A numerical investigation of bubble dynamics based on the potential-flow theory

Abstract

In this paper, the flow field is assumed to be inviscid, irrotational and incompressible, triangular elements are adopted to discretize the boundary of flow field, the boundary integral method is used to solve the flow field and the Mixed-Eulerian-Lagrangian method is applied to simulate the evolution of bubble. Three-dimensional smoothing method is used to smooth the bubble surface and the velocity potential to make the computing process more accurate and stable. In the analysis process, three-dimensional model simulates the dynamics of a bubble in the free field, gravitational field and near the rigid wall respectively, and the calculated results coincide well with the exact results and experimental data, which show that the algorithm and 3D model in this paper are of high accuracy. Calculation process indicates that bubble takes on strong non-linear under the combine effect of gravity and rigid wall.

Keywords

bubble / potential-flow theory / boundary integral / jet / rigid wall / three-dimensional

References

[1] Popinet S., Zaleski S. Bubble collapse near a solid boundary [J]. A numerical study of the influence of viscosity. Journal of Fluid Mechanics, 2002, 464: 137-163

[2] Glimm J., Grove J. W., Li X. L., Shyue K. M., et al. Three-dimensional front tracking [J]. Sci Comput, 1998, 19: 703-727

[3] Mulder W., Osher S., Sethian J. A. Computing interface motion in compressible gas dynamics [J]. Comput Phys, 1992, 100: 29-35

[4] Monaghan J. J. Smoothed particle hydrodynamics [J]. Annual Review of Astron and Astrophys, 1992, 30: 543-74

[5] Swegle J. W., Attaway S. W. On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations [J]. Computational Mechanics, 1995, 17: 151-168

[6] Best J. P., Kucera A. A numerical investigation of non-spherical rebounding bubbles [J]. Fluid Mech, 1992, 245: 137-148

[7] Blake J. R., Gibson D.C. Growth and collapse of a vapour cavity near a free surface [J]. Fluid Mech, 1981, 111: 123-140

[8] Wang Q. X., Yeo K. S., Khoo B. C., Lam K. Y. Strong interaction between a buoyancy bubble and a free surface [J]. Theor Comput Fluid Dyna, 1996, 8: 73-88

[9] Wang Q. X., Yeo K. S., Khoo B. C., Lam K. Y. Nonlinear interaction between gas bubble and free surface [J]. Comput Fluids, 1996, 25(7): 607-628

[10] Wilkerson S. A. A Boundary Integral Approach to Three Dimensional Underwater Explosion Bubble Dynamics [D]. 1990, Baltimore: Johns Hopkins University

[11] Zhang Y. L., Yeo K. S., Khoo B. C., Wang C. 3D jet impact and toroidal bubbles [J]. Comput Phys, 2001, 166(2): 336-360

[12] Wang C., Khoo B. C., Yeo K. S. Elastic mesh technique for 3D BIM simulation with an application to underwater explosion bubbles [J]. Computers and Fluids, 2003, 32(9): 1195-1212

[13] 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, 2005, 537: 387-413

[14] Qi D., Lu C. Growth and collapse of single bubble and its noise [J]. Journal of Shanghai Jiaotong University, 1998, 32(12): 50-54

[15] Qi D., Lu C., He Y. The speciality of two bubbles interaction [J]. Chinese quarterly of mechanics, 2000, 21(1): 16-20

[16] Lu C. J., He Y. S., Zhu S. Q. Transient cavity collapse in the vicinity of a flexible boundary [J]. Hydrodynamics, 1996, 142: 1305-1310

[17] Lu C. 3-D Numerical simulation of underwater explosion bubble [J]. Chinese Journal of Aeronautics, 1996, 9(1): 38-42

[18] Lu C. 3-D Numerical simulation of underwater explosion bubble [J]. Chinese Journal of Aeronautics, 1996, 17(1): 92-95

[19] Rayleigh J. W. On the pressure developed in a liquid during the collapse of a spherical cavity [J]. Philos Mag, 1917, 34: 94-98

[20] Cole R. H. Underwater explosion [M]. 1948, Princeton: Princeton University Press

[21] Brebbia C. A. The boundary element method for engineers [M]. 1978, New York: Halstead Press