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Similarity in Mach stem evolution and termination in unsteady shock-wave reflection

Published online by Cambridge University Press:  03 September 2020

E. Koronio ,
G. Ben-Dor ,
O. Sadot Open the ORCID record for O. Sadot [Opens in a new window]  and
M. Geva
E. Koronio
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer Sheva8410501, Israel
G. Ben-Dor
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer Sheva8410501, Israel
O. Sadot*
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Faculty of Engineering Sciences, Ben-Gurion University of the Negev, Beer Sheva8410501, Israel
M. Geva
Affiliation:
School of Mechanical Engineering, Tel-Aviv University, Tel-Aviv69978, Israel
*
† Email address for correspondence: sorens@bgu.ac.il
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Abstract

Shock-wave reflection over concave surfaces poses a difficulty in its analysis due to the unsteady nature of the reflection process and the occurrence of various types of Mach reflections caused by it. In a pseudo-steady flow, the reflection's configuration is self-similar since the shock wave reflects over a surface with constant inclination. The unsteady Mach reflection introduces an additional complexity as it is affected by the changing inclination of the surface, forcing the reflection to continuously adjust itself to the varying boundary condition. In this study, validated simulations of Mach reflection (MR) over cylindrical concave surfaces with different radii were performed for three inviscid perfect gases with moderate incident shock Mach numbers (Ms) ranging from 1.3 to 1.5. The reflection was investigated up to the point of transition from MR to transitioned regular reflection. A similar behaviour of the configuration and evolution of the Mach stem was observed, one that is independent of the surface radius and type of gas. With regards to different gases, the speed of sound a0 is a dominant factor since it dictates the propagation of wall disturbances. A universal condition of the rate of surface change was found, accounting for different radii, different gases and Ms variation. Analysis based on shock dynamics is employed to explain how disturbances caused by surface variations play a significant role in the behaviour of the reflection. This method successfully supports the similarity that was demonstrated and facilitates a more informed perception of the MR process.

JFM classification

Compressible Flows: Shock waves Compressible Flows: Compressible Flows Waves/Free-surface Flows: Wave-structure interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 902 , 10 November 2020 , A1
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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