An improved single-relaxation-time multiphase lattice Boltzmann model for multiphase flows with large density ratios and high Reynolds numbers. (English) Zbl 1488.76143
Summary: In this study, an improved single-relaxation-time multiphase lattice Boltzmann method (SRT-MLBM) is developed for simulating multiphase flows with both large density ratios and high Reynolds numbers. This model employs two distribution functions in lattice Boltzmann equation (LBE), with one tracking the interface between different fluids and the other calculating hydrodynamic properties. In the interface distribution function, a time derivative term is introduced to recover the Cahn-Hilliard equation. For flow field, a modified equilibrium particle distribution function is present to evolve the velocity and pressure field. The present method keeps simplicity of the conventional SRT-MLBM but enjoys good stability property in simulating multiphase. Apart from several benchmarks, the present model is validated by simulating various challenging multiphase flows, including two droplets impact on liquid film, droplet oblique splashing on a thin film and a drop impact on a moving liquid film. Numerical results show the reliability of present model for effectively simulating complex multiphase flows at density ratios of 1000 and high Reynolds numbers (up to 7000).
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M28 | Particle methods and lattice-gas methods |
| 76P99 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
References:
| [1] | A. K. GUNSTENSEN, D. H. ROTHMAN, S. ZALESKI AND G. ZANETTI, Lattice Boltzmann model of immiscible fluids, Phys. Rev. A, 43 (1991), pp. 4320-4327. |
| [2] | X. SHAN AND H. CHEN, Lattice Boltzmann model for simulating flows with multiple phases and components, Phys. Rev. E, 47 (1993), pp. 1815-1819. |
| [3] | X. SHAN AND H. CHEN, Simulation of non-ideal gases and liquid-gas phase-transition by the lattice Boltzmann equation, Phys. Rev. E, 49 (1994), pp. 2941-2948. |
| [4] | M. R. SWIFT, W. R. OSBORN AND J. M. YEOMANS, Lattice Boltzmann simulation of nonideal fluids, Phys. Rev. Lett., 75 (1995), 830. |
| [5] | M. SWIFT, E. ORLANDINI, W. R. OSBORN, AND J. M. YEOMANS, Lattice Boltzmann simula-tions of liquid-gas and binary fluid systems, Phys. Rev. E, 54 (1996), pp. 5041-5052. |
| [6] | X. Y. HE, X. W. SHAN AND G. D. DOOLEN, A discrete Boltzmann equation model for non-ideal gases, Phys. Rev. E, 57 (1998), 13. |
| [7] | X. Y. HE, S. Y. CHEN AND R. Y. ZHANG, A lattice Boltzmann scheme for incompressible multi-phase flow and its application in simulations of Rayleigh-Taylor instability, J. Comput. Phys., 152 (1999), pp. 652-663. · Zbl 0954.76076 |
| [8] | Z. GUO AND C. SHU, Lattice Boltzmann Method and its Applications in Engineering, World Scientfic, 2013. · Zbl 1278.76001 |
| [9] | S. Y. CHEN AND G. D. DOOLEN, Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech., 30 (1998), pp. 329-364. · Zbl 1398.76180 |
| [10] | R. R. NOURGALIEV, T. N. DINH, T. G. THEOFANOUS AND D. JOSEPH, The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. Multiphas Flow, 29(1) (2003), pp. 117-169. · Zbl 1136.76594 |
| [11] | K. CYRUS, AIDUN AND R. JONATHAN, Clausen lattice-Boltzmann method for complex flows, Annu. Rev. Fluid Mech., 42 (2010), pp. 439-472. · Zbl 1345.76087 |
| [12] | Q. LI, K. H. LUO, Q. J. KANG, Y. L. HE, Q. CHEN AND Q. LIU, Lattice Boltzmann methods for multiphase flow and phase-change heat transfer, Prog. Eng. Combust. Sci., 52 (2016), pp. 62-105. |
| [13] | T. INAMURO, T. OGATA, S. TAJIMA AND N. KONISHI, A lattice Boltzmann method for incom-pressible two-phase flows with large density differences, J. Comput. Phys., 198 (2004), pp. 628-644. · Zbl 1116.76415 |
| [14] | T. INAMURO, T. YOKOYAMA, K. TANAKA AND M. TANIGUCHI, An improved lattice Boltz-mann method for incompressible two-phase flows with large density differences, Comput. Fluids, 137 (2016), pp. 55-69. · Zbl 1390.76726 |
| [15] | L. LEE AND C. L. LIN, A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys., 206 (2005), pp. 16-47. · Zbl 1087.76089 |
| [16] | T. LEE AND C. L. LIU, Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces, J. Comput. Phys., 229 (2010), pp. 8045-8063. · Zbl 1426.76603 |
| [17] | H. W. ZHENG, C. SHU AND Y. T. CHEW, A lattice Boltzmann model for multiphase flows with large density ratio, J. Comput. Phys., 218 (2006), pp. 353-371. · Zbl 1158.76419 |
| [18] | D. CHIAPPINI, G. BELLA, S. SUCCI, F. TOSCHI AND S. UBERTINI, Improved lattice Boltzmann without parasitic currents for Rayleigh-Taylor instability, Common. Comput. Phys., 7 (2010), pp. 423-444. · Zbl 1364.76172 |
| [19] | Q. LOU, Z. L. GUO AND B. C. SHI, Effects of force discretization on mass conservation in lattice Boltzmann equation for two-phase flows, Europhys. Lett., 99 (2012), 64005. |
| [20] | H. W. ZHENG, C. SHU, AND Y. T. CHEW, Lattice Boltzmann interface capturing method for incompressible flows, Phys. Rev. E, 72 (2005), 056705. |
| [21] | A. FAKHARI AND M. H. RAHIMIAN, Phase-field modeling by the method of lattice Boltzmann equations, Phys. Rev. E, 81 (2010), 036707. · Zbl 1263.76053 |
| [22] | J. Y. SHAO, C. SHU, H. B. HUANG AND Y. T. CHEW, Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast, Phys. Rev. E, 89(2014), 033309. |
| [23] | X. D. NIU, Y. LI, Y. R. MA, M. F. CHEN, X. LI AND Q. Z. LI, A mass-conserving multiphase lattice Boltzmann model for simulation of multiphase flows, Phys. Fluids, 30 (2018), 013302. |
| [24] | J. Y. SHAO AND C. SHU, A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast, Int. J. Numer. Meth. Fluids, 77 (2015), pp. 526-543. |
| [25] | C. ZHANG, Z. GUO AND Y. LI, A fractional step lattice Boltzmann model for two-phase flow with large density differences, Int. J. Heat Mass Transfer, 138 (2019), pp. 1128-1141. |
| [26] | C. SHU, Y. WANG, C. J. TEO AND J. WU, Development of lattice Boltzmann flux solver for simulation of incompressible flows, Adv. Appl. Math. Mech., 6 (2014), pp. 436-460. |
| [27] | Z. CHEN, C. SHU, Y. WANG, L. M. YANG AND D. TAN, A simplified lattice Boltzmann method without evolution of distribution function, Adv. Appl. Math. Mech., 9(1) (2017), pp. 1-22. · Zbl 1488.76102 |
| [28] | Y. WANG, C. SHU, H. HUANG AND C. TEO, Multiphase lattice Boltzmann flux solver for incom-pressible multiphase flows with large density ratio, J. Comput. Phys., 280 (2015), pp. 404-423. · Zbl 1349.76746 |
| [29] | Z. CHEN, C. SHU, D. TAN, X. D. NIU AND Q. Z. LI, Simplified multiphase lattice Boltzmann method for simulating multiphase flows with large density ratios and complex interfaces, Phys. Rev. E, 98 (2018), 063314. |
| [30] | H. LIANG, Y. LI, J. X. CHEN AND J. R. XU, Axisymmetric lattice Boltzmann model for multi-phase flows with large density ratio, Int. J. Heat Mass Transfer, 130 (2019), pp. 1189-1205. |
| [31] | A. FAKHARIA, D. BOLSTERA AND L. S. LUO, A weighted multiple-relaxation-time lattice Boltz-mann method for multiphase flows and its application to partial coalescence cascades, J. Comput. Phys., 341 (2017), pp. 22-43. · Zbl 1376.76047 |
| [32] | Y. HU, DECAI LI, XIAODONG NIU AND SHI SHU, A diffuse interface lattice Boltzmann model for thermocapillary flows with large density ratio and thermophysical parameters contrasts, Int. J. Heat Mass Transfer, 138 (2019), pp. 809-824. |
| [33] | H. LIANG, B. C. SHI, Z. L. GUO AND Z. H. CHAI, Phase-field-based multiple-relaxation-time lattice Boltzmann model for incompressible multiphase flows, Phys. Rev. E, 89 (2014), 053320. |
| [34] | J. HUANG, C. SHU AND Y. CHEW, Mobility dependent bifurcations in capillarity driven two-phase fluid systems by using a lattice Boltzmann phase-field model, Int. J. Numer. Meth. Fluids, 60, (2009), pp. 203-225. · Zbl 1162.76043 |
| [35] | Y. Q. ZU AND S. HE, Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts, Phys. Rev. E, 87 (2013), 043301. |
| [36] | Y. QIAN, D. D’HUMIÈRES AND P. LALLEMAND, Lattice BGK models for Navier-Stokes equation, Europhys. Lett., 17 (1992), pp. 479-484. · Zbl 1116.76419 |
| [37] | R. NOURGALIEV, T. N. DINH AND T. THEOFANOUS, A pseudo-compressibility method for the numerical simulation of incompressible multifluid flows, Int. J. Multiphase Flow, 30 (2004), pp. 901-937. · Zbl 1136.76593 |
| [38] | H. DING, P. D. SPELT AND C. SHU, Diffuse interface model for incompressible two-phase flows with large density ratios, J. Comput. Phys., 226 (2007), pp. 2078-2095. · Zbl 1388.76403 |
| [39] | J. L. GUERMOND AND L. QUARTAPELLE, A projection FEM for variable density incompressible flows, J. Comput. Phys., 165 (2000), pp. 167-188. · Zbl 0994.76051 |
| [40] | Y. WANG, C. SHU, J. Y. SHAO, J. WU AND X. D. NIU, A mass-conserved diffuse interface method and its application for incompressible multiphase flows with large density ratio, J. Comput. Phys., 290 (2015), pp. 336-351. · Zbl 1349.76549 |
| [41] | A. BANARI, C. F. JANSSEN AND S. T. GRILLI, An efficient lattice Boltzmann multiphase model for 3D flows with large density ratios at high Reynolds numbers, Comput. Math. Appl., 68 (2014), pp. 1819-1843. · Zbl 1369.76044 |
| [42] | C. JOSSERAND AND S. ZALESKI, Droplet splashing on a thin liquid film, Phys. Fluids, 15 (2003), pp. 1650-1657. · Zbl 1186.76263 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
