Investigation of the PSE Approach for Subsonic and Supersonic Hot Jets. Detailed Comparisons with LES and Linearized Euler Equations Results

Abstract

A Parabolized Stability Equation (PSE) method is applied to hot inviscid Mach 0.7 and Mach 2 axisymmetric jets. The Parabolized Stability Equations are derived from the linearized Euler equations. Spatial development of pressure perturbations is computed in the vicinity of the jet, and the associated radiated noise is obtained by solving the wave equation. A Large Eddy Simulation is performed on the subsonic jet and compared with the results obtained by the PSE analysis of the LES-computed mean flow. Good agreement is found for the spatial growth of pressure instability waves, the spatial damping being slightly under-estimated in the PSE analysis. Only LES predicts acoustic radiation, which may thus be created by the turbulence cascade rather than by the Kelvin-Helmholtz instability waves. PSE method is then applied to the supersonic jet and compared to solutions of Linearized Euler Equations. The common mean flow is analytical. A very good agreement is found for pressure perturbation evolution and for directivity and levels of acoustic radiation.