A new Kirchhoff formulation for transonic rotor noise

A new boundary integral formulation is presented for the evaluation of the noise radiated in an uniform medium by generic sources. The method requires the knowledge of pressure, velocity, and density disturbances on a smooth closed surface surrounding the source, and assumes 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 Kirchhoff approach, but the new integral equations are derived releasing the non penetration condition in the Ffowcs-Williams Hawkings equation. The method is therefore referred as Kirchhoff-FWH. The main advantage of the proposed formulation in respect of Kirchhoff method is that it does not require the knowledge of the surface pressure normal derivative. Two different formulations are presented that differ in the way in which a time derivative is handled. Comparisons with experiment and with Kirchhoff method are presented for a hovering rotor in transonic conditions at various tip Mach numbers.