Direct Navier-Stokes Simulation of Sounds Generatei by Shock-Vortex / Vortex-Vortex Interactions

Abstract

Flow fields generated by the interactions between a shock wave and vortices and between two vortex rings are simulated numerically, and the generation and propagation mechanisms of sounds are studied. The unsteady, compressible Navier-Stokes equations are solved by a finite difference method over the entire acoustic field from near to far fields. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge-Kutta scheme for time integration. The results show that the basic nature of the sounds depends strongly on the generation of reflected shock waves and expansion waves for shock-vortex interaction problems, and on the vortex motions induced by mutual interaction for vortex-vortex interaction problems The results also show that the pressure peaks of the sounds decay in inverse proportion to the distance from the sound source for three-dimensional flows and to the square root of the distance for two-dimensional flows, in agreement with theory.