Correlation and prediction of jet noise

Journal of Sotald and Vibration (I 973) 29(2), 155-168

CORRELATION AND PREDICTION OF JET NOISE K. K. AHUJA~ Department of Mechanical and Aerospace Engineering, Syracuse University, Syracuse, New York 13210, U.S.A.

(Received 19 October 1972, and in revisedform 8 March 1973)

Measurements of subsonic jet noise made on a model jet rig in the anechoic chamber of the National Gas Turbine Establishment are presented. Jet noise spectra for three nozzles of diameters 2"84, 2"4 and 1.52 inches have been obtained. Considerable care has been taken to ensure that unwanted noise from sources such as valves and ducting upstream of the nozzle are insignificant compared with the jet mixing noise. Attempts have then been made to collapse all the data points obtained on to one curve. This is done first of all by normalizing the 1/3 octave and overall sound pressure levels for the theoretical parameters obtained from Lighthill's theory. Empirical schemes are then presented to collapse the data for all the angles and the frequencies. The prediction schemes for I/3 octave SPL, PWL and OASPL and OAPWL are considered. The schemes presented predict noise accurately for cold and clean jets.

1. INTRODUCTION Most o f the published jet noise prediction schemes generally use curves o f overall sound pressure levels (OASPL's) at a given angle to the jet axis as a function of jet velocity. The OASPL's are usually normalized for jet density, distance and the nozzle area. A well-known example of this is by Coles [1 ], which is the original Rolls-Royce scheme and the SAE method. Shortcomings in both these methods have been recognized over the years and the Rolls-Royce method has been substantially modified, first after the merger with Bristol Engines, when opportunity was taken to combine data from both sources and later when the significance o f "excess" noise was appreciated [2, 3]. The outline of the latest Rolls-Royce method has been given in a paper by Bushell [2], although since it is a review paper full details are not given. The SAE method has recently been reviewed by Smith [4] and includes some of the data presented in this paper. The aim o f the study reported in this paper was to take a fresh look at the correlation problem, investigate the difficulties and suggest modifications that may improve the correlation of data. During the past three years, a detailed study of cold subsonic model jets has been made by Ahuja [3, 5] at Rolls-Royce Ltd. and the National Gas Turbine Establishment (N.G.T.E.) and by Lush [6] at the University of Southampton. The data from the former study will be used here. t Formerly at Rolls-Royce Ltd., Derby, and Institute of Sound and Vibration Research, University of Southampton, England. 155

156

K.K. A H U J A

2. DESCRIPTION OF THE DATA The data used in this paper were obtained on a model subsonic jet rig which had a very large contraction ratio (e.g., 250:1 for a nozzle diameter of 1.52 in). Ahuja [3, 5, 7] has shown that this rig was free from upstream noise sources (i.e., valve noise, pipe noise, turbulence noise, etc.) and the turbulence levels in the nozzle exit plane were less than 89%. A full far-field survey was carried out on three nozzles of 2.84 in, 2.4 in and 1.52 in diameter in the anechoic chamber of N.G.T.E., Pyestock. The noise measurements were made at a polar distance of 6 ft from the centre of the nozzle exit plane. The 1/3 octave data as used for the correlation and prediction of jet noise are shown as spectra in Figures 1 and 2. The actual SPL's are presented in a tabulated form in references [3] and [5].

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Frequency(kHz) Figure I. 1/3 octave spectra for nozzle diameter = 1.52 in. Jet velocity values: (a) 1000 ft/s; (b) 900 ft/s; (c) 800 ft/s; (d) 600 ft/s; (e) 400 ft/s; (f) 200 ft]s. Values for 0: x, 30~ +, 45~ [3, 60~ zx, 90~ O, 120~

157

CORRELATION A N D PREDICTION OF JET NOISE

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Figure 2. 1/3 octave spectra for nozzle diameter = 2.84 in. Jet velocity values: (a) 1000 ft]s; (b) 800 ft/s; (c) 700 ft/s; (d) 600 ft/s; (e) 400 ft/s; (f) 300 ft/s. Values for 0: - - , 20 ~ • 30 ~ +, 45 ~ 13, 60 ~ zx, 90 ~ O, 120~

3. THE CORRELATION METHODS U S E D 3.1. 1/3 OCTAVE SPL AND LIGHTHILL'S EQUATIONS

Attempts were made to compare the 1/3 octave noise levels for the "clean" jet noise with Lighthill's [8, 9] theory of jet noise generation. This was done by plotting SPL-

lolog ( ~ ) -lOlogo~- lOlo~1- Mocos0)-s § lOlo~~R/6)= fD

versus

log-r-;-. (1 -- M c c o s 0), vj

(1)

158

K.K. AHUJA

where SPL = 1/3 octave sound pressure levels f r o m Figures 1 and 2, Vj - - j e t exit velocity in ft/s, D = nozzle diameter in ft, 0 -- angle in degrees with the jet axis, R -- distance in feet of the measuring point from the centre of the nozzle, f = I/3 octave centre frequency in Hz, M~ -- convection M a c h n u m b e r = 0.65 Mj, M~ = m e a n jet M a c h n u m b e r = V j / a o , ao -- ambient velocity o f sound in ft/s. Relationship (1) arises from Lighthill's model o f c o n v e c t e d quadrupoles. Since the sources are in motion, convected at M a c h n u m b e r Me, the observed frequencies must be corrected by the D o p p l e r factor to convert to the source frequency: i.e., fsot,,r $6 I

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Figure 3. Normalized 1/3 octave SPL's against Doppler corrected Strouhal number. D = 1-52 in. Values for 0: x, 30~ +, 45~ El, 60~ A, 90~ O, 120~ 36/I LD

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CORRELATION AND PREDICTION OF JET NOISE

159

The source frequency is then normalized as a Strouhal number and this ensures that sources in geometrically similar positions in the jet are considered. These correlations are shown in Figures 3 and 4 for the nozzles of diameters 1-52 in and 2.84 in, respectively. These two figures indicate that, with the exception of the angles of less than 45 degrees to the jet axis, Lighthill's theory holds good at all angles, especially at low frequencies (for (fD/Vj) (1 - Mccos0) < 1). One can thus use these curves to predict noise levels for angles of 45 degrees and higher to an accuracy of 4-1 dB at these frequencies. This scheme, however, demands an improvement in the collapse of the data at small angles to the jet, especially at the higher frequencies. 3.2.

1/3

SEMI-EMPIRICAL SCHEME TO PREDICT

OCTAVE NOISE LEVELS AT SMALL ANGLES

3.2.1. High frequency As can be seen in Figures 1 and 2, the spectra at small angles to the jet axis (i.e., 20 and 30 degrees) show a sharp decrease in levels at high frequencies. In references [3] and [7] this effect has been attributed to the refraction due to the velocity gradients and the scattering of the small wavelength (i.e:, high frequency) sound due to the eddies in the mixing region of the jet. The important aspect of the spectra at these small angles was that their peaks were not dependent upon the jet velocity at all (see Figure 5) and the peak (fp) could be predicted by using

fop

0.2.

=

ao

(3)

Later, some attempts were made to see what velocity laws were followed by the high frequency noise at the smaller angles. The correlation curves were obtained by plotting S P L - 101og(V,) 4 - 101ogD 2 - 101og(1- Mccos 0)-' + 10log ( 6 ) v

versus

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(1 -- Me cos 0).

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Frequency(kHz) Figure 5. Clean jet noise spectra at 0 = 20~(to jet axis). Nozzle diameter = 2-84 inch.

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Values for ~ : x, 1000 ft/s; + , 800 ft/s; O, 600 ft/s; A, 400 ft/s.

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Figure 7. High frequency correlation o f 1/3 octave SPL's for clean jets. 0 = 20 ~ D = 2-4 in, R = 6 ft.

Symbols as in Figure 6 legend.

This is shown in Figures 6, 7 and 8. It is seen that by this means all the high frequency points beyond the spectral peak given by fP=

0 "2ao D

(5)

can be collapsed onto a single curve. Thus, for the high frequency noise at small angles, curve A2B2 of Figure 7 can be used to predict noise to an accuracy o f + l dB.

CORRELATION AND PREDICTION OF JET NOISE

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Figure 8. High frequency correlation of 1/3 octave SPL's for clean jets. 0 = 30 ~ D = 1-52 in, R = 6 ft. Symbols as in Figure 6 legend.

3.2.2. Low frequency A few correlation attempts were m a d e for n o i s e at l o w f r e q u e n c i e s (for s m a l l angles) by plotting 10log

SPL-

- 101ogD s - 10log(1 - M c c o s 0 ) -5 + 10log

- 10log(f) 2

log ( ~ - j ) 9

versus

(6)

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162

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T h u s the above e q u a t i o n completes our methods o f jet noise correlation, a n u m b e r o f w h i c h have been provided.

4. OVERALL S O U N D PRESSURE LEVELS (OASPL's) Figure 11 shows the directivity o f t h c OASPL's for the three nozzles. The theoretical curves are s h o w n in full line. O n an O A S P L basis the theory s e e m s to fit rather well excepting a slight deviation at the highest velocity. Therefore, as a first estimate, one can predict the I

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Angle to jet axis (degrees) Figure 11. Directivities of OASPL's for "clean" jet noise. (a) D = 2.84 in, (b) D = 2.40 in, (c) D = 1.52 in. Values for Vj: x, 1000 ft/s; +, 800 ft/s; Q, 600 ft/s; z~, 400 ft/s; e, 300 ft/s; O, 200 ft/s. ~ , T h e o r y g~ (I -- Mc cos 0) -s.

CORRELATIONAND PREDICTIONOF JET NOISE

163

OASPL's by reading any of the points in Figure 11 and applying an appropriate correction by using Lighthill's equations" i.e.,

I ~ p~ V] D 2 -- Me cos 0) -5,

(8)

at R z(1

Pc

where Pm is the density in the jet mixing region and Pc is the density of the ambient air. However, to make a more accurate prediction, the scheme originally used by Coles [I] and then described by Bushell [2] seems quite adequate for cold jets. The scheme consists of plotting

OASPL-'u'~

~-i]

log,o ~o

t'ersus

(9)

at each angle, where pj = PlSA to = hsA = Aj = =

fully expanded jet density, density of air at International Standard Atmospheric conditions, temperature of the ambient air, temperature of the air at I.S.A. conditions, nozzle exit area.

The above plot for the three nozzles (1.52 in, 2.4 in, 2-84 in) is shown in Figure 12. Plots for angles between 20 and 120 degrees only are available. To predict noise at any other angle, extrapolation should be made by using Figure I 1 in conjunction with Figure 12. In the absence of Figure 12, one can always predict the 1/3 octave SPL's from the other described schemes to the best obtainable accuracy and a value ofthe OASPL can be calculated by adding up 1/3 octave SPL's over a range of frequencies~

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t,'j(fr/s) Figure 12. Jet noise correlation at different angles.

164

K.K. AHUJA

5. P O W E R

WATT

LEVELS

(PWL's)

The 1/3 octave PWL's were calculated by integrating the 1/3 octave SPL's between 0 -- 20 ~ and 0 = 120 ~ (see reference [3]). The resulting I/3 octave PWL spectra are shown in Figure 13. Some extra noise sources appear to be present at the lowest velocity. The corresponding OAPWL's (overall power watt levels) are shown to follow a V~ law (Figure 14). The data are collapsed by normalizing the I/3 octave PWL's with respect to the OAPWL's. Once again, the degree of collapse is rather good. If all three of Figures 15, 16 and 17 are superimposed the degree of collapse is of the order of 4-1.5 dB over most of the frequency range.

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Frequency (kHz) Figure 13. 1/3 octave P W L spectra for the three nozzles. (a) D = 2.84 in, (b) D = 2.40 in, (c) D = 1.52 in. Values for V~: x , 1000 It/s; +, 800 ft/s; D, 600 It/s; zx, 400 ft/s; o , 200 ft/s.

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vj(ft/s) Figure 14. Velocity dependence of O A P W L ' s (normalized with respect to nozzle diameter = 2.4 in). A, D = 2.84 in; O, D = 2.40 in; 0 , D = 1-52 in. - - , Theory V~[(1 + M~)[(1 - M~)'].

CORRELATION AND PREDICTION OF JET NOISE -4

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IOglo(lOl I/i ) Figure 15. Correlation of 113 octave PWL's. D = 2.84 in. Values for Vj: x , 1000 ft/s; + , 800 ft/s; El, 600 ft/s; zx, 400 ft/s.

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logJo(fD/V| ) Figure 16. Correlation of I/3 octave PWL's. D = 2-40 in. Symbols as in Figure 15 legend.

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-I- 6

l

-I.4

I

-I'

f

2

-I.0

I

-0'

I

8 -0'6

f

f

I

-0-4

-0.2

-0.0

I

I

f

I

0"2

0"4

0"6

0-8

1.0

Ioglo(fD/~ ) Figure 17. Correlation of 1/3 octave PWL's. D = 1-52 in. Symbols as in Figure 15 legend.

166

K.K. AHUJA

6. OVERALL POWER WATT LEVELS A scheme similar to OASPL prediction can be used to predict the OAPWL's. For jets at temperatures between 8~ and 25~ the curve o f Figure 14 can be used with reasonable accuracy only by applying the D 2 correction when predicting OAPWL for another nozzle of diameter D. For an accurate prediction the curve of Figure 13 should be used where the normalizing factor is similar to the one in Figure 18 except that the 1/R 2 term is missing. Thus the correlation is obtained by plotting O A P W L - lOlog,o

versus

\7--I

log,o

.

(lO)

160

"-T'._ %

,~176 I

~,~o

140 I 130

o<

v

12O o

o~ 0 I

IlO

10_007

I

I

I

-o6

r

-os

[

I

r

-o4

I

I

-oa

I

-o.2

I

I

-0.,

0

IOg~o (v/ao) L 20O

I 300

I 400

I 5OO

l 600

f 7OO

I 800

I 900

I I000

l/rift~s) Figure 18. Jet noise correlation for overall power watt levels. A, D = 2.84 in; O, D = 2"40 in; El, D= 1-52 in. 7. CONCLUSIONS The existing methods o f jet noise prediction require separate graphs--one for each angle. If the correlations are done at angles relative to the peak noise angle then a supplementary graph showing the variation of the peak angle with the jet velocity is also required. Moreover, some o f the data used in the past is suspected to be coloured with "excess" noise (see the papers by Bushell [2] and Ahuja [3]). The present data are known to be the least affected by any upstream noise sources except at the lowest velocities where the jet noise levels were similar to those o f the measuring electronic equipment. This is illustrated in Figure 19. The schemes presented here predict noise to an acceptable degree o f accuracy and possibly better than any o f the published schemes [I0]. A summary of the prediction schemes is as follows. (1) Use Figure 12 for the prediction of OASPL's. (2) For 0 > 45 ~ use Figure 3; use curve A~B 1 over the whole frequency range. (3) For 0 < 45 ~ use curve A2B2 (Figure 7) for prediction o f 1/3 octave SPL's above fD/ao= 0.2. BelowfD/ao=0.2, curve AaBa (Figure 9) should be used. For the power watt level prediction, Figure 15 in conjunction with Figure 18 will give the best results.

CORRELATION 190

I

I

I

I

I

AND PREDICTION

I

I

I

I

I

167

OF JET NOISE I

I

I

I

I

I

I

I

I

I

I

180

170

16G

% ~ &o ~m

~-

=I

15c

LEGEND 14C

Engines 9 Viper 520 9 Medwoy O l y m p u s 2 2 R v Spoy Olympus 1 0 4 a Polos = Viper 20 e Conwoy 9 Avon

-I

130

Al-t

_o

Airjets

9

mo

t t It

n 0

I 0-78..5 i n 2 Conicol I 2.4 t- 4 5

1250 K 1050 K O05K 470K 300 K

! I0

4 I0 ,, Co~- Di~ 5 0 . 3 " Conical Plug nozzle r cone

llO

I00

I1 I

-0"7

I -O-6

I

I -0.5

I

t

I

300

400

t -0.4

I -03 I 500

600

Stondord

day

I -0.2

I, -0.t

I 700

I

t I O O-I IOg~o ( I,~/o, ) I I I 1

800 900

jet velocity

I000

1200

I

I 0.2

I

I 03

ZO 59 20 45 @3

I

I 04

i

,, j ,,,,,,d " 't t.z~ f,~..,. ~,-~,.~" .I' '''~0"~ d " Conicot

I

I 05

I 06

1.500

(ft/s]

Figure 19. Jet noise correlation,peak polar OASPL. From reference[2]. It is to be noted that the data used in the present work are from cold jets alone. The effect of temperature on jet noise still largely remains to be resolved. The choice of the density function pj Po in equation (9) is still subject to much debate. The earlier form of correlation factor given by Coles [1] contained a density function pZ, as does the SAE method, which, incidentally, appears to be used by most American companies. The factor PjPo was originally used by Bristol Siddeley Engines and was adopted by Rolls-Royce Ltd generally, following the merger of the two companies. A number of investigations are currently under way to determine the most suitable density function. An attempt has already been made by Cocking and Jamieson [1 I] to study the effect of temperature on this density function. It appears that PjPo can be written as (pj)O,where to is a function of both the jet temperature and the velocity. This point, however, needs further investigation. The present results may thus not be of utmost value for the prediction of hot jets but should prove useful as a basis of comparison and as an initial estimate of the jet nois~e. ACKNOWLEDGMENTS The author would like to thank D r K . W. Bushell of Rolls-Royce Ltd. and Professor A . D . Young of Queen Mary College, London, for initiating this project and for their continued interest, useful criticism and many valuable suggestions. Thanks are also due to D r M. J Fisher and many of my colleagues at Rolls-Royce Ltd. and at the Institutelof Sound and Vibration Research for many profitable discussions.

168

K.K. AHUJA

Permission has been given by both Rolls-Royce Ltd and N a t i o n a l Gas Turbine Establishment, Pyestock to publish this work and is gratefully acknowledged.

REFERENCES I. G. M. CoLts 1963.4eronautical Quarterly 14, l-16. Estimating jet noise. 2. K. W. BUSHELL1971 Journal of Sound and Vibration 17, 271-282. A survey of low velocity and coaxial jet noise with application to prediction. 3. K. K. AHUJA 1972 M.Phil. Thesis, University of London. An experimental study of subsonic jet noise with particular reference to the effects of upstream disturbances. 4. M . J . T . SMITH 1972 Rolls-Royce Report, IR00142. Proposals for the jet noise prediction. (Issued to SAE members.) 5. K. K. AnrdJg and K. W. BOSHELL1971 Aeronautical Research CouncilPaper No. 33 110-N749. An experimental study of subsonic jet noise with particular reference to the effects of upstream turbulence and swirl. Part I. Datum tests to determine pure jet mixing noise. 6. P. A. Luslt 1971 Journal of Fhdd Mechanics 46, 477-500. Measurement of subsonic jet noise and comparison with theory. 7. K. K. AtlUJA and K. W. BUSHELLTo be submitted to Journal of Sound and Vibration. An experimental study of subsonic jet noise and comparison with theory. 8. M. J. LIGHTHILL 1952 Proceedings of the Royal Society A211, 564-578. On sound generated aerodynamically: I. General theory. 9. M. J. LIGHTHILL1954 Proceedings of the Royal Society A222, 1-21. On sound generated aerodynamically: II. Turbulence as a source of sound. 10. I. C. CHEESEMAN1972 University of Southampton. Personal communication. I I. B.J. COCKINGand J. B. JAMIESON1971 (August) National Gas Turbhte Establishment, Pyestock, Report. Some preliminary notes concerning the effects of temperature on low velocity jet noise.