Algorithm to integrate the Ffowcs Williams-Hawkings equation on supersonic rotating domain

Abstract

The numerical solution of the Ffowcs Williams-Hawkings equation (Ffowcs Williams, J. E., and Hawkings, D. L., Sound Generation by Turbulence and Surfaces in Arbitrary Motion, Philosophical Transactions of the Royal Society, Vol. A264, No. 1151, 1969, pp. 321-342) on a rotating supersonic domain is discussed. Based on the emission-surface algorithm, the adopted solver performs the integration on the so-called acoustic domain to avoid the Doppler singularity in the integral kernels. The presence of multiple emission times for the supersonic source points and the particular time evolution of the integration domain force the use of a particular data-fitting procedure on both the geometrical and integral quantities. The algorithm may be used in the numerical prediction of the quadrupole source term for helicopter rotors operating at a high transonic regime and in the aeroacoustic analysis of the modern propeller blades, rotating at supersonic tip speed.