Parabolized stability equation models in turbulent supersonic jets

Abstract

The peak noise radiation in the aft direction of high-speed, turbulent jets has been linked to the dynamics of the large-scale structures. We use the parabolized stability equations (PSE) to model these structures as wavepackets associated with instability of the turbulent mean flow. Our past work has demonstrated the utility of these models for subsonic jets; in the present work we extend these methods to supersonic jets. A large eddy simulation database corresponding to an unheated, ideally-expanded Mach 1.5 jet with Reynolds number of 300,000 is employed to extract the necessary input for the PSE (the mean flow and initial conditions) and also to perform comparisons and validations of the computed wavepackets. By contrast with subsonic jets, when the jet exit velocity is supersonic with respect to the ambient speed of sound, linear stability theory predicts that multiple instability modes, related to resonance of pressure waves within the potential core, can be present in addition to the inflectional instability. The possible coexistence of different instability mechanisms, the determination of adequate inlet conditions, and their effect on the wavepackets computed are investigated here. We compare the wavepackets predicted by PSE with fluctuations extracted from the LES data. When performing comparisons, filtering techniques need to be employed in order to extract the coherent, low frequency structures associated with wavepackets. Largescale fluctuations educed using cross-correlation techniques, such as the proper orthogonal decomposition, are shown to compare reasonably well with the PSE wavepackets, but by contrast with subsonic jets, it appears that several POD modes are required to represent the PSE-predicted wavepacket.