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Shock Waves

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Transition boundary between regular and Mach reflections for a moving shock interacting with a wedge in inviscid and polytropic argon

  • J. J. GottliebEmail author
  • M. K. Hryniewicki
  • C. P. T. Groth
Original Article
  • 32 Downloads

Abstract

The transition boundary separating the regions of regular and Mach reflections for a planar shock moving in argon and interacting with an inclined wedge in a shock tube is investigated using flow-field simulations produced by high-resolution computational fluid dynamics (CFD). The transition boundary is determined numerically using a modern and reliable CFD algorithm to solve Euler’s inviscid equations of unsteady motion in two spatial dimensions with argon treated as a polytropic gas. This numerically computed transition boundary for inviscid flow, without a combined thermal and viscous boundary layer on the wedge surface, is determined by post-processing many closely stationed flow-field simulations to accurately determine the transition-boundary 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 for argon 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 1.55, but it deviates upward and above the closely spaced sonic and extreme-angle boundaries by almost \(2^\circ \) at larger shock Mach numbers from 1.55 to 4.0. This upward trend of the numerical transition boundary for this sequel case with monatomic gases like argon (\(\gamma =5/3\)) and no boundary layer on the wedge surface (inviscid flow) is similar to the previous finding for the case of diatomic gases and air (\(\gamma =7/5\)). An alternative method used to determine one point on the transition boundary between regular and Mach reflections, from a collection of Mach-reflection patterns with a constant-strength shock and different far-field wedge angles, by linear and higher-order polynomial extrapolations to zero for triple-point trajectories versus wedge angle, is compared to the present method of using near-field data that are close to and surround the new transition boundary. Such extrapolation methods are shown to yield a different transition-boundary estimate that corresponds to the mechanical-equilibrium boundary of von Neumann. Finally, the significance of the computed inviscid transition boundary between regular and Mach reflections for monatomic and diatomic gases is explained relative to the case of viscous flow with a combined thermal and viscous boundary layer on the wedge surface.

Keywords

Shock-wave reflection Mach reflection Regular to Mach reflection transition boundary Regular reflection persistence 

Notes

Acknowledgements

The contributions of Lucie Freret in making the anisotropic algorithm for adaptive mesh refinement more effective and computationally efficient are greatly appreciated. Important papers on shock-induced boundary layers sent by Hans G. Hornung to the first author are gratefully acknowledged. Mach-reflection discussions with Evgeny Timofeev by the first and third authors were very helpful and much 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, via funding from the Canada Foundation for Innovation (CFI) and the Province of Ontario, Canada.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute for Aerospace StudiesUniversity of TorontoTorontoCanada

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