Scattered noise prediction using acoustic velocity formulations V1A and KV1A

Aeroacoustic scattering prediction generally relies on boundary integral methods which require evaluation of the impermeability condition on the scattering surface. The boundary condition implies zero normal velocity relative to the scattering surface. This condition has been expressed by relating the acoustic velocity to the acoustic pressure gradient, allowing indirect evaluation of the boundary condition by existent acoustic pressure gradient formulations. In the present paper, a direct evaluation of the hardwall boundary condition in scattering problems is demonstrated by time-domain analytic acoustic velocity formulae. Acoustic velocity formulations V1A and KV1A are implemented for acoustic scattering prediction, by hybrid approaches based on the FW-H equation and the Kirchhoff method These formulations can be coupled to any scattering solver, allowing time-domain prediction of the incident acoustic field when broadband noise generation is concerned. Formulation V1A offers mathematical simplicity and computational efficiency, which can be advantageous for realistic scattering applications. Implementation of formula KV1A enables acoustic scattering prediction by existing solvers based on the Kirchhoff method. The validity of the suggested methodology is assessed through the analytical test case of harmonic sound scattered by a rigid sphere. Sound propagation and scattering effects are analyzed by examination of the acoustic velocity field characteristics.