Hostname: page-component-84b7d79bbc-g5fl4 Total loading time: 0 Render date: 2024-07-31T21:20:01.827Z Has data issue: false hasContentIssue false

Shock cavity implosion morphologies and vortical projectile generation in axisymmetric shock–spherical fast/slow bubble interactions

Published online by Cambridge University Press:  10 May 1998

N. J. ZABUSKY
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA; e-mail: nzabusky@caip.rutgers.edu
S. M. ZENG
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA; e-mail: nzabusky@caip.rutgers.edu

Abstract

Collapsing shock-bounded cavities in fast/slow (F/S) spherical and near-spherical configurations give rise to expelled jets and vortex rings. In this paper, we simulate with the Euler equations planar shocks interacting with an R12 axisymmetric spherical bubble. We visualize and quantify results that show evolving upstream and downstream complex wave patterns and emphasize the appearance of vortex rings. We examine how the magnitude of these structures scales with Mach number. The collapsing shock cavity within the bubble causes secondary shock refractions on the interface and an expelled weak jet at low Mach number. At higher Mach numbers (e.g. M=2.5) ‘vortical projectiles’ (VP) appear on the downstream side of the bubble. The primary VP arises from the delayed conical vortex layer generated at the Mach disk which forms as a result of the interaction of the curved incoming shock waves that collide on the downstream side of the bubble. These rings grow in a self-similar manner and their circulation is a function of the incoming shock Mach number. At M=5.0, it is of the same order of magnitude as the primary negative circulation deposited on the bubble interface. Also at M=2.5 and 5.0 a double vortex layer arises near the apex of the bubble and moves off the interface. It evolves into a VP, an asymmetric diffuse double ring, and moves radially beyond the apex of the bubble. Our simulations of the Euler equations were done with a second-order-accurate Harten–Yee-type upwind TVD scheme with an approximate Riemann Solver on mesh resolution of 803×123 with a bubble of radius 55 zones.

Type
Research Article
Copyright
© 1998 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)