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

TL;DR

This paper analyzes three-dimensional shear-layer flows with spanwise stretching, considering reactive and non-reactive cases, revealing how imposed strain influences layer width and burning rate through numerical solutions.

Contribution

It introduces a reduced two-dimensional model for shear layers with spanwise stretching and investigates the effects of imposed strain on flow and combustion characteristics.

Findings

Imposed normal strain significantly affects shear layer width and burning rate.

Constant imposed strain leads to a constant shear layer width downstream.

Decreasing strain rate causes the layer width to grow with the square root of downstream distance.

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 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.