A HYPERSINGULAR INTEGRAL FORMULATION FOR ACOUSTIC RADIATION IN MOVING FLOWS

Abstract

This paper presents a hypersingular integral equation for acoustic radiation in a subsonic uniform flow. The work is motivated by the need for a normal-derivative integral equation to be used in the Burton and Miller method for overcoming the non-uniqueness difficulty in the boundary integral formulation. Although the non-uniqueness, difficulty in the conventional Helmholtz integral formulation has been well studied before, it is shown in this paper that this difficulty becomes more severe in the presence of a mean flow. A generalized normal-derivative operator is defined to derive the hypersingular integral equation. Regularization of the hypersingular kernels is performed to render the integral equation numerically integrable. Theoretical derivation is first given for a general three-dimensional formulation. The resulting hypersingular integral equation is then reduced to the axisymmetric case for numerical implementation. Numerical examples at relatively high frequencies and different Mach numbers are given to verify the formulation.