Assessment of the Taylor-Lorentz transform for boundary element solutions to wave propagation with mean flow

摘要

A boundary element formulation is used in order to solve acoustic wave propagation in non-uniform potential subsonic mean flows. An approach based on a Taylor-Lorentz variable transformation is proposed for low Mach number mean flows. The variable transformation reduces an approximate formulation of the linearised potential wave equation to the standard wave equation with quiescent media. In the transformed domain, a standard boundary element method can then be used. This paper presents a strategy to exploit existing boundary element solvers for wave propagation with quiescent media to compute mean flow effects. The solution is proposed in the frequency domain for prescribed velocity boundary conditions. Numerical experiments are performed to test the proposed variable transformation for three-dimensional applications. A comparison between the results based on either the Taylor-Lorentz or a more conventional Lorentz transform assuming a uniform flow in the entire domain is provided. In the near field, the solutions based on the Taylor- Lorentz transform slightly improve on boundary element solutions based on the Lorentz transform. However, they provide similar results as soon as a region of uniform mean flow is reached.