Electronic Journal Technical Acoustics ISSN 1819-2408

Z. C. Zheng, B. K. Tan, W. Li

On compact Green's functions and asymptotic expansions for flow-induced sound predictions

language: English

received 16.03.2006, published 21.04.2006

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ABSTRACT

Both compact Green's functions and asymptotic expansions are widely used to analytically predict sound generated by low Mach number (M<<1) fluid-dynamic sources, where the acoustic compactness of the source region is satisfied. By mathematically investigating the detailed assumptions involved in each of the two methods and by using two classical examples of flow noise problems, it is shown that the applicability of compact Green's function is restricted to a receiver location, r, at the acoustic far-field with ωr/c₀->inf where ω is the frequency and c₀ is the speed of sound, and that the solution from matched asymptotic expansions can be applied less restrictively starting at ωr/c₀~1. Significant differences between the two solutions are shown when ωr/c₀~1. In the acoustic far-field, the solutions from the two methods are analytically proved identical.

13 pages, 4 figures

Сitation: Z. C. Zheng, B. K. Tan, W. Li. On compact Green's functions and asymptotic expansions for flow-induced sound predictions. Electronic Journal “Technical Acoustics”, http://www.ejta.org, 2006, 8.

REFERENCES

1. Lighthill M. J. On sound generated aerodynamically I. General theory. Proceedings of the Royal Society of London, 1952, A 211, 564–587.
2. Lighthill M. J. On sound generated aerodynamically II. Turbulence as a source of sound. Proceedings of the Royal Society of London, 1954, A 222, 1–32.
3. Howe M. S. Trailing edge noise at low Mach numbers. Journal of Sound and Vibration, 1999, 225, 211–238.
4. Howe M. S. Edge-source acoustic Green's function for an airfoil of arbitrary chord with application to trailing-edge noise. The Quarterly Journal of Mechanics and Applied Mathematics, 2001, 54, 139–155.
5. Howe M. S. Theory of Vortex Sound. Cambridge University Press, Cambridge, U. K., 2003.
6. Kao H. C. Body-vortex interaction, sound generation, and destructive interference. AIAA Journal, 2002, 40, 652–660.
7. Crighton D. C. Radiation from vortex filament motion near a half plane. Journal of Fluid Mechanics, 1972, 51, 357–362.
8. Dowling A. P., Ffowcs Williams J. E. Sound and Sources of Sound. John Wiley and Sons, New York, 1983.
9. Abramowitz M., Stegun I. A. Handbook of Mathematical Functions. Dover, New York, 1965.
10. Kakac S., Yener Y. Heat Conduction. 3-rd edition, Taylor and Francis. Washington, DC, 1993.
11. Ffowcs Williams J. E., Hawkings D. L. Sound generation by turbulence and surface in arbitrary motion. Philosophical Transactions of the Royal Society of London, 1969, A 264, 321–342.
12. Wang M., Moin P. Computation of trailing-edge flow and noise using large-eddy simulation. AIAA Journal, 2000, 38, 2201–2209.

		Z. C. Zheng, Ph.D. (1993, Old Dominion University), is Associate Professor of Mechanical Engineering at Kansas State University. His research interests include fluid mechanics and aeroacoustics. e-mail: zzheng(at)ksu.edu
		B. K. Tan received her M.S. degree from Kansas State University in 2003 and her B.S. degree from University of South Alabama in 2001. She is currently working at IHS, Melaka, Malaysia.
		W. Li received his M.S. degree in Mechanical Engineering from Shanghai Jiao Tong University in 2000. He is a research assistant and a Ph.D. candidate at Kansas State University, Mechanical and Nuclear Engineering Department. Scientific interests: interaction of sound and flow, sound production and propagation, heat transfer and HVAC system. e-mail: wenhua(at)ksu.edu