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 JAMP  Vol.5 No.6 , June 2017
Modeling for Collapsing Cavitation Bubble near Rough Solid Wall by Mulit-Relaxation-Time Pseudopotential Lattice Boltzmann Model
Abstract: Cavitation bubble collapse near rough solid wall is modeled by the multi-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model. The modified forcing scheme, which can achieve LB model’s thermodynamic consistency by tuning a parameter related with the particle interaction range, is adopted to achieve desired stability and density ratio. The bubble collapse near rough solid wall was simulated by the improved MRT pseudopotential LB model. The mechanism of bubble collapse is studied by investigating the bubble profiles, pressure field and velocity field evolution. The eroding effects of collapsing bubble are analyzed in details. It is found that the process and the effect of the interaction between bubble collapse and rough solid wall are affected seriously by the geometry of solid boundary. At the same time, it demonstrates that the MRT pseudopotential LB model is a potential tool for the investigation of the interaction mechanism between the collapsing bubble and complex geometry boundary.
Cite this paper: Shan, M. , Zhu, Y. , Yao, C. , Han, Q. and Zhu, C. (2017) Modeling for Collapsing Cavitation Bubble near Rough Solid Wall by Mulit-Relaxation-Time Pseudopotential Lattice Boltzmann Model. Journal of Applied Mathematics and Physics, 5, 1243-1256. doi: 10.4236/jamp.2017.56106.
References

[1]   Abboud, J.E. and Oweis, G.F. (2013) Themicrojetting Behavior from Single Laser-Induced Bubbles Generated above a Solid Boundary with a Through Hole. Experiments in Fluids, 54, 1438.
https://doi.org/10.1007/s00348-012-1438-6

[2]   Hashmi, A., Yu, G., Reilly-Collette, M., Heiman, G. and Xu, J. (2012) Oscillating Bubbles: A Versatile Tool for Lab on a Chip Applications. Lab on a Chip, 12, 4216-4227.
https://doi.org/10.1039/c2lc40424a

[3]   Naudé, C.F. and Ellis, A.T. (1961) On the Mechanism of Cavitation Damage by Nonhemispherical Cavities Collapsing in Contact with a Solid Boundary. Journal of Basic Engineering, 83, 648-656.
https://doi.org/10.1115/1.3662286

[4]   Li, B.B., Jia, W., Zhang, H.C. and Lu, J. (2014) Investigation on the Collapse Behavior of a Cavitation Bubble near a Conical Rigid Boundary. Shock Waves, 24, 317-324.
https://doi.org/10.1007/s00193-013-0482-3

[5]   Aganin, A.A., Ilgamov, M.A., Kosolapova, L.A. and Malakhov, V.G. (2016) Dynamics of a Cavitation Bubble near a Solid Wall. Thermophysics and Aeromechanics, 23, 211-220.
https://doi.org/10.1134/S0869864316020074

[6]   Magaletti, F., Gallo, M., Marino, L. and Casciola, C.M. (2016) Shock-Induced Collapse of a Vapor Nanobubble near Solid Boundaries. International Journal of Multiphase Flow, 84, 34-45.
https://doi.org/10.1016/j.ijmultiphaseflow.2016.02.012

[7]   Hsu, C.Y., Liang, C.C., Nguyen, A.T. and Teng, T.L. (2014) A Numerical Study on the Underwater Explosion Bubble Pulsation and the Collapse Process. Ocean Engineering, 81, 29-38.
https://doi.org/10.1016/j.oceaneng.2014.02.018

[8]   Zhang, A.M. and Liu, Y.L. (2015) Improved Three-Dimensional Bubble Dynamics Model Based on Boundary Element Method. Journal of Computational Physics, 294, 208-223.
https://doi.org/10.1016/j.jcp.2015.03.049

[9]   Chen, S. and Doolen, G.D. (1998) Lattice Boltzmann Method for Fluid Flows. Annual Review of Fluid Mechanics, 30, 329-364.
https://doi.org/10.1146/annurev.fluid.30.1.329

[10]   Succi, S. (2001) The Lattice Boltzmann Equation: For Fluid Dynamics and Beyond. Oxford University Press, Oxford.

[11]   Gunstensen, A.K., Rothman, D.H., Zaleski, S. and Zanetti, G. (1991) Lattice Boltzmann Model of Immiscible Fluids. Physical Review A, 43, 4320.
https://doi.org/10.1103/physreva.43.4320

[12]   Shan, X. and Chen, H. (1993) Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components. Physical Review E, 47, 1815.
https://doi.org/10.1103/physreve.47.1815

[13]   Shan, X. and Chen, H. (1994) Simulation of Non Ideal Gases and Liquid-Gas Phase Transitions by the Lattice Boltzmann Equation. Physical Review E, 49, 2941.
https://doi.org/10.1103/physreve.49.2941

[14]   Swift, M.R., Osborn, W.R. and Yeomans, J.M. (1995) Lattice Boltzmann Simulation of Non-Ideal Fluids. Physical Review Letters, 75, 830.
https://doi.org/10.1103/physrevlett.75.830

[15]   Chen, L., Kang, Q., Mu, Y., He, Y.L. and Tao, W.Q. (2014) A Critical Review of the Pseudo Potential Multiphase Lattice Boltzmann Model: Methods and Applications. International Journal of Heat and Mass Transfer, 76, 210-236.

[16]   Huang, H., Sukop, M. and Lu, X. (2015) Multiphase Lattice Boltzmann Methods: Theory and Application. John Wiley & Sons Ltd., Chichester.
https://doi.org/10.1002/9781118971451

[17]   Sukop, M.C. and Or, D. (2005) Lattice Boltzmann Method for Homogeneous and Heterogeneous Cavitation. Physical Review E, 71, Article ID: 046703.
https://doi.org/10.1103/physreve.71.046703

[18]   Chen, X.P., Zhong, C.W. and Yuan, X.L. (2011) Lattice Boltzmann Simulation of Cavitating Bubble Growth with Large Density Ratio. Computers & Mathematics with Applications, 61, 3577-3584.

[19]   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.

[20]   Shan, M.L., Zhu, C.P., Xi, Z.H.O.U., Cheng, Y.I.N. and Han, Q.B. (2016) Investigation of Cavitation Bubble Collapse near Rigid Boundary by Lattice Boltzmann Method. Journal of Hydrodynamics, 28, 442-450.

[21]   Shan, M.L., Zhu, C.P., Yao, C., Yin, C. and Jiang, X.Y. (2016) Pseudopotential Multi-Relaxation-Time Lattice Boltzmann Model for Cavitation Bubble Collapse with High Density Ratio. Chinese Physics B, 25, Article ID: 104701.
https://doi.org/10.1088/1674-1056/25/10/104701

[22]   Li, Q. and Luo, K.H. (2014) Thermodynamic Consistency of the Pseudopotential Lattice Boltzmann Model for Simulating Liquid-Vapor Flows. Applied Thermal Engineering, 72, 56-61.

[23]   Kupershtokh, A.L., Medvedev, D.A. andKarpov, D.I. (2009) On Equations of State in a Lattice Boltzmann Method. Computers & Mathematics with Applications, 58, 965-974.

[24]   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.
https://doi.org/10.1103/physreve.86.016709

[25]   Li, Q., Luo, K.H. and Li, X.J. (2013) Lattice Boltzmann Modeling of Multiphase Flows at Large Density Ratio with an Improved Pseudopotential Model. Physical Review E, 87, Article ID: 053301.
https://doi.org/10.1103/physreve.87.053301

[26]   Li, Q., Luo, K.H., Kang, Q.J., He, Y.L., Chen, Q. and Liu, Q. (2016) Lattice Boltzmann Methods for Multiphase Flow and Phase-Change Heat Transfer. Progress in Energy and Combustion Science, 52, 62-105.

[27]   Yuan, P. and Schaefer, L. (2006) Equations of State in a Lattice Boltzmann Model. Physics of Fluids, 18, Article ID: 042101.
https://doi.org/10.1063/1.2187070

[28]   Shan, X. (2008) Pressure Tensor Calculation in a Class of Nonideal Gas Lattice Boltzmann Models. Physical Review E, 77, Article ID: 066702.
https://doi.org/10.1103/physreve.77.066702

[29]   Shi, D.Y., Wang, Z.K. and Zhang, A.M. (2014) Study on Coupling Characteristics between Bubble and Complex Walls at the Same Scale. Acta Physica Sinica, 63, 533-538.

[30]   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.
https://doi.org/10.1017/S0022112071001058

[31]   Guo, Z.-L., Zheng, C.-G. and Shi, B.-C. (2002) Non-Equilibrium Extrapolation Method for Velocity and Pressure Boundary Conditions in the Lattice Boltzmann Method. Chinese Physics, 11, 366.
https://doi.org/10.1088/1009-1963/11/4/310

[32]   Zou, Q. and He, X. (1997) On Pressure and Velocity Boundary Conditions for the Lattice Boltzmann BGK Model. Physics of Fluids, 9, 1591-1598.
https://doi.org/10.1063/1.869307

[33]   Huang, H., Krafczyk, M. and Lu, X. (2011) Forcing Term in Single-Phase and Shan-Chen-Type Multiphase Lattice Boltzmann Models. Physical Review E, 84, Article ID: 046710.
https://doi.org/10.1103/physreve.84.046710

 
 
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