Approximate Solutions of the Transformation of Vortices through a Premixed Flame using Generalized Expansions

Abstract

The vortex-premixed flame interaction is investigated analytically for vortices of different length and velocity scales, l_v and u_v, by expanding the continuity, momentum, vorticity, temperature, and species equations. The terms are written in powers of a small parameter, ϵ. Solutions are separated based on the ratio of u_v to the laminar name speed, S_L, for a strong vortex, S_L/u_v = ϵ « 1, and for a weak vortex, u_v/S_L = ϵ « 1. They are further separated based upon the ratio of l_v to the flame length scale. L_F, resulting in four different cases. For all cases, the leading order equations describing the name and vortex are derived. The vorticity equation which describes to leading order the transformation of the vortices across the flame is solved analytically for l_v/l_F « 1, and qualitatively described for l_v/l_F » 1. This provides the leading order solution for the transformation of the size, velocity, circulation, and vorticity of the vortex across the flame. These solutions have applicability to modeling and predicting the transformation of turbulence across a flame.

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