Pressure-field permeable-surface integral formulations for sound scattered by moving bodies

This paper presents two novel integral formulations for the prediction of sound scattered by moving bodies, derived from the Lighthill and the Ffowcs Williams and Hawkings equations for the pressure field. These are expressed in the frequency-domain, over a permeable (fictitious) surface surrounding the scatterer(s), and are numerically evaluated through application of a boundary element technique. The aims of the paper are the assessment of the influence of the nonlinear terms of Lighthill and Ffowcs Williams and Hawkings equations on sound scattering prediction in the presence of nonuniform mean-flow due to scatterer motion, the assessment of the corresponding limits of applicability of the widely-used linear formulations for solid-wall boundaries, and the development of integral formulations capable to predict accurately and efficiently the noise scattered in the far field by moving bodies. The numerical investigation concerns a non-lifting wing in uniform translation impinged by an acoustic disturbance generated by a co-moving source, and includes the comparison of the results obtained through the proposed scattering formulations with those provided by a boundary-field velocity-potential approach recently validated for moving-body problems. Its main outcomes reveal that, when the proposed pressure-field formulations include the nonlinear terms through application of a suitable permeable-surface, their predictions match those provided by the boundary-field velocity-potential solver, whereas the fully linear versions of both pressure-field approaches yield underestimated scattered noise predictions, significantly less accurate than those given by the linear version of the velocity-potential formulation.