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.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
58 articles.
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