We consider a pressure (density) in a
square flume solid boundaries and no-slip format condition formulation are introduced
to investigate cavitation bubble for the two-dimensional lattice Boltz- mann
method (LBM). Using the coupling Carnahan-Starling equation of state (C-S EOS)
and exact difference method (EDM) based on modified Shan-Chen model, the whole
process of bubble collapse was observed complete and visual with equilibrium
distribution function and rebound format. This paper analyzes the bubble form
evolution, collapse time and dynamic character under the two dimensional press
fields.
References
[1]
Ishida, H., Nuntadusit, C., Kimoto, H., Nakagawa, T. and Yamamoto, T. (2001) Cavitation Bubble Behavior near Solid Boundaries, CAV2001, Session A5.003: Fourth International Symposium on Cavitation.
http://resolver.caltech.edu.sci-hub.org/CAV2001:sessionA5.003
[2]
Nourgaliev, R.R. and Dinh, J.R. (2003) The Lattice Boltzmann Equation Method: Theoretical Interpretation, Numerics and Implications. International Journal of Multiphase Flow, 29, 117-169.
http://dx.doi.org/10.1016/S0301-9322(02)00108-8
[3]
Guo, Z.L. and Shu, C. (2013) Lattice Boltzmann Method and Its Applications in Engineering. World Scientific Publishing Co. Pte. Ltd., Singapore. http://dx.doi.org/10.1142/8806
[4]
Amaya-Bower, L. (2010) Numerical Simulation of Multiphase Flows in Microchannels Using the Lattice Boltzmann Method. Ph.D. Thesis, City University of New York, New York.
[5]
Samiei, E., Shams, M. and Ebrahimi, R. (2011) A Novel Numerical Scheme for the Investigation of Surface Tension Effects on Growth and Collapse Stages of Cavitation Bubbles. European Journal of Mechanics B-Fluid, 30, 41-50.
http://dx.doi.org/10.1016/j.euromechflu.2010.09.002
[6]
Sussman, M. (2003) A Second Order Coupled Level Set and Volume-of-Fluid Method for Computing Growth and Collapse of Vapor Bubbles. Journal of Computational Physics, 187, 110-136.
http://dx.doi.org/10.1016/S0021-9991(03)00087-1
[7]
Chen, L., Kang, Q.J., Mu, Y.T., He, Y.L. and Tao, W.Q. (2014) A Critical Review of the Pseudopotential Multiphase Lattice Boltzmann Model: Methods and Applications. International Journal of Heat and Mass Transfer, 76, 210-236.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.04.032
[8]
Sukop, M. and Or, D. (2005) Lattice Boltzmann Method for Homogeneous and Heterogeneous Cavitation. Physical Review E, 71, Article ID: 04670. http://dx.doi.org/10.1103/physreve.71.046703
[9]
Zhang, X.M. and Zhou, C.Y. (2009) Numerical Simulation of Three Dimensional Cavitation Phenomenon by Lattice Boltzmann Method. Acta Physica Sinica, 58, 8460-8414. (In Chinese)
[10]
Mishra, S.K., Deymier, P.A., Muralidharan, K., Frantziskonis, G., Pannala, S. and Simunovic, S. (2010) Modeling the Coupling of Reaction Kinetics and Hydrodynamics in a Collapsing Cavity. Ultrasonics Sonochemistry, 17, 258-265.
http://dx.doi.org/10.1016/j.ultsonch.2009.05.014
[11]
Chen, X.P., Zhong, C.W. and Yuan, X.L. (2011) Lattice Boltzmann Simulation of Cavitating Bubble Growth with Large Density Ratio. Computers and Mathematics with Applications, 61, 3577-3584.
http://dx.doi.org/10.1016/j.camwa.2010.07.018
[12]
Zhou, X., Shan, M.L., Zhu, C.P., Chen, B.Y., Yin, C., Ren, Q.G., et al. (2014) Simulation of Acoustic Cavitation Bubble Motion by Lattice Boltzmann Method. 4th International Conference on Civil Engineering, Architecture and Building Materials, Haikou, 3098-3105. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.3098
[13]
Shan, M.L., Zhu, C.P., Zhou, X., Yin, C. and Han, Q.B. (2014) Investigation on Cavitation Bubble Collapse near Rigid Boundary by Lattice Boltzmann Method. Journal of Hydrodynamics. (In Press)
[14]
McNamara, G. and Zanetti, G. (1988) Use of the Boltzmann Equation to Simulate Lattice-Gas Automata. Physical Review Letters, 61, 2332-2335. http://dx.doi.org/10.1103/PhysRevLett.61.2332
[15]
Qian, Y.H., d’Humieres, D. and Lallemand, P. (1992) Lattice BGK Models for Navier Stokes Equation. Europhysics Letters, 17, 479-484. http://dx.doi.org/10.1209/0295-5075/17/6/001
[16]
Huang, H.B., Manfred, K. and Lu, X.Y. (2011) Forcing Term in Single-Phase and Shane-Chen-Type Multiphase Lattice Boltzmann Models. Physical Review E, 84, Article ID: 046710. http://dx.doi.org/10.1103/PhysRevE.84.046710
[17]
Sukop, M.C. and Thorne, D.T. (2006) Lattice Boltzmann Modeling: An Introduction for Geoscientists and Engineers, Springer, Verlag.
[18]
Yuan, P. and Laura, S. (2006) Equations of State in a Lattice Boltzmann Model. Physics of Fluids, 18, Article ID: 04210. http://dx.doi.org/10.1063/1.2187070
[19]
Kupershtokh, A.L., Medvedev, D.A. and Karpov, D.I. (2009) On Equations of State in a Lattice Boltzmann Method, Computer and Mathematics with Applications, 58, 965-974. http://dx.doi.org/10.1016/j.camwa.2009.02.024
[20]
Li, Q., Luo, K.H. and Li, X.J. (2012) Forcing Scheme in Pseudopotential Lattice Boltzmann Model for Multiphase Flows. Physical Review E, 86, Article ID: 016709. http://dx.doi.org/10.1103/physreve.86.016709
[21]
Zou, Q.S. and He, X.Y. (1997) On Pressure and Velocity Boundary Condition for the Lattice Boltzmann BGK Model. Physics of Fluids, 9, 1591-1598. http://dx.doi.org/10.1063/1.869307
[22]
He, Y.L., Wang, Y. and Li, Q. (2009) Lattice Boltamann Method: Theory and Applications. Science Press, Beijing. (In Chinese)
[23]
Philipp, A. and Lauterborn, W. (1998) Cavitation Ersion by Single Laser-Produced Bubbles. Journal of Fluid Mechanics, 361, 75-116. http://dx.doi.org/10.1017/S0022112098008738
[24]
Lauterborn, W. and Bolle, H. (1975) Experimental Investigations of Cavitation Bubble Collapse in the Neighbourhood of a Solid Boundary. Journal of Fluid Mechanics, 72, 391-399. http://dx.doi.org/10.1017/S0022112075003448
[25]
Plesset, M.S. and Chapman, R.B. (1971) Collapse of an Initially Spherical Vapour Cavity in the Neighbourhood of a Solid Boundary. Journal of Fluid Mechanics, 47, 283-290. http://dx.doi.org/10.1017/S0022112071001058
[26]
Shen, Z.Z. and Wu, S.J. (2012) Dynamic Behavior of a Cavitation Bubble in Acoustic Field and Electric Field. Acta physica Sinica, 61, Article ID: 124301. (In Chinese)
