Hybrid numerical model for acoustic propagation through sheared flows

Abstract

Simulating the propagation of sound in non-uniform flows remains challenging, especially for large, three-dimensional problems. To account for the sound refraction due to gradients of velocity and temperature, one has to solve the Linearised Euler Equations (LEE) which can be computationally expensive in three dimensions. Alternatively, one can use the Linearised Potential Equation (LPE) which is much cheaper but is limited to potential, isentropic flows. In this paper, a hybrid model combining the LEE and the LPE is proposed in order to simulate the sound propagation in sheared flows at a reasonable computational cost. The LEE are applied only in regions with strong sheared mean flows, the LPE is used everywhere else. The coupling between the LEE and the LPE consists in imposing relations for the characteristic waves propagating at the interface between the LEE and the LPE regions. In this study, the hybrid model is implemented in a high-order finite element solver in the frequency domain. Its performance is first assessed by simulating the propagation of planes waves in a uniform mean flow and the acoustic radiation from a semi-infinite duct in a strongly sheared non-isothermal jet flow. No significant spurious noise is produced at the LEE-LPE interfaces. The applicability of the hybrid model to industrial problems is then demonstrated by simulating the propagation of fan noise through the jet flow exiting from a turbofan exhaust. The use of the proposed hybrid model does not affect the propagation of the sound field while reducing the memory footprint by more than one order of magnitude compared to a full three-dimensional LEE simulation.