A NEW BOUNDARY INTEGRAL FORMULATION FOR THE PREDICTION OF SOUND RADIATION

Abstract

A new boundary integral formulation is presented for the evaluation of the noise radiated in a uniform medium by generic sources. To use the method one requires knowledge of the pressure, velocity, and density disturbances on a smooth closed surface surrounding the source, and to assume that the propagation is linear outside the surface itself. When applied to the prediction of transonic rotor noise the method can be used in the same manner as the Kirchhoff approach, but the new integral equations are derived without requiring the non-penetration condition in the Ffowcs Williams–Hawkings equation. The method is therefore referred as the Kirchhoff–FWH. The main advantage of the proposed formulation in respect of the Kirchhoff method is that it does not require the knowledge of the surface pressure normal derivative. Additionally, it can be applied also for bodies with permeable surface, while the classical FWH equation is not valid in this case. Two different formulations are presented, which differ in the way in which a time derivative is handled, and some general issues on the numerical efficiency of the two formulations are addressed. Comparisons with experiments, and with Kirchhoff and FWH methods, are presented for a hovering rotor in transonic conditions at various tip Mach numbers.