An integral formulation for wave propagation on weakly non-uniform potential flows

TL;DR

This paper introduces an integral formulation for acoustic wave propagation in weakly non-uniform, subsonic flows, using a novel Green's function derived in physical space, with applications demonstrating its accuracy and limitations.

Contribution

It develops a new integral solution based on a Green's function for wave propagation in non-uniform flows, addressing the lack of suitable kernels in existing methods.

Findings

Error increases with frequency and Mach number

Error is localized in regions with flow non-uniformities

Method effectively extrapolates boundary solutions to far field

Abstract

An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels for wave propagation on non-uniform flow. The integral solution is formulated using a Green's function obtained by combining the Taylor and Lorentz transformations. Although most conventional approaches based on either transform solve the Helmholtz problem in a transformed domain, the current Green's function and associated integral equation are derived in the physical space. A dimensional error analysis is developed to identify the limitations of the current formulation. Numerical applications are performed to assess the accuracy of the integral solution. It is tested as a means of extrapolating a numerical solution available on the outer boundary of a domain to the far field, and as a means of solving scattering problems by rigid surfaces in non-uniform flows. The results show that the error associated with the physical model deteriorates with increasing frequency and mean flow Mach number. However, the error is generated only in the domain where mean flow non-uniformities are significant and is constant in regions where the flow is uniform.