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

Published online by Cambridge University Press:  14 December 2007

JOHN H. J. NIEDERHAUS ,
J. A. GREENOUGH ,
J. G. OAKLEY ,
D. RANJAN ,
M. H. ANDERSON  and
R. BONAZZA
JOHN H. J. NIEDERHAUS
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
J. A. GREENOUGH
Affiliation:
Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
J. G. OAKLEY
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
D. RANJAN
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
M. H. ANDERSON
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
R. BONAZZA
Affiliation:
Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI 53706, USA
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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.

JFM classification

Compressible Flows: Shock waves Compressible Flows: Gas dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 594 , 10 January 2008 , pp. 85 - 124
Copyright
Copyright © Cambridge University Press 2008

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Niederhaus et al. supplementary movie

Movie 1. Density (bottom) and vorticity magnitude (top) fields for the interaction of a M=1.68 shock wave with a 2.54-cm-radius helium bubble in an air environment. For this gas pairing, the Atwood number is A=-0.757, and visible here is the development of irregular and divergent shock refraction patterns and the formation of a characteristic vortex ring.

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Video 2.3 MB

Niederhaus et al. supplementary movie

Movie 2. Density (bottom) and vorticity magnitude (top) fields for the interaction of a M=3.38 shock wave with a 2.54-cm-radius argon bubble in a nitrogen environment. For this gas pairing, the Atwood number is A=0.163, and visible here are the very weak nonlinear-acoustic effects associated with low Atwood-number magnitude, resulting in low density contrast at late times and a flowfield dominated by the development of a single large vortex ring. Also visible is the emergence of a small upstrem-directed axial jet.

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Video 892.7 KB

Niederhaus et al. supplementary movie

Movie 3. Density (bottom) and vorticity magnitude (top) fields for the interaction of a M=1.68 shock wave with a 2.54-cm-radius krypton bubble in an air environment. For this gas pairing, the Atwood number is A=0.486, and visible here are the stronger nonlinear-acoustic and turbulence-like effects associated with higher Atwood numbers. Also visible is the development of a prominent upstream-directed axial jet and strong secondary vortices around the primary vortex ring.

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Video 6 MB

Niederhaus et al. supplementary movie

Movie 4. Density (bottom) and vorticity magnitude (top) fields for the interaction of a M=5 shock wave with a 2.54-cm-radius R12 bubble in an air environment. For this gas pairing, the Atwood number is A=0.613, and visible here are the development of very strong nonlinear-acoustic and turbulence-like effects associated with high Atwood numbers, including strong secondary shock waves scattered through the mixing region at intermediate times, and the development of a disordered vorticity field and a large plume of well-mixed fluid at late times.

Download Niederhaus et al. supplementary movie(Video)
Video 5.9 MB