Canadian research in aerodynamic noise

faculteit der luchIvaart· en Ruimtevaarttac:hnlP Kluyverweg 1

2629 HS Dalft

.TTJLY; 1958

BY

B. ETKIN andH. S. RIBNER

CANADIAN RESEARCH IN AERODYNAMIC NOISE j

'

.

BY

B. ETKIN and H. S. RIBNER

This review consists of material assembled for presentation at the "Jet Engines and Noise" session of the lCAS meeting in Madrid, Spain, September 1958. Support was provided by the Defence Research

Board of Canada under DRB Grant No. 9551-02, and by the United States Air Force under Contract No. AF 49 (638) -249, the latter

. monitored by AF Office of Scientific Research of the A ir Research and

SUMMARY

Canadian research on flow noise and some aspects of the aircraft noise problem is described . The work was done at the Defence Research Board, the University of Toronto Institute of Aerophysics and A. V. Roe (Canada) Ltd.

Specific experimental and/ or theoretical investigations include: Aeolian Tones; Boundary Layer Noise (rigid wall and flexible wall); Effects of Boundary Layers and Noise on Aircraft Structures; Distribution of Noise Sources Along a Jet; Ground Run-up Mufflers; Transmission of Sound from, and Acoustic Energy Flow in, a Moving Medium; Sound Generated by Interaction of a Vortex with a Shock Wave.

'J

INTRODUCTION A .1

A.2

JET NOISE

Strength Distribution of Noise Sources Along a Jet Transmission of Sound to or from a M oving Medium Acoustic Energy Flow in a Moving Medium

Sound Generated by Interaction of a Single Vortex with a Shock Wave

Ground Mufflers (UTIA Research)

Ground Mufflers (Orenda Engines Research) BOUNDARY LAYER NOISE

1 1 1 2 2 3 4 5 5 Rigid Wall: Rotating Cylinder Investigation 5 Boundary Layer N oise Theory for Flexible Skin 7 Boundary Layer Noise Experiments with F lexible Skin 8 A.3 AEOLIAN TONES

Theory

Measurements of Intensity and Frequency Measurements of the Pressure

MeasuremenL of the 2-point Correlations Measurement of the Forces

Comparison of Theory and Experiment A.4 UNDERWATER NOISE

A.5 NOISE INDUCED F A TIG UE Effect of Boundary-Layer Noise Effect of Jet Noise

REFERENCES FIG URES Alto A44

8 9 9 10 10 10 11 11 11 11 12 14

( 1 ) INTRODUCTION

This paper describes fundamental and applied research hat has been conducted in Canada during the last few y ars on flow noise, and on some aspects of the aircraft noise problem. The work has been carried out at the Defence Research Board, he Umversity of Toron 0 Institute of Aerophysics. and A . V. Roe (Canada) Ltd.

Financial support for the work at the Institute of Aerophysics has come from the Defence Research Board, the United States A i Forc • and A.V. Roe.

The research described embraces both fundamen al and applied. and both theoretical and experimental investigations. These relate to the generation of sound by jets. wakes and boundary layers;

o he suppression and reduction of such sound; and to lts effects upon structures.

A.I - Jet Noise

along a Jet

Progress in the development of muffle s for jet noise has proceeded largely by empiricism, (cf Ref. Al) guided to a certain extent by LighthiU's basic theory (Refs. A2, A3), Cu io slye ough. it is only recently that the theory has been applied (in different ways. R fs. A4, A5; see also Ref. A6) to assess the distribution of noise-source strength along a jet; yet this information is basic to an under-standing of jet muffler action.

In the Canadian study (Ref. A5) Lighthill's theory is applied to the two regions of 'similar ' profiles in a jet. The analysl. refers to the nois power emitted by a 's lice I of jet (section between two adjace t

planes normal to the axis) as a function of the d'stance x of the slice from the nozzle. It is found that this power is essentially eons an with x: in the initial mixing region (xolaw). then farther do rvnstream (about 8 or 10 diameters from the nozzle) faUs off extremely fast (x,·7 law or faster) in the fully developed jet (Fig. Al). Because of this striking attenuation of strength with distanee. it is concluded ha the mixing region produces the bulk of the noise and must dominate in muffler behaviour; conversely the 'fat' part of the jet must eontribute mueh less to the total noise power than is commonly supposed.

Powell's experiments (Ref, A 7) on the effects of nozzle velocity p ofile on total noise power can thereby be interpreted

qualïatively. The behaviour of multiple-nozzl or corrugated mufflers, both as to overall quieting and as to frequency-shifting. are also

interpreted in the light of the res ults . Because the noise is eoncentrated near the nozzle (Fig. A-I) the possibility emerges that sueh mufflers may be improved without serious thrust loss by the addi ion of a sound-attenuating shroud (Fig. A2).

Transmission of Sound to or from a Moving Medium

The details of the transmission of noise from a high speed jet "to the surroundi.ng quiescent air are not known. Lighthill (Refs. A2, A3) circumvents the details in terms of his Mach number factors for 'self-propelled' noise sources (his analysis does not imply con-vection); however, the factors are open to sus picion in their prediction of infinite energy radiation at M = 1. Thus some examination of the mechanism of the sound transmission is in order, starting with a much simpler case. The problem of the transmission of plane sound waves to or from a moving stream has been investigated in R ef. A 8. The waves are specified as originating in air at rest and imp inging

obliquely on a plane interface with a moving stream. The analysis and the physical interpretation are both simplified by using axes moving with the ripple that must develop in the interface. The acoustic problem is thus changed into th~ aerodynamic problem of the flows above and below a wavy wall - the rippled interface. (Fig. A3).

In this view the angles of incidence, reflection, and refraction are regarded as Mach angles in two supersonic streams. The velocity difference between these two streams is just the veloeity of the original moving stream. The known angle of incidence thereby

leads immediately to an equal angle of reflection and a simply-related angle of refraction (Fig. A4). The angle of refraction is imaginary when the associé):ted velocity • calculated by the velocity-difference rule, is subsonic. This is a condition of total reflection .

The amplitude relations (coefficients of reflection and transmission) are evaluated in closed form. In a graph three zones can be distinguished in the plane of angle of incidence v. Mach number of the moving medium: ordinary reflection and transmission, total reflection, and amplified reflection and transmission (Fig. A5).

lncluded are three loci of infinite reflection: i. e., self-excited waves. The energy balance is examined, and the source of amplification is concluded to be the energy of the moving stream.

Acoustic Energy Flow in a Moving Medium

It was remarked i.n the last' section that Lighthill's Mach number factors for the moving sources in a jet lead to the unacceptable prediction of infinite energy radiation at a jet Mach number of unity. Thus the whole question of acoustic energy flow in a moving stream must come under scrütiny..

It is known thát both acoustic energy density and energy flow are modified by motion of the medium. The classical relation, acoustic energy flo~ equals pressure times velocity • applies only

when the medium is at rest. The derivation of a corresponding relation for"a moving medium offers some difficulty. Comparison has been made (Ref. A9) of similarities and discrepancies in the formulas of

. . - ; 0 ot,. ó.

( 3 )

three investigators (Refs. AS, AlO. A 11) in order to infer a corr ct

formulation.

A convenient form of such a formu tion for pla sound

waves is found to be: energy densit

~ energy flow/unit area =

€

~

(area taken...L energy flow)

(a ve to )

This formalism is that of Ref. AlO; that of Ref. AS is compa ible.

and that of Ref. A 11 errs only by a multiplicati constant.

These formulas for a moving stream can be illustrated with the aid of Fig. A 6. The planes of constant phase move ith t e

'phase velocity' V f different from tht. ordinary speed of sound c. The energy flows with the tray velocity' Vs' F·g. A'? shows ow. for a given wave pattern. progressive variation of the stream velocity can

change the 'linear theory' acoustic energy density - Vlhich is proportional ·to Vf - from positive through zero to negative. with corresponding

changes in the energy flow. For the particular case of zero acoustic energy density and energy flow the convec ion has cancelled out the

propagation so that the sound waves are stationary; they are the familiar

"Mach wave

si'

of steady supersonic flow.

Sound Gmerated by Interaction of a Single Vorte

It is well known that with the appearance of shock waves in a supersonic jet the noise emission is greatly increased. xceeding

the uS law. (cf. Ref. A 1). Theoretical studies have emphasized on the one hand a resonance effect (Ref. A 12). and on the 0 er and the

interaction of convected turbulence kreated by he mixing) with the shock waves (Refs. Al3. A14. A15).

\

The turbulence analyses do no provlde a physical pictur of what happens when a localized "eddy" passes t rough a shock wave 0 To simulate such a situation Hollingsworth and Ric ards made a

schlieren study of the passage of a single columnar vortex 'broadside I through a shock wave (Ref. A 16) and also presented an heuristic theory

(Ref. A 1 '1). The work to be discussed (Ref. AlS) is an attempt at a quantitative thèo:ry of such an interaction.

The analysis exploits the concept t at a vortex can be

de,Q0mposed by Fourier methods into plane shear waves disposed

~jdia.,1:ly .. like the spokes of a wheel (Fig. AB). Each of the shear waves

intéra,cts .. with the shock to produce a refracted shear wave and a plane sound wave according to previous work (Hef'; A 13) (Figs 0 A 9. AlO).

The plane sound waves emanate.· with varying angles. all along the shock

front.

The plane waves possess an envelope that is essentially a growing cylindrical sound wave partly cut off by the shock (Fig. AIO);

that is. the pressure pattern peaks sharply at a cylindrical front (Fig,

A 11). The cylindrical wave i.s centered at the transmiUed (and modified)

vortex co e and its peak ~ttenuates inversely as the square root of the growing radius, The strength varies smoothly around the arc. from compression at one shock intersec ion to rarefaction at the other general

shock intersection. Thes calculated characteristics appear to conform

in a general way with a schlieren photograph of the interaction process obtained in Ref. A 16 .

Ground Mufflers (UTIA Resear ch)

One means of muffling a jet on the ground is to expand it in

a diffuser. The small-di.am ter hi.gh-velocity jet is thereby converted

into one having a large diameter and a low velocity , The eighth-power

law indicates t at the final jet will produce much less noise than the original one. Of course. the noise gen rated inside the diffuser may be

very intense. and must be absorbed by a s uitable acoustic treatment,

Since high pressure-recovery in the diffuser is not a factor • the

appli-cation of short wide-angl diffusers appears attractive. One investigation

along these lines was reported by Geen and Lilley (Ref, A 19) who

found that the diffuser would run fuU if screens we re used to provide

enough internal resistance, T e UTIA investigation was independently

conceived. although informati.on about the Green-Lilley w ork was

received during t e course of the research. The UTIA expe riment (Ref, A20) differed in on s'gnificant respect from that carried out at Cranfield. This difference was the inclusion of air augme tation in the model con

-figuration (R f, A 12~. This feature mig t be necessary in a full-scale

rnuffler for cooling purposes .

After a numb r of trials. satisfactory aerodynamic pe

r-formance was achieved wi two s creens (/j,

'p

I

~ = 3.J) as shown in

Fig. A 13. I can be se en that the diffuser did achieve the objective of

producing a fai Iy uni or~ low-velocity exit jet, The induced flow

achieved was 13,40/0 of'the jet flow. A theoretical analysis given in Ref.

A20 indicates that the velocity profile at the diffuser inlet is an important

factor in determining t e magnitude of the induced flow. and that a longer mixing length would incr ase it.

The acoustic performance of the model muffler tested was

poor. in that more noise was generated with it than without it. This is

attribut d to inadequate acoustic design of the muffler walls. The

Qreen-Lilley experiment was quite successful in this regard.

On the basis of the work cited. it would appear that wide

angle diffusers could be developed into successful mufflers,

:.:~- \

,~. ~

·oi

.,

\.

( 5 )

Ground Mufflers (Orends. Engines Research)

Orenda Engipes Ltd. undertook the development of a light

portable ground muifler which would be suitable for use with

after-burning engines and which would provide a moderate attenuation. The

program began with experimmts on models. and progressed to full

-scale testing of the configuration which evolved Ref. A21~. The

muffler tested is shown sch matically in Fig. A 14. It consists sse

-tia ly of a diffuser. which contains hollo baffles through hieh outside air is drawn into the flow. The resistance of the baffles is such that the flow remains attached to the walls. In this respect it is similar to th screened diffuser ~escribed above.

Cooting is aGcomplished both by the air drawn through th

baffl

s,

and by the ai.r aspirated through the inl t. which is abou.t 60% greater in diameter than the jet exit. No deterioration of the muffler was observed af ter running with the afterburner lito

The diffusion achieved is s ufficient. on the basis of

Lighthill's AV 8

law

.

to produce very large reductions (of the order of 30 db.) in the noise' of the emergent jet. The actual reductions

achieved are of the order of 15 db. at 100 ft. radius. and 450 from the

jet axis. A typical- sound polar is shown in Fig. A 15. It shows the

characteristic field of the unmuffled jet engine and the reduction

achi ved by the muffler - the peak SPL is reduced from 139 db to 127

db. The effect of the muffler on total sound power is shown in Fig. A 16 ,

-the power level is reduced by 9,3 db, in th afterburn'ng condition.

Additional development of the muffler is xpected 0 produce further

gains in performance.

A ,2 - Boundary Layer ~ oise 'I

Rigid Wall: Rotating Cylinder Investigation

The aerodyn~~ic noise radiated by a turbulen boundary layer flowing over a rigiC\ surface (one t at cannot add to t e sound by vibrating) is known to be relatively weak.; thus it is easily ma..c:;ked by

other noises» particuia ly in a wind-tunnel. An experimental

arrange-ment that avoids this mas~ing by other flow-produced noises utiliz s the turbulent boundary l~y r on a rotating cylinder. An investigation

of the noise produced by sllch a boundary lay r has been under way for

some time at UTIA. conducted by L.N. Wilson.

The rotating-cylinder arrangeme t is shown in Fig. A17.

T e cylinder is a thick-walled tube of aluminum 6" in diameter and 18" long. mounted in journal betrings. It is belt driven and has been run

at speeds up to 16.000 rpm. The heavy s upporting structure (Fig. A 17) was enclosed i a heavy plywood sound-isolating box fiU d wi h sand for

the tests reported below. The cylinder assembly is installed in a reverberant chamber that can b calibrated for measurements of total

~Fig. A 18) exhibits a number of sharp peaks projecting above a broad-band continuous spectrum. These peaks occur at multiples of the rotation frequency. Cylinder unbalance and slight out-of-roundness would appear to account for such armonic peaks. These effects and bearing imperfections , can lead to rigid-body modes of motion of the

cylinder.

The sound pressures asBociated with these modes ('bearing noise ') would be expected to be correlated over large areas of the

cylinder whereas that from boundary lay r turbulence would be cor -related over relatively small areas. the size of an "eddy". T here-fore two microp ones were placed close together near the cylinder surface and on -half the square of the difference between the signals was measured. T e co related 'bearing noise' should then cancel out, leaving onl t e uncorrelated noise, which is presumably the true boundary layer noise.

Suc wo-microphone (anti-correlation) near -field

measurements are s own in Fig. A 18 together wit single microphone measuremen s. One curve refers to t e cylinder in t e smooth

condition. using tw 0 microp ones and t e others to the cylinder

roughened wit aluminum 0 ide particles of about .007" to .009"

heig t ( o. 80 A lundum grains) using one and two microphones. The particles were sprayed on the surface in a shellac ve icle. It is clear that roughening raises t e levels substantially, as might be expected. The wide-band noise between the harmonic peaks can be identified as tru oundary layer noise because of the agr ement tere 0 t e singl and double -rnicrophone curves. The peaks, which

appear only on the single-microp one curve, are the e traneous "bearing noise" .

T e roug - all curve 0 uncorrelated pressure (true

boundary layer nois ) Fig. AlS, has been replotted in Fig.A19 on the basis of db/cycl vs. nondirnensional frequency

fD

/

u

(Strouhal number). This and other curves obtained for speeds from 7000 to

13000 rpm have been adjusted to t e same effective speed (10. 000 rpm) and sup rposed.

The relation p2 iI"'V U4 assumed in the adjustment is confirmed by the collapse of the points to a single curve in Fig. A 19. Cross -plots of .db

1

cycle vs. U for fixed fD

Iu

further confirm a U4 law. Apparently, then, the near-field boundary-layer noise is essentially the ydrodynamic (i. e. incompressible) 2ressure field associated locally with the eddying flow. for which p2

=

P 2

U~.

­

Blokhintsev. w 0 as discussed such pressure fields, calls them

( '1 )

Bounda Theory for Flexible Skin

The w ak noise' radiated by turbulent flow past a rigid wall -. g .• the ro ating cylind r described above - is gr atly augmented if the all can vibrat • lik the skin of an airplane. At high subsonic

sp eds such skin vi ration is. in fact, reported to be the major source

of noise within th aircraft (Ref. A23).

A heoretical study has been made ~Ref. A24). The skin

vibration is consider d to be e cited by the fluctuating hydrodynamic

r ssures in the turbul nt boundary layer. These 'pseudo-sound'

pr ssures gr atl exceed th associated compressibly-generated

pressur s that are radiated as sound in the rigid-wall case; this

accounts fo the amplified adiation provided by the sounding-board

f ect of a lexibl wall.

The fluc uating pseudo-sound pressure distribution can be

d compos d y Fouri r methods into a pattern of sinusoidal pressure

waves wit various angl s of yaw (Fig. A20). The pattern is idealized

as rigid a d mo i g u i ormly by convection (the pressure fluctuatmn

at a y po' t is t us caus d by the motion). A rUl1D:ing ripple in the skin

0110'118 und rn ath each wa e. and the noise is ultimately due to these

rippl s. T e acoustic ffec s of the running ripples have been deter-min d or an infini e plan s eet. upersonically moving ripples

radiat t 0 g sound in the for m of Mach waves ~Fig. A21); subsonically

mo mg rippl s g nerate p.o sound unl ss the sheet is finite (or the

ripples unsteady).

For an airplane uselage. howeve • t e infinite plate is

rep aced b a succession 0 fini e pan Is. uccessive panels are

considered to be statistically independent becaus the running waves ar mte rup d y he frames and stringers supporti g the skin. Mor 0 • multipl r flections a the frames and stringers convert

h ning waves into standing waves. An assumption is used to link

wo kinds of waves» and is I ads to provisional estimations of noise Ie ls wi hin aircraft. On this basis the mean square noise

p essure is predicted to vary as

US

b

Yh

5

ç

for t in boundary

laye • changing progressi ely to ~E/h

'7

for thick layers or high

speeds (U

=

flig t speed.

S

=

boundary iayer thickness. h ;;;

p~il z.

thickness. f( = pan 1 damping coeffici nt) . A common factor

.pit//Jp

as been omitted or simplicity from both formulas where

,0

=

interior

air density. ~

=

exterior air density. ~p

=

pan I density.

It is cl ar that increasing the panel damping

'I

is a power

-fu.l means for reducing the noise. For the fixed value

1'/

= .01 the noise

1 el ormulas ar illustrated in Figs. A22 and A23. Shown also on

Fig. A2 are some experimental data for actual aircraft. adjust~d to aJ?ply to the sam pressure altitude. The close agreement with;the

~

=

10" curv is p rhaps fortuitous i.ri view of the uncertain Q-Mrespo

nd-ence 0 the parameters (e. g.

'1

and

t5

)

and the appro imations in

Boundary Layer N oise E

An acousti ally quieted air duct facility has been construeted at the Instïute of Aerop ysics. University of Toronto (UTIA) for the purpose of in estigating noise generated by turbulent flow past a

flexible panel; this is essentially the "boundary layer noise'1 the theory of

which was discussed in the last section. In t is duet the panel is to be

fitted in a cutout portion of one wall flash wi h the inner surface . The facility is basically an open circuit acoustically lined

wind tunnel with a 33 foot duct ection (Figs. A23. A24). Any one of

four interchangeable sections can be used. with respective inside cross

sections 12" wide and 8", 4". 2" or 1" deep to provide fully developed turbulent channel flow befor re~aching the test section . The test

section passeS through a reverberation chamber for measurement of

noise power.

Maximum air speed with the 10 h blower {4" duct) is 200

ps. etails of the design and aerodynamic performance - e. g . • velocity profiles and pressure gradien s - ar given in Ref. A24.

A set of exploratory noise measurements have been made

with a steel pan 1 12" x 12" x 0.002" installed horizontally in the 8"

duct. No grea care was taken, and th t in panel as finally tested

(crudely s pport d in a wooden frame) contained numerO\lS irregularities or wrinkl s in t e surface . Sound pressure 1 el readings were taken

at heights z :: 1 1/2", 6'1,1211

.3011

.36" and 42" vertically above the

centre of the pan 1. The eadings in db (re. 0002 microbar) are

plotted vs. air speed U a e duc inlet in Fig. A26. The curves seem l).ot tb b inconsistent wi h the theo y {Ref. A 2 ) which pre di cts a U5

iaw at low speeds with a transition to a U3 law at high speeds. The

th ory is inadequat. owever. in Us present form, to predict quanti -tetively the position of the observed kn e of the curve.

Tentati.ve measurements ha e also been made on a second .002" steel panel carefully mounted under tension in a machined steel

frame and free of VI" inkles. Spec ra and overall pressure levels for

various air speeds are given i Fig. A27. The overall levels approximate a U 5 law. I is thought that the absence of a transition to a lower power

may be due to the initial tension in the panel: the increased effective stiffness simulates t e properties of a thicker panel wit out tension, for whi.ch the transition point t eoretically occurs at a higher air speed.

A. 3 - Aeolian Ton s

One 0 the goals of research in flow noise has been the

attainment of quantitative experimental verification of the theory. The

classical phenomenon of Aeolian Tones, being relatively simple. offers an attractive possibility for such a verification, and therefore has

( 9 )

the almost-pure notes emitted by a wire or circular cylinder placed in

an airstream; they are closely associated with the periodic shedding of

vortices into the wake.

A theoretical and experimental investigation was started at the UTIA in 1955 {Refs. A25, A26, A27. A28). Initially it comprised an adaptation of Lighthill's theory (Ref. A2) for application to the case

in hand, and some measurements.of the intensity and frequency of the radiated sound. It was soon found that there was insufficient information

available on the unsteady pressures and forces acting on a cylinder to

provide a good quanti a ive c eck on the t eory. The program therefore continued with measurements of t e pressures. the two-point correlations of the pressur<e, and the forces. Some details of the t eoretical and

experimental work follow.

Theory - Lighthill's equations (Ref. A2) could not be applied directly

to the problem because of the presence of asolid boundary in the flow (the surface of the cylinder). The equations were adapted to apply to t is case by imagining that the solid cylinder is replaced by a column of

fluid which is maintained at rest by a suitable distribution of body forces.

The radiated sound field is then found to be that of a distribution of

quadrupole sources associated wi h the turbulence in the wake, and of

dipole sources associated with the body forces. The latter áre uniquely

determined by the surface pressures. This result is exactly the same as that obtained by application of Curle 's theory (Ref. A29). It was

assumed t at in t e experiments the quadrupole sound would be negligible

compared to that from t e dipoles at the cylinder surface . The theory then predicts that the principal radiation is a note at the fundamental frequency of t e wake, radiating as a dipole with its axis cross-stream. This note is associa ed with the alternating lift force on the cylinder . A second note. at double the frequency, and associated with the drag fluctuations ,-radiates as ~ dipole with axis in the stream direction'. The

intensity of the sound in the ar field varies approximately as the sixth

power of the sp ed. a d depends upon the magnitudes of the fluc uating

o ces and on their correlation along the length of the cylinder. No th ory exists for predicting these forces and correlations .

Measurements of Intensity and Frequency

The experiments were carried out in the U TIA subsonic wind tunnel. A number of cylinders were used, varying from 1/8 to

1 3/4 inches in diameter, and the speed range was from about 100 fps

to 225 fps. The results of the frequency measurements are shown in

Fig. A 28. Theyare in general agreement with results obtained by other

investigators.

Intensity measurements were made with the microphone both inside and outside the tunnel. A typical spectrum with the microphone

upstream of the cylinder is shown in Fig. A29. The sound from the cylinder is seen to be significantly louder than the tunnel background

and t . peaks at t e fundamen al and second harmonic frequencies are

learly evident. I terpretation of these in ensity measurements is

somewhat difficult, because of an unknown reverberation effect.

However, the order of magnitude is given by these measurements. Measuremen s of the Pressure

The pressur fluctuations at th cylind r surface we re

measured b mean& of a co denser microphone installed internally.

Typical results are·shown in Figs. A30. A3!, A 32. These show the

nature and magnitude of he rms pr ssure, and ow it varies around

. he circumference. The fundamental component dominates at the sides.

and the second harmonic at the back. This is consistent with the presence of a lift at t e fundamental frequency, and a drag at double

tha t requency. The cu e labe lled "theory" in Fig. A 32 was obtained .

from a simple potential-theory model of t e flow incorporating a p riodic circulation (Ref. A26). It gives the shape of the pressure

curves wit rather surprislng agreement.

Measurem e 2-point Co elations

A series of measuremen s were made of the correlations

of the pressure along the cylinde . -Condenser microphones were used

as pr ssure ransducers, and the quarter-square method was used to obtain the correlation coe ficients. A typi al result. with the holes at

900 to he streani. is s own in Fig. A33. The correlation does not fall 0 f to zero at larg ole separatio s as was expected. Further experimentation is re uired to e plain t is r sult. Until such an explan

-ation is fort coming, it as bee tentatively assumed that the effect is caused by an unknown ex raneous influence. (Possibly a tunnel wall

effect). The correlation curve approp iate to free-field conditions has th refore been as urn d to be giv n by he one shown dotted in Fig. A 33.

Tearea under his curve defines t e t'! fective correlation length. Fig. ~34 s ows ow t is correlatio length varies wit Reynolds number. Measureme

A s rain gage transducer has been designed and built for t11:e. m asurement of the forces acting on a short section of the .

c linder ~one diameter in lengt ). t is shown in Fig. A 35. The transduc~r has b en found to a e satisfactory linearity. sens it iv ity •

and re~lliäbility. In order to calibrate i over tewhole frequency . rang i.f~ been Il cessa y to use bot mec anical and acoustical

means

tö

·supply e calibra ing forces. T e acoustical loading required t e developmen of a special cali ration device.

. .

' . Fig. A36 s OViS the results obtained so ar with this instru-m

n

.

'

It cà,n be seen at t ey are in fair agreement with those

estirrtated from t e pressure distributions, and with those of Fhillips,

obtai.ned at a much low .r Reynolds number. The results of Bingham

,..1

< 11 )

et al (Ref. A3l) are in strong disagreement, however. Unpublished resu ts obtained by Gerrard at Manchester are also in dis agreement

wUh those shown here. Gerrard's experiments we re similar to

McGregor's (Re. A26), and this disagreement has not yet been explained.

Comparison of Theory and Experiment

T e calculated values of the sound pressure in the far field are compared wi h m asured values in Fig. A37. T e data is presented in t e form p* as a function of Reynolds number. p* is a non-dimensional

sound press ure given by

p* :::

4JZ

p

0 0

..L

PU

3

_J[d

w er p is t e rms sound pressure. _{a o} is the speed of sound in the undisturbed air,

p

is t e d nsi y, U is the speed, r is the distance from the cylinder to t e microphone. and 1 and d are cylinder length and diameter. The calculated value is given by

0),

(CL)

rm

s

St

w

À

is the effective correla ion length in diams. (C

d

_rms is the ros valu of the lif coe fkient. and St is t Strouhal number. The

values of these quanti. ies IUsed for the calculated curve are those obtained in he UTIA meas urem nts and hose given by Phillips (R~ef. ASO). T e intensity measurements s ow are t ose of Keefe. Gerrard. and Phi , ips.

A.4 - Underwater Noise

~ udies of sound propaga ion in wa er ha e been carried out at t e Pac' ie Naval Laboratory 0 the Defençe Research Board-. These

hav in olved ome investigations of flow noise, particularly in relation to the use of ydrophones being towed thr ugtn tb;e'water. The noise

associa ed wi th wakes of connecting cables was ound to be important.

tudi save also b en made of t e oise roduced by the flow ov r the ydrophone itself, and 0 t e noise recorded by one ydrophone mounted in t e wak of ano er .

A .5 - Nois lnduced Fatigu

Effect of Boundary-Layer Noise

A P eviou section discussed how he turbulent boundary lay r co ering muc of an airplane in flight can give rise to substantial nois in t e int riol' by exciting vibration in the skin. The question has been raised wh her th skin ,stresses associa ed wi h these vibrations

are suf icient at he high I' speeds to bring in the possibility of fatigue

failure. A heol'etical inv stigation of thes skin stresses was there-fore undel' aken a UTIA under the sponsorship of A 1'0 Aircraft.

For a 1 hu ver ick boundary lay rs the analysis was

based on the idealized boundary-layer oise theory discussed earlier (Re '. A23). The procedures were modified and adapted to yield a

tentative expression for t e mean square stress in the skin as a function of flight speed. boundary layer hickness. panel thickness, panel

fundamental r sonan f e u ncy. damping coefficient. etc. A numerical

exampl was worked ou fo .032" thick dural skin panels of three , sizes (fundam ntal frequ nCl s 37.5. 150. and 600 cps .• respectively).

in which th flig speed was varie,d rom 400 fps to infinity with

neglect of air damping and certain idealizations of the boundary layer. The boundary layer hickness was held constant at about 4 inches.

T ms Si ress for these cases was found to be nearly

constant ov r this entire speed range. showing a flat maximum in the rang 700 to 1100 L p.s. (see Fig. A38). The maximum was far below typical 'i 'inite life' endurance limi s for dural type aHoy •

(e. g. 10.000 p. s. i. for an unfavorable static loading). never exceeding

170 p. s. i. A supplementary study for extremely thick boundary layers (turbul nce scal comparabl wi pa el dimensions) was made by a

on -dim nsional approac developed rom Mil Si ideas (Ref. A3 ).

Indications of rms stress exceeding 10,000 psi were found for boundary layers several feet thick at supersonic speeds.

Effect 0 Jet Noise

Experimental and theoretical investigations of

noise-induced fatigue of built-up structures and simple flat panels have been

ndertaken at Avro Aircraft. The experimental work has been

directed bot at obtaining ad hoc fixes. and at verifying t e theoretical calculations. T e t eoretical work s been directed at predicting the life of flat panels subjected to plane waves. normally incident.

The esting .as been carried out in a specially designed enclosure, using a siren to provide aGoustic pressures of the order of

170 db. The tests conduct d on built-up structures indicated that the

failures tended to occur in the supporting structure, at joints in the

skins throug ri et lines (see Fig. A39). Gene rally , effective means of increasing the life were found to be: reduction of panel size.

applica ion of doublers (see Fig. A 44) and introduction of additional damping.

T e theoretical work (Ref. A34) has indicated that thin

flat panels subjected to intense acoustic loading win achieve large eno!lgh amplitudes t at both "plate-like" and "membrane-like" dis-placements and stresses coexist. The res ult is a stress -time curve

such as that shown in Fig. A40(a). A non-linear theory has been developed to describe this phenomenon (Fig. A40(b».

Comparison of Figs. A40(a) and (b) shows that the

( 13 )

eomparison has been made of the ealculated peak-to-peak stress

interval with measured values. The result is shown on F ig. A41, and the agreement is seen to be very good. The eomparison of measured and predieted fundamental panel frequeney is not so good, however

(Fig. A42).

The theory is applied to prediet the fatigue life of flat panels subjeeted to periodie loading - an example is show n in Fig. A43. No experimental eonfirmation of these predietions is yet

available. A result of some importanee is the predietion that the use of a damping-tape plus edge doubler system (Fig. A44) ean inerease the

'... _.... r-,:, ~ ... .,. Al A2 A3 A4 A5 A6 A7 A8 A9 Fowell, L.R . Korbacher. G.K. Lighthill. M.J. Lighthill, M .J. anders,

.

n

.

R ibner, H. S . Dyer. Ira Powell. Alan Ribner, HS. Ribner, H.S. AlO Blokhintsev. D. L. All Johnson, W.R .• Lapor~e, O. REFERENCES

" A Review of Aerodynamic Noise, UTIA Rev. No. 8, July, 1955

"On Sound Generated Aerodynamically. Part I - General Theory". Proc. Roy.

oc. A. Vol. 211, pp 564-587. 1952

"On Sound Generated AerodynamicaHy Part II - Turbulence as a Source of

ound", Proc. Roy. Soc. A. Vol. 222,

pp 1-32, 1954

"Turbulence N oise Created by Jet Engines". General Electric Lab. Rep.

No. 57GL222, Gen. Elec. Co .• July 1,

1957

"On the Strength Distribution of Noise

Sources along a Jet", UTIA Rep. No.

51. Apr il 1958

"Distribution of Sound Sources in a Jet Stream", Jour. Acous. Soc. Arrer.

{to be published)

"The Influence of the Exit Velocity

Profile on the Noise of a Jet", Aero. Quart .• Vol. IV, Feb. 1954

"Reflection, Transmission and Amplüication of Sound by a Moving Medium", Jour. Acous. Soc. AJrer. ,

Vol. 29. o. 4. pp 435 -441, April 1~57 "Note on Energy Flow in a Moving

Medium", UTIA TN No. 21, April 1958

"Acoustics of a Nonhomogeneous Moving Medium", NACA TM 1399, Feb. 1956,

(translation of 1946 Russian paper)

"The Interaction of Plane and

Cylind-rical Sound Waves w ith a Stationary Shock Wave", Univ. of Mich. Tech. Rep. 2539 -8-T (Project 2539, Dept. of Navy, ONR Contract No.

A 12 Powell, A. A 13 Ribner, H.S A14 Ribner. H.S. A15 Lighthill, M.J. A16 Hollingsworth, M .. A .• Richards. E.J. A 17 HollingsVlort , M. A . • Richards, E.J. A18 Ram. G .S., R ibne r. H. S . A19 Green, D.J., Lilley. G.M. A20 Campbell. A.J. A 21 Wade. J. H. T . 15 )

"On the M echanism and Reduction of

Choked Jet Noise. Part I",

Commun-icated by Prof. E .J Richards, A.R C.

15. 623 F . M. 1858, Dec. 1952

"Convection of a Pattern of Vorticity

Through a S ock Wave" , NACA Rep.

1164, 1954 (Supersedes TN 2864,

Jan. 1953)

"Shock -Turbulence Interaction and the

Generation of Noise", NACA Rep.

1233. 1955 (Supersedes TN 3255.

July 1954)

"On the Energy Scattered from the

Interacti.on of Turbulence with Sound

or Shock Waves". Proc. Cambr. Pqil.

Soc. 49. pt: 3, pp 531-551, July 1953

"A Schlieren Study of the Interaction

Between a Vortex and a Shock Wave in. a hockTube", ARC 17, 985,RM.

2323. Nov. 5, 1955

"On the Sound Generated by the

Inter-action of a Vortex and a Shock Wave.

ARC 18, 257, F .M. 2371. Feb. 29, 1956

"The Sound Generated by Interaction of

a Single Vortex with a Shock Wave", Preprint Heat Transfer and Fluid Mech. Inst. . presented Pasadena California, June 19-21, 1957 (Stanford Univ. Press)

"Preliminary Report on the Use of Wide

Angle Diffuser in Ground Mufflers of

the 11ype used for Silencing J et A ircraft,

College of Aeronautics, Cranfield.

Note o. 27. May 1955.

"Investigation of a Wide-Angle Diffuser with Air Augmentation for use as a Jet

Muffler". UTIA TNNo. 15, Aug. 1957

"Propos al for an Orenda Portable

Gr rund Silencer", 0 renda Engines Ltd. ,

A22 Willmarth, W.W. A23 Ribner, H.S. A24 Maestrello, L. A25 Korbacher, G.K., Etkin, B., Keefe, RT. A26 McGregor, D.M. A27 McGregor, D. M. Etkin, B. A28 Prendergast, V.D. A29 CurIe, N. A30 Phillips, O. M. A31 Bingham, H.H. , Weimer, D.K. Griffi th. W.

"Wall Pressure Fluctuations in a Turbulent Boundary Layer". Jour.

Acous. Soc. Amer. , Vol. 28, No. 6, pp 1048-1053, ov. 1956 A lso

(slightly amplified) , NACA TN 4139, March 1958

"Boundary-Layer-Induced Noise in the Interior of Aircraft" , UTIA Rep. No. 37, April 1956

"UTIA Air Duet Facility for Investi-gation of Vibration Noise Induced by

Turbulent Flow Past a Panel {

Boundary-Layer N oise . UTIA T o. 20,

April 1958

"Acoustic Radiation from a Stationary

Cylinder in a Fluid Stream", UTIA Rep. No. 39, May 1956. Also Jour.

Acous. Soc. A mer. , Vol. 29, No . 1, Jan. 1957

"An E perimental Investi.gation of th

_y

Oscillating Press ures on a Circular Cylinder in a Fluid Stream". UTIA

TN No. 15. June 1957

"Investigation of the Fluctuating

Pres-sures on a Circular Cylinder in an Airstream", P ysics of Fluids, Vol.

1, No. 2, p. 162, 1958

"Measurement of Two Point Correlations of the urface Pressure on a Circular Cylinder", UTIA TN 23, .July 1958 "The lnfluence of 30lid Boundaries

upon Aerodynamic Sound", Proc. Roy. oe. A. , Vol. 231, No. 1187, 1955 "The lntensity of Aeolian Tones", Jour. Fluid Mech. ,Vol. 1, Pt. 6, Dec. 1956 "The Cylinder and Semi-Cylinder in

Subsonic Flow", Princeton Univ. Dept. of Physics .• Tech. Rep. 11-13, 1952

A32 Ribner, H .S.

A33 Miles, J .W

A34 Gould, L. H.

...

· ( 17 )

"On Skin Stresses and Possible Fatigue Associated with Boundary Layer NoiEiel1 (unp ub lis he d)

"On Structural Fatigue under Random Loadingll

, Jour. Aero. Sci., Vol. 21,

No. 11, pp. 75 3 -t7 62, Nov. 1954 "Outline of Research into Acoustic Fatigue of Structures 11, Avro Aircraft

Canada Ltd., Tech. Dept. Rep. No. GEN 1090/346, April 1958

dW dx

o

,

\ I \ \

-7

X

2.

16 Small Jets (D/4 each)

XO

/

-

....

4

6

.... _....

,

x/D 1 Large Jet (D)

8

/0

/2.

/1

FIG Al COMPARATIVE NOISE POWER DISTRIBUTION OF A SINGLE JET AND A

,

. \

r;

:

I l:.L f I '>oL \ _,

FIG. A2 MULTIPLE-NOZZLE JET MUFFLER PLUS

\U

---....

RIPPLE

..

AT

REST

I4'C

I()~

+~

1f,4"'~1

VIEW WITH RI PPLE

a

MOVI NG

~~,,~~,

~

A\~

~~~ ~\,~~

\

\.~~

VIEW WITH RIPPLE STATIONARY

FIGURE A3.

SOUND REFLECTION AND TRANSMISSION

BY A MOVING

MEDIUM IN

TERMS OF MACH WAVES

GENERATED BY RIPPLES RUNNING ALONG THE

-

..

ya 1G.a.

a,

2,

t,

90r---,---r---~lr~rrl~I~I~;__4~---~

60

_M

Cl) lIJ lIJ

30

ct: (!) lIJ 0

~

_,.

z

₀

0 Cl) yalO Cl)

-:E Cl)

z

~. ct:

-30

t-L&.. 0 lIJ ..J (!)

z

«

-60

_90L-______

~

______

~

______

_L~~ _ _ ~ _ _ _ L _ _ _ _ L _ _ _ _ _ ~2

-90

-60

-30

0

30

60

90

ANGLE OF I NCIDENCE,

ex:

OEGREES

AGURE A4 ANGLE OF REFRACTIONOC" VS. ANGLE OF INCIDENCE

11) Cl.) CP ~

~

0~----~~---+---~---+---r---~---1

o ORDINARY ~ - 201---+----,~ REFLECTION ---b~---t---t---t

z

W o (3 Z LL.

o

.2 .4 .6 -40~---~~~--~---H~--+---~----~-~--~ o

w

~-60~---~~----+~~--r----~~---r---~---~

z

<t: -.2

o

FIGURE A5.

2

3

4

5

MACH NUMBER, M

CONTOURS OF CONSTANT REFLECTION IN A GRAPH OF ANGLE OF INCIOENCE OF THE MOVING (SECONO) MEDIUM.

6

7

COEFFfENT, R

Wave Motion

2

I~

Energy Flow Strea;m. U ~

d"

•

--

>

~ ~

'>- /

FIGURE A6 PLANE SOUND WAVE IN A HORIZON.TAL STREAM. THE PLANES OF

CONSTANT PHASE MOVE WITH THE 'PRASE VELOCITY'

Vi

DIFFERENT

FROM THE ORDINARY SPEED OF SOUND

t .

THE ACOUSTIC ENERGY

u

CF

it/ ...

;".s

I /

~

t:

U

(neg,)

U

(neg,)

(a) Vf ) 0 (b) Vf

=

0 (c) Vf

<..

0

FIGURE A7 PLANE SOUND V'IAVES IN A MOVING STREAM: EFFECT OF' STREAM VELOCITY U ON PHASE VELOCITY

Vf

AND RAYVELOCITY

Vs.

ACOUSTIC ENERGY DENSITY '-"""

F KG AB Synthe s is-of vortex from radially disposed shear flows (physical interpretation of Fourier integral).

original vortex

BEFORE

/ shock .vortex, irtual

Sttf°),l

...

'

/ , / '

--

...

-/ /

-\ -\ '

-

--I _{I \ \ "}

,

I " I \ \ "

-\ \ "-\ \ \ \

AFTER

\

\

\

\

\

FliG A9 Convection of vortex through shock wave, I:

focusing of the refracted shear waves.

/

-"

core

shock

shock

Fig. A 10 CONVECTION OF VORTEX THROUGH SHOCK WAVE, II: FORMATION OF

3-

2-N

G(er)

.

1--8

_-4

-

_-

rll-

R

1;"

o

4

FJf.G All Upper and lower bounds to radial pressure profile of cylindrical soünd wave. (Shaded area ior

CT)

I

gives trend only. not bounds.)

9

.

31·~I--~---20

.

1~1-,---~J

o

1 2 3

A

J Al-2/ Aj A3/ A 2

Ao/

Al-2

ft. 2

0.79 2.40 8.0 2.25

---1 . 0 - _{- 0.2 u} , Ut jet L---'----1_.l...-....I-...L_J..I-_ _ - 0 u Ut jet 0 . 5 -1.0 o U 0.5 Ut jet o

POROUS INNER LlNING OUTER SHROUD OUTER CASING TRUNNION

[~=;

~) 7~"'~

Ö

I

I,

:':=:;. ;::; :

~l

~ V "---AMS 5510 STAINLESS BAFFLES I

I'--

-

-

--:-

-

~

~

E

-

::_~IREC~ION ~~~~-~~~HICK)----

-

---

r-:.-lO

AMS 5510 STAINLESS (0·10 THICK)

····~~:~·l;;.:;:.;;:·.·.

- STIFFENERS

SUPPORT ARM SUPPORT ARM

SECTION A-A _{ANCHOR RING}

20 cps -10.000 cps 100% rprn 100 FEET 270 _ _ _ 36,0 I 40 ti) -' w en

hl

_o I -' W __ - - , 130 ~ w 0: :::J (f) ~ 0: a. 120 0 z :::J o (f) IlO z 0 ~ u w 100 0: 0 ~ w ~ 110 120 ~----l130 180140

FIGURE A15 POLAR DIAGRAM OF CFIOO/ORENDA llR NOISE FIELD WITH AND WITHOUT SILENCER

f

..

-

~

.

I

x

AFTERBURNING

~

!!!

I 80

'0

.,

...

-

UNSILENCED

~

17 ol

I

:::;:;;:o"'"~

I

n----~--+-I-I

-l lIJ

G:i

-l

1601

,J,~I

0:: lIJ ~

~ 1501~--4----+----~--~--~----+---~~--~

o

Z : l

o

Cl)

1401

•

o

3000

4000

5000

6000

7000

8000

9000

10,000

THRUST-Ib

FIGURE AI6 SOUND POWER LEVEL VS.ORENDA IIR

FIGURE

Al

17

ROTATING CYLINDER AND BOUNDARY LAYER TRAVERSE GEAR

.

-2

.0

gOr-

-"a

I

I

---

10 log PI

_

2

- -

~

10 logt<P

2-

PI>

..

..J LIJ

>

LIJ ..J

80

1

LIJ

a:

::l U) (t) LIJ

70 I

a:

a..

o

z

::l

060

_U)

J\

~

1\

- - '. -IL---f---,

'.

'I

"

, I

'\ h

I __

----~---I

.

_ - 'l-I\

-I'

1 \

'-~\

ROUGH

SMOOTH

50'

·

2 2 2 3 3

10

2xl0

5xl0

10

2xl0

FREQUENCY,

Cps

FIGURE AI8

SPECTRA OF NEAR FIELD BOUNDARY LAYER NOISE PRESSURES

FOR SMOOTH AND

.

ROUGH S" ROTATING CYLINDERS, MEASUREO WITH A SINGLE'

MICROPHONE

(p2)

AND WITH ANTICORRELATED MICROPHONES

t

(R-

Pt

)2

.,

ü 100 90 >-~ 80 ,g ~

-

..

cI,-IN ~ I G.jl ca. o ~ 70 o

-~ LIJ

>

60 LIJ ~ 2 ;:) ~ 50 () LIJ Q. (I) 40 30 Ol A~

~~~~

.~~

_x+ 0

xtl~.

~

.

~ lIt~ A I3,OOOrpm -fI. V 12,000rpm

~

.

o II,OOO~pm X 10,000rpm

4~

~.

+ 9000rpm

+~~

• 8000rpm

~~~o~""

I> 7000r m

\..rvtè+

1>1> .1 I fO

STROU

H

A

L

NUMBE~

St-1ï

10

FIGURE AI9-SPECTRUM OF NEAR-FIELD BOUNDAR

Y

LAYER

NOISE FOR ROUGH CYLINDER WITH ANTI-CORRELATED

MICROPHONES 21n. FROM SURFACE.

DATA FOR 7000 rpm

TO 13,000 rpm ADdUSTED TO 10,OO<? rpm ON BASIS

p2"'U

4 .1 t

•

J I

J

100

FIG A20 MOVING PRESSURE WAVE. AN ASSEMBLAGE OF SUCH WAVES OF ALL ORIENTATIONS, WAVELENGTHS, AND SPEEDS CAN REPRESENT A RANDOM FLUCTUATING DlSTRIBUTION OF SURFACE PRESSURE

u

_..

FIG A21 GENERATION OF MACH WAVES BY FLEXURAL WAVE TRAVELLING

db

130

120

110

100

90

o

4

8

12

Boundary- Layer Thickness,

FIG A22 BOUNDARY-LAYER-INDUCED NOL3E PRESSURE LEVELS CALCULATED

FOR EXAMPLE AIRPLANE ALONG CENTERLINE OF AF'! END OF

FUSELAGE. HIGHLY REVERBERANT CONDITIONS, NO INSULATION.

ALTITUDE 18,000 FT., FUSELAGE PRESSURIZED TO 8,000 FT.

I

I

-

I

ó"

16

db

140

120

100

80

60 50

₁₀₀

₂₀₀

₄₀₀

₈₀₀

_ft/sec.

Flighf Speed, U

FIGURE A 23 BOUNDARY-LAYER-INDUCED NOISE PRESSURE LEVELS CALCULATED FOR EXAMPLE AIRPLANE ALONG CENTERLINE OF AFT END OF FUSELAGE. HIGHLY REVERBERANT CONDITIONS, NO INSULATION. ALTITUDE 18,000 FT., FUSELAGE PRESSURIZED TO 8,000 FT. EXPERlMENTAL POINTS ARE CORRECTED FOR ALTITUDE.

E E i i 90 a: w !;g' IL.

I

21.75

,---+---,L.l

SECTION D-D

OUCT N..ET ANO OUTLET

REPLACED WITH DueT

32.687 SECTION E-E

F

----==--=--ïl 11 -_. '---:RATlON 11 I" 56 'I

'T--t1

I I

11

SECTION B-B REPLACEAEl..E BY SECTIONS 8x12,4xl2,2xl2,Ixl2 10 Wo MOTOR 5 N. FLEXIBLE COUPLING ,

f[H

~15~

I

82.25 SECTION A-A o

ro

1

~

I

A - - A

6

~

SECOlID CORNER '

I

Tt.ONI<G VANES

ffij

5 SCREENS _{TURNING VANES} FIRST CORNER

_I

SECTION CoC

-=fo

I

I _{I .}

\\\.'I;.

I

;

RAPID e!xPANSION

24.75 \\." 1 FIRST DIFFUSER OUCT

!

SECTION

\

-1

~'I;.

I

;

I \'1;.

~I

d

_II

,I

_I

I

!

:

:

:

1 I ' I 11 11

I

I

I IJ I1 10 - _______ .lJ ~20__+_15.5 14 -1-9.5 2 '..I :1%1 1 26.75 r.;~ Q 1---2415 1 62.45 3,96 .,...---11- 10 I. fII - - - --+---26.75 6;JO.95 I I I 1 o 10 20 30 40 50

FIGURE A24 SCALE; INCI-ES

GENERAL ARRANGEMENT

BOUNDARY -LAYER-NOISE DueT

o

o

o

CO slaq!~aa

o

l éfS

o

<..0

0

0

~

0

0

N

0

lO

o ·

o~

-~

::::>

>;

+-'0

0

o-a;

lO>

~

+-u

:::J 0 ..J W

z

«

Cl. 0::

«

w

Z ..J W

>

W ..J W 0:::

::::>

Cf) Cf)

w

0:: Cl. <.0 C\J

«

W 0::

::::>

(!) LL

B

*

OCTAVE ANALYSIS

OISTANCE FROM MICROPHONE TO PANEL Z= 16" 8/1 DUCT

.002-

PANEL

./

/ / /

.~

"~

OVERALL LEVELS ./~ ,

~

/

h-

~

0

/

__

0

~

t:7-.-~X--::

""O~~~$

__

~

~.

/'

/'

~-..;---

-e~-0--2-x

... ..,,,,-

"0

/ v

~"

.~~~

'W-eq

~

~

'X

0

6 Ot·

A-A

'VI

/A--~~-'W/

~/

.

--w--w-v, "'" "'"

V

...

~

~

/ ...

~

,

'X

0

i

8 - 8

· A - -

8 ,

·

--A /

...

~

__

~

__

~ v.~"

'"

~

~El-e.

" / X

"'0

:g

~/E1-~ ~/~~"'~-"""8

~

V "" ""'0

..J

I

//'''-...El~''''''''''''''El

- - 9 " "

\

~

X

\.~

Q.. . / " ' "

8",

~

\

\

.

\'~

en

es / /

'E1~

'e

\

X~S" O~.,

4OJ.

U//

" "

\

w~

\

' \

F1 :c.'Ó \ . "

-""El ..

~

~ V""X\ 0

"'v

8.

' "

V

X

El " " "Ä

FREQUENCY

CpS. " ' E l 8

IpO

'P,O

0

10,0,.00

la

100

1,000

_

DUCT

c..

VELOCITY, U fps.

FIGURE A27. FAR FIELD MEASUREMENTS OF ACOUSTIC RADIATION

FROM .002 INCH STEEL PANEL.

a:::

w

·2S

·26

·24

al

.22

~ :::>

z

.20

..J ~ ::J: .18 ::>

o

a:::

ti

·16

·14

r

I

-

"

-

"

-I L

.,2 ,

2

10

I I I I

I

I

T I I

_I

T

I

I

I

I

_I

I

_T

_I

T

, 1 1 1 1 I

1--1.

1 <I

1

!

1

1

1

1 I

- l •

"V~n~~

• •

I

•

SI

I

'-'--

I . , - xx

1

I · .!- <I ... ... ,

J -

I

•• -

·

IT

jo;

xx~~xx!txx

Xx xx

~6"''''

1 T I

I

1

., x

r-r. • •

• •• --'"

1

.xXJf.·1

I' ,

' T 11

~fo°

I

1

-,"X • -

1

I ' , '

r~

_I 1

I

1

1

1

e-lil :

1

I

1

I

1

1

I 1

11]

4 6 SI

2

46S1

2

46S1

2

100

1000

10,000

4 6

SI

2

100,000

4

6

SI

1,000,000

REYNOLDS NUMBER

1 FIGURE A; 28

VARIATION OF FUNDAMENTAL STROUHAL NUMBER WITH REYNOLDS NUMBERS

o

UTIA - 1955 • Roshko - 1953

() Kovasznay - 1949 (after Lehnert) • Relf - 1924

" DVL Hiebtone - 1919 (af ter Lehnert)

100

t - - - - + - - - - I I - - - + - + - - f -

tOIA-

CYLINDER

· 90

I + -.0 "C I

~80

en

IN TUNNEL

TUNNEL

70

1---4--___+___+_

EMPTY

~--4----+--4--+

2 3

I

100

5

1000

2 3

5

IQ

000

2

FREQUENCY- C.RS. ..

FIGURE A 29

1 SPECTRUM OF CYLINDER NOISE

"3

oetave band analysis uneorreeted for microphone response. U

=

225 ft. Isee .•

mierophone in settling ehamber (Fig. 10. Configuration C)

Run No.

o -

100 • - 101 Description eylinde r in tunnel tunnel empty

o 0

60

0

80

100 1200

~

40·

140·.

20°

160

0

0 - .

' 1 8 0 °

-Cp~.003

FIG A30 OSCILLOGRAPH PICTURES OF OVERALL PRESSURE FLUCTUATIONS AT

VARIOU3 LOCATIONS AROUND THE CYLINDER. U = 75 ft /sec., BAND WIDTH: ZERO SELECTIVITY

FREQUENCY

-FUNDAMENTAL

FRËQUENCY

·3.---.--

-·2 - -

.-

--

- -

-

- - -

-

---

----

--

-.... 0. ·1 - - - ---- + -U

..: ·05

z

9=180

9=90

9

=

135

w

o

-lL lL. W

o

o

IJJ

0: :::>

9=45

.01

J - - - + - -

-

-

+ l -~·005J--~----4--~---~~

w

a::

0..

9=0

O--cr---"V ·oo,~---~--~---~~~~--~ 10 !SO 100 500 IOÓO 2000

rREQUENCY -

cps

FX ~.\31

PRESSURE SPECTRA AT VARIOUS LOCATIONS AROUND THE CYLINDER. U

=

211 FT./sEC. BAND WIDTH: 1/30CTAVE

c: :::J

-.... 0. U

...

Z W U lL. lL. W

o

u

w

a:::

:J Cf) Cf) W

a:::

a..

,

1

A32 COMPARISON OF THEORETICAL AND EXPERIMENTAL PRESSURES.

Cp = r.m.s. VALUE OF PRE.3SURE FLUCTUATIONS AT FUNDAMENTAL

fun FREQUENCY-'::::: (1/2)

r

UZ

I'----'

1.0

~

V

-, :. _X

MEASURED

~ \ ~CORRELATION 0 \

.8

R( x} .6 \

I

'--'"

\

CORRECTEO

\

~

l.--- CORRELATION

!4 \ \ 0 \ 0 0 \ u 0 0 \ X 0

"

.2

"-x ... _ X

I -

x-

X _X - - - - v_ ,

o

2 4 6 8 10 12 14 16 X 18 2.0

x diameters

FIGURE A33

2 POINT PRESSURE CORRELATION ON

A

I IN. DIA.

5.0

4.0

À

_3.0

2.0

LO

o

0

o

l

-____ _ I _ _

r___

....

20

40

60

80

100

120

140

160

180

-~

R.(xIO )

-

FIGURE

A

3~

.

CORRELATION

LENGTH

'I'

REYNOLD

S.

NUMBER

?( ?(

(--... r ---"'),

- - -.-<.":' _,.,,'1 I _{L _ _} I

,

_,

~Î I I ( - - - - . . ... 1 ) ...

_---

'

-

!,--I \ \ I \ \ , I I 1'--, I

'

_.... I I

'i

_-<

_-.

I I ./ "./

r---~

~---

-I ./

-t

"-:,.

./

f'

.J

cID

cID

-x

(

\

I , I I I I

-~

\ \ I I I .J

FIGURE A35 STRAIN GAUGE BALANCE FOR MEASURING UNSTEADY COMPONENTS OF LIFT AND DRAG

·8

·7

·6

·5

C ·4

L

rm.

-3

·2

·1

o

---r I I I I I

I

I I I

I

-r-r-n-

'

I

I

I

1

I

1

11

r-

I 1

I

I "

1

"

•

.'1

"1

" 1 1 1 1

I

~I

"

'

1 "1

E

'

EFE

---

0

1

K

r J - 1 - - r

j -

I'

PHJLLJPS

McGREGOR

_

,

..

~ ~

-

I

Ijl ,

1

I I

_

1

1

' 1 1

1

,-- I 1

l.q

1

1 11 _ .L 1 1

l

1

1 1

~

I

100

1,000

10,000

100,000

REYNOLDS NUMBER

...

.~ C!)

o

..J

o

-I

-2

~

-~

-~

-~

- I-....,

~

,$Q.Q,O

~

@~

.q:<P

=

: 35.ptl.

I

I

1 -

....

I!I

5 P't1

I

6 pts.

71l~S.

~p1

s.

ME A SU RE 0 :

_

~

0 KEEFE -,.. 8 pl..

I

GERRARD

-~

-.

!IJ[

PHJLLIPS

~

-CALCULATED:

.

-~

-.

_1-~~~-L~~

__

LI~I~I~I~I~I~I_~II~I~1

~

I I I ' I _L 102.

₁₀

3

REYNOLDS NUMB-ER

4

10

10

5

200 150

.

~

·

Ol

·

0.-m U) ril ₁₀₀ . ~ E-4 Ul

·

Ol

·

S

·

s.. 50

I

panel.fundamental freq., 37.

I

~ CPS

I

j

I

.

.'

.1

I ~r-- <

.

150 c.p.s . ~

~

.J •

--.

.

600 c. p. s .

~

/

<. < , ,. 400 800 1600 F LIGH T SP EE D, U, f. p . s . ,

.

'.

'

-

-

.

~ ~

_~

! S 1

~

.,

1

ç

I Asymptote

~

- T

.,

~ ~ \

(

-00

FIG A38 Skin stress associated with boundary-layer noise according to example computations based on an idealized model. Dural skin 0.032" thick, boundary

EL

BIS

• . - . _ )< , 9 " . , . "

(

,.

' -

~'- ".,..,~. - " ' .

.'

_{- ._,}

,

,-,~ -~:v"""" -~_W8.~ . . ~ Lt. . . __ . . . . _.~~~,_{.t . .} ~ iW_

_

_

~.

-

""'7'

D

.

4!!lI_. J 'U'il\~~ ," .,._ .. ~._,._..--' '

l

.-

..

ei

b

20,000

15

,0 00

10,000

(a) THEORETICAL

5,000

...-....--- I CYCLE

----~~

I

-

5 ,00 0

(b) EXPERIMENTAL

FIGURE A40. CVeLIC VARIATION OF fiBER