Abstract
The acoustic analogy proposed by Lighthill in 1952 in his jet noise theory provides an exact governing equation of noise generation away from the flow region. The generalization of Lighthill’s equation in the presence of moving surfaces by Ffowcs Williams and Hawkings in 1969 was a major advance. The primary impact of the governing equation of noise generation known as the Ffowcs Williams-Hawkings (FW-H) equation has been in the prediction of the noise of rotating blades such as high speed propellers and helicopter rotors. Since the mid-seventies many researchers have derived solutions to the FW-H equation in both the time and frequency domains. Sophisticated computer codes for noise prediction based upon the acoustic analogy have been developed with highly realistic blade geometry, kinematics and aerodynamic input. As a result of the demand by aeroacousticians, much effort has gone into the development of high resolution aerodynamics for use in acoustic codes. The acoustic analogy is now in a mature stage. The aircraft industry is beginning to rely on codes based on the acoustic analogy to control aircraft propulsion system noise. In this paper, we argue that, because of the exact nature of the FW-H equation, the availability of high quality aerodynamic data, sophisticated acoustic codes and high performance computers, the acoustic analogy is an important and useful tool of computational aeroacoustics. Some examples for advanced propellers and rotors are presented.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baeder, J. D., McCroskey, W. T., and Srinivasan, G. R., 1986. “Acoustic propagation using computational fluid dynamics,” In Proc. of the 42nd AHS Annual Forum & Tech. Display.
Brentner, Kenneth B., 1986. “Prediction of helicopter rotor discrete frequency noise-a computer program incorporating realistic blade motion and advanced acoustic formulation,” NASA TM-87721.
Brentner, Kenneth S. and Farassat, F., 1992. “Helicopter noise prediction: The current status and future direction,” In Presented at the DGLR-AIAA 14th Aeroacoustics Conf. (to appear in J. Sound Vibration, 1993), Aachen, Germany, May 11–14, 1992.
Burton, D. E., Schlinker, R. H., and Shenoy, R., 1985. “The status of analytical helicopter noise prediction methods,” NASA CR-172606.
Crighton, D. G. and Parry, A. B., 1992. “Higher approximation in the asymptotic theory of propeller noise,” AIAA Journal 30(1), pp. 23–28.
Curie, N., 1955. “The influence of solid boundaries upon aerodynamic sound,” Proc. Roy. Soc. A 231, pp. 505–514.
Dunn, M. H. and Farassat, F., 1992. “High-speed propeller noise prediction — a multidisciplinary approach,” AIAA Journal 30(7), pp. 1716–1723.
Dunn, Mark H., 1991. The Solution of a Singular Integral Equation Arising from a Lifting Surface Theory for Rotating Blades, Ph.D. Thesis, Old Dominion University.
Farassat, F., 1977. “Discontinuities in aerodynamics and aeroacoustics: The concept and applications of generalized derivatives,” J. Sound Vibration 55(2), pp. 165–193.
Farassat, F. and Brentner, K. S., 1988. “The uses and abuses of the acoustic analogy in helicopter rotor noise prediction,” Journal of the AHS 33, pp. 29–36.
Farassat, F., Lee, Yung-Jang, Tadghighi, H., and Holz, R., 1991. “High-speed helicopter rotor noise — shock waves as a potent source of sound,” In Proc. of the AHS/RAeS International Technical Specialists’ Meeting on Rotorcraft Acoustics and Rotor Fluid Dynamics, Philadelphia, PA.
Farassat, F. and Myers, M. K., 1986. “Aerodynamics via acoustics: Application of acoustic forumulas for aerodynamic calculations,” AIAA-86–1877.
Farassat, F. and Myers, M. K., 1988. “Extension of Kirchhoff formula to radiation from moving surfaces,” J. Sound Vibration 123(3), pp. 451–460.
Farassat, F. and Myers, M. K., 1991. “Aeroacoustics of high speed rotating blades: The mathematical aspect,” To appear in the Proceedings of 3rd IMACS Symposium on Computational Acoustics, Cambridge, MA, June, Harvard University.
Farassat, F., Padula, S. L., and Dunn, M. H., 1987. “Advanced turboprop noise prediction based on recent theoretical results,” J. Sound Vibration 119(1), pp. 53–79.
Farassat, F. and Succi, G. P., 1983. “The prediction of helicopter rotor discrete frequency noise,” Vertica 7(4), pp. 309–320.
Ffowcs Williams, J. E., 1984. “The acoustic analogy — thirty years on,” IMA Journal 32, pp. 113–124.
Ffowcs Williams, J. E. and Hawkings, D. L., 1969. “Sound generated by turbulence and surfaces in arbitrary motion,” Phil. Trans. Roy. Soc. A 264, pp. 321–342.
George, A. R., 1978. “Helicopter noise — state of the art,” Journal of the Aircraft 15(11), pp. 707–715.
Gel’fand, I. M. and Shilov, G. E., 1964. Generalized Functions, Volume 1 of Properties and Operations, Academic Press, New York.
Hanson, D. B., 1991. “Unified aeroacoustic analysis for high speed turboprop aerodynamics and noise (Vol. 1), Development of theory for blade loading, wakes and noise,” NASA CR-4329.
Hanson, D. B. and Fink, M. R., 1979. “The importance of quadrupole sources in prediction of transonic tip speed propeller noise,” J. Sound Vibration 62(1), pp. 19–38.
JanakiRam, R. D., 1990. “Aeroacoustics of rotorcraft,” AGARD-R-781.
Jones, D. S., 1982. Generalized Functions, McGraw-Hill Publishing Company, London, Second Edition.
Kanwal, R. P., 1983. Generalized Functions- Theory and Technique, Academic Press, New York.
Lele, S. K., 1992. “Direct computation of aerodynamic noise,” In these Proceedings.
Lighthill, M. J., 1952. “On sound generated aerodynamically — I. General theory,” Proc. Roy. Soc. A 211, pp. 564–587.
Lowson, M. V., 1992. “Progress towards quieter civil helicopters,” Aeronautical Journal 96(956), pp. 209–223.
Magliozzi, B., Hanson, D. B., and Amiet, R. K., 1991. “Propeller and propfan noise. Aeroacoustics of flight vehicles: Theory and practice, Vol. 1: Noise sources,” NASA Ref. Publ. 1258.
Morgans, W. R., 1930. “The Kirchhoff formula extended to a moving surface,” Phil. Mag. 9, pp. 141–161.
Schmitz, F. H., 1991. “Rotor noise,” NASA RP-1258.
Schmitz, F. H. and Yu, Y. H., 1979. “Theoretical modelling of high speed impulsive noise,” Journal of the AHS 24(1), pp. 10–19.
Tadghighi, H., Holz, R., Farassat, F., and Lee, Yung-Jang, 1991. “Development of shock noise prediction code for high-speed helicopters — The subsonically moving shock,” In Proc. of the 47th Annual Forum & AHS Technology Display, Phoenix, AZ.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag New York, Inc.
About this paper
Cite this paper
Farassat, F. (1993). The Acoustic Analogy as a Tool of Computational Aeroacoustics. In: Hardin, J.C., Hussaini, M.Y. (eds) Computational Aeroacoustics. ICASE/NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8342-0_7
Download citation
DOI: https://doi.org/10.1007/978-1-4613-8342-0_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4613-8344-4
Online ISBN: 978-1-4613-8342-0
eBook Packages: Springer Book Archive