The Uses and Abuses of the Acoustic Analogy in Helicopter Rotor Noise Prediction

This paper is theoretical in nature and addresses applications of the acoustic analogy in helicopter rotor noise prediction. It is argued that in many instances the acoustic analogy has not been used with care in rotor noise studies. By this it is meant that approximate or inappropriate formulations have been used. By considering various mechanisms of noise generation, such abuses are identified and the remedy is suggested. The mechanisms discussed are thickness, loading, quadrupole, and blade-vortex interaction noise. The quadrupole term of the Ffowcs Williams-Hawkings equation is written in a new form which separates the contributions of regions of high gradients such as shock surfaces. It is shown by order of magnitude studies that such regions are capable of producing noise with the same directivity as the thickness noise. The inclusion of this part of quadrupole sources in current acoustic codes is quite practical. Some of the difficulties with the use of loading noise formulations of the first author in predictions of blade-vortex interaction noise are discussed. It appears that there is a need for development of new theoretical results based on the acoustic analogy in this area. Because of the impulsive character of the blade surface pressure, a time scale of integration different from that used in loading and thickness computations must be used in a computer code for prediction of blade-vortex interaction noise.

[1]  L. J. Bober,et al.  Numerical evaluation of propeller noise including nonlinear effects , 1986 .

[2]  F. Farassat,et al.  A new capability for predicting helicopter rotor and propeller noise including the effect of forward motion , 1977 .

[3]  J. E. Ffowcs Williams.  The Acoustic Analogy—Thirty Years On , 1984 .

[4]  F. Farassat,et al.  Theory of Noise Generation From Moving Bodies With an Application to Helicopter Rotors , 1975 .

[5]  F. H. Schmitz,et al.  Transonic rotor noise: Theoretical and experimental comparisons , 1980 .

[6]  W. R. M. M.Sc.  XIV. The kirchhoff formula extended to a moving surface , .

[7]  D. B. Hanson,et al.  The importance of quadrupole sources in prediction of transonic tip speed propeller noise , 1978 .

[8]  W. R. Splettstoesser,et al.  Acoustic results of the blade-vortex interaction acoustic test of a 40 percent model rotor in the DNW , 1987 .

[9]  Roger C. Strawn,et al.  Prediction of high-speed rotor noise with a Kirchhoff formula , 1987 .

[10]  Fredric H. Schmitz,et al.  Theoretical Modeling of High‐Speed Helicopter Impulsive Noise , 1979 .

[11]  C. Kitaplioglu,et al.  A study of the far-field sound due to unsteady shocks on rotors , 1977 .

[12]  Albert R. George,et al.  Transonic blade-vortex interactions - The far field , 1987 .

[13]  F. Farassat.  Linear Acoustic Formulas for Calculation of Rotating Blade Noise , 1981 .

[14]  Mahendra C. Joshi,et al.  Prediction of blade-vortex interaction noise using measured blade pressures , 1987 .

[15]  G. P. Succi,et al.  The prediction of helicopter rotor discrete frequency noise , 1982 .

[16]  D. L. Hawkings.  Noise Generation by Transonic Open Rotors , 1979 .

[17]  F. Farassat,et al.  Quadrupole source in prediction of the noise of rotating blades - A new source description , 1987 .

[18]  F. Farassat,et al.  Extension of Kirchhoff's formula to radiation from moving surfaces , 1988 .

[19]  Kenneth S. Brentner.  A prediction of helicopter rotor discrete frequency noise for three scale models using a new acoustics program , 1987 .

[20]  F. Farassat,et al.  A numerical technique for calculation of the noise of high-speed propellers with advanced blade geometry , 1980 .

[21]  J. Baeder,et al.  Acoustic propagation using computational fluid dynamics , 1986 .

[22]  D. L. Hawkings,et al.  Sound generation by turbulence and surfaces in arbitrary motion , 1969, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[23]  F. Farassat.  Theoretical analysis of linearized acoustics and aerodynamics of advanced supersonic propellers , 1985 .

[24]  Y. Nakamura,et al.  Prediction of blade-vortex interaction noise from measured blade pressure , 1981 .

[25]  Donald B. Hanson,et al.  Compressible Helicoidal Surface Theory for Propeller Aerodynamics and Noise , 1983 .

[26]  F. Farassat,et al.  Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations , 1986 .