Study on the Mach and regular reflections of shock wave

  • Kexin Wu
  • Guang Zhang
  • Heuy Dong Kim
Regular Paper


While a moving incident shock wave moves through a sharp compression ramp with the fixed angle, θr, the incident shock wave is reflected by the ramp surface and the induced pseudo-steady flow behind it is deflected by the ramp corner. It is known that four basic shock reflection patterns can be obtained, including regular reflection, single-Mach reflection, transitional-Mach reflection, and double-Mach reflection. Previously, the shock reflections were mainly studied by various experimental methods with different test gases in the shock tubes, which include air, nitrogen, helium, and argon. In this paper, in order to clearly illustrate the transitional properties between Mach and regular reflections, theoretical and numerical analyses were carried out. Detachment and mechanical equilibrium criteria were established by the theoretical analysis based on the two- and three-shock theories. Further, which criterion is more suitable and accurate to explain the transitional processes between the Mach and regular reflections was illustrated. The generation and variation of the reflected shock waves were clearly captured based on the total variation diminishing scheme within Fluidyn software. A series of 2D (two-dimensional) models were simulated at different operating conditions that the incident Mach numbers (1.1, 1.5, 2.03, 3, 4 and 5) and compression ramp angles (27°, 50°, and 60°) were changed, respectively. The detailed properties on Mach and regular reflections were illustrated in the present studies. In addition, some new and constructive conclusions for transitional processes between the Mach and regular reflections of shock wave were obtained.

Graphical abstract


Unsteady Inviscid Shock reflection Detachment criterion Mechanical equilibrium criterion 



This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2016R1A2B3016436).


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Copyright information

© The Visualization Society of Japan 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringAndong National UniversityAndongRepublic of Korea
  2. 2.College of Mechanical Engineering & AutomationZhejiang Sci-Tech UniversityHangzhouChina

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