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The wall-jetting effect in Mach reflection: theoretical consideration and numerical investigation

Published online by Cambridge University Press:  01 April 2003

L. F. HENDERSON
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
E. I. VASILEV
Affiliation:
Department of Computational Mechanics, Volgograd State University, Volgograd, Russia
G. BEN-DOR
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
T. ELPERIN
Affiliation:
Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel

Abstract

The jetting effect often appears in the Mach reflection of a shock and in more complicated irregular shock reflections. It also occurs in some natural phenomena, and industrially important processes. It is studied numerically using a W-modification of the second-order Godunov scheme, to integrate the system of Euler equations. It is shown that there is no correspondence between the shock reflection patterns and the occurrence of jetting. Furthermore, there are two kinds of jetting: strong which occurs when there is a branch point on the ramp surface where the streamlines divide into an upstream moving jet and a downstream moving slug; and weak which has no branch point and may occur at small and large values of the ramp angle $\theta_{w}$. The width of the jet for Mach and other reflections is determined by the angle of the Mach stem at the triple point (also called the Mach node or three-shock node). Strong jetting is unstable and the primary instability is in the jet itself. The contact discontinuity is also unstable, but its instability is secondary with respect to the jet instability. Two types of irregular reflection are identified in the dual-solution-domain. They are a two-node system comprising a Mach node followed by a four-shock (overtake) node; and another which seems to be intermediate between the previous system and a three-node reflection, which was first hypothesized by Ben-Dor & Glass (1979). An approximate criterion for the jetting $\,{\leftrightarrow}\,$ no-jetting transition is presented. It is derived by an analysis of the system of Euler equations for a self-similar flow, and has a simple geometrical interpretation.

Type
Research Article
Copyright
© 2003 Cambridge University Press

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