Wall-Cavity Acoustic Green's Function at Low Mach Number

Abstract

Analytical approximations are developed for the low Mach number, aeroacoustic Green's function for a rectangular or circular cylindrical open cavity in a plane, rigid wall. The formulae can be used to predict the sound radiated into the main flow from a knowledge of the hydrodynamic flow near the cavity. At low Mach numbers the sound is a small by-product of the main flow, whose hydrodynamic properties can first be determined from observation or from a numerical treatment of the incompressible Navier-Stokes equations. Detailed predictions are made of the lowest order, open cavity resonance frequencies, and it is shown how a resonance is excited by the unsteady drag, and also by the lift or drag force experienced by a small bluff body placed in the flow close to the cavity. The cavity resonance frequencies are complex, with imaginary parts depending primarily on radiation damping, which can be sufficiently large for a shallow, open cavity, that a distinct resonance peak is absent from the acoustic spectrum – for a square cavity such peaks are predicted only when the cavity depth exceeds about half the cavity length. For very shallow cavities the efficiency of sound production by volumetric pulsations within the cavity is comparable to that of free field turbulence quadrupoles, and therefore negligible at low Mach numbers.

Get full access to this article

View all access options for this article.

References

Howe

M. S.

1997 Edge, cavity and aperture tones at very low Mach numbers. Journal of Fluid Mechanics 330, 61–84.

Howe

M. S.

2002 Mechanism of sound generation by low Mach number flow over a wall cavity. Journal of Sound and Vibration (in press).

Batchelor

G. K.

1967 An Introduction to Fluid Dynamics, Cambridge University Press.

Taylor

1978 A transformation of the acoustic equation with implications for wind tunnel and low speed flight tests. Proceedings of the Royal Society of London A363, 271–281.

Howe

M. S.

1998 Acoustics of fluid-structure interactions, Cambridge University Press.

Powell

1961 On the edgetone. Journal of the Acoustical Society of America 33, 395–409.

Rayleigh

Lord

1945 Theory of Sound, Volume 2. New York: Dover.

Morse

P. M.

and Ingard

K. U.

1968 Theoretical Acoustics. New York: McGraw-Hill.

Abramowitz

and Stegun

I. A.

(editors) 1970 Handbook of Mathematical Functions (Ninth corrected printing), US Department of Commerce, National Bureau of Standards Applied Mathematics Series No.55.

10.

Lighthill

M. J.

1952 On sound generated aerodynamically. Part I: General theory. Proceedings of the Royal Society of London A211, 564–587.

11.

Rossiter

J. E.

1962 The effect of cavities on the buffeting of aircraft. Royal Aircraft Establishment Tech. Memo. 754.

12.

Rockwell

1983 Oscillations of impinging shear layers. American Institute of Aeronautics and Astronautics Journal 21, 645–664.

13.

Rockwell

and Naudascher

1978 Review – self-sustaining oscillation of flow past cavities. Transactions of the American Society of Mechanical Engineers, Journal of Fluids Engineering 100, 152–165.