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, A 0 , is uniform. We restrict our attention to cases where the typical distance 2r 0 between the vortices-or the characteristic vortex ring radius r 0 -is large compared to both the thickness, ␦ v , of the vorticity core and the thickness, ␦ m ϳ(/A 0 ) 1/2 , of the mixing layer. In addition, we consider that the ratio, ⌫/, of the vortex circulation, ⌫, to the kinematic viscosity, , is large compared to unity. Then, during the interaction time, A 0 Ϫ1 , the viscous and diffusion effects are confined to the thin vorticity core and the thin mixing layer, which, when seen with the scale r 0 , 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.

Ignition, Liftoff, and Extinction of Gaseous Diffusion Flames

“…As sketched in Figure 4, this vortex-flame configuration can be characterized by the unperturbed strain experienced by the flame prior to the interaction, given by the value A A on the air side of the mixing layer, the characteristic radius of the vortex ring r 0 , the vortex strength , and a characteristic diffusivity of the system (e.g., the thermal diffusivity D T or kinematic viscosity ν of the oxidizer stream) (Vera & Li ñán 2004). Additional parameters include the temperature and composition of the fuel and oxidizer streams, which determine the critical strain rate at extinction A e and the overall air-to-fuel mass stoichiometric ratio S.…”

On the dynamics of flame edges in diffusion-flame/vortex interactions

“…This paper represents an extension of the previous work by Vera and Liñán [45] (herein referred to as VL) on the unsteady response of reacting mixing layers (or diffusion flames) perturbed by vortices. For the sake of brevity, in this sequel paper we will focus our attention on axisymmetric flame/vortex interactions, which are the configuration typically found in the experimental literature.…”

A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

“…In addition, (r c (t), z c (t)) denote the motion of the center of the vortex core, defined explicitly in [43,58] as a function of time. This expression assumes that, at time t = 0, the vortex crosses the plane z c (0) = 0, having a non-dimensional, unit size r c (0) = 1.…”