A computational parameter study for the three-dimensional shock–bubble interaction

Abstract

The morphology and time-dependent integral properties of the multifluid compressible flow resulting from the shock–bubble interaction in a gas environment are investigated using a series of three-dimensional multifluid-Eulerian simulations. The bubble consists of a spherical gas volume of radius 2.54 cm (128 grid points), which is accelerated by a planar shock wave. Fourteen scenarios are considered: four gas pairings, including Atwood numbers −0.8 < A < 0.7, and shock strengths 1.1 < M ≤ 5.0. The data are queried at closely spaced time intervals to obtain the time-dependent volumetric compression, mean bubble fluid velocity, circulation and extent of mixing in the shocked-bubble flow. Scaling arguments based on various properties computed from one-dimensional gasdynamics are found to collapse the trends in these quantities successfully for fixed A. However, complex changes in the shock-wave refraction pattern introduce effects that do not scale across differing gas pairings, and for some scenarios with A > 0.2, three-dimensional (non-axisymmetric) effects become particularly significant in the total enstrophy at late times. A new model for the total velocity circulation is proposed, also based on properties derived from one-dimensional gasdynamics, which compares favourably with circulation data obtained from calculations, relative to existing models. The action of nonlinear-acoustic effects and primary and secondary vorticity production is depicted in sequenced visualizations of the density and vorticity fields, which indicate the significance of both secondary vorticity generation and turbulent effects, particularly for M > 2 and A > 0.2. Movies are available with the online version of the paper.

Two-fluid simulations of shock wave propagation and shock-bubble interaction in collisionless plasma

“…13 The round bubble was deformed at first into a concave shape and then finally into a vortex ring. [13][14][15][16] Similar deformation processes were observed in an experiment in a solid 17 and in an experiment using a plasma-ball generated by laser energy deposition in a gas. 18 The deformation morphologies of the bubble have been studied mainly with the aim of understanding compressible turbulence.…”

“…In the ion-fluid, the bubble was deformed into a concave shape due to the baroclinic vortex. [13][14][15][16] The transmitted shock wave could be observed inside the bubble. The streaky density distribution appeared upstream of the bubble.…”

“…The number of cells and the order of accuracy in the present scheme were insufficient for capturing the fine turbulent structure at the late stage of bubble deformation, but it was enough for the qualitative observation of the shock-bubble interactions at the very early stage. In the previous computations of the conventional shock-bubble problems in neutral gases, Niederhaus et al 15 used 128 cells for the radius of the bubble in the three-dimensional simulation, while Picone and Boris 16 used 50 cells in the two-dimensional simulation. Both these studies successfully produced similar results at the early stages.…”

Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations

“…Samtaney & Zabusky (1993) have also proposed an analytical density-ratio dependence on the baroclinic circulation initially deposited at a planar light-to-heavy interface. In shockbubble interactions (Giordano & Burtschell 2006;Niederhaus et al 2008;Layes, Jourdan & Houas 2009, among recent studies that consider various gas pairings), the refracted portion of the incident wave results in a complex wave distortion process in the interior of the bubble, particularly at high density ratios. The reverberation of these reflected and/or diffracted waves is analogous to Richtmyer-Meshkov growth after reshock.…”

Application of Multigrid Ghost Fluid Method to the Interaction of Shock Waves with Bubbles in Liquids

“…(1) (ESWL) (2) Ghost Fluid (6) , (7) Lagrange Euler ( ) (8) Quirk & Karni (9) Niederhaus (10) Haas & Sturtevant (11) Riemann (12) Takahira (3) , (4) ( Ghost Fluid )…”