Surface and volume quadrupoles in the prediction of propeller noise

Starting with some results from recent theoretical investigation on quadrupole source of Ffowcs Williams-Hawkings equation, an attempt is made of improving the performance of a propeller noise prediction procedure. In particular, surface terms coming from splitting the volume quadrupole source are implemented: they refer to the blade surface, but it is also possible to apply the same method to other nonmaterial surfaces where a mathematical discontinuity (for example, a shock wave) occurs in the flow. In the former case, knowledge of the blade kinematics and aerodynamics is effective in describing the source term; in the latter case, the three-dimensional structure of the flow field makes it difficult to achieve as accurate results as for blade surface terms. Nevertheless, when the supersonic portion of the transonic flow field on the blade is quite small, the contribution of shock quadrupole may not be relevant, and the implementation of blade surface terms proves to be very effective in improving linear theory prediction. At higher transonic tip Mach number the contribution of surface terms is also very important, but the predicted peak pressure is quite far from achieving good agreement with the experimental waveform: in this case, it is necessary to account for the strong shock in the tip blade region.