Boundary integral methods for sound propagation with subsonic potential mean flows

Abstract

This work deals with including non-uniform mean flow effects into boundary integral solutions to acoustic wave propagation. A time harmonic boundary integral solution is proposed for low Mach number potential flows with small non-uniform mean flow velocities and a free-field Green’s function is recovered to solve the corresponding kernel. The boundary integral formulation can be used as a means of solving both wave extrapolation and boundary element problems. For boundary element solutions to external sound propagation, the non-uniqueness issue is worked around by extending the conventional combined Helmholtz integral equation formulation and the Burton–Miller approach to non-uniform mean flows. Nonetheless, the proposed integral formulation is shown to be consistent with a combination of the physical models associated with the Taylor and Lorentz transforms. The combined Taylor–Lorentz transformation allows mean flow effects on acoustic wave propagation to be resolved by using a standard boundary integral formulation for the Helmholtz problem with quiescent media in a transformed space.

Numerical experiments are performed to benchmark the proposed integral formulations against finite element solutions based on the linearised potential equation. Numerical examples are also used to validate a weakly-coupled approach exploiting the proposed integral formulations in order to predict forward fan noise installation effects. Nonetheless, the integral formulations in a transformed space are used to simulate mean flow effects based on standard boundary element solvers for quiescent media. The results suggest that, for low Mach numbers, boundary element solutions to wave propagation with non-uniform mean flows represent a good approximation of finite element solutions based on the linearised potential equation. It is shown that the boundary element solutions including non-uniform mean flow effects improve on the corresponding approximations assuming a uniform flow in the whole computational domain. This is observed when sound propagation is predicted in the near field and in a region where the non-uniformity in the mean flow velocity is significant.

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