Aeroacoustic Integrals Accelerated by Fast Multipole Method

Abstract

The calculation of acoustic field solutions due to aeroacoustic sources is performed for a large number of observer locations. Sound is predicted by a hybrid method that uses direct calculation for near-field source computations and the Ffowcs Williams―Hawkings equation as the acoustic analogy formulation. The integrations of surface dipole and volume quadrupole source terms appearing in the Ffowcs Williams―Hawkings formulation are accelerated by a three-dimensional wideband multilevel adaptive fast multipole method. The three-dimensional wideband fast multipole method presented here applies a plane-wave expansion formulation with fast spherical filtering and interpolation and diagonal translation for calculations in the high-frequency regime and a partial-wave expansion formulation with rotational―coaxial translation in the low-frequency regime. The method is described for the solution of a three-dimensional Green's function that incorporates convective effects. The sound generated by the unsteady flow past a cylinder in the proximity of a NACA0012 airfoil is studied and the interaction of both geometries is analyzed for different cylinder positions. The developed numerical capability allows the analysis of each noise source individually. Therefore, the effects of dipoles and quadrupoles for each configuration are investigated. Results for acoustic field solutions obtained by the accelerated Ffowcs Williams―Hawkings formulation are up to 2 orders of magnitude faster than with the conventional computation of Ffowcs Williams―Hawkings equation.