Modeling Symmetric Coherent Mode Interactions in a Supersonic Rectangular Jet

Abstract

This work presents the use of a reduced-order model (ROM) to predict coherent structure modes and their interaction with one another in a supersonic rectangular jet. The ROM formulation is unique in that it utilizes an integral technique and models the energy exchange between harmonically related modes, which can give insight on how to excite the jet in an experiment or computation. This ROM is used in conjunction with a linearized Euler equation solver to obtain shape functions for various disturbance frequencies. Work is limited here to symmetric modes of the coherent structure, and hence the disturbance in the upper and lower shear layers is in phase. Nonlinear solutions are first obtained without mode–mode interactions, giving a most amplified Strouhal number of 0.15 based on the height of the jet, which is assumed to be the dominant noise source in the jet, referred to as the fundamental frequency. The fundamental’s interaction with either the subharmonic or harmonic is assessed based on their ability to reduce the fundamental. Adding the harmonic is found to be more effective at reducing the peak of the fundamental, and thus this is concluded to be possibly an effective mechanism for noise reduction.