On the differences in noise predictions based on solid and permeable surface Ffowcs Williams–Hawkings integral solutions

Abstract

The Ffowcs Williams–Hawkings equation is widely used in computational aeroacoustics to post-process unsteady simulations and provide the sound at distances beyond the accurate range of the grid. It distinguishes the monopole/dipole contributions from solid surfaces Σ and that from quadrupoles present in the volume of the fluid. Curle showed that at low Mach numbers, the solid-surface terms are stronger than the volume term. Very few studies have included the volume term itself, but many have used a permeable Ffowcs Williams–Hawkings surface Σ, which in principle surrounds the quadrupoles, giving valid results independent of Mach number; in reality for external flows, the surface cannot surround all the quadrupoles. However, in spite of doubts over the solid-surface approach even at low Mach numbers, it is widely used because of its simplicity and the difficulties associated with turbulence crossing the permeable surface. We consider Mach numbers M up to 0.25, which challenges approximations based on the property that “M ≪1.” An additional attraction of the solid-surface approach is the idea of identifying the “true” source of the sound by computing separately the Ffowcs Williams–Hawkings integrals for different components. We wish to determine whether this “self-evident” argument gives an effective approach, and in general to assess Curle’s approximations, using a sphere-dipole problem and three model problems related to landing-gear noise, namely an isolated rectangular body, a fuselage with a cavity, and one with a bluff body under it. One key test is the shielding of sound toward various directions; any approach that misses this shielding is suspect. The overall conclusion is, again, that Curle’s approximations succeed in some cases but are quite inaccurate in the audible range for an airliner in approach and for high-speed trains, and also that separating the components’ contributions is often misleading. In contrast we verify that, for our model problems and with adequate grid resolution and surface placement, the permeable-surface results are as accurate as the simulation itself is, irrespective of distance, direction, or Mach number.