A Comparative Use of the PSE and LES Approaches for Jet Noise Predictions

Abstract

A Parabolized Stability Equation (PSE) method is developed for inviscid axisymmetric jets. The Parabolized Stability Equations are derived from the linearized Euler equations, and are parabolic without neglecting any terms. This approach is applied on a Mach 0.7 hot axisymmetric jet, on which a Large Eddy Simulation (LES) has also been performed, as well as experimental measurements. The LES-computed mean flow is used as an input for the PSE analysis, which provides easily the physical disturbances, even in the region where the basic flow is stable. This is the main advantage of the PSE approach compared to the classical parallel-flow stability theory. Indeed in the stable region the classical stability theory requires the use of integration contours in the complex plane to construct the disturbances functions. All these complicated mathematical developments are avoided by the PSE approach. 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. The PSE results are compared to the LES ones and to measurements in a region close to the jet. 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, for the particular studied jet, by the turbulence cascade rather than by the Kelvin-Helmholtz instability waves.