Steady rotation of a Mach shock: experimental and numerical evidences

This experimental and numerical work reports on the dynamical behaviour of a shock in an inert gas at the concave wall of a hollow circular chamber. The gas in the chamber was air or He + O2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm O}_{2}$$\end{document} + 2  Ar at initial pressures pc0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{{\rm c0}}$$\end{document} ranging from 2 to 12 kPa and initial temperature T0 =288 K. The shock was generated using a detonation driven shock tube. The shock dynamics were characterized through high-speed shadowgraph recordings and high-resolution numerical simulations. For each gas and pc0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_\text {c0}$$\end{document}, the experiments evidenced the formation of a Mach reflection along the wall and identified a range of initial pressures for which this configuration rotates with constant stem heights and constant velocities larger than those at the chamber entry. The numerical simulations were capable of capturing the dynamics quantitatively. These results extend to inert gases our previous work with a reactive gas for which we reported on the possibility of a steadily rotating overdriven Mach detonation. The steadiness range is narrower with the inert gases, likely because of the smaller initial pressure ratios at the chamber entry and lower support from the subsonic flow behind the shock. The initial support in the reactive case was more efficient because the discontinuities at the chamber entry were self-sustained Chapman–Jouguet detonations. Further investigations of these Mach rotating regimes should rely only on specific experiments and numerical simulations, for example, on the effect of the chamber dimensions, because of the complex non-dimensional formulation of the problem.