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Interaction of a strong shockwave with a gas bubble in a liquid medium: a numerical study

Published online by Cambridge University Press:  11 May 2012

N. A. Hawker  and
Y. Ventikos
N. A. Hawker
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
Y. Ventikos*
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
*
†Email address for correspondence: yiannis.ventikos@eng.ox.ac.uk
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Abstract

The interaction of a shockwave with a gas bubble in a liquid medium is of interest in a variety of areas, e.g. shockwave lithotripsy, cavitation damage and the study of sonoluminescence. This study employs a high-resolution front-tracking framework to numerically investigate this phenomenon. The modelling paradigm is validated extensively and then used to explore the parametric space of interest. We provide a comprehensive qualitative analysis of the collapse process, which we categorize into three phases, based on the principal feature dominating each phase. This results in the characterization of numerous previously unidentified features important in the evolution of the process and in the emergence of peak temperatures and pressures. For example, we discover that the peak pressure does not occur as a result of the impact of the main transverse jet (also called the re-entrant jet) but later in the collapse. We perform fully three-dimensional simulations, showing that three-dimensional instabilities are limited to the small-scale details of collapse, and continue by comparing collapse of cylindrical and spherical bubbles. We detail a parametric investigation varying the shock strength from 100 MPa to 100 GPa. A counter-intuitive discovery is that the maximum gas density decreases with increasing shock strength.

JFM classification

Drops and Bubbles: Bubble dynamics Compressible Flows: Shock waves Drops and Bubbles: Sonoluminescence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 701 , 25 June 2012 , pp. 59 - 97
Copyright
Copyright © Cambridge University Press 2012

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Hawker and Ventikos supplementary movie

1GPa - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 12.9 MB

Hawker and Ventikos supplementary movie

1GPa - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 8.7 MB

Hawker and Ventikos supplementary movie

1GPa Vorticity - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows a numerical schlieren image whereas the right hand side shows vorticity.

Download Hawker and Ventikos supplementary movie(Video)
Video 8.1 MB

Hawker and Ventikos supplementary movie

1GPa Vorticity - A 2D simulation of the interaction of 1GPa shockwave in water with a 1mm air bubble. The left hand side shows a numerical schlieren image whereas the right hand side shows vorticity.

Download Hawker and Ventikos supplementary movie(Video)
Video 8.2 MB

Hawker and Ventikos supplementary movie

100GPa - A 2D simulation of the interaction of 100GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 15.6 MB

Hawker and Ventikos supplementary movie

100GPa - A 2D simulation of the interaction of 100GPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 13.1 MB

Hawker and Ventikos supplementary movie

100MPa - A 2D simulation of the interaction of 100MPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 24.6 MB

Hawker and Ventikos supplementary movie

100MPa - A 2D simulation of the interaction of 100MPa shockwave in water with a 1mm air bubble. The left hand side shows density and the right hand side shows the pressure, only in the liquid, and the temperature, only in the gas. A numerical schlieren image, visualising magnitude of gradient of density, with a tailored colour and opacity map is overlaid over both, making the shock structures clearer.

Download Hawker and Ventikos supplementary movie(Video)
Video 16.8 MB