Abstract
The transition boundary separating the region of regular reflection from the regions of single-, transitional-, and double-Mach reflections for a planar shock wave moving in air and interacting with an inclined wedge in a shock tube is studied by both analytical methods and computational-fluid-dynamic simulations. The analytical solution for regular reflection and the corresponding solutions from the extreme-angle (detachment), sonic, and mechanical-equilibrium transition criteria by von Neumann (Oblique reflection of shocks, Explosive Research Report No. 12, Navy Department, Bureau of Ordnance, U.S. Dept. Comm. Tech. Serv. No. PB37079 (1943). Also, John von Neumann, Collected Works, Pergamon Press 6, 238–299, 1963) are first revisited and revised. The boundary between regular and Mach reflection is then determined numerically using an advanced computational-fluid-dynamics algorithm to solve Euler’s inviscid equations for unsteady motion in two spatial dimensions. This numerical transition boundary is determined by post-processing many closely stationed flow-field simulations, to determine the transition point when the Mach stem of the Mach-reflection pattern just disappears and this pattern then transcends into that of regular reflection. The new numerical transition boundary is shown to agree well with von Neumann’s closely spaced sonic and extreme-angle boundaries for weak incident shock Mach numbers from 1.0 to 1.6, but this new boundary trends upward and above von Neumann’s sonic and extreme-angle boundaries by a couple of degrees at larger shock Mach numbers from 1.6 to 4.0. Furthermore, the new numerically determined transition boundary is shown to agree well with very few available experimental data obtained from previous experiments designed to reflect two symmetrical moving oblique shock waves along a plane without a shear or boundary layer.
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Acknowledgements
The contributions of Lucie Freret in making the anisotropic algorithm of AMR more efficient are greatly appreciated. Computational resources for performing all of the calculations reported in this research were provided by the SciNet High-Performance Computing Consortium at the University of Toronto and Compute/Calcul Canada, through funding from the Canada Foundation for Innovation (CFI) and the Province of Ontario, Canada.
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Communicated by B. Skews.
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Hryniewicki, M.K., Gottlieb, J.J. & Groth, C.P.T. Transition boundary between regular and Mach reflections for a moving shock interacting with a wedge in inviscid and polytropic air. Shock Waves 27, 523–550 (2017). https://doi.org/10.1007/s00193-016-0697-1
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DOI: https://doi.org/10.1007/s00193-016-0697-1