Super-equilibrium increase of chemical reaction rate in the detonation front and other effects in the detonation wave initiated by a shock wave

In the present work the problem of detonation wave formation in a shock tube was considered in one-dimensional formulation. The Monte Carlo non-stationary method of statistical simulation (MCNMSS), also known as DSMC, was used for simulation. The method automatically takes into account all details of mass and heat transfer. At an initial moment, the low-pressure channel (LPC) of the shock tube was filled with gas A while the high-pressure chamber (HPC) was filled with gas C. The cross-sections of the HPC and LPC, as well as the temperatures of gases A and C were equal to each other. At the beginning of the simulation the ratio of pressures in the HPC and LPC was equal to 100. It was assumed that chemical reactions A+M→B+M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{A}}+\mathrm{{M}} \rightarrow \mathrm{{B}}+\mathrm{{M}}$$\end{document} (M=A,B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{M}}=\mathrm{{A}},\, \mathrm{{B}}$$\end{document} and C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{C}}$$\end{document}) took place. The ratio of molecular masses of gases A,B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{A}},\, \mathrm{{B}}$$\end{document} and C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{C}}$$\end{document} was taken as 20:20:1. Different reaction thresholds were considered. For the case of a low reaction threshold, the velocity of the resulting detonation wave was found to be higher than the Chapman–Jouguet velocity. A region with constant values of flow parameters inside product was observed. An increase of the reaction threshold led to disappearance of this region and gave rise to something similar to an expansion wave, with peaks of flow parameters at the leading part of the detonation wave. The values of these peaks were found to be constant in time. The velocity of the detonation wave became appreciably lower than the Chapman–Jouguet velocity. Further increase of the reaction threshold led to disappearance of detonation. The reactions A+B→B+B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{A}}+\mathrm{{B}} \rightarrow \mathrm{{B}}+\mathrm{{B}}$$\end{document} and A+C→B+C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{{A}}+\mathrm{{C}}\rightarrow \mathrm{{B}}+\mathrm{{C}}$$\end{document} turned out to be very important for initiation of detonation.