Quadrupole Noise Prediction Through the Ffowcs Williams-Hawkings Equation

The problem of the high speed impulsive (HSI) noise prediction from hovering rotors is faced and solved through the numerical evaluation of the nonlinear terms of the governing FWH equation. Two particular resolution forms are used. The former performs the integration on a three-dimensional grid rigidly attached to the body, where the fluid velocity components are known. The latter preliminarly integrates the Lighthill stress tensor in a direction normal to the rotor plane, thus reducing the quadrupole volume integrals to some surface integrals. By using a new algorithm developed at CIRA, this last approach allows to extend the computations outside the sonic cylinder and to account for the occurrence of multiple emission times. Both the solution forms are implemented into a retarded-time algorithm, ehere the integrals are determined on the present configuration of the computing grid, and en emission-surface algorithm, where the integration is performed on a retarded domain. An analysis of the main features and limitations on the different approaches is presented, with a comparison of the corresponding numerical results and computational costs.