Correlation of jet noise data in terms of a self noise-shear model

CO~ION OF JEI' NOISE DATA IN TERMS OF A SELF NOISE-SHEAR NOISE MODEL

Tfa~~

n ..

:~ r~~s~~·:;:,;"~r:~. '.'~ ~ ',1

VUfiGTU1G['OU·v". :<U:':'":·E by

Nagy Sabet Mikhai1 Nosseir

7

J L! 1~75

January, 1975 urIAS TECHNICA!. NarE NO. 193

CN ISSN 0082-5263 AFOSR-TR 75-0496

CORRELATION OF JET NOISE DATA IN TERMS OF A SELF NOISE-SHEAR NOISE MODEL

by

Nagy Sabet Mikhai1 Nosseir

Submitted January,1975.

January, 1975. UTIAS Technica1 Note No. 193

Abstract

The theoretical formalism of Ribner

(1964

and

1969)

was applied in the

analysis of a large body of experimental jet noise data. It was found that the ffbasic direct;i.vityff which results on excluding convection and refraction effects could be decanposed unambiguously into self noise and shear noise. The basic self noise spectrum peaked approximately one octave higher than the shear noise spectrum, and the peak amplitudes were roughly in the ratio two to one. opon frequency shifting and normalizing alignments, the two spectra were found to match well in shape. All these properties are in accord with the theory. The self noise-shear noise spectral similarity was applied in a formalism for jet

noise prediction utilizing the theory. .An empirical input - the value of ~ ~

shear noise peak/self noise peak (the approximate theoretiCal value ~ ::: 2 works

nearly as well) - is applied to generate narrow band directivity curves re 8 ::: 900 relative to the jet ax;i.s. Agreement with experiment was generally very

good within the range 300

_<

₈

_<

₁₁₀0_{, which excludes the refraction-dominated}

--- ---I. II. lIl. IV. Tab1e of Contents Acknow1edgement Abstract List of Symbo1s INTRODUCTION

1.1 Survey of Previous Work

1.2 Qut1ine of Present Investigatiqn

ANALYSIS OF EXPERIMENTAL DATA IN TEEMS OF SELF NOISE-SHEAR NOISE :MODEL

2.1 Corre1ation Model 2.2 ResUlts and Discussion

PROPOSED METEODS FOR CO~UTING FAR~FIELD NOISE

CHAR.A.CTERISTICS

3.1 The Quadrupole Theory: Expres~ion fOT the Intensity

in

Any

Direction

3.2 First Method: Measurement~ Ej.:t Ninety Degrees

3.3 Second Method: Un:i,versal Se1f Noise SpectrUlll

CO~CLUDING REMARKS ii iii iv 1 1 1 2 2

4

8 8 9 10 11 REFERENCES 13

b c o C

cs

D dB f H I L M M c n p r R Re

s

SPI. u U x y List of Symbols self noise spectral density shear noise spectral density

amb~ent spee~ of sound

convect~on factor C

=

source Strouhal number, CfD/U.

J

jet exit diameter decibe:)..

fr~quency

4

2

cos

e

+ cos

e

directivity factor H(e)

=

acoustic intensity scale of turb14ence

~ch numb~r, Uj/Co

convection Mach number, U /c _c

0 2

exponent in the convective amplific~tiQn (taken

= 4)

aeQus ti c power

turb.ulence intensi ty, u/U j observer dist~ce

Reynolds number, U.D_J. ./,v

0

observed Strouhal ~uIDber, fD/U.

J

sound pressure level

foot mean square of t~bulent velocity local mean velocity

convection v~locity (taken ~

&./2)

J

jet exit velocity

distanee along the jet ~is

radial di$tance from the jet axis

Symbo1s

0: constant ( ::: 0.55)

13 ratiO'-of-Shear noise to self noise, b(CS)/a(2CS)

e

angle with jetexhaust axis

~m mean gas density .

density of ambient air '

''basic directi vi tyff spectrum 1/3 octave band intensity

~K constant bandwidth intensity

v

o kinematic viscosity of ambient air

radian frequency

Subscripts

m mean value

ma.x maximtun value

o properties of ambient air

p at peak

se self noise

"

I. INTRODUCT ION

The introduction of large jet engine aircraft has added a major source,

of noise to our environment.' The jet noise created by the mixing of exhaust gas

with ambient air causes a real annoyance in airports as well as in the surrounding

cpmmunities, and may even cause sonic fatigue damage to the aircraft structure.

Many scientists, attracted by the jet noise problem, have carried' on theoretical

and experimental investigations wîth the aim to understand the mechanism of noise

generation, estimate the noise levels, and to control the high sound levels radiated

from jet engines. A short account of some of this work is given below.

1.1 Survey of Previous Work

The theory of sound gener'ated aero'dynamically, given by Lighthill' in

his two fundament al papers (1952 ahd 1954), has provided a basis for ·the

under-standing of sound produced by a free jet. Re described the sources of sound in

turbulent flow by means of an acoustic quadrupole distributed in .a 'uniform medium

at rest. This work has stimulated a great volume of further efforts, both

theo-retical and experimental.

All of the known theories ,dealing withJet noise require a knowledge of

the turbulence structure of the jet. The experimental work in Refs.

6,

7

and

8

appear to be useful in this regard. These experiment

al

measurements show that

both the turbulent and the mean velo~ity' components posse~s self-similar profiles

along the jet axis in the mixing region.

One of the current theories was presented,by Ribner in 1964, and in a

more refined form in 1969. Re applied a two-point, space-time quadrupole

correla-tion technique to the case of an isotropio turbulence superimposed on mean shear

flow. Excluding the effe cts of refraction and convection, he showed that the basic

directivity consists of a self noise arising from turbulence alone and a shear

noise due to cross-coupling of turbulence and the mean shear flow. 'Ris ailalys'is

showed that, ,dth the self noise spectrum shifted an octave lower, both shear noise

and self noise spectra, reformulated to a unity peak~ shoUld collapse into 'one

curve. In the Appendix, the similarity between the self noise, and the shear noise

spectra is predicted and discussed using Ribner's equations and an assumed

self-similar turbulent and mean velocity profiles along the jet axis.

Some authors have questioned the importance of considering the directional

shear noise when dealing with the basic directivity. Indeed, a stronger convection

factor can modify the basic directivity Il).uch like the shear noise. This questiop.

concerning the role of the she'ar noise motivated the present work... It was d!,=sired

to see (1) whether the shear noise and self noise can be extracted unambiguously

from experi:rrental jet noise data, (i) to what extent they fit Ribner' s theoretical

model, and (3) how important the shear noise is to the directional pattern. Earlier

efforts along these lines by Grande (Ref. 15) and by MacGregor et al. (Ref. 9) have

provided guidance.

1.2 Outline of Present Investigation

In Section II, the extensive measurements by Ahuja (Refs. 10 and 11) and

by Mollo-Christensen et al. (Ref. 12) with the unpublished work of Chu, were used

to examine the "basic directivity" of the jet'. Avoiding small angles to the jet

possible to predict the directional shear noise as well as the nondirectional self noise in the ''basic directivity" pattern. Furthermore, similarity between self no1se and shear no1se spectra, with~;the former peaking nearly an octave higher, was ex;plored.

In Section III, the theory (Refs. 1 and 2) is used to derive an expression for the intensity in any direct10n in terms of (1) the intensity in a direction perpendi cular to jet axis, and (2) the ratio between the shear nois e and sel f nois e spectra peak~,~. The intensity at a direction perpendicular to jet axis can be deiivedd1rectly from the self noise spectrum .a(es). Observations on the different selt no1se spectra led to the possibility of presenting a universal self noise spectrum using an effective source Strouhal number. With ;this universal spectrum and ~ proper va.lue for the factor ~, the theory is usêd to construct a simple method ta ca.lculate the different characteristics of jet noise.

II. ANALYSIS OF EXPERIMENTAL DATA IN TERMS OF SELF NOISE-SHEAR NOISE MODEL 2.1 Correlation Model

In an extens1ve work by Ribner in 1964 (Ref. 1), he derived mathematical forms to express the major features of jet noise ä.long with physical explanations • Start1ng from the basic equations of motion and employing certain similari ty re-lat10ns for the turbulence, his expression for the idealized spectrum of the complete jet has the form

p(e,f) ""

(1)

where p(e,f) is the acoustic energy flux in direction e per unit solid angle per cycle. po!PiD.··.t,he ambient air and mean gas densitiesjQ(v) = v2/(1 + v2 )2, where v

=

fe/f*,is a semi-empirical spectrum with asymptotes satisf~ng the f2 and f-2 laws. f* is a special value of typical frequency f, and

2 2 2 1/2

e

=

[(l-M cose) _c +

ex

M ]

0 (2)

is the convection factor with M = U /co,U = vel 0 city of convected sources, taken as (jet velocity U

j)/2 and ex isca coRstantCtaken as

0.55.

The corrected directivity factor Hee) by Ribner (Ref .2)

H(e)

=

4

cos e + cos e 2 2

replaced the incorrect cos4e of Ref. 1, where e is the angle between observation direct10n and jet axis.

In fact, the assumed spectral density function, Q(v) and Q(v/2) replac~ the shear noise spectral density b(eS) and the self noise spectral density aCes) respectively. Hence, E~n.

(1)

in a more general form, is

where P(8,CS) "" p c

5

.0 0

4

2 ~ (8 CS) [(CS) + b(CS) cos 8 + cos 8] 'PB'

=

a 2 (4 ) (5) ~s the "basic dire ctivity" spectral density, CS = CfD/U. is the source Strouhal

J number.

By definition, the intensity spectral density in directio~ 8,r(8,CS) is equal to p(e,CS)/R2 where R is the distanee b~tween the observer and the source

el~ment. C0l1sequently, Eqn. (4) can be written as .

4

2

r(8,CS)

=

KC-4(8}1J

B(e,cS) ==

KC-4_{(8)[a(CS)+ b(CS) cos 8 ; cos 8] (6)}

The constant K in Eqn. (6) depends mainly on the Mach number M = U./c , the Re,rnolds number Re _{v·, .} = U .D/v and on the observation distanee R. _{J O '} J 0

. The oonvective ~li~ication in the appears as a vertical shift CO' in the source a Dopp+er Shift c-l.

observed spectrum r(8,S), Eqn.

(6),

spectrum 1J

B(8,CS), Eqn.

(5),

plus Shear Noise and Self Noise Density Spectra

i

Equation (5) can be solved to give the self noise spectral density a(ÇS) and the shear noise spectral density b(CS) using two different directions of observation, makjng the angles 8

1 and 82 with the jet axis, as follows:

with H(8) =(cos

4

8 +

cos2~/2

from Eqn.

(3).

Subtract Eqns.

(7)

and

(8)

to get

Multiply Eqn. (7) by H(8

2) and Eqn. (8) by H(8l) and subtract to get

a(CS)

-H(82~~B(8l'CS) _{- H(8l )1JB(82,CS)} H(s2) - H(8l )

If 9

1 was chosen to be 90 0

, i.e., H(9

l ) ~O.O, and 9 replaces 92 in

Eqns. (9) and (10), a simpler form would be

and

(9c)

(9d)

Equation (9) shows that the self noise is constant tn all directions, aresult derived before in Ref. 2, due tothe assumed isotropic turbulence, and that the "basic direct:1.vity" reduces to the self noise alone at a direction perpendicular to the jet axis.

In order to make use of the 1/3 octave intensity measurements of Ahuja (Ref. 11) and Chu (unpublished), arelation betweert basic spectral den-sity CPB and 1/3 octave intenden-sity 11>113' with bandwidth M_where M = ~f (constant percentage bandwidth) is given as I(9,CS)M

=

11>1/3

~

C 4(9)CPB(9,CS)f. Using Eqn. (6),

(lOa)

Similarly, for the case of const. ant bandwidth measurements I1>K' (Möllo-Christensen et al, Ref. 12) M = ~ (constant bandwidth). Then Eqn.(6)· gives

I(9,CS)M

=

I1>K - C-4(9)CPB(9,CS)k

2, i.e.,

(lOb)

The present method of calculation avoids the small-angle refraction effect by limiting the narrow band intensity measurements 11>(9

l ,CS) and 11>(92,CS), to two directions making angles 9

1 and 92 greater than 40 0

• Then Eqns.(lO) are applied to these measurements to eliminate the effect of convection and to produce the "basic directivity" spectra CPB ( 9_p CS) and CPB ( 9

S'CS). Equation (9)

is then used to derive the self noise a(CS), and the shear noise b(CS) density sl'ectra.

In the 1/3 octave measurements of Ahuja (Ref. 11) and Chu (Unpublished), Equations (lOa, 9c and 9d) were used with 9

=

450• On the other hand, Eqns. (lOb, 9a and 9b) were applied to the constant bandwidth SPL of Mollo-Christensen et al., Ref. 12, with 9

1

=

45 0

and 9₂

=

600• 2.2 Results and Discussion

Basic Directivity: Extraction of Self Noise and Shear Noise

points, calculated from the 1/3 octave measurements of Ahuja (Ref. 11) at 900 and 450 • With these two curves, namely the self noise spectrum a(CS) and the basic spectrum at 45 0 ~B(CS), the extracted shear noise spectrum b(CS) is also shown. In the same way, ,Figs. 14 to 16 show results from Chus(unpublished) measurements.

The basic directivity spectra at 8

1

= 45

0

and 8₂

= 60

0 from the constant bandwidth SPL measurements of Mollo-Christensen et al. (Reference l2)are presented in Fig. l7a. From these spectra, the extracted self noise and shear noise spectra in the form a(es)/a _ma.x and b(CS)/a _ma.x respectively are shown in Fig. 17. Table I, illustrates the flow conditions related to each figure and the corresponding ref-erence. All spectra are drawn against the source Strouhal number (CS), up to (CS)

=

1.5 , and the vertical axis does not indicate an absolute value of b(CS) or a(CS). All figures show clearly the shear noise b(CS) and the self noise spectra a(es); the latter peaks at higher source Strouhal number. The ratio of the self noise to the shear noise peak Strouhal numbers [(CS~e/(CS)sh] is listed in Table I for each case. This ratio ranges around the value 2, in

ag~eement

with one form of the theory (Refs. 1 and 2).

Figure

4

shows self noise and shear noise peaks of the same order of magnitude, a considerable difference from the general trend in all other cases.

The reason may be due to an overestimation in convective ~lificition e- 4 at

this high Mach number (M

=

0.91) where C

=

[(1-McCOS8)2 + ex Mc2 ]1 2. Overestima-tion of convective a.trq?lificaOverestima-tion is expected to result in less directivi ty be-tween ~B(45o,es) and ~B(900,CS) as shown in the figure. The same was predicted in Fig. 16 of Chu with M

=

0.96.

Similarity Between Shear Noise and Self Noise Spectra

From Eq. (1), the theory predicts one function Q.(v) for both the shear noise and the self noise densi ty spectra, provided that the self noise is shifted an octave lower. This has been examined by plotting the self noise and the shear

noise in the forms a(2eS)/a and b(CS)/b respectively, in Figs. 18 to 32.

max max

All figures show the similari ty in general. Figures 23 to 26 show a small deviation at small source Strouhal numbers and Figs. 27 and 28 show a deviation at high source Strouhal numbers.

A convective amplification in the form C-n where n = n (CS,M) is examined

in Fig. 33. The value of the exponent n is chosen to cancel the small deviation observed at small and high source Strouhal numbers. The figure shows that n changes slightly around the fixed theoretical value of 5. On the other hand,the figure shows that Mani1s convective amplification exponent in his recent work varies strongly wi th source frequency. Ris strong convective amplificatfu n at low source frequencies appears to compensate approximately for neglect of the shear noise.

TABLE I

MACH NO.

FIG. REFERENCE JEI' VEL. M

1 400 0.362 2 600 0.543 3 800 0.714 4 1000 0.905 5 300 .273 6 Ahuja (11) 400 0.364 7 600 0.546 8 800 0.728 9 1000 0.901 10 400 0.362 11 600 0.543 12 800 0.718 13 1000 0.905 14 743.1 0.69 15 Chu (unpub.) 887.5 0.85 16 999.1 0.96 17 Mo11o-Christensen 650* 0.8 (12) ,

*

This value was estimated in the present

analysis. NOZZLE DIAM. Din. 2.84 2.84 2.84 2.84 2.4 2.4 2.4 2.4 2.4 1.52 1.52 1.52 1.52 2 2 2 1 Average

Basic Directivity: Contribution of Shear Noise and Self Noise

[

lCS)se~

{CS)sh 2.00 1.70 2.25 2.00 2.00 1.84 2.00 1.92 1.78 1.82 1.73 2.00 1.66 1.80 2.00 2.20 1.92

The theory (Ref. 1) assumes a contribution of shear noise and self noise of the ratio 2 to 1 in the ''basic directi irity " spectrum (Eq. 1), i.e., the shear noise spectral density b(CS) is the shifted säf noise spectral density

a(2CS), multiplied by a factor 13. This factor 13 is equal to about 2 (Eq. 1).

In other words, the theory suggests that the factor 13, which equals b(CS)lá(2CS)

should exhibit a constant value against different source frequencies (anSl

direc-tion

8).

Figure 34 shows the variation of 10 log 13( CS) with source Strouhal number

(CS) • It is shown that all points in each figure collapse to a mean value, 10

log 13. The only deviations expected are at small and large (CS).

The mean value, f3 , can fairly represent the ratio of shear noise and self noise for all values ~f (CS). ,The numerical value of f3, where the subscript m is dropped for convenience, varies with the Mach number M and the Reynolds number :Re (or U and D). The values of 10 log f3 for each case from measurements of Ahuja

(Eef. 11) are listed in Table II.

TABLE II

D

=

1.52 in D

=

2.4 in D

=

2.84 in

U. M

6

logf3

6

10 logf3

6

10g~

J RexlO 10 RexlO RexlO 10

1000 0.90 0.84 2.31 1.32 2.22 1.57

----800 0.73 0.67 2.24 1.06 3.28 1.26 4.23

600 0.54 0.50 2.35 0.80 4.11 0.94 4.93

400 0.36 0.34 2.73 0.53 4.15 0.63 4.81

(i) Variation of 10 log f3 with M

Figure 35 shows the variation of 10 log f3 ~th the Mach number M(or u./e ) for each nozzle diameter D. The figure show$ a very small variation of 10

10~

f30 for M for D

=

2.84 in. and 1.52 in. A decrease of about 2 dB is shown in the case

of D

=

2.4 between M = 0.90, and M = 0.36. (ii) Variation of 10 log f3 with D

Figure 36 shows an increase 'in 10 log f3 in direct proportion with nozzle dd.ameter D for Mach numbers 0.71 and belO\>f. The diameter dependence appears to disappear at M = 0.90.

(iii) Variation of 10 log f3 with Re

Figure 37 presents the variation of 10 log f3 with the nondimensional p ara-meters, the Reynolds number Re = U .D/v where v is the kinematic viscosity of air

J 0 0

at the ambient temperature and the Mach number M = u./e

o' The figure shows a linear variation between 10 log f3 and Re, with inclination ihat decreases with increasing Maoh number M. This merely reflects the dependences on D' and M shown earlier.

An interesting result could be derived from both Fig. 37 and the theory. Figure 37 suggests the follovling linear relation:

10gf3

=

KJ.Re (11)

where Kl

=

KJ.(M). On the other hand, the theory of Refs. 1 and 2 give the ratio of shear noise to self noise as

f3 = K 2

(~

)2 (12) or K 2 = -2 r

r is the turbulence intensity, u/U, ~ is a constant that depends on the shear. Erom Eqs. (11) and (12), we have

log r

=

log K₂

KJ.

2 -

2"

Re (13)

ExperimentaJ. meas.urements of the variation of turbulence intensi ty wi th Reynolds number Re from Ref. 8 are. shown in Fig. 38. The linear variation be-tween log r and Re in the figure appears to satisfy an Eq. of the form (13) as predicted from the theory and Fig. 37.

IrI. PROPOSED METHODS FOR COMPLJrING FAR-FIELD NOISE CHARACTERISTICS

Two m.ethods for computing the far-field jet noise characteristics are pre-sented and eompared wi th experiment.

The quadrupole theory as developed by Ribner, (Refs. 1,2), is used to derive', an expression for the intensity measured in any direction in terms of the intensity in direction perpendicular to the jet axis. The two methods use this expression along with results deve10ped in Section II from experimental data of Ref. 11. '

3.1 The Quadrupole Theory: Expression for the Intensity in any Direction From equation (9c) of Section II, we can write

The theory states

b( CS)

=

t3a(2CS)

(14)

(15) where 13 is a constant with respect to source frequency; in general 13 = t3(M,Re) from experimental results , Fig. 37. The two· ·propos ed methods will refer to Fig. 37 to co~ute the v~ue of t3(M,Re), rather than t1:e value of about 2 sugges-ted by the theory with turbulence data insersugges-ted (Eq. (1)). The agreement between the theory with values of 13 from Fig. 37, and the measurements of Ref. 8.

(Section 1I-3), was in favour of using Fig. 37 as a universal reference for va1ues of 13. Equations (14) and (15) and :(9d) give

~B{e,CS) - ~B{90o,CS)

t3

=

H(e) $B(900,2CS) (16a)

or

(16b)

and with Eq. (6), the above equation can be written as

The 1/3 octave bandwidth intensity can be written as <I>J/3(e,cs)

=

~fI(e,CS)'"

~U/D SI(e,CS). Substitute in Eq. (17), we get

<I>1/3(e,cs)'"

4

S

[~B(900,CS)

+

~H(e)~B(900,2CS)J

C (e)

(18)

Equation 18 expresses the 1/3 octave intensity <I>1/3(e,cs) in terms of the ''basic directi vi ty" spectrum at e

=

900• ~he first term on the right hand side is the self noise and the second term is the shear noise. The convective ampli-fication c-

4

(e) multiplies the Doppler shifted basic self noise and the shear no"ise spectra. Th~ frequency in the Strouhal number S gi ves the constant per-centage bandwidth intensity <I>1/3( e ,Cp). The refraction effects which dominate' at small angles to the jet axis are not included.

Using Eq. (lOa), Eq. (16b) can be put in the form

<I>1{3(e,cs) <I>1/3(900,CS)

or in a decibel basis

10 log <I>1/3(e,cs) = 10 log + 10 log

3.2 First Method: Measurements

0 <I>1/3(90 ,CS)

C5~900~

[1 + ~H( e)

<PB(900,2CSlJ

C5 (e) ~B(900,CS) at Ninet;y DeSirees (19a) (19b)

This method suggests that only experimental measurements at e

=

900, with

Eq. (19), are enough to calculate the noise characteristics at any direction.

The steps are as follows:

(1)

(2)

(3)

Equations (l()) are used to convert the narrow band measurements <I>1/3(900,CS) to the "basic directivity" speqtrum ~B(900,CS). The value of ~(M,Re) is taken from Figs. 36 or 37.

Substi tute in Eq. (19) to get the narrow band intensity at any

direction ~1/3(e,cs).

Co~arison with EAperiment

The directivi ty C'UTves of the 1/3 octave intensity <I> 1/3 are cOIq?ared to Ahuja's measurements, Ref. 11, in Fig. 39. The curves were fitted at 900 with the measurements. Th~ directi vi ty curves are calculated for a source Strouhal number (CS) that ranges from 0.03 to l.O.

In Figs. 39a, b, c and d the method shows gooa agreement with experiment •

.An overestimation by the method at e = 1200 is shown in Figs. 39a, b andoc.

The sensitivity of the resuJ..ts to the value of t3'was tested for M = 0.54

and D = 2.84 in. In Fig.3ge, t3 is the measured value taken from Fig. 37 and

is equal to 2.82. The calculated curve agrees with experiment, except it again

overestimates <1>1/ at e = 1200 for all source frequencies. In the same figure

the value t3 = 2.03from the theory (Ref. 1) is used and the curve shows the same trend with little difference.

The value' of t3 = 0 is used in Fig. 3ge, which is the condition of neglecting

the shear noise contribution. For t3 = 0, Eq. (19) gives 10 log <1>lj~(e,cs) =

10 log <1>lj~(900,CS) + 50 log C(900)jC(e). It is clear that the preaiction is

substantihlly impaired: the error runs as high as 5-6 dB. This implies - in

agreement with the theory - that the shear noise and self noise magnitudes are camparable.

3.3 Second Method: Universal Self Noise Spectrum

Variations 'of the source Strouhal number of the self noise peak (CS) with

Reynolds nurnber and Mach number are examined in Figs. 40 and 41 using Ahuja's data, Ref. ll.

Figure 40 shows a very small variation of (CS) with Re for each M. A

constant (CS)p for each Re (or diameter D) is

ass~R

and Fig. 41 shows a linear

relation between (CS)p and M which may be put in the farm, (CS)p= K

3- 0.1 M where

K3 is a constant (or a very weak function of Re) •

A universal self noise spectrum can then be extracted by replotting the

different self noise spectra in such a way that,

(1) they are shifted to peak together, i.e., by using a new source Stroupal number that satisfies the relation

(CS) = (CS) + 0.1 M;

e

(2) they are all of unity peak, i.e., in the form a(CS) ja •

e max

(20)

In Fig. 42; the differenia~ self noise spectra from Ahuja' s measurements

are shown to collapse reasonably to a universal curve. Chu' s measurements at M = 0.85 were used as a check and are shown to agree well with the eiiIpirical universa1 self noise spectrum.

Method of Solution

The narrow band directi vity <1>( el) at each source Strouhal nurnber (CS) can

be calculated by the following steps: ·

(1)

(2)

Evaluate (CS) from Eq. (20).

e

From the universal self noise spectrum, Fig. 426 evaluate the ratio cJ>B[900 , (2C.S) e]/cJ>B[900, (CS) e ]which equalw cJ>B(90 ,2CS)

jcJ>B

(900 ,CS) • Evaluate t3(M,Re) from Figs. 36 or 37.

(4) Substitute in Eq. (19) to obtain th~ narrow band directivity ~(8,CS).

(5) Repeat to yie1d directivity ~(8,CS) for different source Strouhal number.

(6) A cross-plot will produce the spectrum at any direction 8.

(7) The overall sound pressure level (OSPL) at direction 8 can then be

derived by integration of the spectrum over source Strouhal number

(CS). All values of 8 must be greater than 400 in order to avai d

the zone where the neglected refraction-diffraction effect is important. COrnparison with Experiment

(i) 1/3 Octave Directivity Curves

The directivity curves of the 1/3 octaveintensity ~l/ are compared to

measurements by Ahuja (Ref. 11), Chu {unpublished) and Lush (Ref. 14) in Figs. 43 to 45. These curves are calculated for a source Strouhal number that ranges from 0.03 to l.O.

All figures show gene rally good agreement with experiment. This deteriorates

in Fig. 43 for M

=

0.71 and Fig. 45 for M

=

0.87 at small Strouhal nwnber CS and

at small angles with the jet axis.

The refraction effect must be brought into the theory at small 8, which wi1l reduce the intensity to show "refraction valley" for the hot jet.

(ii) 1/3 Octave Intensity Spectra

The 1/3 octave intensi ty spectra at di~ections 1200, 600 and

45

0 with the

jet axis are compared with Ahuja's measurem~nts (Ref. 11) in Fig. (46).

Compari-son with measurements by Chu (unpublished) is in Fig. (47).

Figure 46 shows that the method overestimates the intensity spectrum at

8 = 1200 conrpared to Ahuj a' s experimental values.

However, the method shows a better agreement wi th Chu' s me as urements • In

Fig. 47 the agreement is fairly good at large angles (8

=

1100) , while the only

discrepansy is that the calculated intensity is higher by 2 dB over the experiment

at 8

=

45 and cs

=

l.O.

Dl. CONCLUDING REMARKS

The present work is one of several attempts to verify, use and compare Ribner's development of Lighthill's theory with experimental measurements. The following are some conc1uding remarks about the present study:

1. The "basic directivity" of jet noise which results on excluding the effects

of convection and refraction, could be unambiguously decomposed into self noise and shear noise components. These had the general form predicted by the theory.

2. The basic self noise spectrmn peaks approximately an octave higher than the

basic shear noise spectrmn as suggested by one version of the theory (the ratio of the peak frequencies average 1.92 and varied from 1.66 to 2.25).

3.

4.

The predicted ~imi1arity between the shifted se1f noise spectrum a(2CS) and the shear noise spectrum b(CS) was most apparent for source Strouhal number (cs) ranges between 0.3 and l.O. (The ratio b(CS)/a(2CS)= ~ was near1y constant wi th CS.)

This simi1arity was exp10ited in a forma1ism for jet noise prediction uti1izing the theory with a minimum of empiricism. In the "First Method" a mean empirica1 va1ue of ~ (average over a spectrum) is used at given D and M, together with jet noise measurements at 900 at Cf and Cf/2; directivity curves re 900 are generated for e~ch f. In the "Second Method" a universal curve of se1f noise at 90 is used.

The ca1culated directi vi ty patterns showed very good agreement wit h experiment within the range 300

<

9

<

1100, whi1e an overestimation is

0

.

' 1. Ribner, H. S. 2. Ribner, H. S. 3 • Lighthi11, M. J. 4. Lighthi11, M. J. 5. Ribner, H. S. 6. Laurence, J. C. 7. Davies, P.O.A.L. Barratt, A. L. Fisher, M. J. 8. Lassiter, L. W. HUbbard, H. H. 9. MacGregor, G. R. Ribner, H. S. Lam, H. 10. Ahuja, K. K. 11. Ahuja, K. K. Bushe11, K. W. REFERENCES

"The Generation of Sound by Turbulent Jets", Advances in App1ied Mechan~cs, Vol. 8, 103-182, 1964.

"Q,ua.drupo1e Corre1ations Governing the Pattern of Jet Noise". J. of F1uid Mech., August 1-24, 1989. "On Sound Generated Aerodynamica11y. I. General Theory". Proc. Roy. Soc., A211, 564-587, 1952. "On Sound Generated Aerodynamica11y. 11. Turbulence

as a Source of Sound". Proc. Roy. Soc., A222, 1- 32, 1954. "Aerodynamic Sound from F1uid Di1ations - A Theory of Sound from Jets and Other F1ows", University of Toronto Insti tute for Aerospace Studies, urIAS Report 86,

1962.

"Intensity, Sca1e and Spectra of Turbu1ence in Mixing Region of Free Subsonic Jet". NACA Report 1292, 1956.

"Turbulence in the Mixing Region of a Round Jet". ARC 23, 728-N200-FM3181, 1962.

"Some Resu1ts of Experiments Re1ating to the Generation

of Noise in Jets". J. Acoust. Soc. Amer., Vol. 27, No.3, 431-437, 1955.

" 'Basic' Jet Noise Patterns Af ter De1etion of Convection and Refraction Effects: Experiments vs. Theory". J. of Sound and Vibration, 27(4), 437-454, 1973.

"Corre1ation and Prediction of Jet Noise". J. of Sound and Vibration, 29(2), 155-168, (1973.)

"An Experimental Study of Subsonic Jet Noise and Com-parison wi th Theory". J. of Sound and Vibration, 30( 3) , 317-341, 1973.

12. Mo11o-Christensen,E. "Experiments on Jet F10ws and Jet Noise Far Field Spectra Kolpin, M. A. and Directivity Patterns". Mass. Inst. of Tech.,

Martucce11i, J. R. Aeroe1astic and Struct. Res. Lab. ASRL TR 1007, 1963. 13. Mani, R.

14. Lush, P. A.

15. Grande, E.

"A Moving Source Prob1em Relevant to Jet Noise". J. of Sound and Vibration, 25(2), 337-347,1972.

"Measurements of Subsonic Jet Noise and Conrparison with Theory". J. of F1uid Mech., 46, 477-500, 1971.

"Refraction of Sound by Jet Flow or Jet Temperature" • University of Toronto, Institute for Aerospace Studies, TN 110, (NASA CR-840 (1967)).

APPENDIX: SIMILARITY BETWEEN SIIEAR NOrsE AND SELF NOISE SPECTRA

The following is a mathematical analysis that uses Ribner's equations

(Refs. 1 and 2) with experimental observations (Refs. 6 and 7) to show that both

the shear noise and the self noise can be expressed in one form. This is shown to be valid in the mixing and the transition regions of the jet.

The power emitting from unit volume at distance x along the jet axis

(Ref. 2) J!.:S.-'; ;:

P(x,9 )

~

C- 5[A + B cos4

e ;

cos2

eJ

where A ,.., p2W4U4L3/p C5 is the basic self noise spectra

m 0 0

(A.l)

B ,.., p2w4u2ifL3/p C5 is the basic shear noise spectra. w is the source frequency,

m 0 0

L if;l the scale of turbulence, and u, U are the turbulent and local mean velocity

components respectively.

The emission from a volume elemept in the form of an annular ring

dV

=

2ny dy dx (Fig. A.l) is dP

=

d~(w/C)6(w/C)

y

dy

D x

FIGURE A.l: CO-ORDINATE SYSTEM

where d~(W/C) is the spectral density from dV, and 6(w/C) is the frequency

band-width which is proportional to the observed frequency w/C for the case of constant percentage bandwidth, i.e.,

(A.2)

From Eqs. (A.l) and (A.2), the self noise and shear noise density spectra from dV can be written as

dep

~ sh P 2 w

3

u2 uf L

3

4

2 _m~--=,.--.-__ dV cos e +2 cos e

c

5

é

Po 0

The terms of the right hand side of Eq. (A.~) can b~ expressed in terms of the variables y and x. C = [(1 - M

ccdte)2 + w2L /77CQ2 ]1/2tne convection factor. In the mixing region the conditions M

=

U ./2C and w2L'~ /77C 2 constant, are

c 2J 0 / 0

approximated. Hence C

=

[(l-M cose)2 +

a

M 2] 1 2 E c(e,M). L is the scale of

c c

turbulence and can be wriiiten as

L = L (0_.:l!:, - M) (A.4a)

in the three regions of the jet. w is the source frequency and can be expressed in the form

u

max W " '

-L (A.4b)

where u (x) is the maximum value of the turbulent velocity component u at a gi ven

max

location x. Thus w is taken to be invariant in a "slice" of jet. Then, Eq. (A.3)

is written as

P 2 H(e)

&Psh(y,x)"" m u3 (x) u2(y,x) uf(y,x) Y dy dx P C 5 C4 max

o 0

By integrating along a "slice" of jet,

The constants

IS

and K3 are mainly functions of the Mach number, M, and the

Reynolds number, Re. .

The self-similarity il1 the turbulent velocity component u and the mean veloçity components U in the mixing and the transition regions can be used in evaluating the integrals in Eq. (A.5), i.e"

(A.6)

4

2

,.. U. x

J

(lb)

J

(~J d~

_J

where T) ;:: y + D/2/x. The experimental results in Ref. 7 show,

(A.7) dep se (x) == [K₄U4 2 3 j; (I1+ I2)]x umax(x) dx

}

(A.8a) dep sh (x) 4 x2u3 (x) 'CE{ ;:: [K₅U_j (I₃ + I₄)] max

where I).., I2' I3 and I4 are pure number s which can be evaluated from Eqs. (A.6) and (A.7) with F1(T}) and F

2

(T})

at certain value af (D/~) from Ref. 7.

Equation (A.8a) can be written as

d!P

se 2 3

dx (x);:: K6 x umax(x)

}

(A.8b)

~Sh

2

3

where K6 and

K7

are constants.

Equations (A.4a) and (A.4b) show that the source frequency is a function of :lÇ only, i. e • ,

The function F (x) can be evaluated from Refs. 6 and 7. From (a.9) and (A.8), the self noise

~d

shear noise density spectra from the jet can be evaluated using,

(A.10)

Equations (A.8) to(A.10) show the similari ty between the self noise and the shear noise density spectra if calculated along the mixing and the transition regions. In using Eqs. (A.9) and (A.10) to derive the self noise and the shear noise density spectra, the theory's assumption of an octave difference between them must be taken into consideration.

In fact, Eqs. (A.8) te (A.10) can be used to evaluate the "basic directivity" spectrum and then proceed to evaluate the other jet noise characteris tics by the theoryas in Sections

(n)

and (lIl).

i

t' D :: :A C ~ c: ~ ~ ~ :ö ~ o o 0.5 0.5 / b(cs) SHEAR NOISE 1.0

(I)

1.0 Ahuja 0"2.84 In UJ"400 ftll x 1.5 (CS) Ahuja 0"2.84 in UI "600 ftll 1.5 (CS)

i

t' ~ = ~

..

~ ~ ~ :ö .'i o Q5

(3)

0.25

(2)

(4)

bICS) :CS) "+.(90") 10 0.5 Ahuja 0" 2.84 In UI" 100ft" (CS) Ahuja 0" 2.84 in Uj" 1000 ft/. (CS) Q75

I! ~ r: ~ i ~

.

.:

_::l ,., E :ö .'i o o 0.5 1.0

(5)

bCCS) 4>8 C45°) 0.5 1.0

(6)

Allljo D- 2.4 In Uj- 300 fil. x (CS) Ahuja D-2.4in Uj-400ft/ • x (CS) J! ·ë ::l t' ~ :ö ~

=

·E ::l t' ~ :ö .'i o o 0.5 bICS) 0.5 accs) - •• C9O") 1.0

(7)

4>8C45°) lO

(8)

FIGS. 5-8. BASIC SELF NOISE SPECl'RUM a (CS) , WITH SPECI'Rm1 FIOi MFASUREMENTS AT

8=45 DEGREES, AND THE EXTRACTF.D BA..c;rc SHEAR NOISE SPEX:'I'RUM b(CS).

(CONrINUED) • AhuJa D -2.4 In Uj-SOOft/. Ahuja D-2.4 in Uj-eOO ft/. (CS) (CS)

•

!

t'

:

i

! ë ~ t' ~ :a C 0 o ales) -+'190'\ -: 0.5

(9)

4>.(~ 0.5

,

(10)

Ahuja o -2.4 In UJ-IDDO fth - - - e 1.0 ales) - 4>.(90") x CS IB Atalja o -U12in ut-400ft,. (CS) Q !! -i: ~ l:' ~ :a C J!

'

"

~ ,.. ~ :a C Ahuja 0- L1111. IIJ-tOOft/. / bt;s)

~~

0 - - ' - ', ' ' . .' " ·t,OO"I _ a -' 0.5 '

(11)

4>. (45°) 0.5

(12)

a (es) -4>.(90") 1.0 (CS) Ahuja o -l52 In UI-800ft/. _ _ 13 cs

.

=

c ~ ~ g ~

"

i ~ ,., Ii ~ :Q è

•

.S

(13)

+.

(4SO) '" Ahuja 0-1.52111 ~.IOOOft" a (CS) ' . . 190'1 Chu 0·21n Uj.743.lftll (CS) o • i ~ ~ g :<i .'i o O.S a(CS) ",-190")

(15)

<10.14,.) 1.0

l~

./

~~

!! 'ë ~ ~ g o

~

/ a(cs) , / ',,(90") \

x'

,

Ir

0

"-

~

₀ 0

-.-O.S 1.0 (CS)

(14)

~

"

o

,

_,

X---.

(16)

"

_"

.... 'x lO

FIGS. 13-16. BASIC SELF mISE SPECl'RUM a(CS), WITH

sp~UM

FRGi MFASUREMENI'S AT

8-45 DOOREES, ANI) '!HE EXTAACTED BASIC SHEAR NOISE SPB:TRUM b(CS)

«(X)Nl'INUED) • Chu 0·2 •

\4-"'.5"'.

)c o (CS) Chu o -21n Uj -989.1 ftll (CS)

~ ë, J ~ ~ ~ c:( o +. (4~·)

•

1.0

+.

(60·) 2.0 Molla Christen .. n et ol 0-1.0 In M

-0.,

(UJ.6~ ft/Il 3.0 (CS)

FIG. 17a. SPECl'RA FR:M MFASUREMENI'S AT 6=45° and 60°.

l! 'ë J ~ ~ .Q .'i o .5 ~(CS)/Omo~ [0 (CS)/Omax] 1.0 Molla Christensen et al o alO in M-O.'(Uj"6~ft/.; 1.5 (CS)

1.0~ ~ e ~ ol I 0 DJ 10 Q o x o x GIl I 0.2 x o GD ~ ~ )( 0 I 0.3

(18)

•

o x X 0 I 0.4 o x )( 0 I O.~ o x Ah.Ija 0- LIS21n UI-400ft'" @) O(2CS)/Omal X b(CS)/bmal ~ I 0.6 0.7 Aroja o -l~2In Uj-600 ft/a e O(2CS)/Omax X _{b(CS)/ b mal} o x CS

0'

I I I I I ' ! o al 02 0.3 0.4 0.5 0.6 07 CS

(19)

Ahujo 0- 2.4 In UJ-!OO ft/I e o(2CSlIO max 1.0 lil X b(CS)/bmal ~ ~ ~ ~

•

Cl< ~ I!!

•

~ 0 0 0.1 02 0.3 04 á5 a6 07 (CS)

(20)

FIGS_ 18-20:

COMPARISON OF NORMALIZED SELF NOISE

ANI) SlIEAR NOISE SPECTRA (the se1f

noise has been down-shifted one octave)

1.04- lID 0 x 'j(

ol

I 0 0.1 Aruja 0-2.4in Uj-aOOftls x el a(2CS)/a_maa 0 x _X b (CS)/bmal 0 _x 0 1'1 ₀ 1.0~ GIl _GIl <:> X <:> X )( 0 ~ X <:> <:> x 'X ₀ X 0 x X I I I I I I 0.2 Q3 0.4 0.5 0.6 07 CS

ol

I I I I 0 0.1 0.2 0.3 0.4

(22)

(24)

·

Ahlja o -2.84 In Uj -4ooft/, tl _{o(2CSI/O maa} X blC.SI/bmax x <:> _X <:> X 0 I I I 0.5 0.6 0.7 CS

LOt- _{0 ~} 0 X 0 X X. 0 X Ol , , 0 0,1 02 1.0l- ₀ & _~ 0 X 0 X x

ol

I I 0 0.1 0.2 Ahuja D -L52 I" Ahuja US-100ft.,. _{D -2.4111} UI-IOOOft/, t> o(2csl/amaa 1.0

"

X b(CSl/bmaa ₀ <:> e a(2CSl/Omax

"

<:> " x b (CS) /b maa 0 0 ~ X <:> X 0 " <:> <:> )( ₀ ~ x <:> " <:> <:> X 0 x l<. " x , , , , 0 , 0,3 0.4 0.5 0.6 0.7 CS 0 Ol 0.2 Q3 0.4 ~ 0.6 0.7

(25)

(27)

Ahuja D -2.84 Ahuja UI-600ft/, _{D -1.52 In} Uj-IOOOft/,

E> a(2csl/O maa

X X bC CSl/ b maa 0 X 0 X 0 ~ lil 0.3 Q4 0.5 0.6 I.Ot- a!! _x 0 ~ o a(2CS)/amaa 6 _~ X bCcs)/b maa 0 ~ 0 ₀ X X 0 0

J

X X X I I I I I I 0.7 CS 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

(26)

(28)

: FIGS. 25-28: COMPARISON OF NORMALIZED SELF NOISE AND SHEAR NOISE SPECTRA

(the self noise bas been down-shifted one octave)(CONTINUED)

CS

Ahujo Chu

D "2.84 In D-2 in

ut"eoo ftll Uj-887.5ftll

1.0 ... _{~ tf. 'IC.} 1.0 0 e _x

0 'IC. ~ a (2CSl/o mox x 0 (!) O(2CSl/<lmox

0

x b (C_{Sl/b max} x x b(CSlI b max

x 0 0 0 lID 'IC. ₀ ~ Q _Q 0 ~ ~ x e X (;) 0 y. 0 x ol I I I I I I I 0 0 al 0.2 0.3 04 0.5 0.6 0.7 _CS 0 Ol 0.2 0.3 04 05 06 07 CS

(29)

(31)

Chu Mollo Christensen

0-2 in 0-1 in Uj -743.1 ftll M -0.8 (Uj"SSO ft/s) 1.0+ 0 lil x _{o o(2CSl/Omax}

'"I

Ö _{~ O(2CSl/omax} 0 x x b(CSl/b mOlt lil X b(CSl/b mox x 0 0 <lil _I!S 0 lil x x _{0 \11} x Q 0 lil x 0 e x 0 Q x 0' I I 1 1 1 1 1 0 0 0.1 Q2 0.3 0.4 05 0.6 0.7 CS 0 0.1 0.2 0.3 0.4 0.5 0.6 (CS)

(30)

(32)

n

_Mani

_{

_:,

M = 0.91

} Mc=0.65M

M - 0.54

{

~

M - 0.91 ,

0

-2..

-4 ..

8

k7,v

Ahuja

M = 0.73

.0

=1.52

11

M = 0.54

.0

=2. 4

ti

"

M = 0.36

.0

=2.4

11

"'"

~

6

4

"-2

'"

x

o

o

0.5

1.0

cs

log SHEAR NOISE (CS) log

f3

SELF NOISE

(2CS)

cs

:E

AHUJA 0 0= 2.4 in M=0.54 0 0 0 _~ 0

0

0 0 0

:[

0 M=0.71 0 <:) ₀ 0 0 0---{;) _{0 0}

:E

M=0.90 al

_0----0

0 0 (3 ₀ 0 ~

..

0 ₀

CQ

Ct 0=2.84 in M=0.36 0

-

5

0 0 0

0

MOLLD- CHRISTENSEN 0= 1.0 in M=0.80

:[

0

_0--0---0

0 0 0

0-:F

CHU 0=2.0 in M=0.85 0 0 0

~

0---0

0 ₀ 0 0

0

0.25

0.5

CS

10 log IJ +10

~

~

Oal.!J2 In +0 I 1 1 Q5 1.0 M o

FIG. 35. VARIATION OF f3 WITH MACH NUMBER M

(FJO.1 MEASUREMENTS OF REP. 11).

10 leg ,9 +10 M o 0.90 o Q. 71 A 0.54

o

036

~

o I I I I o 1.0 2.0 3.0 0 il)

FIG. 36. VARIATION OF f3 WITH JET DIAMETER D (FRC»1 MEASUREMENl'S OF REF. 11). +20-10100,9 +10 ~~

~~o:~

.

--~

_~

0. .

_---0----_ _---0----_ _---0----_ . _ _ . 0.72 ' I

...::::~ ~

- ' V ".O.90 -o. f §==§§f

-===-- -

-

-

"

o _{0.2 0.}I _{4 06} I _{I I I} . 0.8 1.0 1.2 Rex 10-6

FIG. 37. VARIATION OF f3 WITH REYOOIDS NtJ.1BER Re

(FJO.1 MEASUREMENrs OF REP. 11).

leg r u = log Uj +0.5 o -0.5 o o L assiter et al X/D -3.0 Y/D -0.5 -lO I I I I I o Ol 0.2 0.3 0.4 106 x Re

'FIG. 38: DEPENDENCE OF TURBULENCE INTENSITY

r

=

u/U. ON REYNOLDS NUMBER Re

4>

1/3

(dB)

J..

IOdB

T

0= 1.52in. 0=2.4in. _{0 = 1.52in. 0= 1.52in.}

M=0.36(Uj =400ft/a) M=0.36(Uj =400ft~ _{M=O.54(Uj=600ft/s) M=O.9(Uj=IOOOft/s)}

o

30 60 90 120

8°

(a)

(b) _{(c) (d)}

o

Ahuja

_{Thaory (}

_Ist

_Mathod)

0=2.84In.

M=0.54(Uj =60Oftll)

M (CSlp

I

'" 036 0.6 ~ 054 e 0.12 o Q9() 0.4' 'il' 0.36 0.54 6 ê A ~12 a '" e 0 110,...0_.90 _ _ _ 0 0.2 Ol , ! ! , 02 04 0.6 oe 10 1.2 1.4 1.6 Re X 106

FIG.

40:

VARIATION OF SOURCE STROUHAL NUMBER

OF SELF NOISE SPECTRUM PEAK (CS)

WITH REYNOLDS NUMBER Re. P

(C5I Peak O.~' 0.2 0.1 o 0.5 1.0 _M

FIG. 41: VARIATION OF SOURCE STROUHAL NUMBER OF SELF NOrSE SPECTRUM PEAK (CS)

WITH MACH NUMBER M. P

a

ainax

o

C> c;] G •

•

M.0.9} M • 0.71 (Ahuja) M '0.53 M • 0.341 M • 0. 8~ -(ChII) (CS). -CS+OIM

FIG" 42: EMPIRICAL UNIVERSAL SELF NOISE SPECTRUM a(CS)e/amax"

D= 1.52in.

M=0.54(Ut600ft.ls.)

<PI''''~---'

(dB)

10

80

70

80

7 0

1 - ' - - ' _ . . . L - - - L - - - I

o

30 60 90 120

•

D=2

.

84in

.

D=2.4in.

M= O

.

71(Ut800ftJs)

M=0.9(Uj =IOOOft./sJ

90

80

100

8 0

~I - - - '

90 ,--'

--'_-'----L~

8

0

t P l / ' " ' r - - - ,

(dB) .---__ 90 80 90

o

=2in. M=0.85 {Uj=887.5ft./sJ

o

Lush Theory (!) CS=.03 [lkliVersai O{CS)e/Omax] A 0.1

o

0.3 " 1.0

< P 1 / 3 r - - - .

(dB) 80 0= 2il. M=0.69 (Uj= 743 ft./s.) CS=1.0 80~--~--~~~~=-~~)

o

20 40 60 80 100 90 60 60 50 40 30

v

0 15 30 45

8

0

8

0 <:) Chu Theory (45) (44)

FIGS. 44-45: DIREX:TIVITY OF 1/3-a:::TAVE INTENSITY: CCWARISON WITH EXPERIMENTAL DATA OF

CffiJ ANI) liJSH.

Ma_O.87

M=0.37

•

q,1/3

[dB)

100

100

90

70

60

50

0

Ahuja

o

8=120

o

---Theory

.

~

~~:

[Universal C(CS),/Crnax ]

o

o

o

o

o

0.5

D=2.4in

M=O.90

o

D=2.84ïn

M=O.71

0=1. 52in.

M=0.54

CS

FIG. 46: SPECrRA OF 1/3--ocTAVE INTENSITY AT DlRECI'IOOS

e

=

45°, 600 and 120°: aNARISCN WI'IH

EXPERIMENT AL DATA OF AHUJA.

<1>1/3

(dB)

100

90

60

0

Chu

Theory

[Universal

a(cs), /a

_max]

o

8=110

0 Cl

70

0 A

45

0

~_A

____

--~A~---~t:.

[~

D

~

~

0

-0= 2.01n

M= 0.85(Uj =887.5 ft/s)

~B

~

t:.

g

V

0

D=2in

M=0.69(U =743.lft/s)

0.5

1.0

FIG. 47: SPOCTRA OF lj3-cx:::TAVE JNl'ENSI'I'Y AT DIRECTIrns

9

=

45°, 70° and 110°: CCMPA'RISrn WITH

EXPERIMEN'I7\L DAT].\. OF CHU.

CS

UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

REPORT DOCUMENT ATION PAGE _{BEFORE COMPLETING FORM} READ INSTRUCTIONS

I. REPORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

AFOSR-TR 7s-04Q6 .

4. TITLE (and Subt/tle) 5. TYPE OF REPORT 8< PERIOD COVERED

CORRELATION OF JET NOISE DATA IN TERMS OF _INTERIM

A SELF NOISE-SHEAR NOISE MODEL

6. PERFORMING ORG. REPORT NUMBER

illIAS TEeR. NOTE NO. 193

7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)

Nagy Sabet Mikhail Nosseir AFOSR-70-1885A

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK

AREA 8< WORK UNIT NUMBERS

University of Toronto, 681307

Institute for Aerospace studies 9781-02

Toronto Ontario (!::ln.<",'lA ];1102F

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE

Air Force Office of Scientific Research/NA, Jenuary 1975 1400 Wilson Blvd., Arlington, Va. 22209, U.S.A. 13. NUMBER OF PAGES

41

14. MONITORING AGENCY NAME I!t ADDRESS(if dillerent Irom Contro/lin~ Office) IS. SECURITY CLASS. (ol thls report)

UNCLASSIFIED

15a. DECLASSI FI CATI ON/ DOWNGRADI NG

SCHEDULE

16. DISTRIBUTION STATEMENT (ol thls Report)

Approved for pUblic release, distribution unlimited.

17. DISTRIBUTION STATEMENT (ol the abstract entered In Block 20, if diflerent Irom Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side iI necessary and Identlly by block number)

1. Acoustics 2. Jet Noise _{3. Aerodynamic} Noise

20. ABSTRACT (Continue on reverse slde 11 necessary and Identily by block number)

The theoretical formalism of Ribner (1964 and 1969) was applied in the

analysis of a large body of experimental jet noise data. It· was found that the "basic directivity" which results on excluding convection end refraction

effects could be decomposed unambiguously into self noise and shear noise. The basic self noise spectrum peaked approximately one octave higher then the shear noise spectrum, end the peak amplitudes were roughly in the ratio two to one. upon frequency shifting end normalizing alignments, the two spectra were

DO

FORM

UNCLASSIFIED

SECURITY CL.ASSIFICATION OF THIS PAGE(When D.I. Enlered)

found to match weil in shape. All these properties are in accord with the

theory.. The self noise-shear noise spectral similarity was applied in a _I

formalism for jet noise prediction utilizing the theory. An empirical input

- the value of ~ ~ shear noise peak/self noise peak (the approximate

theoretical value .~

=

2 works nearly as well) - is applied to generate narrow

band directivity curves re 9

=

90° relative to the jet axis. Agreement with

experiment was generally very good within the range 30°

<

9

<

110°, which

excludes the refraction-dominated valley. -

tJrIAS TECI!IIICAL NarE NO. 193

Institute for Aerospace Studies, University of T oronto

CORRELATION OF

=

NOISE DATA IN TERMS OF A SELF NOISE-SIIEAR NOISE MlDEL

Nosseir, Nagy Sabet M1khail 20 pagea (approx) 50 figurea

l. Acoustics 2. Jet Nolse 3. Aerodynamic Helse

I. Nosseir, N. S. M. 11. UI'IAS Teelmical Hote No. 193

The theoretical formalism of Ribner (1964 and 1969) was appl1ed in the analysis of a

large body of experimental jet noise data. It was found that the "basic directivity"

,.,hich results on excluding convectlon and refraction effects coUld be decanposed

un-ambiguously into sel.f noise and shear nois.!. The basic selt nolse spectrum peaked

approximatel.y one-octave higher than the shear noise spectrum, and the peak. amplitudes

were roughly in the ratio wo to one. Upon frequency shifting and normal.izing

align-rnents, the two spectra were found to match weil in shape. All these properties are in

accord with the theory. The self noise-shear noise spectra.l. sim1larity was appl1ed in a formalism for jet noise prediction utili zing the theory. An ~irica.l. input is

the value of ~ ~ shear noise peak/self noise peak (tbe approx1ma.te tbeoretica.l. va.l.ue

~ = 2 works nearly as weU), is appl1ed to generate narrow band directivity curves re

900 • exc1uding tbe "refraction valley". Agreement with experiment was gene rally good: very good witbin tbe range 0.3 to 1.0 in aource Strouhal number. Discrepancy outside

th1s range could be accounted for by postulat1ng varlable convectlve ampllfication as

a fWlctlon of f'requency (ct. recent 'WOrk of Mani).

~

tJrIAS TECI!IIICAL NarE NO. 193

Institute for Aerospace Studies, University of T oronto

CORRELA1'ION OF

=

NOISE DATA IN TERMS OF A BELF NOISE-SIIEAR NOISE MlDEL

Nosseir, Nagy Sabet Mikball 20 pagea (approx) 50 figures

1. Acoustles 2. Jet Nolse 3. Aerodynamic Nelse

I. N08selr, N. S. M. 11. 11rIAS Technic&l. Hete No .• 193

The theoretical formaJ.1sm of Ribner (1964 and 1969) was appl1ed in tbe analyaia of a

large body of experimenta.l. jet noise data. It was found that the "basic directivity"

wbicb results on excluding convect1on and refraction effects could be decanposed un-ambiguously into self noise and sbear noise. Tbe basic self noise spectrum peaked

approximately one octave higher than the sheu noise spectrum, and the peak amplit\dea

were rouglUy in the ratio two te one. Upon frequency shiftlng and normallz1ng &llgn ..

ments, the two spectra were found to match weU in shape. All these properties are in

accord with the tbeory. The selt nolse-shear nolse spectral similarity was applled

in a formalism for jet noise prediction utili zing the theory. An empirica.l. input is

tbe value of ~ ~ sbear noise peak/self noise peak (the approximate tbeoretica.l. v.a.l.ue

~ = 2 works nearly as weU), is applied to generate narrow band directivity curves re

900 , excluding the "refraction valley". Agreement witb experiment was genera.l.ly good: very good witbin the range 0.3 to 1.0 in source Stroubal number. Discrepancy outside

tbis range could be accounted for by postulating variable convecti ve amplification as a function of freQ.uency (cf. recent werk of Man1).

~

Available co pies of th is report are limited. Return this card to UTIAS, if you require a copy. Available copies of this report are limited. Return this card to UTIAS, if you require 11 copy.

tJrIAS TECIINICAL NOTE NO. 193

Institute for Aerospace Studies, University of T oronto

CORRELATION OF

=

NOISE DATA IN TERMS OF A SELF NOISE-SIIEAR NOISE MJDEL

Nosseir. Nagy Sabet Mikhall 20 pages (approx) 50 figures

1. Acoustics 2. Jet Noise 3. Aerodynamic Noise

I. Nosseir, N. S. M. II. tJrIAS Technica.l. Note No. 193

The theoretica.l. formaJ.ism of Ribner (196" and 19(9) was appl1ed in the analysis of a

large body of experiment al. jet noise data. It was fO\U'1d that the "basic directivity"

which results on excluding convection and refractlon effe cts could be decatrposed

Wl-ambiguously lnto selt' nolse and shear noise. The basic self nolse spectrum peaked

approximately one octave higher than the shear noise spectrum, a':'ld the peak. amplitudes

were roughl.y in the ratio two to one. Upon frequency shifting and normal .... zing

align-ments, the two spectra were found to match weil in shape. All these properties are in

accord with the tbeory. The self noise-shear noise spectra.l. sim11arity was applied

in a formalism for jet noise prediction utili zing the theory. An empirica.l. input is

the va.l.ue of ~ ~ shear noise peak/self noise peak ·(the approximate theoretica.l. va.l.ue

~ = 2 works nearly as well), is applied to generate narrow band directivity curves re

900, excludlng the "refraction valley". Agreement with experiment was generally goo<1:

very good within the range 0.3 to 1.0 in source StrouhaJ. number. Discrepancy outside th1s range could be accounted for by postulating variable convective ampli:flcatlon as

a t'unctlon of frequency (ct. recent werk of Ma.n1).

~

Available copies of th is report are limited. Return this card to UTIAS, if you require a copy.

tJrIAS TECI!IIICAL NarE NO. 193

Institute for Aerospace Studies, University of T oronto

CORRELAT ION OF

=

NOISE DATA IN TERMS OF A SELF NOISE-SIIEAR NOISE lilDE!.

Nosseir, Nagy Sabet Mikhail 20 pages (approx) 50 figurea

1. Acoustics 2. Jet Noise 3. Aeroc!ynamic Noise

I. Nosseir, N. S. M. Il. tJrIAS Technica.l. Note No. 193

The theoretical formalism of Ribner (1964 and 19(9) was applied in the analysis of a

large body of experimenta.l. jet noise data. It was found that the "basic directivity"

which results on excluding convectlon end refractlon effects cOuld be decamposed

un-ambiguously into self nolse and shear nolse. The 'basic selt nolse spectrum peaked

approximately one octave higher then the shear nolse spectrum, and the peak amplitu:les

were roughly in the ratio two to one. Upon frequency shifting end normallzing

align-ments, the two spectra were found to match weil in shape. All these propertles are in

accord witb tbe tbeory. The self noise-shear noise spectra.l. aim1larity was applied

in a formalism for jet noise prediction utili zing the theory. An ~irica.l. input is

the value of ~ ~ shear noise peak/ self noise peak (tbe approx1ma.te theoretical value

~ = 2 works nearly as weU), is applied to generate narrow band directivity curvea re

900_{, excluding tbe "refraction valley". Agreement with experiment was genera.l.ly good:}

very good witbin tbe range 0.3 to 1.0 in aource Strouhal number. Discrepancy outaide

tbia range could be accounted tor by postulating variable convecti ve amplification as

a function of freQ.uency (cf. recent wrk of Mani).

~