Quadrupole Noise Predictions Through the Ffowcs Williams-Hawkings Equation

The problem of high-speed impulsive noise prediction from hovering rotors is studied and solved in the time domain through the numerical evaluation of the nonlinear terms of the governing Ffowcs Williams-Hawkings equation. Two particular resolution forms are used. The former performs the integration on a three-dimensional grid rigidly attached to the body, where th efluid 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. This last approach allows extending the calculations outside the sonic cylinder and accounts for the occurrence of multiple emission times. Both the solution forms are implemented into a retarded-time algorithm, where the integrals are determined on the present configuration of the computing grid, and into an emission-surface algorithm, where the integration is performed in the retarded domain. An analysis of the main features and limitations of the different approaches is presented, with a comparison of the corresponding numerical results and computational cost.