Benchmarking of different wave models for sound propagation in non-uniform flows

Weak forms of the second-order Pierce wave operator and of third-order Pridmore-Brown wave operator are discretized in frequency-domain by using a standard Galerkin approach and verified against model problems of practical interest, for which analytical or numerical reference solutions are available. The weak form of the Pridmore-Brown operator, on which the Lilley’s equation is based, constitutes an original contribution of this paper. The well known effects of two modelling errors associated with the second order operator are highlighted: a refraction error in the presence of sheared flows and a Kutta-condition error in the presence of an edge. The application of these wave models to the solution of a realistic aero-engine aft noise radiation problem, for which no one of the wave models is in principium appropriate, reveals an appreciable influence of the model only in the backward radiation arc.