Two-dimensional weak shock-vortex interaction in a mixing zone

Abstract

The interaction between a vortex or a pair of vortices and a shock is studied by using two-dimensional direct numerical simulation. The deformation of the shock structure is analyzed and the mechanisms leading to the formation of triple points are underscored. It is shown that they are related to the appearance of pressure gradients in the direction parallel to the shock resulting from the shock-vortex interaction. A distribution of an inert chemical species, i.e., mixture fraction, is prescribed within the vortex. From its time evolution, one analyzes the coupling between the response of the shock to the disturbance and the change in mixing rate. Modifications of the maximum of the scalar gradient are observed in the direction perpendicular to the shock and also, to a smaller extent, in the direction parallel to the shock. Nomenclature A(s) = stretching function of the mesh a,b,c,d = coefficients of the FADE scheme D = diffusion coefficient of the inert chemical species L = reference length of the problem M = Mach number N = total number of grid points in streamwise direction P = pressure Pr = Prandtl number q, qr = mesh stretching ratio and stretching rate R = radius of the vortex Re = acoustic Reynolds number (r, ft) = polar coordinates s = position on the uniform mesh