On the interaction of vortices with mixing layers

Abstract

We describe the perturbations introduced by two counter-rotating vortices—in a two-dimensional configuration—or by a vortex ring—in an axisymmetric configuration—to the mixing layer between two counterflowing gaseous fuel and air streams of the same density. The analysis is confined to the near stagnation point region, where the strain rate of the unperturbed velocity field, A0, is uniform. We restrict our attention to cases where the typical distance 2r0 between the vortices—or the characteristic vortex ring radius r0—is large compared to both the thickness, δv, of the vorticity core and the thickness, δm∼(ν/A0)1/2, of the mixing layer. In addition, we consider that the ratio, Γ/ν, of the vortex circulation, Γ, to the kinematic viscosity, ν, is large compared to unity. Then, during the interaction time, A0−1, the viscous and diffusion effects are confined to the thin vorticity core and the thin mixing layer, which, when seen with the scale r0, appears as a passive interface between the two counterflowing streams when they have the same density. In this case, the analysis provides a simple procedure to describe the displacement and distortion of the interface, as well as the time evolution of the strain rate imposed on the mixing layer, which are needed to calculate the inner structure of the reacting mixing layer as well as the conditions for diffusion flame extinction and edge-flame propagation along the mixing layer. Although in the reacting case variable density effects due to heat release play an important role inside the mixing layer, in this paper the analysis of the inner structure is carried out using the constant density model, which provides good qualitative understanding of the mixing layer response.