New perspectives in the use of the Ffowcs Williams-Hawkings equation for aeroacoustic analysis of rotating blades

The Ffowcs Williams-Hawkings equation represents a standard approach in the prediction of noise from rotating blades. It is widely used for linear aeroacoustic problems concerning helicopter rotors and aircraft propellers and over the last few years, through the use of the so called porous (or permeable) surface formulation, has replaced the Kirchhoff approach in the numerical solution of nonlinear problems. Nevertheless, because of numerical difficulties in evaluating the contribution from supersonic sources, most of the computing tools are still unable to treat the critical velocities at which the shock delocalization occurs. At those conditions, the attention is usually limited to the comparison between the noise prediction and the experimental data in the narrow time region where the pressure peak value is located, but there has been little attention paid to the singular behaviour of the governing equation at supersonic speeds. The aim of this paper is to couple the advantages of the porous formulation to an emission surface integration scheme in order to show if and how the singularities affect the noise prediction and to demonstrate a practical way to remove them. Such an analysis enables an investigation of some interesting and somewhat hidden features of the numerical solution of the governing equation and suggests a new solution approach to predicting the noise of a rotor at any rotational velocity.