Reacting and Non-reacting, Three-dimensional Shear Layers with Spanwise Stretching

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 imposed strain creates a counterflow that stretches the vorticity in the spanwise direction. The 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 the several of parameter inputs such as Damk\"ohler number, 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 \kappa is predicted by ordinary differential equations based upon 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 imposed normal strain rate is constant. A similar solution with layer width growing with the square root of downstream distance is found when imposed strain rate decreases as the reciprocal of downstream distance.