Reacting and non-reacting, three-dimensional shear layers with spanwise stretching

Abstract

A three-dimensional, steady, laminar shear-layer flow spatially developing under a boundary-layer approximation with mixing, chemical reaction, and imposed normal strain is analyzed. The purpose of this study is to determine conditions by which certain stretched vortex layers appearing in turbulent combustion are the asymptotic result of a spatially developing shear flow with imposed compressive strain. The imposed strain creates a counterflow that stretches the vorticity in the spanwise direction. Equations are reduced to a two-dimensional form for three velocity components. The non-reactive and reactive cases of the two-dimensional form of the governing equations are solved numerically, with consideration of several parameter inputs, such as the Damköhler number, the Prandtl number, chemical composition, and free-stream velocity ratios. The analysis of the non-reactive case focuses on the mixing between hotter gaseous oxygen and cooler gaseous propane. The free-stream strain rate κ* is predicted by ordinary differential equations based on the imposed spanwise pressure variation. One-step chemical kinetics are used to describe diffusion flames and multi-flame structures. The imposed normal strain rate has a significant effect on the width of downstream mixing layers as well as the burning rate. Asymptotically in the downstream direction, a constant width of the shear layer is obtained if the imposed normal strain rate is constant. The one-dimensional asymptotic result is an exact solution to the multicomponent Navier–Stokes equation for both reacting and non-reacting flows, although it was obtained using the boundary-layer approximation. A similar solution with the layer width growing with the square root of downstream distance is found when the imposed strain rate decreases as the reciprocal of downstream distance. The reduced-order asymptotic solutions can provide useful guidance in developing flamelet models for simulations of turbulent combustion.