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Numerical Simulations of Shock Emission by Bubble Collapse Near a Rigid Surface

With Applications to Shock-Wave Lithotripsy (SWL) and the Spallation Neutron Source

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Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 106))

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Abstract

The event central to cavitation erosion is bubble collapse. Yet, the detailed physics of the process are not well characterized. In recent years, direct simulations of the Euler equations have been used to study the collapse of a single bubble and the subsequent shock emission, in contexts ranging from naval engineering to biomedical applications. In the present work, shock-induced collapse and Rayleigh collapse of a single gas bubble are examined, with emphasis on cavitation damage in biomedical applications and the Spallation Neutron Source (SNS). After an overview following Johnsen [32], the non-spherical bubble dynamics are considered in detail for problems in which the collapse time is on the order of the time scale of shock propagation through the bubble. The pressures generated by bubble collapse near a solid surface are measured, and it is shown that the resulting wall pressure may be larger than that of the incoming shock. The current work is then applied to shock-wave lithotripsy, a procedure developed to treat renal calculi. In particular, one-way coupled fluid and elastic wave propagation simulations are used to investigate damage to kidney stones. Two stone comminution mechanisms are proposed: shock-induced bubble collapse and spallation due to shocks emitted by bubble collapse. The results suggest that the coupling between the fluid and solid mechanics are important in terms of understanding cavitation erosion. In the context of the SNS, the effect of confinement on the bubble dynamics and the pressure generated by collapse are examined.

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Acknowledgments

Part of this work was supported during the author’s Ph.D. studies by NIH Grant PO1 DK043881 and ONR grant N00014-06-1-0730. The more recent work was partly supported by Oak Ridge Associated Universities through the Ralph E. Powe Junior Faculty Enhancement Award. The author gratefully acknowledges helpful conversations with Tim Colonius, Robin Cleveland, Bernie Riemer and the Consortium for Shock Waves in Medicine.

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Authors and Affiliations

  1. Mechanical Engineering Department, University of Michigan, Ann Arbor, USA

    Eric Johnsen

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  1. Eric Johnsen
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Correspondence to Eric Johnsen .

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Editors and Affiliations

  1. Office of Naval Research, Arlington, Virginia, USA

    Ki-Han Kim

  2. DYNAFLOW, Inc., Jessup, Maryland, USA

    Georges Chahine

  3. Laboratoire des Ecoulements Géophysiques et Industriels (LEGI), Grenoble, France

    Jean-Pierre Franc

  4. Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland

    Ayat Karimi

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Johnsen, E. (2014). Numerical Simulations of Shock Emission by Bubble Collapse Near a Rigid Surface. In: Kim, KH., Chahine, G., Franc, JP., Karimi, A. (eds) Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction. Fluid Mechanics and Its Applications, vol 106. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8539-6_16

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  • DOI: https://doi.org/10.1007/978-94-017-8539-6_16

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