Deformable-boundary integral formulation for the solution of arbitrarily-forced acoustic wave equation

The propagation of perturbations in fluids is governed by an acoustic wave equation. This paper, first, introduces an arbitrarily-forced wave equation which, properly adapted, gives rise to equations describing specific phenomena of signal perturbation propagation in fluids (like, for instance, the Lighthill and Ffowcs-Williams and Hawkings equations for radiation and scattering). Then, its solution is determined through a novel boundary integral formulation based on the free-space Green function, which is applicable to fluid domains bounded by solid or porous deformable surfaces. Different versions of the proposed boundary integral formulation can be derived, depending on the frame of reference in which they are expressed. The numerical investigation begins with the comparison of the results obtained by the presented formulation against analytical solutions concerning both a pulsating solid sphere and a deformable porous surface that encloses pulsating sources. Then, the equivalence of the formulations expressed in different frames is examined for a bending and twisting non-lifting wing translating at different Mach numbers. Finally, the aeroacoustic field generated by a helicopter rotor model in forward flight is examined to assess the effect of the body deformation on the radiated noise and the accuracy of the numerical simulations by comparison with experimental data. The results of the numerical investigation have provided a comprehensive validation of the deformable-boundary integral formulation presented for the analysis of wave propagation in fluids, and confirmed its capability to study problems of engineering interest.