenuation

along the refracted ray path. The significance of tone broadening was

determined from the spectrumshape.

Contrary to the tone burst methodused in the refraction amplitude

correction experiment a continuous discrete tone wasused in the scattering experiment. This simplified the discrete tone spectrumacquisition

and interpretation. To avoid contamination of the far-field microphone

signal by sound reflected from the collector, the sideline distance was

decreasedto y = 0.91 m so that the direct radiation arriving at the

microphonedominated the reflected sound.

In addition to the experimental effort the existing turbulence scattering analysis of Lighthill (ref. 24) wasmodified to provide an estimate

of the discrete tone amplitude reduction. Themodified analysis was also

used to drive an expression for predicting the onset of turbulence scattering. Experimental results were comparedwith the resulting analysis.

Theanalysis of Lighthill assumedsingle scattering. An alternate

approach is to assumemultiple scattering as in the analysis of Howe

(ref. 25). Unfortunately, this approachneglects the time dependenceof

the turbulence so that there is no frequency scattering for a discrete

tone signal. However,by adding meanflow to the analysis, the frozen

turbulence restriction can be,removedas reported by Amiet in reference

26. Themodified analysis assumeda Doppler shift due to the motion of

the turbulence. In this way frequency scattering was introduced into the

56
multiple scattering problem. Comparisonsbetweenthe modified analysis

of Amiet and the present experiment are provided.

ParametersControlling Scattering

Whena soundwavepasses through a region of turbulence, it encounters both frequency and direction scattering. The first mechanismextracts

energy from one frequency bandand redistributes it in adjacent frequency

bands. If the acoustic signal contains a discrete tone, the frequency

scattering results in a broadenedspectrum. The direction scattering on

the other hand scatters soundto newangles resulting in a changeof the

discrete tone directivity pattern.

It is not the purpose of this section to give an original treatment of

the scattering of soundby turbulence. The theoretical and experimental investigations conductedby the authors cited in the bibliography of references 24 and 25 are considered adequate. Instead, the present section will

link the physical parameters controlling the scattering phenomenonwith the

results observedin the experiments.

The first parameter to be considered in the turbulence scattering phenomenonis the magnitude of the turbulence intensity. The general trend

established by the various theoretical analyses suggeststhat turbulence

scattering _ncreasesas the absolute value of the intensity increases. An

increase in the open jet Machnumber, therefore, creates stronger scattering.

Turbulent eddy size is another parameter which controls the scattering

mechanism. Direction scattering maybe considered to becaused by a reflection of sound from the turbulent eddies similar to that of Bragg reflection

where X rays are scattered from a crystal. For the case of sound the acoustic waveis only reflected by the componentof turbulence which possessa

wavenumbercomparableto the acoustic wavenumber(ref. 24).

Directional scattering is a prerequisite to frequency scattering. The

latter phenomenonis observed as a Doppler shift of the discrete tone by

the turbulent eddy. The resulting Doppler shift can be explained by the

schematic in figure (63a). Consider the direction scattering of soundto

be modeledas a two step process consisting of an initial absorption of the

soundpropagating in direction, e + e . Angle e defines the scattering s

represents the edd_convection s velocity. Theresulting Dop- angle while Uc

pier shift in the new propagation direction is then given by the equation

&f = foUc

[cos(ec+ as) - cosec]

[co - uc cos (ac +es)]

(2])

57
It follows from equation 21 that the Doppler shift is zero along

the ray path for which the scattering angle is zero.

Figure 63a neglects the mean velocity gradient and the resulting refraction which takes place across the shear layer. Such velocity gradients,

however, do not create a Doppler shift if the observer is stationed on the

refracted ray path. Sound reaching the far-field microphone station

(figure 63b) at the original source frequency then represents the portion

of the acoustic energy which is not scattered out of the refracted ray

path. Any reduction of the discrete tone amplitude measured at the observer

station is then due to scattering of sound to a new direction given by 0 t + 0s.

Monitoring the decrease in the tone amplitude at the acoustic source

frequency provides a method for calibrating the direction scattering

phenomenon. Admittedly, acoustic energy can arrive at the 0bserver station

after being direction scattered from other turbulent regions in the shear layer.

This is illustrated by the ray initially propagating at angle 0' in figure

c

63b. However, the direction scattered sound which now arrives at the observer station has a Doppler shifted frequency which is different from the

original source frequency. Scattering volumes located downstream of the

refracted ray path shear layer crossing-point, Xo, in figure 63b result

in a Doppler shift to lower frequencies based on equation 21. In contrast,

upstream scattering volumes cause a shift to high frequencies. This explains how tone broadening can occur in the spectrum at the observer station in the absence of a Doppler shift of the discrete tone center frequency. If the scattering is sufficiently strong the resulting measured

spectrum will be a broad hump with no perceptible discrete tone. In this

case the initial energy in the acoustic wave front has been scattered to

new directions and the measured spectrum represents the energy, Dopplershifted by the turbulence volumes upstream and downstream of station X o.

It should be emphasized that the far-field microphone in figure 63b

will always sense some of the acoustic energy at the original source frequency. This is because for every microphone station, there exists a

unique refracted path along which Doppler shifts are non-existent. If

direction scattering is weak, the sound sensed at the microphone station

is then dominated by the original discrete tone frequency. For strong

scattering, the tone is not perceptible in the spectrum. It is replaced

by a broad-band hump with a maximum at the original source frquency. The

adjacent frequency bands now contain energy due to scattering of sound from

turbulence volumes upstream and downstream of the refracted ray crossing

point.

58
Theabove described frequency and direction scattering effects become

stronger as the acoustic propagation path length in the turbulent medium

increases. This follows due to the increase in the numberof interactions

betweenthe acoustic wavefront and the turbulent eddies in the flow.

Discussion of Experimental Results

Comparisonsbetweenthe in-flow and far-field measuredspectra are

presented first for the case of soundradiating normal to the openjet

axis from a source situated on the centerline at X/Ro = 0.53. The acoustic source and microphonearrangementcorrespondedto Test Configuration 9

in Table III. The openjet Machnumberdependence,and hence, shear layer

turbulence intensity dependenceis assessedin figure 64 over the frequency

range of f = 5 kHz to 15kH_ All far-field soundpressure level amplitudes

are plotted relative to the in-flow measurement. The latter measurement

wasnormalized to unity amplitude or zero decibels. A 50 Hz analyzer bandwidth was used for all spectrummeasurements.

In-flow sound pressure levels in figure 64 were corrected for the

refraction amplitude changeand the corresponding inverse square-law

decay betweenthe in-flow microphoneand the non-refracted sideline

observer position (station D in figure 23). In addition, corrections were

also applied for the nose cone directional sensitivity characteristics

determined from continuous discrete tone calibration Curves similar to

those in figure 49. The resulting spectra then correspondedto the sound

pressure levels measuredat the far-field microphonestation in the

absenceof refraction and scattering. The far field spectra were then plotted

relative to the corrected in-flow spectra. The peak amplitude difference between

the two spectra calibrated the magnitudeof the scattering effect.

Figure 64 showsa gradual decrease in the tone amplitude and a simultaneousbroadening of the spectrumwith increasing Machnumber. The tone

amplitude decrease demonstratesthe occurrence of direction scattering of

sound to newangles. Since these angles are not on the refracted ray path

linking the in-flow and far-field microphonestation, a decrease in tone

energy is sensedat the observer station. Spectrumbroadening occurs due

to soundarriving at the measurementstation from turbulence scattering

volumes upstreamand downstreamof the acoustic ray cross-over point in

the shear layer. The strength of the scattering phenomenonis seen to

increase as the acoustic source frequency increases betweenfigure 64a and

64c. This follows since the acoustic wavelength is approaching the size

of the turbulent energy bearing eddies responsible for the scattering phenomenon.

To investigate the effect of increasing the propagation path length

through the turbulent mediumin addition to changing the turbulent eddy

size, spectra were measuredat different radiation angles given by 0c = 50°

59
and 30°. Here a decrease in e results in an increase of the propagation C

path length, L, based on the approximation L = _/sin e . In addition, the

C

turbulence length scales were expected to increase since they are known to

scale with the local shear layer thickness. THe results shown in figure 65

verify the previously described trend of increased scattering effects when

the propagation path length increased. Both discrete tone amplitude attenuation and spectrum broadening become stronger as 0c approaches the open jet

axis. Thus, experiments limited to ec = 90 ° are not sufficient for determining the severity of the discrete tone scattering phenomenon. It should be

noted that the turbulence intensity is approximately constant downstream of

the open jet exit plane (figure 19). Thus, the trend observed here is not

due to differences in the turbulence intensity at the acoustic ray shear layer crossing points associated with the different radiation angles, 0

C

To further investigate the effect of propagation path length changes on

the scattering phenomenon, the acoustic source was shifted downstream to

station X/R = 2.66. The test geometry in this case corresponded to Test

O

Configuration I0 in Table III. Figure 66 shows the open jet Mach number dependence over the frequency range of f = 5 kHz to 15 kHz for sound radiating

at ec = 90 ° • When compared to the upstream source position results described

earlier (figure 64) the tone broadening becomes stronger for downstream acoustic source positions. Figure 66 also shows a small increase in the discrete

tone amplitude attentuation. This amplitude change is not as dramatic as the

tone broadening change between the upstream and downstream source station.

This is because only a small amount of scattered acoustic energy is needed to

broaden the spectrum at the -25 dB level in figure 66c.

To further assess the propagation path length changes and the turbulent

eddy size changes at this downstream source station measurements were also

conducted at radiation angles other than e = 90 ° . The results shown in figC

ure 67 for a range of frequencies at a fixed Mach number, M = 0.3, indicate

severe scattering for angles close to the open jet axis. The discrete tone

peak amplitude at f = 15 kHz, 8c = 40 ° has decreased by i0 dB relative to the

0 c - 30 ° measurement in figure 65. Scattering effects are also stronger at

the lowest frequency of f = 5 kHz when compared to the results shown for the

upstream station in figure 64. In this case the shear layer thickness has

increased sufficiently to provide large scale energy bearing eddies comparable in size to the acoustic wavelength.

Far-field spectra in figure 67 show less scattering at e = 120 ° than at

e = 90 ° for f = 5 kHz and i0 kHz. At these frequencies theCacoustic wavec

length is considered large relative to the local shear layer thickness at

_c = 120° resulting in weak scattering. A further increase in source frequency to 15 kHz changes the ratio of wavelength to eddy size sufficiently

to create stronger scattering at 0c = 120 ° than at 8 = 90 ° . The reversal

c

is explained by the magnitude of t_e turbulence intensity vector. At e = 90 °

C

60
the fluctuating velocity vectors coinciding with the acoustic rays arriving

at this angle have approximately a single componentin the radial direction.

On the other hand, both axial and radial fluctuating velocity componentscombine to form the fluctuating velocity vectors coinciding with soundrays arriving

at ec = 120° . The turbulence vector is then larger in this direction of propagation.

Assumingscattering to be related to the magnitudeof the fluctuating velocity

vector, scattering would be expected to be stronger at 0c = 120° • This argument

can be generalized to explain the stronger effects at all angles for which 8c # 90° .

Conservation of acoustic energy betweenthe in-flow and far-field microphoneis demonstratedin figure 67c. Total acoustic energy arriving at the

far-field microphonewas obtained by integrating the spectra in the frequency

domain. The resulting intensity, represented by the open-circle symbols, is

approximately equal to the discrete tone amplitude at the in-flow microphone

station. This suggests a two-step scattering process. First acoustic energy

is scattered to newdirections resulting in a decreasetone amplitude at the

source frequency. Simultaneously, sound is scattered in the direction of the

far-field microphonefrom the remainder of the open jet shear layer. This

soundarrives at Doppler-shifted frequencies which broaden the spectrum. The

integral of this energy is comparableto the energy decreaseat the acoustic

source frequency. The total energy in the spectrum, therefore, remains unchanged. Although this explanation satisfies the conservation of acoustic

energy observed at the far-field microphonestation, the authors recognize

that it maybe too simple an explanation.

Changesin the degreeof scattering due to changesin acoustic source position are summarizedin figure 68. Here the source frequency, radiation angle,

and open jet Machnumberwere held fixed to isolate source position changes.

Themeasurementsdemonstrate that turbulence scattering effects are more

pronouncedat downstreamstations.

The degree of tone broadening and reduction in the peak amplitude of the

far-field spectra in the previous figures is a function of the analyzer bandwidth. A large bandwidth, such as the 50 Hz value used in figures 64-68,

narrows the spectrum and increases the peak amplitude. The latter effect

occurs becausethe filter band can pass acoustic energy at the Doppler shifted

frequencies surrounding the acoustic source frequency. In the case of strong

tone broadening the soundpressure level associated with the filter band is

large since it passesboth the narrowbandrandomenergy and the discrete tone

energy. On the other hand, decreasing the filter bandwidth to 1 Hz results in

a lower soundpressure level at the peak position in the spectrum.

Theabove described trends will nowbe demonstratedusing the experimental

results obtained in the present investigation. Figure 69a contains the inflow and far-field spectra previously presented in figure 67c using a 60 Hz

61
analyzer bandwidthwith f = 15 kHz. Figure 69b showsthe spectrumobtained

for the sametest condition using a 0.25 Hz analyzer bandwidth. As expected

the amplitude of the far-field soundpressure level measuredwith the 0.25

Hz filter had decreased significantly relative to the 50 Hz bandwidth

measurement. Surprisingly, the 0.25 Hz spectrumalso showsthe remnant

of the original discrete tone. This wasnot expected from the tone broadened

spectrumin figure 69a. Oneadvantageof the smaller bandwidth is, therefore,

the ability to isolate the discrete tone in the presence of the broadened

spectrum. The tone amplitude in figure 69b is weakwhencomparedto the

narrowbandrandomsoundpressure levels at adjacent frequencies. This is

demonstratedby integrating the randomnoise level in a 50 Hz band centered

at the discrete tone in figure 69b. The randomnoise level in this case is

approximatedby the constant amplitude line. The total energy in the 50 Hz

band, obtained by logarithmically summingthe randomnoise and discrete tone,

corresponds to the peak amplitude (-8.5 dB) of the broad-bandpeak in figure

69a. In comparison, the discrete tone by itself has a -24 dB amplitude

verifying that the major contribution to the spectrumin figure 69a is obtained from the broad-bandnoise in the 50Hz filter band.

A 0.25 Hz bandwidth spectrumanalysis wasalso conductedfor the in-flow

microphoneto check for the presenceof randomnoise in the measurementwith

the 50 Hz analyzer bandwidth. The detailed spectrum, shownin figure 69b,

indicates a discrete tone 3 dBweaker than the amplitude measuredin figure

69a. The difference betweenthe two discrete tone amplitudes is due to the

randomnoise shownin figure 69b. Whenthe integral of this noise, approximatedby a constant level of -26.5 dB, is addedto the discrete tone amplitude,

the total energy in figure 69a is recovered. In conclusion detailed comparisons of the discrete tone amplitude changesbetweenthe in-flow and

far-field microphoneshould, therefore, use as small a bandwidth as possible.

Figures 70a and 70b showthe samefar-field microphonespectra presented

in figures 69a and 69b with the addition of an absolute frequency scale on

the horizontal axis. The spectrumin figure 70a has beennormalized by the

peak soundpressure level. Arrows identify the soundpressure level obtained

from integrating the 0.25 Hz narrowbandrandomspectrumas well as the discrete tone amplitude in figure 70b. For the 15 kHz acoustic source frequency, the 50 Hz bandwidth measurementis dominatedby randomnoise. If the

acoustic source frequency were decreased, scattering would be expected to be

weakerwith the discrete tone comprising a larger portion of the soundpressure level measuredin the far-field. This is demonstratedin figures 70c -

70f where the 50 Hz and 0.25 Hz bandwidth spectra are compared. Basedon

the trends observedin figure 70a, 70c, and 70e a large analysis bandwidth

(such as 50 Hz) can qualitatively demonstrate the importance of the scattering

phenomenonand identify trends associated with parametric changes. However,

the large analysis bandwidth cannot provide quantitative measurementsof the

discrete tone amplitude reduction and, hence, the magnitudeof the direction

scattering. Suchmeasurementscan only be madeusing small (such as 0.25 Hz)

bandwidth spectra like those shownin figure 70b, 70c, and 7Of.

62
A calibration of the magnitudeof the direction scattering can be obtained

from the amplitude difference betweenthe in-flow and far-field 0.25 I1zbandwidth

spectra like those in figure 69b. Figure 71 showsthis difference for a range

of frequencies and radiation angles, 8 . Changesin the latter parameterrepre- c

sent changesin the acoustic propagation path length through the turbulent shearlayer in addition to changesin turbulent eddy size. Thediscrete tone amplitude

attenuation is seen to increase dramatically above5 kHz. In comparisonto figure

67 the attenuation is observedto be stronger whenmonitored with a 0.25 Hz

bandwidth analyzer. In this case the actual discrete tone amplitude is measured

instead of an integral of the soundpressure o_er a finite bandwidth.

Prediction of Turbulent Scattering Effects

In its present form the shear layer correction does not account for the

scattering of discrete tone soundby shear layer turbulence. As shownby the

refraction amplitude correction measurements,scattering presents a source of

error, and someestimate should be madeof its importance.

Lighthill (reference 24) gives an estimate of the energy E scattered in new

directions from a unit volume of turbulence per unit time as

8Tr2L I (VI') 2

E- I

X2 Co2 (22)

where = Intensity of incident sound

(v1

L 1

= wavelength of incident sound

= mean-square velocity of turbulence

= macro scale of turbulence in the direction of the

incident sound

c o = sound speed

This result does not assume any particular type of turbulence, but does assume

that %/L 1 is less than unity.

This result can be used to estimate the fraction of the incident energy

which is direction scattered. Consider a volume of turbulence with an area

normal to the incident beam of A and thickness L. The energy incident per

unit time is AI. The fraction R s of the incident energy which is scattered is

ALE 8_2Li L (vi') 2

Rs : AI : X 2 c_ (23)

63
The Lighthill theory is a single scattering theory so the above relation is

valid only for small R values. However, it should be possible to obtain from

it an indication of when scattering affects a significant fraction of the incident energy.

Equation 22 can be used to relate the scattering from two different test

cases designated as (a) and (b). If Rs is the same for two cases, the degree of

scattering should be the same. Equation 23 gives

[L I

xz

L. (Vl)

co2

2 ]

o

= [LIL

x2

(V'z)

Co2

2 ]b

(24)

The mean square perturbation velocity, (v')2_ will generally be proportional to

the mean velocity U. Thus,

[LLM2] o [LLM2] b

(25)

If the turbulent length scale is taken to be equal to the shear layer thickness,

o b

(26)

Replacing the acoustic wavelength by the expression f/c ° and assuming that the

sound speed is the same in both cases gives the scaling parameter,

( fM]0:IL,Mlb

Two operating conditions which satisfy the equality in equation 27 should then

provide the same degree of scattering. Consequently, attentuation of the discrete tone amplitude would be the same for two such cases.

A crude check of equation 27 can be made using the results shown in figure

64. Here the test conditions, corresponding to M = 0.i, f = 15 kHz and M = 0.3,

f = 5 Hz, satisfy equation 27. The experimental measurements both show a 2.5 dB

reduction in the tone amplitude. Equation 2? is also satisfied for the M = 0.2,

f = 15 kHz and M = 0.3, f = i0 kHz test conditions. Both spectra in this case

show approximately a 3 dB reduction.

In figure 66 the shear layer thickness, 5, at the acoustic ray cross-over

point on the open jet lip line is about five times that of figure 64 assuming

64
a constant spreading angle. The M = 0.i, f = 5 kHz case in figure 66 gives

a 1 dB reduction in the tone while the M = 0.2 f = 15 kHz case in figure 64

gives a 3 dB reduction. This comparison is not as good as the comparison

in figure 64 but, further work would be needed to give a more definitive

evaluation of equation 27. Also, future comparisons should be made using

the 0.25 Hz analysis bandwidth instead of the 50 Hz bandwidth.

Equation 22 can also be used to derive an equation predicting the onset of

turbulence scattering. A criterion must, however, first be set to determine

the discrete tone amplitude attentuation for which scattering is considered to

be important. Here the value of Rs at which scattering is deemed significant

will be taken to be 0.5. Then assuming L = L 1 as above, and also that the

root-mean-square turbulence velocity is 15% of the open jet velocity, equation

23 becomes

or

(fML) = 0.5c o _9)

Assuming a spreading half angle of 7° for the shear layer, the shear layer

thickness is approximately 0.3 m at the acoustic ray cross-over point for the X/R o =

2.66 source position. Taking co = 355 m/sec gives f M = 558; thus, for M = 0.i

scattering will become important at f = 5580 Hz. From figure 66a for M = 0.i

and f = 5000 Hz the peak of the tone is one dB below that for no scattering,

indicating that there has been measureable scattering.

Equation 28 can be compared to the onset of turbulence scattering

deduced experimentally in figure 53. Where scattering was shown to occur

when L/% _ i0. ;For this condition, equation 28 gives M = 0.05 as the

Mach number for which scattering becomes important. Figure 53 shows

that for L/% _ i0 a idB attenuation in discrete tone amplitude occurs

at M = 0.05. This Mach number is equivalent to the value calculated from

equation 28. The good comparison between theory and experiment verifies

that equation 28 can be used to predict the onset for turbulence scattering.

The above result of Lighthill assumes single scattering. An alternate

approach is to assume multiple scattering as in the analysis of Howe (ref. 25).

Similar to the Lighthill model, Howe's approach assumes no mean flow, and

because of this, gives no scattering in the frequency domain for the case of

frozen turbulence.

65
By assuminga Doppler shift due to the motion of the turbulence, the Howe

theory has been modified by Amiet in reference 26 to account for a meanflow.

Becausethe analysis is a high frequency theory and assumesmultiple scattering

it cannot be used for predicting the onset of significant scattering. Also,

becauseof the multiple scattering assumption, the scattering is independent

of frequency. Thus, in comparingthe results of the theory and experiment,

the experimental results for the highest frequency will be chosensince this

best satisfies the multiple scattering assumption. To further satisfy this

assumption, theory will only be comparedwith experiment at the farthest downstream source position corresponding to X/R° = 2.66.

Using the 50 Hz spectrumanalysis results in figure 66c the peak for the

M = 0.3, f=15 kHz case is expected to be 3 dB below the M = 0.i case. The

modified Howetheory gives a I0 dB difference in the peak level for these two

cases. Thus, there is a significant difference betweenthe theory and experiment. It is possible that this difference is due to the experiment not being

in the applicable range of the theory; i.e., the theory assumesmultiple

scattering, whereas this assumptionis not satisfied by the experiment.

In conclusion, additional work is neededon the multiple scattering theory

in order to predict the experimental results. It is possible that a modification applied to the Howetheory will give a better prediction of the experimental

results.

66
CONCLUS IONS

A theoretical and experimental study was conductedto determine the effects

of refraction and scattering on soundtransmission through a circular open-jet

shear layer. A generalized refraction theory was assessedexperimentally for

angle and amplitude changesacross the shear layer. Both on-axis and off-axis

source locations were investigated as frequency varied from 1 to i0 kHz and

freestream Machnumbervaried from 0.i to 0.4. Discrete tone scattering

phenomenawere investigated over the sameMachnumberrange as frequency varied

from 5 kHz to 15 kHz. Attenuation of discrete tone amplitude and tone

broadening were measuredas a function of acoustic source position and radiation

angle. The following conclusions are nowavailable from this investigation.

a.

b.

c.

d.

Refraction Effects for 0n-Axis Source

Far-field noise directivity patterns measured in open-jet acoustic test

facilities are significantly altered at test Mach numbers of 0.i and greater

due to sound wave refraction by the open-jet shear layer. This is evident

from measurements of the wavefront angle and amplitude changes associated with

sound propagation through the shear layer.

For on-axis source locations, the refraction angle and amplitude changes for

a circular cross-section open jet were well predicted by the zero thickness

shear layer theory of Amiet over the Mach number range of 0.i to 0.4 employed

in the present experiment.

For the range of shear layer thicknesses considered in the present experiment,

the refraction angle and amplitude changes were independent of shear layer

thickness. This is evident from wavefront angle change measurements conducted

at axial source positions between 0.6 and 4 jet radii downstream of the nozzle

exit. Amplitude changes were also verified to be independent between 0.53 and

2.66 jet radii from the nozzle exit. This independence of shear layer thickness and shear layer divergence confirms a previous theoretical prediction.

The refraction anEle and amplitude changes were independent of frequency over

the 1 kHz to I0 kHz range considered in the present experiment. This independence

confirms a previous theoretical prediction. Experimental verification of the

amplitude independence using a discrete tone was complicated by the presence

of sound scattering by the turbulent shear layer at high frequencies.

67
So

b,

c.

Refraction Effects for Off-Axis Source

The generalized off-axis refraction angle and amplitude correction

theory developed in the present program predicts large differences between onaxis and off-axis corrections.

The off-axis angle and amplitude correction theory was confirmed experimentally

for the case in which the observer and source were located in a plane passing

through the open-jet axis and the source-to-shear layer distance was greater

than one open jet-radius. Mach number dependence and frequency independence

of the zero thickness shear layer refraction theory were validated.

For an off-axis source situated at a source-to-shear layer separation distance

less than one jet radius, measurable differences between theory and experiment

occurred for the refraction angle change. The disagreement, at present, is not

understood. This result precluded conducting the amplitude correction study

since placement of the far-field microphones requires knowledge of the angle

change across the shear layer.

a.

bo

c,

d_

Scattering of Sound by Turbulence

Scattering is a combined function of the open jet absolute turbulence intensity

(which scales with Mach number), acoustic source frequency, and propagation

path length through the turbulent medium. Scattering effects were observed to

increase as each of these individual parameters increased.

Several trends were observed in the experimental study. These were:

i) Scattering is stronger at angles close to the open jet axis than at 90 ° ,

2)

3)

Scattering becomes stronger as the acoustic source position shifts downstream,

Scattering becomes significant as the ratio of shear layer propagation path

length to acoustic wave length approaches a value of i0.

Reduction of the discrete tone amplitude on the refracted ray path is caused

by direction scattering of sound to new angles. Tone broadening of the spectrum measured on the refracted ray path is caused by Doppler-shifting of sound

waves by turbulent regions upstream and downstream of the acoustic ray shear

layer cross-over point. The existence of tone broadening (or frequency scattering) implies the occurrence of direction scattering.

The frequency at which the onset of turbulence scattering occurs can be estimated using an analysis developed during the present study.

68
APPENDIXA

Derivation of Shear Layer Correction For An Off-Axis

Acoustic Source

Figures 21 and 22 show the basic geometryand the coordinate system used in the

following derivation. Thesefigures were previously described in the section entitled

"Theoretical Formulation of the Refraction Problem."

Refraction An$1e Change - The angular change of a ray on passing through the

shear layer is determined by treating the waves on either side of the shear layer

as plane waves and matching phase across the shear layer. This planar assumption

should be valid as long as the wavelength is smaller than the open jet radius.

The small disturbance pressure field produced by an arbitrary source can be

written as a Fourier composition of plane waves of the form

Pi: e-i(@-kz_Z) (A.I)

where

G--_t +k_x+kyy

and k and k represent wavevectors in the x, y, z coordinate system.

z

tion _f equation (A.I) in the wave equation

D m O +U 8

Dt _" -_"

(A.2)

Substitu-

(A.3)

gives

kzl : (l-Mk x) - kx z-k_

(A.4)

where the overbar on k indicates normalization by w/C ; i.e., _ = k C /9.

o o

The normal to a wavefront is found by taking the gradient of the phase of

equation (A.I) giving

^ _x_+- kyjA + k,z,k ^ (A.5)

ne = I- Mk x

69
Since the wavefronts produced by a source in a stream are spheres with their center at

the retarded source position, this normal vector points from the retarded source

connectingposition tot xl'he YI'' Zl'" The direction of energy propagation (the line

present source position to Xl, YI'' Zl') can be found by adding

i M to equation (A.5). Thus.

^ A a /_,2 A A_ ^ he+ iM i(M + kx)+j ky+ kkzl

- (A.6)

y f

The transmitted wave at point Xl, Yl ' Zl can be written

Pt =T e-t(e+kz2Z) (,4.7)

Substitution in equation (A.3) but with M = 0 gives

- 2 -2 z (A.8)

kz2 = I-k x-ky

Taking the gradient of the phase of equation (A.7) gives for both the normal to a

wavefront above the shear layer and the direction along which energy is

propagated

^ -- A -- A A

nz=k xi+ kyj+kz2k (A.9)

Equations (A.6) and (A.9) give the relation between the ray paths for the

incident and transmitted rays. Rather than have this relation in terms of the

parameters k and k (which must be equal in equations (A._ and (A.9) in order for

the phase of Xthe incident and transmitted waves to be equal across the shear

layer) it is more useful to put the relation in terms of the angles e and ¢.

Then, x , Yl and z can be written as 1 1

XI: rlCOS8 C

Yl = rl sin ec cosy¢ (A.lO)

zI = r, sin 8c sin)" c

with

r I =

o sin e o (sin Yc- gsin @c)

COS@c sine c sin 8c (A.]I)

7O
and y - _ +

g --- I- h/o

The first equality in equation (A. II) can be verified from figure 14, and the

second equality is found from equation (A.20), to be derived later. The normal

along rI is then 1

^ A A A

n I=icos8 c+jstn8 ccos 7c +k sin8 c sinyc (A.12)

Comparisons of equations (A.6) and (A.12) show that

or

Also

COS 8c =

M +;32kx

%/I + M 2 [(I-M_x)2-kx 2] (A.13a)

I [ cos ec ]

-- M

ky =

sin 8c COS Yc

JI- M2 sin28c (A. 13b)

_ sin 8c sin 7¢

kzl = ,_1_ M2 sin2ec (A. 13c)

For the transmitted wave the normal n2 along r2 can be written

A A A A

n2=i cos 81+jsin8 tcosyt +ksine lsin),t (A.14)

Comparison with equation (A.9) gives

kx = COS e I

(A. 15a)

71
ky --sin 8 t cos 7t (A. 15b)

Ezz = sin 81 sin ¥t (A.15c)

By equating the values of [ and [ given by equations (A.13) and (A.15),the

X

incident and transmitted angles ar_ found to be

cos 8c - M

#2 cose,= v/'-M2sin_&

(A.16)

sin ec cos Yc

sin 8 t cos Yt = jl_MzsinZe c

(A.17)

Equation (A.16) can also be written

tan 8c =

_t

_ZCOS 8 t + M

(A.18)

where 2

_t =(I-Mc°set) z-cos 28 t

which agrees with equation i of reference 6. Other useful relations are

sinec= _,/, + M2__

_t = sin 8 c

(A. 19)

The angle a can be related to

figure 22. Thus,

by applying the sine rule to triangle SAB in

C

72
cos )"c: g cos #c (A.20)

Using equation (A,I9), equation (A.17) can be rewritten

I__ sin e t COS Yt : COS )'C r,,

(A.21)

The above relations determine completely the angle change needed in the shear

layer correction.

Refraction Amplitude Correction - The amplitude correction will now be determined

by calculating the ray tube divergence. Consider a ray tube beneath the shear layer

formed by varying 8c and ¢c by amounts de c and de c, respectively. This produces a

ray tube with cross-sectional-area at the shear layer

dA_: r,2sin ec d % d%

Above the shear layer the angle variatfons are

aat

det = _"'_c dSc

a_t a_t

d_,--7_cdec+--a#c %

(A. 22)

(A. 23a)

(A.23b)

Note from equation (A.16) that _et/_ c = 0 since ec and ¢c are independent variables.

Therefore, this term does not appear in equation (A.23a). The partial derivatives

can be found from equations (A.16) and (A.21) to be

3

_St _t

88c sin8 t sin28c (A. 24)

g _jtsin#c cla

sin 71 sin e t a_c

(A.25a)

73
acl sin _c

-g I

c_,_c sin )'c

(A. 25b)

cI@t COS ytcotStsinSc-COS ycCOSec

= sin ),,sin St(l- M2s,n_Sc)S/2

(A. 26)

In order to find the area which the ray tube intercepts on the tangent

plane, note that zI will remain constant in equation (A.10) as0 and _ are

varied. From equation (A.]0) c c

x_ _ cot 8c

z, sin Yc

Yl

zl C01 Yc (A, 27)

Thus,

d,, [dec+ cose co, J

sin8 c

dy, = -r, _ d,c

(A. 28)

A variation de gives a contribution to dx , while a subsequent variation

c 1

d; c gives both a dx I and dy I contribution. This indicates that the ray tube

area intercepted by the tangent plane is a parallelogram; its area dA 2 is the

dec contribution to dXl times the d_c contribution to dy I , or

d4 2= r_d_de c = dA,

sin Yc sin )'c sin 8c (A.29)

The cross-sectional area dA 3 just above the shear layer is then, by a similar

argument

dA 3 : dA 2 sin Yt sin 81 (A. 30)

74
Equation (A.30) can also be derived by setting r2 = 0 in equations (A.34) to be

derived later.

The rate of ray tube divergence changes on passing through the shear

layer, and the ray tube cross-sectional area must now be calculated for a

point at an arbitrary distance above the shear layer. The equations for a

point x2, Y2' z2 are

x2=x_ +_ cos 8t =r cOSe m

Y2 = Yl + rz sin 8t COSYt

(A. 31)

with r 2= x2Z+ Y22+z_

z2=z I+r zsin8 tsinh

By varying first 8c and then _c, the point x2, y^Z' z 2 will trace out two

sides of an area. By taking the cross product of the vectors defining these ^

two sides and then taking the dot product with the unit vector n^ given by

z

equation (A.14), the ray tube cross-sectional area will be determined. In

taking the derivatives of equation (A.31), r2 will be taken as constant, as the

variation of r 2 with @ and _ is irrelevant in the final area result. Thus, c c

clx2 = -rl clet

aec s,rTec- - r2 sin e, as c

C_YZ-r z cos8 tcosyt ---sine I sin )'t

c)e----_c - aec aSc !

ae-_ =azz rz (cos e, sin Yt _caSt + s,n8_cos 7, aec !

(A.32)

75
where z] is constant and the variation of x I and Yl with ec

equation (A.28). Also,

ax 2

_$ =-r Icos8 coot

ay z slne c a@,

_c - rl rz sin et sin ×t sin ¥c a_c

az 2 a_,

_@c - r2 sin 8tCOS Yt _c

was found using

(A. 33)

The cross-sectional area dA 4 is then

8x 2 A aY2 ^ #Z2 )

d("-'_l : _'"_0 c + J-_c + k _--_-c dSc (A. 34a)

c_xz _ '_Y2 ^ c_zz t

dr-'-!2 = '_-"cc + J "_c + k _c / d_c (A. 34b)

dA4 = _2(d.._£t x d('2) (A. 34c)

Thus,

dA4 (I r z sin8 c a8 t r z sinyc sin8 t a_T

(,,o (,,oe, f

(A. 35)

76
Equation (A.35) gives the ray tube divergence behavior above the shear layer.

This equation allows one to calculate the sound level just outside the shear

layer in terms of the far-field sound.

The incident pressure just inside the shear layer is now needed, and will

be calculated from the shear layer transmission coefficient. In crossing the

shear layer, the wavefront can be treated locally as being plane. Then the

velocity potentials for the incident, reflected and transmitted waves can be

written

_i : e-i (® +kziZ)

_r = _ e-i (_--kzlZ)

(A.36)

¢:'t = T¢_e'i(e + kzzZ)

where _ is given by equation (A.2), kzl by equation (A.4) and kz2 by equation (A.8).

The pressure and fluid displacement will be matched across the shear

layer. The pressure is related to the velocity potential by

D_ (A. 37)

P =-P0_F

_tching the pressure across the shear layer at z I gives

(,-M_x) [e-'Z,kz' + Rei z'kz'] :T_ e-'z'kzz (A.38)

To match the fluid displacement across the shear layer, the interface can be

considered to be rippled by the acoustic waves, the ripple moving in the x

direction with velocity k /U . If the observer moves in the x direction with

the ripple, the mean flowXve_ocity outside the shear layer will be -_/k x while

that inside will be U ° -w/k x. Denoting the perturbation z velocity by w and

equating flow slopes gives

Wi+ Wr

w I = (A. 3'9)

I - Mk" x

77
Then, using the fact that w = _¢/az and using equations (A.36), equation (A.38)

becomes

T_ kz2 (I-M_ x) e-izlkzz = kz t (e-iZlkz_ -Re i Z_kzr) (A.4O)

Combining equations (A.38) and (A.40),

T®[..(_-M_,f,,2/k,,] :2(,-M_,)e",(k,2-",. )

(A.41)

T_is the transmission coefficient for the potential. The transmission coefficient

for pressure is found by noting from equation (A.37) that

TPl : ipll _ (l-Mkx)CI:) o i JTo = l-Mk X

(A.42)

Thus,

2

[Tpl= ,+ (,-ML) 2 kzz/kz,

(A.43)

From equations (A.13c), (A.15c), and (A.19)

kz2 stne I sin Yt

" kzl _Isin 7c (A.44)

The final result for the amplitude correction can now be given. Equation

(A.35) gives the ratio of the square of the pressure just outside the shear layer

to that at the observer. Equations (A.43) and (A.44) give the ratio of pressure

just outside to the incident pressure just inside the shear layer. Thus, the

incident pressure just inside the shear layer can be calculated from that

measured at the observer position. By extrapolating this calculated pressure

by the factor rl/r , the corrected pressure at a distance r from the source can

be calculated. The final result for the correction factor is then

78
+ +

r sLn281s_nSct r sin), t sin8 c a':/:'c

2 sin 8c

J sin _,_a T/a %

sin8 Tsin Yt [ I +(,I_M COS St) 2 sin 8tsin Yt Jl _]tsin Xc

(A.45)

where 3_t and 3_t are given by equations (A.25a) and (A.26) respectively

a¢c _¢c

79
Listing of Computer Program for Generalized

Refraction Theory

The computer program listed on the following pages solves the angle and

amplitude corrections for a sound source off axis inside a cylindrical zero

thickness shear layer. This program gives the results of Eqs. (A.16) and (A.17)

for the angle correction and Eq. (A.45) for the amplitude correction with relevant parameters in these equations given by Eqs. (All), (AI8), A(25a), A(26) and

A(31). The necessary inputs to the program are

A = shear layer radius = a

G = i- h/a

Z = sideline or constant radius distance

M = tunnel Mach number

PHC = _c = one of the two corrected angles

The angles and various geometric parameters are defined in Figs. 21 and 22. This

program does not give an explicit solution in that the measured observer angles

are not specified as input, but are output. A program does exist at UTRC which

allows input of the measured observer angles, but this requires iteration. The

observer distance from the source is an input to the above program, however. The

angle _c is 90 ° for the case with the source, the observer and the tunnel axis in

the same plane. For the case _c = 90o' the parameter g is 1 for the case where the

source is just inside the near shear layer, while g = -i represents the case where

the source is just inside the shear layer on the far side of the tunnel. For a

source on the tunnel axis g = o. Also, the case(g _-go' _c o)is the same as

(g = go, _c = -_co) for any values go and _co

The outputs of the program are

THC = e c = corrected angle

THM = B = measured angle

m

THR = Or = corrected angle

THT = 0 t = transmitted angle

PHM = #m measured angle

PHT = _t = transmitted angle

ALPH= _ = angle

measured from retarded source position

8O
t,_lll,lLlil_m,i, ,,i,ii ,, ......... _ .... i ,11 ........................................................

_q FO _ g9

O O O O _ ",/

O O O OO

0 t1_.. I_h ii I11t --I .'__,"0--t--.-!1 ii q -',1,_-I1 H II il Ii ,'_ II l..q :_H ::_---Iti:;_:_:_--IR'T_

11 X _ U II ::_ fi I! Ii II :_ II II II !1 O ::I>ITI :_tTI ::_:I>ITI _1.

C.,- .,--Z:_.*_:;O.-.'4";"-X---_,.-)(,.(-_:_-X--.,I--I(_.C_.4_:: i ;C_.--IG._C'_ ,"...1--1._-.':;i_:r..rY_.,::_. ("_.:Z_'J::_.r..9-pz--,XXrJ.I_.-,O_-,,M _. ,0".._ .._ Z

::I).r.-._.-(a'):;:r_..-_-::}_.-)_--4-Z:_:ZC'_i--_--_C.'_::::9. b-3--I_i--(:3I:)- £,K.'-0.,L"0o _.-_--_-._F-,.vO')_-,_-_--_ r_q::_.-'O. _v_ ,,v Xv

rrIT--I _--_::I> ::D,-

,- -C') - - C'_Z

X_I II M:) :_._1

_ .. --r.l._ ::_:-.,

:Z:: OX-

--I * - -D W

X r..Nl X II

:I> - "t3."rl

r-.-4 -I-,,0 -0.

"_."r . -r

::I:: O t.J

X_.I _ _ v

,,X -rl -

_" @- ::_9.

:_.--I r-, !!

ITI "T" "-N

II

m

H

n) c:

0

0 H,

I_- I_

0 0

0

H,

H,

0

H0

II

0 H,

(b c-t

0.,

_b

C)

0

Co

C')

f-t

0

r't

0

0

f't

H.

0

c_

_n

0.,

u_

I"I

0

c_

('b

HI-I"

Cr0

0

0

CD CD

Ph

r_ 0

0

0 I"t

M _

N
5('. 0

,:,0

DBR = DBF' + RRRC

CNR = CNT/(I.-M)_CNT)

!SNI:_= SQRT(I.-CNR_(2)

X2 = X1 + R2_CNT

Y2 = YI 4' R2_SNT_(CF'T

Z2 = Z1 4. R2._SNT_SE"r

(?.N M = _(2 ! I:;_

SNM = SORT(I,-CNM_2)

CPH = Y2/(R_SNM)

:._F'M := Z2/(R_SNH)

[M = 57.2"958_ATAN2(SNM,CNH)

TK' ....52" 2758)_ATAN2 (SNR, CNR)

i'l -- 57*2958_(ATAN2(SNT,CNT)

PM = 57.2958)_ATAN2(SPM,CF.M)

WR I TE (5,500) T I ,TH, TR, TT, F'M, F'T,ALF' ,DBF', DBR

:ORMAT ( IX,F5 .i ,8( IX, F6.1 ) )

CONTINUE

GO TO 10

ENB

A sample printout is given below for a sideline microphone geometry

with M = 0.3. The predictions correspond to an on-axis acoustic source

and far-field microphone position situated in a plane coinciding with

the jet axis. Under these conditions #m = 90o and #t = 90o (not included

in printout) and _ = 0°. The parameter RETD is not included in the printout. The resulting table of 8c versus 0m and 0m (or 0c) versus PRESS was

used to plot the angle corrections and amplitude corrections in figures

28 and 30. Angles are given in degrees while the amplitude corrections,

PRESS, are given in decibels. The input distances, A and Z, can be entered

in any system of units. The example presented here uses the English system

of units with the shear layer radius, A, and the observer distance, Z,

given in inches.

82
INiaUT A, G, Z, M, PH C

18, (_, 72, .5,90

A : 18._0

G " 0.(_0

M : 0.3 _0

PH C - 90.0

TH C TH M T_ R TH T PH M

5.0 14.9 6.5 A(_.I 90.1_

1_.{_ 23.7 13.8 41 .I 90.(*

15.0 29.8 19.5 ,_2.7 98.F

2_.8 34.8 25.9 4A._ 9(_.(_

25.0 39.3 32.3 A7.6 90._

3(_.(_ 43.7 38.6 5t_.7 9_._

35._ AI8.1 44.9 54.3 9_.I_

40.B 52.6 51,I 58.1 90.{_

A5.0 57.2 57.2 62.3 90.t_

5_.0 6I .9 63 .3 66.7 90._

55.0 66.8 69.2 71 .,.3 9ft. P,

6_.0 71 ,_ 75. I 76.P. 9_._

65.0 76.9 80.8 81.2 90.t_

70.0 82.2 86.4 86.4 9(_._

75.0 87.6 91.8 91.9 9(_.0

F0.0 9,3 . I 97.2 97.5 90.(_

85.0 98.8 102.4 1_3.3 9_.0

9[_.0 104.7 107.5 lf19.2 90.0

95.0 110.8 I12.4 115.5 9t_.(_

100.0 117.1 1!7._ 1P2.0 90._1

105.0 123,8 121.8 128.8 90.8

!!_.0 151.1 126.4 136.2 90.0

!15.0 139,3 130.8 1_4.3 90,0

12g.0 149.3 135,1 154.0 90,0

125.0 165.5 139.2 168.5 90._

83
APPENDIX B

Wavefront Angle Change Calculation

According to equation(5) derived earlier

(5)

Using the trigonometric identity for the sum of two angles and expanding in a

Fourier series gives

A'-aT =_-oft (_o+ /'L°s +"') cosHf + (I- T + ) sin/_ s

- +...)] (/'_o + 3

(B.I)

Since Po was consistently held at values less then 0.016 radians, higher order

terms may be neglected leaving

nLr-AT /_ ° (C°S/'Zl-I) ]: fc'_ S+n_, [ '+ s,n#,

(B.2)

or

(B.3)

The maximum.contribution from the second term in equation (B.3) occurs

when p I = 7/2. Then

[,.o] (B .4)

Here _ provides a negligible contribution to the phase difference.

o

an adequate approximation for the phase difference is

f_

&IT - A'r = -_o stn_l

This expression is valid to within .016 cycles. Finally,

ALt= sin-_[ CQ(AIT-AT)]f_

Hence,

(B.5)

(B.6)

.+_ 84
APPENDIX C

Shear Layer Angle Correction Calculation

Figure 72 depicts the ray path as the acoustic wave is transmitted through

the shear layer. The point, X ,at which the sound emerges from the airstream

O

is given by

Xo= X2-X 3 (C.I)

But

X2: r sin(90-8 m) (c.2)

and

X 3 :(Y-h) ton (90-Sm-Mq) (C.3)

Thus

X 0 : r sin (90- 8 m) + (Y-h) tan (M-i- 90 + 8 m) (c.4)

or

X o = r cos 8 m -(r sin 8 m-h) COt (Mq + 8m)

(c.5)

Finally the original propagation angle inside the flow is given by the expression

85
APPEhrDIXD

Microphone- Acoustic Driver Cross-Correlation Technique

Facility backgroundnoise contributed significantly to the two microphone

cross-correlation function at Machnumbersgreater than 0.i. This effect can be

demonstratedanalytically. The net pressure, P, sensedby microphonem2 in figure

73 is

P2(t)= B 2 COS [wt-27/'(A+A2) ] + p'2(t)

(D.I)

I

Here B 2 represents the frequency dependent discrete tone amplitude while P2

denotes the facility random background noise. The time dependence is expressed

relative to the signal generator which drives the acoustic source in figure 73

The parameter A represents the total phase lag between the signal generator

output and the microphone input. Here

A:_o+ As+_P (D.2)

where Ap is the propagation phase delay between the speaker and the microphone.

A similar expression exists for the signal at m I except that the pure tone is

out of phase by _' relative to m2:

(D.3)

or

The resulting cross-correlation function S, is then

S,,2 (r): <P,(t)P2(t)'> fD.4)

S_.2 (r):B, B2 <COS [wt-2Tr (A +A' +A_)] • (D.5)

COS [wt- 2Tr(A +A2)]>

+ <PI' (t + r) P_ (t)>

The second term in equation (D.5) corresponds to the random noise contribution which

dominates the correlation trace in figure 34.

86
An alternate approach for extracting only the periodic component is to

separately cross-correlate each microphone signal with the acoustic driver signal.

This technique, described by Schlinker in reference 23, was applied to the

measurement of standing waves in a duct using flush mounted wall microphones. The

microphones sensed both the acoustic pressure fluctuations and the random turbulent

boundary layer pressure f]uctuations.

The method is illustrated schematically in figure 73. The output voltage,

V2, from m 2 is cross-correlated with the signal generator voltage, Vs(t ) V o cos_t,

resulting in

(D.6a)

Since the cross-correlation between the periodic driver signal and the random background noise is zero, this term is not included in equation D.6a.

Note that the microphone system sensitivity, G2, has been used to link the

acoustic pressure and the voltage output. Replacing the trigonometric

terms by the complex notation for the cosine function gives

s2,s(:-)=

4

where 4" = 2_ (A + A2).

in equation D.6b is zero.

G282Vo<e 2i_tei(_:-¢)+ e-2i_'e-i(_t-_*)

+ ei(_T+_*)+ e-i(_r +_*)>

(D.6b)

The time average of the first two periodic terms

Hence,

The measured cross-correlation shown in figure 36 can be represented by a peak

voltage amplitude H 2 and a phase between V s and P2

(D.7)

where n is an integer.

S2,S(T) = H 2 COS I_T- 2_" (rl2+I,/2)]

(D.8)

87
Comparinglike terms in equations (D.7) and (D.8) provides

•r/2 = A +_2- n 2 0_< "r/Z< I (D.9)

The value for _2 is obtained from the microphone - signal generator cross-correlation

curve in figure 36. The time delay, _2, to the first maximum is used to solve

for n 2. Notice that the location of the first maximum was defined as the midpoint

between two cross-over points in the correlation function. By using two cross-over

points, irregularities in the correlation function trace were averaged.

Figure 36 represents the same operating condition as in figure 34. The

background noise which dominated in the first figure has been eliminated from

the second figure. To verify that the background noise did not influence the

results, the cross-correlation function for microphone m 2 was measured at each

test condition with the acoustic source turned off.

Cross-correlating P1 and Vs, it can be shown that

f_': (_,+n2)- A -A i,O<__, <_co (D.IO)

Here the number of integer cycles phase delay is referenced to m 2. Hence, _2 - nl

can exceed one cycle.

Finally,

(D. I1)

Substituting equation (D.IO) and (D.9) for &' and n 2 gives

/'_T - AT =('_t- _2 ) - AT

(D.12)

88
APPENDIX E

Cross-Correlation Technique in Presence

of Reflected Sound Waves

Consider the net pressure, P, sensed by microphone m 2 in figure 8 to

contain a direct acoustic ray represented by amplitude B2, a reflected wave

represented by B2,R, and the background noise given by _2" If the microphone output voltage is cross-correlated with the acoustic driver voltage

then the cross-correlation function between m 2 and the driver signal is

similar to equation D.7. In the present case,

(E.I)

As in Appendix D, the microphone sensitivity, G2, has been used to link the

microphone acoustic pressure input signal and voltage output signal.

The second term in equation E.I corresponds to the cross-correlation

between the reflected acoustic signal arriving at the microphone and the

acoustic driver voltage signal. Note that the reflected signal has an arbitrary phase shift AR, relative to the direct acoustic ray. The cross-correlation between the periodic driver signal and the random background noise is

zero so this term is not included in equation E.I. Replacing the trigonometric

terms in equation E.I by the complex notation for the cosine function and

noting that the time average of the periodic terms is zero gives

(E.2)

B2, R CO$,[_r R + 2_ (A+ g2 + AR)]

The importance of the second term in equation E.2 can be determined by

considering the reflected wave to be n_/2 radians out of phase with the

direct propagating wave arriving at microphone m 2. Under this condition,

the reflected wave has a maximum effect on the zero cross-over points used

to determine the phase difference, q2" Hence, if 2_A R = n_/2, where n = i,

3,5, etc., then the zero cross-over condition, S2,S(_R )= 0 gives

89
s_,_c_-_ :o:oo_[_,_-_ +2-(,_+,_]+

Bz

(E.3)

Simplifying the above equation gives

- = tan COT"R + 2Tr (A+A2)

B2,R (E.4)

Solving for the phase difference, _R f, between acoustic driver signal and

the combined direct and reflected sound waves gives

r R f = _ arctan (Ba/B2,R) _ (/_. + Z_2)

2-rr (E.5)

Here, the time difference, TR, has been multiplied by the frequency, f, to

express the zero cross-over delay point in the cross-correlation function in

terms of cycles.

In the absence of a reflected wave the zero cross-over point is determined by the equation

F 3

s_,_(_)=o=cosL_t-2_ (A+_2)J (E.6)

Solving for the phase difference between the acoustic driver and the direct

sound wave gives

I

TDf = _ - (A +A 2) (E.7)

The difference between TD and TR represents the error in identifying the zero

cross-over point in the presence of the reflected wave. The error, in cycles,

is

('I'D-'rR) f =

I I

4 2Tr arc tan (B2/B2,R)

(E.8)

It now remains to determine the ratio of direct-to-reflected sound wave

amplitude which represents the experimentally observed input to the right

side of equation E.8. Free-field decay measurements indicated a variation of

90
+

- 0.5 dB about the mean line defining the ideal inverse square-law curve.

A worst case calculation would assume these deviations to be generated by

direct and reflected waves which are either in phase or 180 ° out of phase.

the first case the sound pressure level is a maximum corresponding to the

+ .5 dB variation. Her E the noise level is controlled by the amplitude

coefficient (B 2 + B 2 R) • For the 180 ° phase shift, corresponding to the

-0.5 dB deviation, t_e noise is controlled by the amplitude coefficient

(B2 B2,R )2. The 1 dB difference between the + 0.5 and - 0.5 deviations

defines the ratio of the amplitude coefficients given by the expression

In

+ B2' )2 I (E.9) 1 dB = 10 log L'_cB2 BZ,R) 2

Solving for the ratio of the reflected-to-direct sound wave amplitude gives

B2,R/B 2 = 0.0574.

Substituting the calculated wave amplitude ratio into equation E.8 gives

(T D - TR)f = 0.0091 as the phase error in the zero cross-over point used to

determine q2 in equation i0. This error is comparable to the experimental

accuracy of the phase measurement and is less than the 0.02 cycle accuracy

required in the experiment. Based on the error analysis in Appendix F, this

would result in at most a 0.8 ° error in the experimentally determined value

of Oc .

91
APPENDIX F

Error Analysis for Shear Layer Angle Correction Experiment

It is worthwhile to perform an error analysis to determine the

sensitivity of the corrected angle, 8c, to errors in the measured phase

difference in equation i0. Based on the chain rule the variation of 0

c

relative to the phase diffcrence is controlled by the equation

d8.._._c= dSc dx o dffl

dA* dX o d/z I dA* (_.z)

where

(F.2)

Using the corresponding expressions for 0 c (equation 7), X o (equation 8)

and #i (equation 6), the above expression becomes

Simplication gives

dA* = [X2o+,h2 sin2(Fj+ 8m)J If cosff," co]

d49c (r/h)(sin 8rn- I) c o

d--_" = - sin 8 c sin2(/zJ+Sm ) tf cos/z,

(F.3)

(E.4)

The error in Oc will be calculated for the case of Om = 90 ° where the

magnitude of the phase difference is a minimum (see figure 37). Small errors

in the measured phase difference are then significant relative to the magnitude of the phase difference. Letting em = 90 ° , _ = 0.48 m, M = 0.4 and

h/r = 0.25 (based on Test Configuration i), the sensitivity of 0c to changes

in the phase difference is estimated by the differential expression d0 c =

-1.6 d(g*). Here, d8 c is expressed in radians.

Assuming a 0.02 cycle error in the measurement of A* the error in e is

c

calculated to be 0.032 radians or 1.8 ° . This is small in comparison to the

magnitude of 0 c which in this case is 72 ° . Thus, the accuracy of the phase

measurements had a negligible effect on the experimentally determined value

of 0

c

92
REFERENCES

1.

2.

3.

.

o

6.

7.

.

9.

i0.

ii.

12.

13.

Schlinker, R.H., Amiet, R.K.: Experimental Assessment of Theory for Refraction

of Sound by a Shear Layer, NASA CR-145359, 1978. Also AIAA Paper 79-0628.

Ribner, H.S.: Reflection Transmission and Amplification of Sound by a Moving

Medium. J. Acoust. S,c. Amer., vol. 29, 1957, pp. 435-441.

Miles, J.W.: On the Reflection of Sound at an Interface of Relative Motion.

J. Acoust. S,c. Amer., vol. 29, 1957, pp. 226-228.

Gottlieb, P.: Sound Source Near a Velocity Discontinuity. J. Acoust. S,c.

Amer., vol. 32, 1960, PP. 1117-1122.

Graham, E.W. and Graham, B.B.: Effect of a Shear Layer on Plane Waves of

Sound in a Fluid. J. Acoust. S,c. Amer., vol. 46, 1969, pp. 169-175.

Amiet, R.K.: Propagation of Sound Through a Two-Dimensional Shear Layer with

Application to Measurements in the Acoustic Research Tunnel. United Technologies Research Center Report UAR-L40, 1972.

Amiet, R.K.: Correction of Open Jet Wind Tunnel Measurements for Shear Layer

Refraction. Progress in Astronautics and Aeronautics, Ed. Martin Summerfieid,

1976, pp. 259-280. Also AIAA Paper 75-532, 1975, and UTRC Report NII1208-I,

1974.

Jacques, J.R.: Noise from Moving Aircraft: Some Relevant Models. Ph.D.

Thesis, Cambridge University, 1975.

Tester, B.J. and _rfey, C.L.: Developments in Jet Noise Modeling - Theoretical Predictions and Comparisons with MeasUred Data. J. Sound and Vib., vol. 46,

1976, pp. 79-103.

Amiet, R.K.: Refraction of Sound by Shear Layer. AIAA Paper 77-54. Also, to

be published in J. Sound and Vib., vol. 58, No. 3., 1978.

Candell, S. M.: Application to Geometrical Techniques to Aeroacoustic Problems.

AIAA Paper 76-546, 1976.

Tester, B.J. and Burrin, R.H.: On Sound Radiation From Sources in Parallel

Sheared Jet Flows. AIAA Paper 75-57, 1975.

Mani, R., Clapper, W.S., Stringas, E.J. and Banarian, G.: Development of a

Technique for Inflight Jet Noise Simulation - Part II. AIAA Paper 76-532,

1976.

93
REFERENCES(Cont'd)

14.

15.

16.

17.

18.

19.

22.

25.

26.

94

Candell, S.M., Guedel, A. and Julienne, A.: Refraction and Scattering in an

OpenWindTunnel Flow. Proceedingsof the 6th International Congresson

Instrumentation in AerospaceSimulation Facilities, IEEE, September1975,

pp. 288-299.

Ahuja, K.K., Tester, B.J., Tanna,H.K.: TheFree Jet as a Simulator of Forward Velocity Effects on Jet Noise. NASACR-3056,1978. Also AIAAPaper

77-1266, 1977.

Ozkul, A., Yu, J.C.: An Experimental Investigation of Acoustic Radiation

from a Source Inside a Large Turbulent Free Jet, J. Acoust. Soc. Amer.,

vol. 65, part 2, 1979, pp. 336-344.

Paterson, R.W., Vogt, P.G., and Folery, W.M.: Design and Developmentof the

United Aircraft ResearchLaboratories Acoustic ResearchTunnel. J. Aircraft,

vol. i0, No. 7, 1973, pp. 427-433.

Schlinker, R.H., Fink, M.R., and Amiet, R.K.: Vortex Noise from Nonrotating

Cylinders and Airfoils. AIAAPaper 76-81, 1976.

Paterson, R.W., and Amiet, R.K.: Acoustic Radiation and Surface Pressure

Characteristics of an Airfoil Dueto Incident Turbulence. AIAAPaper 76-571,

1976.

Rajarathnam,N.: Turbulent Jets. AmericanElsevier Publishing Co., 1976.

Candell, S. M., Guedel, A., and Julienne, A.: Radiation, Refraction and Scattering of Acoustic Wavesin a Free Shear Flow. AIAAPaper 76-544, 1976.

Paterson, R.W.: Acoustic ResearchTunnel Test Summary#29; Passageof High

FrequencyPure TonesThrougha Turbulent RoundJet. Report UAR-MII2,United

Aircraft ResearchLaboratories, August 1973.

Schlinker, R.H.: Transmissionof Acoustic Plane-Wavesat a Jet Exhaust.

J. of Aircraft, vol. 16, No.3, 1979, pp. 188-194.

Lighthill, M.J.: Onthe EnergyScattered from the Interaction of Turbulence

with Soundor ShockWaves. Proc. Camb.Phil. Soc., vol. 49, 1953, pp. 531-

551.

Howe,M.S.: Mulitple Scattering of Soundby Turbulence and Other Subhomogeneities J. Soundand Vib., vol. 27, 1973, pp. 455-476.

Amiet, R.: Scattering of Soundby Turbulence . United TechnologiesResearch

Center Report UTRC79-112,1979.
Table I -- Refraction Angle Correction Test Conditions.

TEST

GEOMETRY

NUMBER

SOURCE

LOCATION

x h

Ro Ro

1 33 1

266 1

4.0 1

1.33 0,55

133 144

RADIAL

LOCATION

h

[

0.25

025

025

014

0.16

MACH

NUMBER

M

01,02, 03, 04

02. 04

02, 04

0.1, 02, 0.3, 04

04

SOURCE

FREQUENCY

kHz

1,25,5. 10

]

5,10

Table II -- Refraction Amplitude Correction Test Conditions.

TEST

GEOMETRY

NUMBER

SOURCE

LOCATION

h

Ro Ro

053 1

266 1

053 1.67

SIDELINE

STATION

h

Y

025

0.25

042

MACH

NUMBER

M

0.1. 02. 03. 04

I

't

01,0.2,03

SOURCE

FREQUENCY

kHz

125, 25,5, 10

95
Table III -- Turbulence Scattering Test Conditions.

TEST

GEOMETRY

NUMBER

9

10

11

SOURCE

LOCATION

X h

Ro Ro

O53 1

166

266 'I

SIDELINE

STATION

h

Y

05

MACH

NUMBER

M

01,02, 03

SOURCE

FREQUENCY

f, kHz

5, 10, 15

i

J

'r

96
TURBULENCE LINED ACOUSTIC CORNERS__ I--r_--._

_ SCREENS /-----ACOUST,C WEDGES _-"-" ___]

\ CONTRACTION / FREE JET _ III _ [--_"

AIR _ O UT L E.-T-z_/-- C O L L ECT O R XXX_ l_Ij'_u _ -

"ONEYCOMB--_ /_ 1ll _ \1 TO_. l

HEATER AND_ lJ_ _ _CONTROL ROOM "_ PARALLEL

MUFFLER AND

__ BAFFLES

INLET ANECHOIC

CHAMBER

_,_-

TOP VIEW

46m --_

DIFFUSER / MUFFLER 1 DRIVER t

CENTRIFUGAL FAN ---j DRIVE MOTOR

SIDE VIEW

Figure 1 - UTRC Accoustic Research Tunnel.

97
_D

00

Figure 2 - Anechoic Chamber Test Arrangement for Refraction Angle Correction Ex_neriment.

e
co

-o

z_

03

ACOUSTIC SOURCE FREQUENCY

f=l kHz

INVERSE SQUARE LAW

25 kHz

DISTANCE FROM SOURCE, m

Figure 3-- Intensity-Distance Variation for Acoustic Source Employed in

Refraction Angle Correction Experiment with Discrete

Frequency Excitation.

99
C_

Figure 4- Acoustic Source and Microphone Arrangement for Free

Field Verification Tests Prior to Refraction Amplitude

Correction and Scattering Experiments.

illlrrl
tll

Z)

I--

£L

<

UJ

>

Ill

Cr

_-','-DISCRETE TONE SOURCE

E ___ / POINTING DOWNSTREAM

I-_,._ _ _ DISCRETE TONE SOUERNCEjE z AXIS

I _ _ _._._. f.,_E_S_

- I-'- _c?_sT;cn_ _ _ / LAW

, _ F,_o/- _ --_ --..../..._

T "

_h :-_owo_ _ _,_o,_,c_o_o__

STAT,O, '_i STAT,ON /

I i 11 l i i ! 1 ! ! fl

0.1 0.2 0.3 0,4 0,5 0.6 0.8 1.0 1.5 2.0 2.5

DISTANCE, m

Figure 5 -- intensity Versus Distance Variation for Acoustic

Source Employed in Refraction Amplitude Correction

Experiment with 1.25 kHz Discrete Tone and Tone Burst,

0m =90 °.

lOt
CO

t--

<_

J

LLJ

0.

ACOOSTC FREE

l

IN-FLOW MICROPHONE '--_

STATION

1 I I 1 I I I

0.2 0.3 0.4 0.5 0.6 0,8

DISTANCE, m

1

1.0

ILl

1"--

2

<=

,,J

ILl

Pc FAR-FIELD MICROPHONE_

I I STATIONI 1

1.0 1.5 2.0 2.5 3.0 3.5

DISTANCE, m

Figure 6 -- Intensity Versus Distance Variation for Acoustic

Source Employed in Refraction Amplitude

Correction Experiment with 1.25 kHz Tone Burst, _m =30°.

102
INLET NOZZLE

WITH TABS

Figure 7-Acoustic Source and Far Field Microphone Arrangement for Refraction

Angle Correction Experiment.

103
JET CONTRACTION

X

JEt- AXIS

-- NOZZLE LIP

EXTENSION ':Y,2,_ ,i,..--_90°--..._, / em

UPSTREAM WALL

> WITH WEDGES

> MICROPHONE SEPARATION, I _

Figure 8 -- Plan View of Open Jet, Acoustic Source and Far -- Field

Microphone Arrangement for Refraction Angle Correction

Experiment.

104
INLET NOZZLE

I ijj II!

}OURCE

COLLECTORPLAN VEW

A_US; JC

DRIVER

V

3E CHANNEL _

_n

Figure 9 -- Anechoic Chamber Test Arrangement for Refraction

Amplitude Correction and Scattering Experiment,
SOURCE

MICROPHONE, m 3

IN-FLOW TRAVERSE

LINE

LAYER

JET CONTRACTION JET AXIS

NOZZLE LIP

LINE EXTENSION

_ UPSTREAM WALL

> WITH WEDGES

>

>

"-_ OUT-OF-FLOW

TRAVERSE LINE

RAY Om

J

OUT-OF-FLOW

MICROPHONE, m 4

Figure 10-- Plan View of Open Jet, Acoustic Source and Microphone

Arrangement for Refraction Amplitude Correction

Experiment.

106
1.0 --

0.8 -

0.6 --

0.4 -

I

o 0.2

z)

>:

1.-

5 o

O

.,.,J

LI..J

>

£3

uJ

U 1.0

J

<

rr

o

z 0.8

-8

0.6 -

0.4 -

0.2 -

0 I

0.4

O° o

[] o

An o

0

0

A o

n

A

o

o

I , I I., I _

a) M = 0.2

A

0

o

X/Ro

O 0.66

n 20

A 40

[]

0 O Z_ Z_ Z_

I OOl_

_o o

0

z_ 0 o

z_ o

O

z_

0

I , I , I

O.6 O.8 1.0

R

E_

8

o O z_

z_

, J

1.2 1.4 1.6

NORMALIZE RADIUS, R/R o

b) M=0.4

Figure 11-- Variation of Normalized Velocity Profiles with Axial

Station, Tabs Installed.

107
O

53

53

>-

I-'-

O

d

LU

£3

1.0

0.8

06

0.4

0.2

DO

-- A

, I i ! I

X/Ro

O 0.66

O 20

A 40

£[3 A

0D A

0 A

0 [] A

0 El AA

a) M:0.2

LLI

U

--I

dE

o

Z

1.0

0.8

Z_ 130

1,oo

_ Z_

0.6 --

0.4--

0.2--

0

0.4

Eb

OA

D

co zx

Z_

OD &

0 D Z_

D Z_

0 D A

O I1_ Z_

1.0 1.2 1.4 .6

NORMALIZED RADIUS, R/Ro

b) M=0.4

Figure 12 -- Variation of Normalized Velocity Profiles with Axial

Station, Tabs Removed.

108
NOZZLE LIP -._ ]

l'

.o I

1'

I

6

-- _ U/Uo- 05

R

I _

_JET CENTERLINE

Figure 13-- Shear Layer Conditions.

109
O

£E

£E

o5

E3

<

_E

£3

UJ

U

J

<

EE

O

Z

1.6

14

1.2

1.0

0.8

0.6

0.4

O

O

O

O

m O

O

[3 D [] O

A

U/U o

O 0.1

O o5

Z_ 09

A

A

A

__, 1 j I I I ,

0 1 2 3

NORMALIZED AXIAL COORDINATE, X/R O

Figure 14 -- Axial Variation of Average Shear Layer Characteristics,

Tabs Installed.

Ii0
1.6

UtU O _ MEASURED INTERMITTENCY

BOUNDARY, M = 0.4 A 01

-- TRAVERSE LINE

0.4 I I i I , !

0 1 2 3 4

NORMAL AXIAL STATION, X/R o

i

Figure 15 -- Axial Variation of Average Shear Layer Characteristics,

Tabs Removed.

111
O

CO

LU

Z

",Z

O

I

I,--

n'-

U,J

>-

<

,,_1

rr

<

iii

I

CO

g_

N

_J

<

m

O

z

0.8

0.6

04

0.2

O TABS REMOVED

[] TABS INSTALLED

n

CANDEL

D

ID

0

[]

0

[D

0

GOETLER SOLUTION

, I , I J L ,

1 2 3

NORMALIZED AXIAL COORDINATE, X/R o

Figure 16 -- Axial Variation of Average Shear Layer.Thickness.

112
O

t--

©

_J

UJ

C3

LId

U

..J

OC

o

Z

1.2

1.0

0.8

0.6

0.4

0.2

0

1.2

1.0

0.8

0.6

0.4

0.2

0

_ )qRo

O 133

_.. _A_ [] 20

---_,l-lanhl I l I I I I I I

a) M=0.2

.6 -1.2 -0.8 -0.4 0 0.4 0.8

SIMILARITY PARAMETER, l 1

b) M = 0.4

.2

Figure 17-- Similarity of Velocity Profiles at Various Axial

Stations. Tabs Installed.

113
X/R o

a) M = 0.2

0.6

0.4

0.2

0

z_

.6 -1.2 -0.8 -0,4 0 0.4 0.8 1.2

SIMILARITY PARAMETER, 1]

b) M = 0,4

Figure 18 --Similarity of Velocity Profiles at Various Axial Stations,

Tabs Removed.

114
>_-

I--

Z

LU

I--

Z

0.20

0.16

0

0.12

0.08

0.04

O

n

A

m A AA% A

A

z_nOno A

- o o

430 --O'oA

A OA

oo ooz_

Z_

- o d_

tz 8,,

_ &o _

g_ 0

_ A 0

I 1 I I 1 I 1 I I I

.6 -1.2 -0.8 -0.4 0 0.4

SI M ILARITY PARAMETERS, 1]

X/R o

066

20

40

nA

0 o

oO

°_ u

I I

0.8 1.2

Figure 19 -- Similarity of Turbulence Intensity Profiles at Various Axial Stations,

M = 0.4, Tabs Removed.

115
0.20

0.16;

O

o12i

>_-

I--

Z

tli 0.8

Z

0,4-

0

-1.6

% m

0

0

0

5

06, °8

o

M

O 02

n 0.4

t ! _ i : I i I I I I

-12 -0.8 -0.4 0 0.4 1.2

SIMILARITY PARAMETERS,r/

O

8

oa

013

0

, I

0.8

Figure 20 -- Similarity of Turbulence Intensity Profiles at Different Mach Numbers,

X/R o = 4.0, Tabs Removed.

116
/

/

/

iii

li

/I

DIRECTION

PARALLEL TO

AXIS OF JET

x

II

II

Ii

/I

/

Y'I, Z'l

PLANE TANGENT TO SHEAR LAYER AT POINT

(Xl, Y'I, Z'l)WHERE RAY CROSSES

Figure 21 -- Geometry for Theoretical Model.

117
h

/

/

I

I

PROJECTION OF r2 ON

PLANE PERPENDICULAR

TO DIRECTION OF FLOW

TANGENT TO

SHEAR LAYER AT

POINT (x 1, yl _ z_)

Vt

SHEAR

LAYER

Figure 22 -- Cross-Sectional Geometry for Theoretical Model.

118
M

--up,,.

SHEAR LAYER

M=0

_Xo_

SOURCE _ S

RAY PATH

Y

WAVEFRONT, M = 0

_1 = e,-em

SIDELINE TRAVERSE J

IN-FLOW

MICROPHONE, m 3

WAVEFRONT

M_0

NON REFRACTED

RAY PATH

Z-- CONSTANT RADIUS

C_ STATION

/ \

/ \

f

O

CONSTANT SIDELINE

STATION

)BSERVER OR OUT-OF-FLOW

MICROPHONE, m 4

Figure 23 -- Geometry for Transmission of Sound Through

a Shear Layer.

119
180

"0

UJd

(..g

z

<

E_

LU

o

LW

OS

nO

0

160

140

120 --

100

80--

60--

40--

20--

0

0

M

01 h =025

r

O2

0.3 h

0 4 Ro

! I

/

I I 1 1 J

20 40 60 80 100 120 140 160

MEASUREMENT ANGLE, 9m, deg

Figure 24 -- Theoretical Refraction Angle Correction as a Function of Mach Number,

on Axis Acoustic Source Location, Constant Radius Microphone Geometry.

120
180

160

140

120

O3

"I3

_ 100

UJ

_J

(.9

Z

<

£3

"' 80

iii

rr

n"

0

o

6O

40

20

h

Ro

0

10

20

J

J

J

0 m

0 20 40

10

0

-10

h

w

r

0

025

05

MEASUREMENT ANGLE, 8m, deg

Figure 25 -- Theoretical Refraction Angle Correction as a Function of Off.Axis

Source Position for M = 0.3, Constant Radius Microphone Geometry.

121
Q3

-O

O

I--

O

L,LJ

r_

CE

o

L_

Lt.J

E3

t--

g

(3-

<_

10

5 --

0 m

-5

0

M

h

0.2 m = 0.25

r

O4

h

-1

Ro

f

f

I

J

J

I

/

/

I ,1 1 I I I t I !_ 1 I ! 1 I I

20 40 60 80 100 120 140 160

MEASUREMENT ANGLE, em, deg

Figure 26 -- Theoretical Refraction ._.mplitude Correction as a Function

of Mach Number on Axis Source Location, Constant Radius

Microphone Geometry.

122
co

-o

o

I--

O

uJ

rr

o

O

ILl

r_

I--

J

Q-

<

15

10

-5

-10

-15

0

h

-- Ro g

-- 0 10

-- 1 0

-- 20 -1 0

20 4O 60

h

r

0

025

05

f jg:.l

Z_o=o oN -Tf

g= +1 "--/ I OBSERVER

L_

80 100 120 140 160

MEASUREMENT ANGLE, 0m, deg

Figure 27 -- Theoretical Refraction Amplitude Correction as a Function of

Off-Axis Source Position for M =0.3, Constant Radius

Microphone Geometry.

123
©

W

C3

6

<3D

..J

(3

Z

<

I---

o

L_

fT

f_

Q

t80

160

140

120

100

80

60

40

20

M

0t

02

03

0.4

h =025

Y

h =1

R o

, ! I I i I I__ I ! i !

60 80 100 120 140

MEASUREMENTANGLE,Dm, DEG

160

Figure 28 -- Theoretical Refraction Angle Correction as a Function

of Mach Number, On-Axis Acoustic Source Location,

Sideline Microphone Geometry.

124
(.9

UJ

J

z

<

D

LLI

t--

O

U,J

rr

rr

O

(.3

160

140 "--

120 --

100 --

80--

60--

40--

20--

h h

Ro g y

0 1.0 0

1 0 0 025

20 - 1.0 0.5

/

I 1 l I

20 40

g= +1

1 i 1

80 100

1 I 1

0 60 160

Jl OBSERVER

i 1 i I

120 140

MEASUREMENT ANGLE, 8m, DEG

Figure 29 -- Theoretical Refraction Angle Correction as a Function

of Off-Axis Source Position for M 0,3, Sideline Microphone Geometry

125
10

: oM_h ,/

0 2 _" = 0.25 / / /

F-6 -5- I I i I I 1 I I I ! l I i I I

L3 0 20 40 60 80 100 120 140 160

MEASUREMENT ANGLE, 8m, DEG

a) AMPLITUDE CORRECTION VERSUS _m

I: / I

i

.6

0 20 40 60 80 100 120 140 160

CORRECTED ANGLE, 8c, DEG

b) AMPLITUDE CORRECTION VERSUS ec

Figure 30 -- Theoretical Refraction Amplitude Correction as a

Function of Mach Number, on Axis Acoustic

Source Location.

126
LZI

•/uletuoeo euoqdoJO!lN eu!leP!S '£'0 = IN JOl uo!|tSOd

eoJnos slxv-|tO lo uo!;oun-I e se UO!lOeJJOO epnl!lduJv uol|oeJ|e_l leo!|eJoeq/-- _£ eJn6L-I
I

Ii RAY PATH,

M_'O

RAY PATH I DNT

M=O M=O

I

I

WAVEFRONT

I M_O

,_ = 0.15,0.3, 0.48 m

_r <0.25 cm.

m!

Figure 32 -- Model of Wavefront Angle Changes at Far-Field

Microphone Location.

128
Z LJJ

LU n

8_

©

cE LLJ

m

'1"

f

MID POINT

DELAY TIME

q=0

Figure 33 -- Two Microphone Cross.Correlation Function at M = 0.

129
LU

l---

r_

<_

LU

>

pLLI

rr

-1

-2

[ ACOUSTIC SOURCE FREQUENCY:

1,, I=5 kHz

'_ " R

/ f'_ souCEON

- Vr

, I I l J I I

0 160 320 480 640

DELAY TIME, #sec

Figure 34 --Two Microphone Cross-Correlation Function at Mach

Number, M =0.4, Measurement Angle, 8m =37.5 o,

Test Configuration 1.

130
=_

=_

.J

£L

CO

LU

>

_J

LU

ACOUSTIC SOURCE

FREOUENCY: f = 5 kHz

--fm #-

i I J I J I i

3 4 5 6 7

FREQUENCY, f, kHz

Figure 35- Typical Far.Field Microphone Spectrum at Mach

Number, M =0.4, Measurement Angle, 0m -37.5 °,

Test Configuration 1.

131
3r

LLI

E3

:)

I--

.._J

<

III

I.--

<

d

LLI

rr

-1

-2

0

CROSS-CORRELATION FUNCTIONS

T1 = t]l/f _i

._T]2/f """''= $2, s ( ) SOURCE ON In__St ,s()SOURCE

2 -- _" _ s2, s ( ) SOURCE OFF

f,_", /3-, 7x',

/,,"i /

H\, I/ \', I/ \', /i

i _ _ _ I _Zo_oss.ov_\, I/ / \,, // \, //

! M,DPO,_'"_ , / I / \ ', / i ! _ / /"

'- _ '. / ' ZCROSS-OVER _ ', J i I _ / ,

,. / ! ,,,o_O,NT\ "_ / / \ \ / /

k:',/,,' \v,, \v,,

I "4 " I I ""'" I I "T'"

160 320 480 640

DELAY TIME,T, #sec

Figure 36 --Microphone-Signal Generator Cross-Correlation at Mach

Number, M =0.4, Frequency, f = 10 kHz Measurement

Angle, Bm =37.5 °, Test Configuration 1.

132
co 1.0

U..I

,,_1

o

>...

o 0.8

<3

t

I--

0,6

LU

o

z

Lu 0.4-

131

UJ

L.L

U...

0.2-

U.I

03

"la_ 0

0

_ /--.THEORY. _ EXPERIMENT,_:048m

\ "Z'

THEORY, "*" _

,_:048 m _ _ _

MICROPHONE

SPACING _

I I I I I I I I I i I i I ! I I I I I i i !

10 20 30 40 50 60 70 80 90 100 110 120

MEASUREMENT ANGLE,Om, DEG

Figure 37 -- Comparison of Measured and Theoretical Phase

Difference at Mach Number, M = 0.3, Frequency,

f = 2.5 kHz, Test Configuration 1.

133
L,,,;,

4L_

LU

t---

.<

w

X

o

n13_

o_

<

n

z

<

i,..-

o

<

X

LU

Z

ILl

W

rn

rr

o

[12

IT"

,Z

U.I

o

rr

col

n

CO

Z

o_

i--

3

o

0

30

_. MICROPHONE SPACING:

- "_ -0= 0,48 m

M =0,1 '__ _.

__ M=02 "_

I I t I I 1 I 1 l I i 1 i

40 50 60 70 80 90

AVERAGE MICROPHONE MEASUREMENT ANGLE, em, DEG

100

Figure 38 -- Assessment of Error Due to Plane-Wave Propagation

Assumption,
120

100

8O

6O

4O

8O

6O

4O

2O

THEORY, M=0.1

M

O01

no3

0 20 40 60 80 100 120

MEASUREMENT ANGLE, 8m, DEG

b) f= 10 kHz

Figure 39 -- Comparison of Measured and Theoretical Refraction Angle Correction as

a Function of Mach Number and Frequency, Test Configuration 1.

135
©

W

C3

UJ

J

©

z

<

o

W

I--

o

LU

rt"

nO

c.)

120

100

8O

6O

4O

2O

0

120

B

-- O

[]

02

04M /

-

THEORY, M = 0,2 f

_ o_.,,d

_--- JJ "

I 1 , I l I I I I I_.,

C) f -- 5 kHz

100

8O

6O

4O

2O

B

m

I

I

0

o

THEORY, M = 01__

o,3_/

1 I 1 l 1 l l I I

20 40 60 80 100 120

MEASUREMENT ANGLE, 8m, DEG

d) f=5 kHz

Figure 39 -- Contir_ued.

136
C5

I.JJ

tm

L_

IdJ

._1

©

z

<

d_

LIJ

tO

LLI

m

cE

©

o

120

t00

80--

60--

40 -

20--

0 I

120

100

80

O 02 ,,,'

I-]o4

THEORY, M=0 2_ _/.1_"

o4 ,_ ''D

//

1 I 1 I I , I _ !. I

e) f = 2.5 kHz

M

O 0._

[] 0.3

THEORY, M =01

0.3--_

60

40

20 40 60 80 100

MEASUREMENT ANGLE, _m, DEG

f) f= 2.5 kHz

Figure 39 -- Continued.

120

137
IJJ

L_

uJ

z

LU

I--

o

I,,U

nCC

0

0

120

100

80

60

40

20

0

120

100

80

60

--002

D 04 A

THEORY, =__d

_

, , i , I , l , I, , I ,

g) f= 1 kHz

THEORY,M

40

0

20 40 60 80 100

MEASUREMENT ANGLE, 8m, DEG

h) f = 1 kHz

120

Figure 39 -- Concluded.

138
120

cb

LU

IE)

.=P

u./

J

(.9

Z

<

£3

UJ

f--

o

UJ

t'T

5

o

100

80

60

40

20

0

120

100

80

60

40

20,

TEST CONFIGURATION 2:

X

-_o = 2 66

- h = I THEORY,_ /

_o M=04

p_l-I O 0.4 10

J [] 04 5

J I , I _ I , I , I ,

a) f=10,5 kHz

f

M kHz

0 0.4 2.5

17 0.4 1.0 ._

• =

, I _ 1 i I I I , I

0 20 40 60 80 1O0 120

MEASUREMENT ANGLE, 8m, DEG

b) f =2,5, 1 kHz

Figure 40 -- Comparison of Experimental and Theoretical Refraction Angle

Correction as a Function of Mach Number and Frequency,

Test Configuration 2.

139
tm

u./

._1

(..9

z

<

ill

(3

ill

n-

©

(3

120

100

80

60

40

20

0

[]

M

02

0,4

THEORY, M

20 40 60 80 100

MEASUREMENT ANGLE, 8m, DEG.

c) f = 5 kHz

Figure 40 -- Concluded.

120

140
z

120

1CO

80

60

40

LLI

o 20

(5

L.U-

-J

(3 0

z

<:

120

LU

I--

0

ILl

rr

rr 100

O

(.3

80

60

40

20

TEST CONFIGURATION 3:

x

-4

_._h =_ ,z"O

R0 THEORY,_

S ,.,.

,,_ M kHz

o o4 ,o

I , 1 , 1 , I ,,, I , I

a) f = 10, 5 kHz

1

M kHz E

O 04 2.5

[] 0.4 1.0 .,,_ C

. =

J I , I ' I , 1 , 1 , I

20 40 60 80 100 120

MEASUREMENT ANGLE, 8m, DEG.

b) f =2.5, 1 kHz

Figure 41 -- Comparison of Experimental and Theoretical Refraction Angle

Correction as a Function of Mach Number and Frequency,

Test Configuration 3.

141
L.IJ

uJ-

_1

(.9

Z

D

LIJ

I--

0

UJ

rTnO

o

120

100

80

60

40

20

[] 04 THEORY, M=02_ .X_".,_fj m .,_] U

I I I , I , I , ! _ 1 I

20 40 60 80 100 120

MEASUREMENT ANGLE, 8c, DEG.

c) f = 5 kHz

Figure 41 -- Concluded.

142
i

UJ

D

,:¢:>

uJ

J

(5

Z

O

UJ

I0

ILl

n'-

cc

0

o

120

100

8O

6O

4O

2O

0

120

100

8O

TEST CONFIGURATION 4:

X

-- = 1.33

Ro THEORY,

h

-- = 055

Ro

[]

[3

[]

a) f = 10 kHz

O

[]

M

0,1

0.3 THEORY, M =

6O

4O

2O

0 20 40 60 80 100 120

MEASUREMENT ANGLE, 8m, DEG.

b) f = 10 kHz

Figure 42 Comparison of Measured and Theoretical Refraction Angle

Correction as a Function of Mach Number and Source Frequency,

Test Configuration 4.

143 '
LU

£3

J

(.9

z

<

£3

UJ

po

iii

orr

©

o

120

1O0

80

60

40

20  ̧

0

1

100

80

60

40

20

M

0 02 ,_f D 04 = 0,2---_

THEORY, M

/7 D -

/z/o

I i I I I I I J I-i

C) f = 5 kHz

M

O o_

[] 0.3

THEORY, M =

0.3-_

20 40 60 80 100

MEASUREMENT ANGLE, _m, DEG,

d) f = 5 kHz

Figure 42'-- Continued.

120

144
-Z

UJ

£3

u./

J

©

z

tm

u.J

I--

0

Ill

rr

0

0

120

IO0

80--

60

40

20

120

100

80

60

40

0

20

M

017 020.4 THEORY. M = 0.2_ ,_

,4,,_

I i l _ I , I , I ,

e) f = 2.5 kHz

o:, /

oo.3

/o

•

i I L I I I , I I I , J

20 40 60 80 100 120

MEASUREMENT ANGLE, 8 m, DEG

f) f = 25 kHz

Figure 42 -- Concluded.

145
UJ

C)

_.J

(.9

Z

<

tm

UJ

o

LU

rr

rr

o

o

120

100

8O

6O

4O

2O

0

120

100

8O

6O

4O

2O

TEST CONFIGURATION 5:

X = 1.33 /

R° ///

-_- = 1.44 THEORY,_ C3#//_)/'4_

o M= 02 _ _/-/E:]

h.__ : 0.36 0.4"__ ,_

13 o.4

I I t J I I 1 I I J

a) f= 10 kHz

THEORY, M

2O 40 60 80 100

MEASUREMENT ANGLE, em, DEG

b) f = 5 kHz

120

Figure 43 -- Comparison of Experimental and Theoretical Refraction Angle

Correction as a Function of Mach Number and Frequency,

Test Configuration 5.

146
t-n

-o

O

O

LU

tT

Or"

O

O

LLJ

O

I--

,_J

13-

<

10

0

-5

0 120

m

-- /-- CONSTANT RADIUS,

I ! 1 I I I I l I I I

20 40 60 80 1O0

CORRECTED ANGLE, 8c, DEG.

Figure 44 -- Comparison of Theoretical Refraction Amplitude Correction

for Sideline and Constant Radius Far Field Microphone

Location with M = 0.4, Source On.Axis.

147
/-- TONE BURST

"7"- 0 / SIGNAL

> I TIME

TO AUDIO -- i

AMPLIFIER

AND ACOUSTIC

DRIVER

TONE

BURST

GEN

PREAMP

PREAMP

}_ SWITCH

AMPLIF H

/-- PULSE

= 0 / SIGNAL

TIME

FILTER

H SIGNAL I

ENH

Figure 45a -- Schematic of Signal Enhancement Circuitry Used to Capture Tone Burst.

148
LLI

Z

O

13.-

AMPLITUDE, B4, 5

2 .,3 4 ,k--[- ,6- ,;,, ,8-, ;, _o L /'X I\ I\ !\ / \ i _ ,, '. 1 , ,,--..

[ V V- V V _ \7 ',..,/ '_1' """ TIME

T T+AT 'T+2&T

Figure 45b -- Tone Burst Signal Recovered from Signal Enhancement.

149
rn

7:3

O

C)

U.J

rr

O

O

LU

D

I--

,_J

Q.

<_

2

0 0 0 0 0 0

0 0 0

i

-2 I I I I I I I _J

20 40 60 80 100

CORRECTED ANGLE, Pc, DEG.

Figure 46 -- Comparison of Measured and Theoretical Amplitude Correction,

M =0, f = 5 kHz Tone Burst, Test Configuration 6.

150
il III ,I, id I, m,,

,

"T1 C

-,,4I

""m

II"

..E°

- Q.

w,

o5

--I ""

"1'1

,.,._

O_"

m,

o.=

'_ "rl

D, o3

ZT0

"!00

"I

w_ 0

0

II 00

mi-_mo

RELATIVE AMPLITUDE

.4-

00

/
/ACOUSTIC

SOURCE

JET

CIFNTERLINE

RAY

M

I

I

i t

SHEAR J

LAYER

MICROPHONE

_'- IN-FLOW

TRAVERSE

LINE

MICROPHONE

Figure 48 -- Acoustic Ray Orientation Relative to Microphones.

152
0

Z3

__1

13..

,<

_>-1

._J

ill

rr

-2

-3

ACOUSTIC

WAVEFROIT _

MICROPHONE CARTRIDGE

L ..ANDPREAM_L,F,ER

I, 'C OENCEANG

O NOSE CONE MICROPHONE

|= lOkHz TONE BURST

[] REFERENCE MICROPHONE

! = 10kHz TONE BURST

A NOSE CONE MICROPHONE

l= 10kHz ONE-THIRD

OCTAVE BAND RESPONSE

'-I II

I

'L-NOSECONE

RAY PATH

Cl D O E] 0 O O O o 0 0 O O D O O 0 O D 0 E30_

TldB

CORRECTIONS WERE BASED

FOR TONE BURST

i I I I i I _ I i I l,,, I _ I. _

0 20 40 60 80 100 120 140 160

INCIDENCE ANGLE, deg

Figure 49 -- Nose Cone Directional Sensitivity to Tone Burst and Random Noise Signals.

153
"pePnlOUOO -- 61_ aJnS!-I

6ep '399NV 30N30IONI

09 L 0_ I. 0_ I- 00 I. 08 09 0t' 0_

I I I I i I I I I I I I I I

01. V

£Z []

_ 3NO9 3SON .8 O3SN3£

S3ION3RO3EIJ 1sEIn8 3NO1 " " " T %

8P I m

qNI7 B9VW3AV 7

o

0

0

0

--4

o

0

u'7
0

O

-- -2

I"-

O

UJ

riCE

O

O

LU

E3

P- 5

O

-5

2O

TEST CONFIGURATION 6

X/R o = 053

hlR o = 1.0

o

I I I I I I I

a) M=0.1

m

! 1 I I I I I

40 60 80 100

b) M=0.2

CORRECTED ANGLE, ec, DEG.

Figure 50 -- Comparison of Measured and Theoretical Refraction Amplitude

Correction as a Function of Mach Number for f = 1.25kHz, Test

Configuration 6.

155
-5

r'n

Z

o

I--

(,..)

IJ,J

t-'r

r'r-

©

(D

LLI

5

2

2

0

-5,

20

m

-- O O

I I I I I I I

c) M=0.3

l, kHz /

0 125 /

-- 0 25 /

I I 1 I I i 1

40 60 80

d) M:0.4

CORRECTED ANGLE, 8 c, DEG

Figure 50 -- Concluded.

100

156
5

5

80o

2

2

< -5

f, kHz TEST CONFIGURATION 6

-- O 125 X/Ro = 0 53

_ _ 25 h/R o = 1.0

m

I I I ,I I I I

0 0.1 0.2 0,3 0.4

MACH NUMBER, M

Figure 51 -- Comparison of Measured and Theoretical Refraction Amplitude

Correction as a Function of Mach Number for _c =30°,

Test Configuration 6.

157
0

o -5

I--

C)

LU

rc

rr

o

o

L.U

a

Z)

t- 5

<=

0

-5

20

m TEST CONFIGURATION 6

_ X/Ro=O 53

i

, I ! 1 _1 I 1 1

a) f --- 1.25kHz

,, 1 I .11 I I 1 1

40 60 80 100

b) f = 25kHz

CORRECTED ANGLE, ec, DEG

Figure 52 --Comparison of Measured and Theoretical Refraction Amplitude

Correction as a Function of Frequency for M = 0.3

Test Configuration 6.

158
-5

- O _ O_

THEORY--/

I 1 I I I ! I

c) f = 5kHz

a3

Z_

O

I,--

c)

LLI

n'-

rr

O

(D

UJ

C3

:)

I--

._.1

(3-

.<

10

m

_ O

5

-- 0

-- 0

0

-5 I I I I I I I

20 40 60 80 100

d) f = 10kHz

CORRECTED ANGLE, 6c, DEG

Figure 52 -- Concluded.

159
rn

"13

u5

O

Z

LU

cr

UJ

LL

LL

UJ

E)

I---

d

o_

<

10

-5

5

0

-5

0

f = 1.25kHz DATA POINT AT

0c : 25"

! ! I I I I

a) 0 c = 30 °

l, kHz L/)-,

O 125 0.32

O 25 0.64

_, 5 129

_, 10 2.58

0

I 1 I ! I I 1

0.1 0.2 0.3

MACH NUMBER, M

b) 0c=89 °

0.4

Figure 53 -- Difference Between Measured and Theoretical Refraction Amplitude

Correction as a Function of Frequency, Mach Number, and Corrected

Angle, Test Configuration 6.

160
O3

-o

©

f--

L.LJ

n'-

o

O

LU

pJ

Q_

f O RANDOM NOISE, 1t3 OCTAVE BAND

D TONE BURST

-_':',:,°,.,,.,,.,o_

_ __. ×_Ro--O_

THEORY h/Ro = 1

i

-5 I I I I I I i

20 40 60 80 100

CORRECTED ANGLE, e c, DEG

Figure 54 -- Comparison of Measured and Theoretical Refraction Amplitude Correction

for Tone Burst Noise Source and Random Noise Source, f =10kHz, M =0.2,

Test Configuration 6.

161
cn

©

I--

O

LU

CC

or-

©

LU

(E3

t---

d

o_

<

-2

5

TEST CONFIGURATION 6 m

X/R o = 053

htR O = 1.0

J 1 I i

a) M=0.1

-5

5

-5

2O

m

l I ! I ! l I

b) M = 0.2

w

- O

, I I I I I I I

40 60 80 100

CORRECTED ANGLE, ec, DEG

c) M=0.3

Figure 55 -- Comparison of Measured and Theoretical Amplitude Correction as a

Function of Mach Number for f = 2.25kHz, Test Configuration 6.

162
r'n

z

O

I,,-

O

LU

Q::

cr

O

O

LLI

n

:3

I--.

n

,<

Figure 56 --

-2

TEST CONFIGURATION 6

X/R o = 053

h/R O= 10

a) M=0.1

0

-5

B

I I I i I .] 1

CORRECTED ANGLE, ec, DEG

b) M=O,2

Comparison of Measured and Theoretical Amplitde Correction as a

Function of Mach Number for f - 5kHz, Test Configuration 6.

" ; " : . ;_ : _ : _: -;i. - I

163
10

cn

-o

Z.

o

I--

O

Lu

t'r

rr

O

o

LU

- TEST CONFIGURATION 6

- X/R o = 2 66

-- htR o = 10 ,_

5

0

a) f = ].25kHz

1()

C_

_J

I3_

<

5- _ O

O

0

-5 , I i i , t , i ,

20 40 60 80 100 120

CORRECTED ANGLE, {)c, DEG

b) f= 5kHz

Figure 57 - Comparison of Measured and Theoretical Refraction Amplitude

Correction as a Function of Frequency for M =0.3,

Test Configuration 7.

164
1313

"O

©

I--

(.9

UJ

rr

crO

C)

LI.J

C)

D

t.--

Q_

10

M

" 0 01

#

-- O 0.3 I

5 Z S_',,,_. THEORY

jjJrl U =0.3

M=0.1

f TEST CONFIGURATION 7

X/R o = 266

htRo = 1.0

-5 I I .... ! I I

a) M =0.1, 0.3

10

0 q

M I

- O o2

-- I_ THEORY

ooA o_-o /

- / / Z ,,//°

- / O

.2

l

-5 I I I ! I

80 100 120

CORRECTED ANGLE, 0c, DEG

b) M =0.2, 0.4

140

Figure 58 -- Comparison of Measured and Theorectical Refraction Amplitude

Correction in the Forward Quadrant for Varying Mach Number with

f = 1.25kHz, Test Configuration 7.

165
rY_

7O

z

©

pO

LLJ

rV

CE

©

o

LLJ

D

l--

._J

o,_

<

10

-5

10

5

q

0

B

TEST CONFIGURATION 7

-- X/R o = 2.66

Z h_/R°=lO A

".,-THEORY

w

B

, ! i I !

a) f = 1.25kHz

- 0

-- 0 0

N

I

-5 L , 1

8O

I n I i

100 120

CORRECTED ANGLE, Pc, DEG

b) f = 5kHz

140

Figure 59 -- Comparison of Measured and Theoretical Refraction Amplitude

Correction in the Forward Quadrant for Varying Source Frequency

with M = 0.3, Test Configuration 7.

166
"111

(Oc

(,r'l I

¢) Oomc

O,,

coo

C) O

33

33

Itl z

-r r-- N rlq

E_

r'rl

O

AMPLITUDE CORRECTION, dB I I I I O I I I

",.,4
5

zo

F- -5

(_

LU

rr

EE

o

L_

LU

C)

_- 5

-5

20

0

TEST CONFIGURATION 8

X/R o = 0.53

_ h/R o= 167 THEORY,_

-- o e

, I I ,.I ! I ! l

a) f= 1.25kHz

I I ! I i ! I

40 60 80 10(

RADIATION ANGLE, ec, DEG

b) f = 5kHz

Figure 60 -- Comparison of Measured and Theoretical Refraction Amplitude

Correction as a Function of Frequency for M = 0.3,

Test Configuration 8.

168
691

c

@

I

m3

=r_..

Zc

C a,

3m

=r o

II "

_o

o

==m

¢.,._

5"_

3

m

m,

O.

0

@

('I

i,

0

0

AMPLITUDE DIFFERENCE, dB

I ' I

ZONE OF SILENCE

W I ' I

I

.-.,

o

m _ m m m m i .

I

"m

m

m m

m m

_ m

_z

o8

I-<

E_

_m

_5

g_

m

o
O, I

2

<=

UJ

rr

GAC: REFERENCE-TO-IN-FLOW CROSS-SPECTRUM

GAB: REFERENCE-TO-FAR-FIELD CROSS-SPECTRUM

_ ""-- GAC(f)

i

•"_ _1.2 13.6

1

1 I I I 1 ! I 1 1 I I I I I

4 8 12

FREQUENCY, kHz

16

Figure 62 -- Cross-Power Spectra, #c =90°, X/Ro =4, M = 0.225.
AL_ ACOUSTIC

SOURCE /-" LINE PARALLEL TO

MEAN VELOCITY

o!

• _ _ _-'-Uc

_0 S _NO_ S£ A'Iq'ERED

SCATTERED RAY PATH

RAY PATH

Figure 63a -- Schematic of Direction Scattering by Turbulent Eddy.

171
Xo

f SOURCE

LINE PARALLEL TO

MEAN VELOCITY

INITIAL RAY

PAT HS

SHEAR

LAYER

M=0

SCATTERED

RAY PATH

0T+ 0 S SCATTERED

RAY PATH

FAR FIELD

MICROPHONE

REFRACTED

RAY PATHS

Figure 63b -- Schematic Showing Refraction Angle Change and Scattering by

Different Regions of Shear Layer.

172
-10

-20

-25 00H[_--

_30_ i •

03

m

d

13-

,<

I,1

>

III

ix:

0

J

a) f = 5kHz

-5-

-10 -

-t 5 -

-20 -

-25 -

-30

b) f : 10kHz

Figure 64 -- Variation of Discrete Tone Spectrum with Mach Number and

Frequency for 0 c -90 °, X/R o --0.53, BW = 50Hz, Test

Configuration 9.

173
:7 i |

rn

tm

I,--

¢t

<I:

tll

:>

i11

1:12

0

-5 - j

IN-FLOW

SPECTRU M

-10

-15

-20

-25 00H

-30

_- M =0.1 _02 _0,3

, //

C) f = 15kHz

Figure 64 -- Concluded.

174
0[ NFLow_1

tSECTU o,rsoo -5 0 c = 90

. _ I I FAR FIELD-" II

_ -15

_ -20

-25 OOH

-3C

Figure 65 -- Variation of Discrete Tone Spectrum with Radiation Angle for

f = 15kHz, X/R o -- 0.53, M - 0.3, BW = 50Hz, Test Configuration 9.

175
9LI

• LL uo!leJn6i)uoo iSel 'ZH0S = M8 ' 99"_ = °kl/X 'o 06 = °e JOl _ouenbeJ-I

pue JequJn N qoelN ql!M uJnJ|oeds euo£ eleJos!Q |o uo!le!JeA -- 99 eJnSL-I

ZH_O L: _ (q

0£-

_ cj8-

08-

-cjL-

--0L0

33

ITI

I'-"

"-4

ITI

3>

q3

1-"

--4

C

E_

rrl

OO3
-5

cn

1o

u.]

-10

E3

t--

J

(3._

-15

.<

LU

>

I'-"

< -20

d

LU

rr

-25

-30

M=01

f02 •

FAR FIELD

SPECTRUM

_ 500Hz

c) f = 15kHz

Figure 66 -- Concluded.

177
-5

-10

-15

-20

rn -25

0

-30 t--

...J

.<

uJ 0

t--

.J

uJ -5

r'r-

-10

-15

-20

-25

-30

IN-FLOW

- SPECTRUM

-%

_ 500Hz

= 120 °

/- 90 °

a) f = 5kHz

b) f = 10kHz

Figure 67 -- Variation of Discrete Tone Spectrum with Radiation Angle and

Frequency for M = 0.3, X/R o -2.66, BW = 50Hz, Test Configuration 11.

178
i

5

-5

2

-10

-15

-20

i -25

i -30

O FAR FIELD INTENSITY

O

O O

IN-FLOW-_ _ ec=12o o

-- SPECTRUM "_ I / " • 90 °

I I FAR FIELD-_ _ Af _ __50 °

- IISPECT'UM'_// /\ /Y

c) f = 15kHz

Figure 67 -- Concluded.

I79
ED

FJ

EL

<

LIJ

>

LU

Q2

-5

-10

-t5

-20

-25

-30

IN-FLOW

_SPECTRUM

FAR FIELD-_

__ SPECTRUM ",

-- 500Hz /

f XIR o = 0.53

1.66

\

Figure 68 -- Variation of Discrete Tone Spectrum with Axial Source Location for

_c =90°, t =15kHz, M =0.3, BW=50Hz.

180
rn

u..i

t--

J

(3_

<

LU

I'--

<

d

i11

rr

0

-5

-10

-15

-20

-25

-30

DISCRETE __'--TOTAL ACOUSTIC

TONE

-- ENERGY IN

__ 14 975-15.025kHz BAND_

IN-FLOW I _ _- FAR FIELD

DISCRETE TONE

LEVEL

500Hz

a) SPECTRUM WITH BW = 50Hz

-5

-20

-25

-30

-35

-40

IN-FLOW

SPECTRUM

--..t _oHzF-

__ ,.__.ow_.o_o_.o.E

APPROXIMATE RANDOM

NOISE LEVEL

- t,

It

DIFFERENCE

l

FA._R F ,z.,.FAR FIELD

ELD MICROPHONE SPECTRUM

APPROXIMATE RANDOM NOISE LEVEL

b) SPECTRUM WITH BW = 0.25Hz

Figure 69 -- Comparison of Spectra Obtained with Different Analyzer Bandwidths

for 0c - 50 o, X/Ro -_ 2.66, f = 15kHz, M = 0.3, Test Configuration 11.

18t
cn

tm

z3

I--

a_ 0

,<

LLI

>

-5-

uJ

rT

-10 --

-15

-20

-25

-30 _

14.975

5

0-

-5 --

-10 -

-15 -

-20 -

-25

11

,i#,_..-_-----_ TOTAL ACOUSTIC ENERGY

z BAND

DISCRETE TONE --------.mAMPLITUDE LEVEL

I I I I I I I

13 15 17

FREQUENCY, kHz

a) SPECTRUM FOR f= 15kHz, BW=50Hz

19

r" APPROXIMATE

/ RANDOM

_ A/NOISE LEVEL

! i

I I I I i !

15.0

FREQUENCY, kHz

b) SPECTRUM FOR f= 15kHz, BW=0.25Hz

15.025

Figure 70 -- Far Field Microphone Spectra Obtained with Different Bandwidths for

ec = 50 °, X/R o -- 2.66, M =0.3, Test Configuration 11.

182
cn

u..[

C)

:3

I,-

,,_1

rl

<

LtJ

o

I..U

rr

-5

-10

5

0--

-5

-10 B

-15 -

-20

-25

6

DISCRETE TONE •

AMPLITUDE LEVEL

TOTAL ACOUSTIC

ENERGY IN

9975-10 025kHz BAND

J..... i I i I i

8 10 12 14

FREQUENCY, kHz

c) SPECTRUM FOR f= 10kHz, BW=50Hz

-15 -

/-- APPROXIMATE RANDOM

/ NOISE LEVEL

-25

-30 I ! t I

9.975 10.0 10.025

FREQUENCY, kHz

d) SPECTRUM FOR f-- 10kHz, BW=025Hz

Figure 70 -- Continued.

183
I::I3

1D

u5

d3

E3

l,-

d

(3..

,<

LLI

>- 0

t,-

'1

LLI

rr -5

-5

-10

-15

-20

-25

-30

__

B

DISCRETE TONE

AMPLITUDE LEVEL

TOTAL ACOUSTIC ENERGY IN

4 975-5.025kHz BAND

l 1 1 I ......

3 5 7

FREQUENCY, kHz

e) SPECTRUM FOR f = 5kHz, BW= 50Hz

9

-10

-15

-20

-25

-30

-35

4.975

I I

APPROXIMATE RANDok,

I

I , I I

5.0

FREQUENCY, kHz

f) SPECTRUM FOR f : 5kHz, BW = 0.25Hz

I 1 1

5.025

Figure 70 -- Concluded.

184
GO

'o

z

o

z

LU

I--

F-

<

LLJ

Z

o

t--

LU

t--

LU

CE

O

CO

C3

3O

20--

i

10--

i

0--

-1

0

ec

0 4O

rII 50

9O

120

I I i I I I I

5 15 20

0L

FREQUENCY, kHz

Figure 71 -- Discrete Tone Attenuation as a Function of Frequency and Radiation

Angle for X/R o = 2.66, M = 0.3, BW - 0.25Hz, Test Configuration 11.

185
Y

t

h

X 2

•q_----_-- X 0 _! ._----- X 3

M

\

. • B SHEAR LAYER

Pl " 01 -Om _

0

Figure 72 -- Geometry for Angle Correction Calculation.

186
!

SIGNAL

GENERATOR

M %%

M=O

V{t- A a/f)

AMPLIFIER }

CORRELATOR

PRESSURE SIGNAL,

P(t-(_a + A s)/f)

SHEAR

LAYER

V2= V 2 (t- (A+ _2)/f)

Vl= Vl(t-iA* _'÷ ,-_1) /f)

A =_a+ As*,_p

i °

Fig. 73 -- Schematic Showing Phase Lag Between Signal Generator•

and Far-Field Microphone Output,

187
I, Report No. 2. Government AccesSion No.

NASA CR-3371

4. Title and Subtitle

REFRACTION AND SCATTERING OF SOUND BY A SHEAR LAYER

7. Author(s)

Robert H. Schlinker and Roy K. Amiet

g Performing Organization Name and Addre_

United Technologies Research Center

East Hartford, Connecticut 06108

12 Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546

3. Recipient's Catalog No.

5. Report Date

December 1980

6. Performing Organization Code

8. Performing Organ;zation Report No.

10, Work Unit No.

'11. Contract or Grant No.

NASl-15339

13, Type of Report and Period Covered

Contractor Report

14. Sponsoring Agency Code

; 15 _pplementary Notes

Langley Technical Monitor:

Final Report

James C. Yu

16 Abstract

A theoretical and experimental study was conducted to determine the angle and amplitude

changes for acoustic waves refracted by a circular open-jet shear layer. The generalized refraction theory was assessed experimentally for on-axis and off-axis acoustic

source locations as source frequency varied from i kHz to i0 kHz and free stream Mach

number varied from 0.I to 0.4. Angle and amplitude changes across the shear layer

showed good agreement with theory. Experiments confirmed that the refraction theory

is independent of shear layer thickness, acoustic source frequency, and source type.

A generalized theory is, thus, availg01e for correcting far field noise data acquired

in open-jet test facilities.

A theoretical and experimental study was also conducted to investigate the effect of

discrete tone scattering by the open-jet turbulent shear layer. Scattering effects

were investigated over the same Mach number range as frequency varied from 5 kHz to

15 kHz. Attenuation of discrete tone amplitude and tone boradening were measured as a

function of acoustic source position and radiation angle. Scattering was found to be

stronger at angles close to the open jet axis than at 9°o . In addition, scattering

becomes stronger as the acoustic source position shifts downstream. Thus, corrections

for discrete tone amplitude changes across the shear layer must account for both

refraction and scattering amplitude changes. A scattering analysis provided an estimate

of the onset of discrete tone scattering.

17 Key_Words(Suggested by Author(s))

Refraction of Sound

Scattering of Sound

Sound Propagation Through Shear Layer

Shear Layers

Turbulence Scattering

19. Security Oa_if, (of this re_rtl 20. Security Cta_if. (of this _ge)

J , ,

Unclassified :Unclasszfled

18. Distribution Statement

Unclassified - Unlimited

21. No. of Pages

189

Subject Category 71

22. Price

A09

For sale by the National Technical Information Service, Springfield, Viri_inia 22]6!

NASA-Langl ey, 1980