Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets

Abstract

Parabolized stability equation (PSE) models are being developed to predict the evolution of low-frequency, large-scale wavepacket structures and their radiated sound in highspeed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer. Here we show they also in very good agreement with hot-wire measurements at the jet centerline in the potential core, for a different set of experiments. When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large-scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative importance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that nonlinearity has a very limited impact on the evolution of the wavepackets for St ≥ 0.3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper.