Evaluation of PSE as a Model for Supersonic Jet Using Transfer Functions

Abstract

Parabolized Stability Equations (PSE) have been shown to model wavepackets and, consequently, the near field of turbulent jets with reasonable accuracy. Because of these capabilities, PSE is a promising reduced-order model to derive control laws that could be employed to reduce the sound generation of a jet. The purpose of this work is to apply PSE to obtain time-domain transfer functions that could estimate both the fluid-dynamic and the acoustic fields of a supersonic jet. The results of this model were compared to results obtained from a database of a well-validated large-eddy simulation of a supersonic jet. Based on the unsteady pressure data at a input position, the time-domain pressure field was estimated using transfer functions obtained using PSE and an empirical method based on the LES data. The prediction scheme employed is a single-input-single-output (SISO), linear model. The unsteady pressure predicted by PSE showed good agreement with the LES results, especially if the input position is outside the mixing layer. For this region, the prediction capabilities of PSE are comparable to those of empirical transfer functions. The agreement is good even for output points taken in the acoustic field, showing that it is possible to estimate the time-domain behaviour of Mach-wave radiation using transfer functions. This indicates that PSE could not only be used to predict the sound generation, but also to open up new potentialities to attenuate noise by means of closed-loop control of the flow. The exploration of the regions where the method displayed good agreement, presented in this work, can guide the positioning of sensors and actuators for experimental implementation of closed-loop control in a jet.