Some Analytic Results for the Study of Broadband Noise Radiation from Wings,Propellers and Jets in Uniform Motion

Abstract

Alan Powell has made significant contributions to the understanding of many aeroacoustic problems, in particular, the problems of broadband noise from jets and boundary layers. In this paper, some analytic results are presented for the calculation of the correlation function of the broadband noise radiated from a wing, a propeller, and a jet in uniform forward motion. It is shown that, when the observer (or microphone) motion is suitably chosen, the geometric terms of the radiation formula become time independent. The time independence of these terms leads to a significant simplification of the statistical analysis of the radiated noise, even when the near field terms are included. For a wing in forward motion, if the observer is in the moving reference frame, then the correlation function of the near and far field noise can be related to a space-time cross-correlation function of the pressure on the wing surface. A similar result holds for a propeller in forward flight if the observer is in a reference frame that is attached to the propeller and rotates at the shaft speed. For a jet in motion, it is shown that the correlation function of the radiated noise can be related to the space-time cross-correlation of the Lighthill stress tensor in the jet. Exact analytical results are derived for all three cases. For the cases under present consideration, the inclusion of the near field terms does not introduce additional complexity, as compared to existing formulations that are limited to the far field.

Get full access to this article

View all access options for this article.

References

Powell

: On the Aerodynamic Noise of a Rigid Flat Plate Moving at Zero Incidence, J. Acoust. Soc. Am., 31(12), 1959, pp. 1649–1653.

Hubbard

H. H.

(Editor): Aeroacoustics of Flight Vehicles – Theory and Practice, Volume 1, Noise Sources, Acoustical Society of America, 1995.

Meecham

W. C.

: Surface and Volume Sound From Boundary Layers, J. Acoustical Society of America, 37(2), 1965, pp. 516–522.

Siddon

T. E.

: Surface Dipole Strength by Cross-Correlation Method, J. Acoustical Society of America, 53(2), 1973, pp. 619–633.

Meecham

W. C.

: Theory of Air Frame Noise: J. Acoustical Society of America, 57(6), Part II, 1975, pp. 1416–1420.

Miller

W. R.

and Meecham

William C.

: Large Scale Model Measurements of Airframe Noise Using Cross-Correlation Technique, J. Acoustical Society of America, 71(3), 1982, pp. 591–599.

Brooks

T. F.

and Humphreys

W. M.

: Flap-Edge Aeroacoustic Measurements and Predictions, J. of Sound and Vibration, 261, 2003, pp. 31–74.

Lighthill

M. J.

: On Sound Generated Aerodynamically. I. General Theory, Proceedings of the Royal Society of London, A 211, 1952, pp. 564–587.

Williams

Ffowcs J. E.

and Hawkings

D. L.

: Sound Generation by Turbulence and Surfaces in Arbitrary Motion, Philosophical Transactions of the Royal Society, A 264, 1969, pp. 321–342.

10.

Powell

: Thoughts on Boundary Layer Noise, Aeronautical Research Council (Great Britain) Report A.R.C. 16727, F.M. 2061, April 1954.

11.

Powell

: Aerodynamic Noise and the Plane Boundary, J. Acoust. Soc. Am., 32(8), 1960, pp. 982–990.

12.

Curle

: The Influence of Solid Boundaries on Aerodynamic Sound, Proc. Roy. Soc. (London), A231, 1955, pp. 505–514.

13.

Farassat

and Succi

G. P.

: The Prediction of Helicopter Rotor Discrete Frequency Noise, Vertica, 7(4), 1983, pp. 309–320.

14.

Brentner

K. S.

: Prediction of Helicopter Rotor Discrete Frequency Noise- A computer program incorporating realistic blade motions and advanced acoustic formulation, NASA Technical Memorandum 87721, October 1986.

15.

Casper

and Farassat

: A New Time Domain Formulation for Broadband Noise Prediction, Int. J. of Aeroacoustics, 1(3), 2002, pp. 207–240.

16.

Farassat

and Brentner

K. S.

: The Uses and Abuses of the Acoustic Analogy in Helicopter Rotor Noise Prediction, J. American Helicopter Society, Vol. 33, 1988, pp. 29–36.

17.

Brentner

K. S.

: An Efficient and Robust Method for Predicting Helicopter High-speed Impulsive Noise, J. Sound & Vibration, 1997, 203(1), pp. 87–100.

18.

Morris

P. J.

and Farassat

: Acoustic Analogy and Alternative Theories for Jet Noise Prediction AIAA J., 40(4), April 2002, pp. 671–680.

19.

Gelfand

I. M.

and Shilov

G. E.

: Generalized Functions: Properties and Operations, Volume 1, Academic Press, New York 1964.

20.

Farassat

: Introduction to Generalized Functions With Applications in Aerodynamics and Aeroacoustics, NASA Technical Paper 3428, 1994 (Corrected April 1996), Available at: http://techreports.larc.nasa.gov/ltrs/PDF/tp3428.pdf

21.

Farassat

and Myers

M. K.

: An Analysis of the Quadrupole Noise Source of High Speed Rotating Blades, Computational Acoustics – Scattering, Gaussian Beams, and Aeroacoustics, Lee

Cakmak

Vichnevetsky

, Editors, Vol. 2, pp. 227–240, 1990.

22.

Ribner

H. S.

: Theory of Two-Point Correlations of Jet Noise, NASA Technical Note, TND-8330, 1976.

23.

Williams

Ffowcs J. E.

: The Noise from Turbulence Convected at High Speed, Philosophical Transactions of the Royal Society of London, Vol. 255, 1964, pp. 469–503.