Flow Structures and Sound Radiation in Supersonic Mixing Layers with Nonlinear PSE Method

The nonlinear stability, flow structure, and sound radiation of supersonic mixing layers are studied using nonlinear PSE methods. The nonlinear evolvements of unstable waves in the mixing layers are modeled using spatial marching method. The coherent structures such as vortex roll-up, pairing,. vortices and hairpin-vortex etc. are simulated by adding all harmonic waves to basic flow, which demonstrates nonlinear PSE a fast way to simulate the nonlinear flow structures. Since the stability solution is applicable for supersonic far field, the sound radiation from the vortex pairing to the supersonic far field is studied. The results demonstrate that the linear effects increase the dominating modes rapidly, and the nonlinear effect redistribute the energy in the Fourier domain through transferring energy from basic flow and low frequency modes to high order modes. PSE method can well capture the two- and three-dimensional large scale vortex structures in supersonic mixing layers. In the far field, the time averaged pressure is no longer uniform when the amplitude gets large enough. Sound radiate downstream from the location of vortex structures for supersonic mixing layers.