Development of an Improved Kirchhoff Method for Jet Aeroacoustics

Research in the development of an improved Kirchhoff method is described. The Kirchhoff method is a means of evaluating radiated sound from flow acoustic quantities on a computational surface. The linear, homogeneous wave equation is assumed to be valid in the propagation region, outside this surface (the Kirchhoff surface). The surface quantities are generally obtained from a computational fluid dynamics (CFD) calculation of the acoustic near field. We outline the development of a Kirchhoff method for use when the linear, homogeneous wave equation is not valid in a portion of the region outside of the Kirchhoff surface. The new method is derived through the use of a permeable-surface formulation of the Ffowcs Williams-Hawkings equation. This modified integral equation allows the Kirchhoff methodology to be employed in problems with large, noncompact source regions that extend beyond the limits of the CFD calculation. Test calculations are presented in an attempt to validate the method for use in jet aeroacoustics studies. However, the method is presented in a manner to make it easily applicable in cases where Kirchhoff methods have been used in the past.