A three-dimensional numerical study on instability of sinusoidal flame induced by multiple shock waves

The instabilities of a three-dimensional sinusoidally premixed flame induced by an incident shock wave with Mach = 1.7 and its reshock waves were studied by using the Navier–Stokes (NS) equations with a single-step chemical reaction and a high resolution, 9th-order weighted essentially non-oscillatory scheme. The computational results were validated by the grid independence test and the experimental results in the literature. The computational results show that after the passage of incident shock wave the flame interface develops in symmetric structure accompanied by large-scale transverse vortex structures. After the interactions by successive reshock waves, the flame interface is gradually destabilized and broken up, and the large-scale vortex structures are gradually transformed into small-scale vortex structures. The small-scale vortices tend to be isotropic later. The results also reveal that the evolution of the flame interface is affected by both mixing process and chemical reaction. In order to identify the relationship between the mixing and the chemical reaction, a dimensionless parameter, η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}, that is defined as the ratio of mixing time scale to chemical reaction time scale, is introduced. It is found that at each interaction stage the effect of chemical reaction is enhanced with time. The enhanced effect of chemical reaction at the interaction stage by incident shock wave is greater than that at the interaction stages by reshock waves. The result suggests that the parameter η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document} can reasonably character the features of flame interface development induced by the multiple shock waves.