Velocity-potential boundary-field integral formulation for sound scattered by moving bodies

This paper presents a boundary-field integral formulation suitable for the prediction of noise scattered by moving bodies. Although based on the same flow modeling assumptions, linear formulations derived from velocity potential or pressure disturbance wave equations provide different predictions when the scatterer is not at rest. Indeed, the discrepancies reside in the different influence of the neglected nonlinear terms. Here, a velocity potential-based approach is developed by extracting the first-order contributions from the nonlinear terms. This yields a linearized boundary-field, frequency-domain formulation for the scattered potential that, extending the standard linear boundary integral approach, takes into account the effects of mean flow nonuniformity. The influence of the additional field contributions is examined for different scatterer velocities, with the aim of assessing the domain of validity of the fully linear formulation and the rate of growth of the field contributions with increase of velocity. Specifically, the numerical investigation concerns the noise scattered by a moving, nonlifting wing, when impinged by an acoustic disturbance generated by a co-moving point source.