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Vortex ring modelling of toroidal bubbles

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Abstract

During the collapse of a bubble near a surface, a high-speed liquid jet often forms and subsequently impacts upon the opposite bubble surface. The jet impact transforms the originally singly-connected bubble to a toroidal bubble, and generates circulation in the flow around it. A toroidal bubble simulation is presented by introducing a vortex ring seeded inside the bubble torus to account for the circulation. The velocity potential is then decomposed into the potential of the vortex ring and a remnant potential. Because the remnant potential is continuous and satisfies the Laplace equation, it can be modelled by the boundary-integral method, and this circumvents an explicit domain cut and associated numerical treatment. The method is applied to study the collapse of gas bubbles in the vicinity of a rigid wall. Good agreement is found with the results of Best (J. Fluid Mech. 251 79–107, 1993), obtained by a domain cut method. Examination of the pressure impulse on the wall during jet impact indicates that the high-speed liquid jet has a significant potential for causing damage to a surface. There appears to be an optimal initial distance where the liquid jet is most damaging.

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Authors and Affiliations

  1. Maritime Research Centre, Division of Environmental and Water Resources Engineering, School of Environmental and Civil Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 630798, The Republic of Singapore

    Q. X. Wang

  2. Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore, 19260, The Republic of Singapore

    K. S. Yeo, B. C. Khoo & K. Y. Lam

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  1. Q. X. Wang
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  2. K. S. Yeo
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  3. B. C. Khoo
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  4. K. Y. Lam
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Correspondence to Q. X. Wang.

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Communicated by J. R. Blake

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Wang, Q.X., Yeo, K.S., Khoo, B.C. et al. Vortex ring modelling of toroidal bubbles. Theor. Comput. Fluid Dyn. 19, 303–317 (2005). https://doi.org/10.1007/s00162-005-0164-6

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  • DOI: https://doi.org/10.1007/s00162-005-0164-6

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