Improved three-dimensional bubble dynamics model based on boundary element method. (English) Zbl 1349.76420
Summary: Some new theoretical and numerical techniques are adopted in an improved 3D bubble dynamics model based on Boundary Element Method. Firstly, a numerical model under the incompressible potential assumption is established for 3D bubble dynamics, and the traditional technique for the vortex ring induced potential at the reference point in axisymmetric model is extended to arbitrary location in 3D model. Then, to homogenize the boundaries’ mesh density, new Density Potential Method is put forward inspired by the Elastic Mesh Technique. It’s combined together with the topology optimization based on edge swapping procedure to maintain a desirable mesh for the large deformation problem. Through the verification and the comparison by simulating a benchmark case, the improved model demonstrates good accuracy and stability. Particularly, more toroidal bubble evolution detailed features are captured which are in accordance with the axisymmetric model. Finally, bubble dynamics under different circumstances are simulated with the improved 3D numerical model presented in this paper, which shows that the improved model is also robust.
MSC:
| 76M15 | Boundary element methods applied to problems in fluid mechanics |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |
| 76L05 | Shock waves and blast waves in fluid mechanics |
Keywords:
bubble dynamics; boundary element method; surface mesh optimization; toroidal bubble; density potential methodReferences:
| [1] | Cole, R. H., Underwater Explosion (1948), Princeton University Press: Princeton University Press Princeton, USA |
| [2] | Wilkerson, S. A., A Boundary Integral Approach to Three-Dimensional Underwater Explosion Bubble Dynamics (1990), Department of Mechanical Engineering, The Johns Hopkins University: Department of Mechanical Engineering, The Johns Hopkins University Baltimore, Maryland |
| [3] | Best, J. P., The Effect of Non-Spherical Collapse on Determination of Explosion Bubble Parameters (2002), DSTO Systems Sciences Laboratory |
| [4] | Geers, T. L.; Hunter, K. S., An integrated wave-effects model for an underwater explosion bubble, J. Acoust. Soc. Am., 111, 4, 1584-1601 (2002) |
| [5] | Wang, C.; Khoo, B. C.; Yeo, K. S., Elastic mesh technique for 3D BIM simulation with an application to underwater explosion bubbles, Comput. Fluids, 32, 9, 1195-1212 (2003) · Zbl 1140.76386 |
| [6] | Klaseboer, E.; Hung, K. C.; Wang, C.; Wang, C. W.; Khoo, B. C.; Boyce, P.; Debono, S.; Charlier, H., Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure, J. Fluid Mech., 53, 7, 387-413 (2005) · Zbl 1138.76303 |
| [7] | Wang, Q. X., Non-spherical bubble dynamics of underwater explosions in a compressible fluid, Phys. Fluids, 25, 7 (2013) · Zbl 1320.76116 |
| [8] | Ziolkowski, A., A method for calculating the output pressure waveform from an air-gun, Geophysics, 21, 137-161 (1970) |
| [9] | Vaage, S.; Ursin, B.; Haugland, K., Interaction between airguns, Geophys. Prospect., 32, 676-689 (1984) |
| [10] | Ziolkowski, A., Measurement of air-gun bubble oscillations, Geophysics, 63, 2009-2024 (1998) |
| [11] | Brujan, E. A.; Nahen, K.; Schmidt, P., Dynamics of laser-induced cavitation bubbles near an elastic boundary: influence of the elastic modulus, J. Fluid Mech., 433, 283-314 (2001) · Zbl 0968.76508 |
| [12] | Klaseboer, E.; Khoo, B. C., An oscillating bubble near an elastic material, J. Appl. Phys., 90, 5808-5818 (2004) · Zbl 1067.76067 |
| [13] | Liu, X. M.; He, J.; Liu, J.; Ni, X. W., Nonlinear dynamics of laser-induced bubble near elastic boundaries, Proc. SPIE, 6839, 68391J1-6 (2007) |
| [14] | Blake, J. R.; Gibson, D. C., Cavitation bubbles near boundaries, Annu. Rev. Fluid Mech., 19, 99-123 (1987) |
| [15] | Best, J. P.; Kucera, A., A numerical investigation of non-spherical rebounding bubbles, J. Fluid Mech., 245, 137-191 (1992) · Zbl 0825.76472 |
| [16] | Zhang, Y. L.; Yeo, K. S.; Khoo, B. C.; Wang, C., 3D jet impact and toroidal bubbles, J. Comput. Phys., 16, 6, 336-360 (2001) · Zbl 1030.76040 |
| [17] | Wang, Q. X.; Blake, J. R., Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave, J. Fluid Mech., 659, 191-224 (2010) · Zbl 1205.76263 |
| [18] | Dadvand, A.; Khoo, B. C.; Shervani-Tabar, M. T.; Khalilpourazary, S., Boundary element analysis of the droplet dynamics induced by spark-generated bubble, Eng. Anal. Bound. Elem., 36, 11, 1595-1603 (2012) · Zbl 1351.76139 |
| [19] | Pearson, A.; Cox, E.; Blake, J. R.; Otto, S. R., Bubble interactions near a free surface, Eng. Anal. Bound. Elem., 28, 295-313 (2004) · Zbl 1070.76040 |
| [20] | Wang, C.; Khoo, B. C., An indirect boundary element method for three-dimensional explosion bubbles, J. Comput. Phys., 19, 4, 451-480 (2004) · Zbl 1100.76542 |
| [21] | Blake, J. R.; Gibson, D. C., Growth and collapse of a vapour cavity near a free surface, J. Fluid Mech., 111, 123-140 (1981) |
| [22] | Gibson, D. C.; Blake, J. R., The growth and collapse of bubbles near deformable surfaces, Appl. Sci. Res., 38, 1, 215-224 (1982) |
| [23] | Best, J. P.; Blake, J. R., An estimate of the Kelvin impulse of a transient cavity, J. Fluid Mech., 261, 75-93 (1994) · Zbl 0812.76012 |
| [24] | Best, J. P., The formulation of toroidal bubbles upon collapse of transient cavities, J. Fluid Mech., 251, 79-107 (1993) · Zbl 0784.76011 |
| [25] | Wang, Q. X.; Yeo, K. S.; Khoo, B. C.; Lam, K. Y., Strong interaction between a buoyancy bubble and a free surface, Theor. Comput. Fluid Dyn., 8, 73-88 (1996) · Zbl 0874.76010 |
| [26] | Wang, Q. X.; Yeo, K. S.; Khoo, B. C.; Lam, K. Y., Nonlinear interaction between gas bubble and free surface, Comput. Fluids, 25, 7, 607-628 (1996) · Zbl 0898.76005 |
| [27] | Wang, Q. X., The evolution of a gas bubble near an inclined wall, Theor. Comput. Fluid Dyn., 12, 29-51 (1998) · Zbl 0912.76064 |
| [28] | Klaseboer, E.; Khoo, B. C.; Hung, K. C., Dynamics of an oscillating bubble near a floating structure, J. Fluids Struct., 10, 2, 1-10 (2005) |
| [29] | Zhang, A. M.; Wang, S. P.; Huang, C.; Wang, B., Influences of initial and boundary conditions on underwater explosion bubble dynamics, Eur. J. Mech. B, Fluids, 42, 69-92 (2013) |
| [30] | Zhang, A. M.; Yang, W. S.; Huang, C.; Ming, F. R., Numerical simulation of column charge underwater explosion based on SPH and BEM combination, Comput. Fluids, 71, 169-179 (2013) · Zbl 1365.76245 |
| [31] | Wang, Q. X.; Yeo, K. S.; Khoo, B. C.; Lam, K. Y., Vortex ring modelling of toroidal bubbles, Theor. Comput. Fluid Dyn., 15 (2005) · Zbl 1112.76322 |
| [32] | Li, Z. R.; Sun, L.; Zong, Z.; Dong, J., Some dynamical characteristics of a non-spherical bubble in proximity to a free surface, Acta Mech. Sin., 2331-2355 (2012) · Zbl 1307.76078 |
| [33] | Wang, Q. X., Unstructured MEL modeling of nonlinear unsteady ship waves, J. Comput. Phys., 210, 17 (2005) · Zbl 1154.76371 |
| [34] | Milne-Thomson, L. M., Theoretical Hydrodynamics (1968), Dover Publications: Dover Publications New York · Zbl 0164.55802 |
| [35] | Sussman, M.; Smereka, P.; Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114, 146-205 (1994) · Zbl 0808.76077 |
| [36] | Sussman, M.; Fatemi, E., An efficient, interface-preserving level set redistancing algorithm and its applications to interfacial incompressible fluid flow, SIAM J. Sci. Comput., 20, 1165-1191 (1999) · Zbl 0958.76070 |
| [37] | Wang, Q. X.; Yeo, K. S.; Khoo, B. C., Toroidal bubbles near a rigid wall (1996), unpublished technical report · Zbl 1081.76526 |
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