Stability and Thermodynamic Consistency in the Coexistence Curve Of Liquid-Vapor in A Modified Pseudo-Potential Model

Document Type : Research Article

Authors

1 زنجان-مهندسی- گروه مهندسی مکانیک

2 Department of mechanical engineering/ Faculty of engineering/ University of Zanjan /Zanjan/ Iran

Abstract

In this paper, the conditions of convergence and thermodynamic consistency of the Kupershtokh model for simulating a 2D droplet are investigated. Hence, the coexistence curve of liquid and vapor phases is divided into four levels according to the constant of the potential function, k and the weight coefficient of the intermolecular forces, A. Accordingly, a range is reported for k at each level. This range for level 1 with the lowest density ratio is kmin= 0.05 to kmax = 0.22 and for the fourth level with the highest density ratio is kmin=0.002 to kmax = 0.01. Also, the appropriate weight coefficient for inter- molecular forces, Afit is obtained for yielding the thermodynamic consistency at levels 1 to 4 equal with 0.25, 0.025, -0.082 and -0.125, respectively. Results show that the choice of A=0.5 produces symmetric and A=0 causes asymmetric forces in the interface. Finally, the problem of mass conservation in four levels is investigated. Results show that Kupeshtokh model has a better behavior in controlling the mass of the droplet in the high density ratios. So, the change in the mass of the droplet at level 1 is more than 20% and at the level of 4 is less than 1%

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References

[1]  H. Huang, M. Sukop, X. Lu, Multiphase lattice Boltzmann methods: Theory and application, John Wiley & Sons, 2015.
[2]  H. Deng, K. Jiao, Y. Hou, J.W. Park, Q. Du,  A lattice Boltzmann model for multi-component two- phase gas-liquid flow with realistic fluid properties, International Journal of Heat and Mass Transfer, 128 (2019) 536-549.
[3]A.A. Mohamad, Lattice Boltzmann method: fundamentals and engineering applications with computer codes, Springer Science & Business Media, 2011.
[4]  M. Sukop, DT Thorne, Jr. Lattice Boltzmann Modeling Lattice Boltzmann Modeling, (2006).
[5]  G. Házi, A.R. Imre, G. Mayer, I. Farkas, Lattice Boltzmann methods for two-phase flow modeling, Annals of Nuclear Energy, 29(12) (2002) 1421-1453.
[6]  X. Shan, H. Chen, Lattice Boltzmann model for simulating flows with multiple phases and components, Physical Review E, 47(3) (1993) 1815.
[7]  L. Chen, Q. Kang, Y. Mu, Y.-L. He, W.-Q. Tao, A critical review of the pseudopotential multiphase lattice Boltzmann model: Methods and applications, International journal of heat and mass transfer, 76 (2014) 210-236.
[8]  A.L. Kupershtokh, D.A. Medvedev, I.I. Gribanov, Thermal lattice Boltzmann method for multiphase flows, Physical Review E, 98(2) (2018) 023308.
[9]  P. Yuan, L. Schaefer, Equations of state in a lattice Boltzmann model, Physics of Fluids, 18(4) (2006) 042101.
[10] M. Nemati, A.R.S.N. Abady, D. Toghraie, Karimipour, Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid– vapor for multi-phase flows, Physica A: Statistical Mechanics and its Applications, 489 (2018) 65-77.
[11]  S. Khajepor, J. Wen, B. Chen, Multipseudopotential interaction: a solution for thermodynamic inconsistency in pseudopotential lattice Boltzmann models, Physical Review E, 91(2) (2015) 023301.
[12] Q. Li, K. Luo, Thermodynamic  consistency  of  the pseudopotential lattice Boltzmann model for simulating liquid–vapor flows, Applied Thermal Engineering, 72(1) (2014) 56-61.
[13] Q. Li, K. Luo, Achieving tunable surface tension in the pseudopotential lattice Boltzmann modeling of multiphase flows, Physical Review E, 88(5) (2013) 053307.
[14]  A. Kupershtokh, D. Medvedev, D. Karpov, On equations of state in a lattice Boltzmann method, Computers & Mathematics with Applications, 58(5) (2009) 965-974.
[15] Q. Li, K.H. Luo, Q. Kang, Y. He, Q. Chen, Q. Liu, Lattice Boltzmann methods for multiphase flow and phase-change heat transfer, Progress in Energy and Combustion Science, 52 (2016) 62-105.
[16] S. Son, L. Chen, D. Derome, J. Carmeliet, Numerical study of gravity-driven droplet displacement on a surface using the pseudopotential multiphase lattice Boltzmann model with high density ratio, Computers & Fluids, 117 (2015) 42-53.
[17] K. Timm, H. Kusumaatmaja, A. Kuzmin, The lattice Boltzmann method: principles and practice, in, Springer: Berlin, Germany, 2016.
[18] A. Kaplun, A. Meshalkin, Behavior of the heat capacity C V at the liquid-vapor critical point and in the two-phase region of a thermodynamic system, in: Doklady Physics, Springer, 2005, pp. 434-437.
[19]   X. He, X. Shan, G.D. Doolen, Discrete Boltzmann equation model for nonideal gases, Physical Review E, 57(1) (1998) R13.
[20]   Z. Qin, W. Zhao, Y. Chen, C. Zhang, B. Wen, A pseudopotential multiphase lattice Boltzmann model based on high-order difference, International Journal of Heat and Mass Transfer, 127 (2018) 234-243.
[21]   R. Zhang, H. Chen, Lattice Boltzmann method for simulations of liquid-vapor thermal flows, Physical Review E, 67(6) (2003) 066711.
[22]  A.L. Kupershtokh, Simulation of flows with vapor- liquid interfaces using lattice Boltzmann equation method, Siberian Journal of Pure and Applied Mathematics, 5(3) (2005) 29-42.
[23]     A. Kupershtokh, C. Stamatelatos, D. Agoris, Stochastic model of partial discharge activity in liquid and solid dielectrics, in: IEEE International Conference on Dielectric Liquids, 2005. ICDL 2005., IEEE, 2005, pp. 135-138.
[24]    A. Kupershtokh, D. Karpov, D. Medvedev, C. Stamatelatos, V. Charalambakos, E. Pyrgioti, D. Agoris, Stochastic models of partial discharge activity in solid and liquid dielectrics, IET Science, Measurement & Technology, 1(6) (2007) 303-311.
Amirkabir Journal of Mechanical Engineering
Volume 52, Issue 11
February 2021
Pages 3091-3106

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