Numerical Simulation of Vorticity Production in Shock Diffraction

Abstract

Space-time conservation element and solution element method is employed with Euler and laminar Navier-Stokes solvers to investigate the vorticity production in shock diffraction and the interaction of the reflected shock wave with the main vortex for incident shock waves of various strengths diffracting around convex corners of different angles. The numerical results show that, in the Euler simulation, the flow structures are self-similar before they impinge on the bottom wall and that, in the laminar Navier-Stokes simulation, the flow structures are self-similar other than when they are influenced by the boundary-layer effect. Neither solver yields evidence of the rollup of small vortices along the slipstream. The major vorticity production is formed to be along the slipstream with the Euler solution. Different circulation production rates are observed between the Euler and Navier-Stokes solutions as a result of the vorticity contribution of the boundary layer and the secondary vortex in the latter. The degree of vorticity production is found to be dependent on the strength of the incident shock wave and the diffracting angle when the bottom wall effect is not considered.