Implementation of a Vortex Sheet in a Finite Element Model Based on Potential Theory for Exhaust Noise Predictions

Abstract

Predicting sound propagation through the jet exhaust of an aero-engine presents the specific difficulty of representing the refraction effect of the mean flow shear. This is described by the linearised Euler equations, but this model remains rather expensive to solve numerically. The other model commonly used in industry, the linearised potential theory, is faster to solve but needs to be modified to represent a shear layer. This paper presents a way to describe a vortex sheet in a finite element model based on the linearised potential theory. The key issues to address are the continuity of pressure and displacement that have to be enforced across the vortex sheet, as well as the implementation of the Kutta condition at the nozzle lip. Validation results are presented by comparison with analytical results. It is shown that the discretization of the continuity conditions is crucial to obtain a robust and accurate numerical model.