广义守恒相场简化多相流格子Boltzmann方法

章诗婷; 肖鸿威; 周锦翔; 牛小东

doi:10.7638/kqdlxxb-2021.0327

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

广义守恒相场简化多相流格子Boltzmann方法

专栏——格子玻尔兹曼方法及应用 | 更新时间：2026-05-28

- 广义守恒相场简化多相流格子Boltzmann方法
- Generalized conservative phase-field model based lattice Boltzmann method for multiphase flows
- 空气动力学学报 2022年40卷第3期页码：75-86
- 作者机构：
  
  1. 汕头大学工学院,汕头,515063
  2. 汕头大学智能制造技术教育部重点实验室,汕头,515063
- 作者简介：
  
  章诗婷（1996-），女，浙江人，硕士研究生，研究方向：格子Boltzmann方法，磁流体多相流. E-mail：19stzhang@stu.edu.cn
  牛小东*（1969-），男，辽宁人，教授，研究方向：格子Boltzmann方法，磁流体多相流. E-mail: xdniu@stu.edu.cn
- 基金信息：
  
  国家自然科学基金（11772179）;国家自然科学基金（12172203）
- DOI：10.7638/kqdlxxb-2021.0327
  中图分类号： O359
- 纸质出版：2022
- 稿件说明：
移动端阅览
章诗婷, 肖鸿威, 周锦翔, 等. 广义守恒相场简化多相流格子Boltzmann方法[J]. 空气动力学学报, 2022, 40(3): 75−86.

ZHANG Shiting, XIAO Hongwei, ZHOU Jinxiang, et al. Generalized conservative phase-field model based lattice Boltzmann method for multiphase flows[J]. 2022, 40(3): 75-86.
章诗婷, 肖鸿威, 周锦翔, 等. 广义守恒相场简化多相流格子Boltzmann方法[J]. 空气动力学学报, 2022, 40(3): 75−86. DOI： 10.7638/kqdlxxb-2021.0327

ZHANG Shiting, XIAO Hongwei, ZHOU Jinxiang, et al. Generalized conservative phase-field model based lattice Boltzmann method for multiphase flows[J]. 2022, 40(3): 75-86. DOI： 10.7638/kqdlxxb-2021.0327.

摘要

针对不可压缩、非混溶的复杂多相流问题，提出一种广义守恒相场简化多相流格子Boltzmann方法。此方法运用早前发展的简化多相流格子Boltzmann方法（simplified multiphase lattice Boltzmann method，SMLBM），通过采用带有拉格朗日算子的广义守恒相场方程来控制界面的演化并确保每个相的体积和总质量守恒。此外，在单松弛格子Boltzmann方法框架内，SMLBM是通过预测-校正策略来模拟流体系统和跟踪界面演化，其计算过程中仅需要考虑平衡态分布函数的演化，并且平衡态分布函数可直接从宏观量计算得到，因而具有良好的稳定性、高计算效率和边界条件易于实施的优点。本方法继承了SMLBM的优势，能够解决由不同流体组分之间的大密度比和大黏度比引起的界面处大压力梯度问题。为了验证本方法的稳定性和准确性，模拟了包括拉普拉斯定律、液滴透镜、三相泊肃叶流以及复合液滴铺展在内的四个多相流算例。结果表明，本方法能有效地模拟密度比达1200和黏度比达500的复杂界面算例。

Abstract

A generalized conservative phase-field simplified lattice Boltzmann method is proposed

which is suitable for incompressible and immiscible complex multiphase flow problems. This method extends our earlier simplified multiphase lattice Boltzmann method (SMLBM) by using a generalized conservative equation with Lagrange multiplier to control the evolution of the interface and ensures the conservations of the volume and total mass of each phase. Moreover

the SMLBM mimics the fluid systems and interface dynamics with a predictor-corrector scheme in the frame of single-relaxation lattice Boltzmann method by considering only the evolution of equilibrium distribution function

which can be directly calculated from the macroscopic variables. Therefore

this method inherits the advantages of good stability

high computational efficiency

and easy implementation of boundary conditions of the SMLBM

which is utilized for solving the interface problems with large gradients induced by large density ratios and large viscosity ratios between different fluid components. To validate the present method

four multiphase flow examples including Laplace law

spreading of a liquid lens

Poiseuille flow with three phases and spreading of a compound droplet are simulated. The results show that this method can effectively simulate complex interface multiphase flows with the density ratio of 1200 and the viscosity ratio of 500.

关键词

Keywords

references

CHEN Z, SHU C, TAN D, et al. Simplified multiphase lattice Boltzmann method for simulating multiphase flows with large density ratios and complex interfaces[J]. Physical Review E, 2018, 98(6): 063314. DOI:10.1103/physreve.98.063314

UTADA A S, LORENCEAU E, LINK D R, et al. Monodisperse double emulsions generated from a microcapillary device[J]. Science, 2005, 308(5721): 537-541. DOI:10.1126/science.1109164

DONG S. Physical formulation and numerical algorithm for simulating N immiscible incompressible fluids involving general order parameters[J]. Journal of Computational Physics, 2015, 283: 98-128. DOI:10.1016/j.jcp.2014.11.039

YUAN X, LIANG H, CHAI Z, et al. Phase-field-based lattice Boltzmann model for immiscible incompressible N-phase flows[J]. Physical Review E, 2020, 101(6-1): 063310. DOI:10.1103/physreve.101.063310

BOYER F, LAPUERTA C, MINJEAUD S, et al. Cahn-Hilliard/Navier-Stokes model for the simulation of three-phase flows[J]. Transport in Porous Media, 2010, 82(3): 463-483. DOI:10.1007/s11242-009-9408-z

GARCKE H, NESTLER B, STOTH B. A MultiPhase field concept: numerical simulations of moving phase boundaries and multiple junctions[J]. SIAM Journal on Applied Mathematics, 1999, 60(1): 295-315. DOI:10.1137/s0036139998334895

KIM J. Phase field computations for ternary fluid flows[J]. Computer Methods in Applied Mechanics and Engineering, 2007, 196(45-48): 4779-4788. DOI:10.1016/j.cma.2007.06.016

HIRT C W, NICHOLS B D. Volume of fluid (VOF) method for the dynamics of free boundaries[J]. Journal of Computational Physics, 1981, 39(1): 201-225. DOI:10.1016/0021-9991(81)90145-5

GUEYFFIER D, LI J, NADIM A, et al. Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows[J]. Journal of Computational Physics, 1999, 152(2): 423-456. DOI:10.1006/jcph.1998.6168

OSHER S, SETHIAN J A. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations[J]. Journal of Computational Physics, 1988, 79(1): 12-49. DOI:10.1016/0021-9991(88)90002-2

SMITH K, SOLIS F, CHOPP D. A projection method for motion of triple junctions by level sets[J]. Interfaces and Free Boundaries, 2002: 263-276. DOI:10.4171/ifb/61

UNVERDI S O, TRYGGVASON G. A front-tracking method for viscous, incompressible, multi-fluid flows[J]. Journal of Computational Physics, 1992, 100(1): 25-37. DOI:10.1016/0021-9991(92)90307-K

TRYGGVASON G, BUNNER B, ESMAEELI A, et al. A front-tracking method for the computations of multiphase flow[J]. Journal of Computational Physics, 2001, 169(2): 708-759. DOI:10.1006/jcph.2001.6726

GINGOLD R A, MONAGHAN J J. Smoothed particle hydrodynamics: theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society, 1977, 181(3): 375-389. DOI:10.1093/mnras/181.3.375

CAHN J W, HILLIARD J E. Free energy of a nonuniform system. I. interfacial free energy[J]. The Journal of Chemical Physics, 1958, 28(2): 258-267. DOI:10.1063/1.1744102

ALLEN S M, CAHN J W. Mechanisms of phase transformations within the miscibility gap of Fe-rich Fe-Al alloys[J]. Acta Metallurgica, 1976, 24(5): 425-437. DOI:10.1016/0001-6160(76)90063-8

BAO W Z, DU Q. Multiscale modeling and analysis for materials simulation[M]. World Scientific . Imperial College Press, 2011. doi: 10.1142/8212

LEE H G, CHOI J W, KIM J. A practically unconditionally gradient stable scheme for the N-component Cahn-Hilliard system[J]. Physica A: Statistical Mechanics and Its Applications, 2012, 391(4): 1009-1019. DOI:10.1016/j.physa.2011.11.032

LEE H G, KIM J. An efficient numerical method for simulating multiphase flows using a diffuse interface model[J]. Physica A: Statistical Mechanics and Its Applications, 2015, 423: 33-50. DOI:10.1016/j.physa.2014.12.027

LEE H G, KIM J. A second-order accurate non-linear difference scheme for the N-component Cahn-Hilliard system[J]. Physica A: Statistical Mechanics and Its Applications, 2008, 387(19-20): 4787-4799. DOI:10.1016/j.physa.2008.03.023

KIM J. A generalized continuous surface tension force formulation for phase-field models for multi-component immiscible fluid flows[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(37-40): 3105-3112. DOI:10.1016/j.cma.2009.05.008

ELLIOTT C M, LUCKHAUS S. A generalised diffusion equation for phase separation of a multi-component mixture with interfacial free energy[R]. IMA Preprints Series #2486. https://www.ima.umn.edu/sites/default/files/887.pdf

DONG S. An efficient algorithm for incompressible N-phase flows[J]. Journal of Computational Physics, 2014, 276: 691-728. DOI:10.1016/j.jcp.2014.08.002

DONG S. Wall-bounded multiphase flows of N immiscible incompressible fluids: Consistency and contact-angle boundary condition[J]. Journal of Computational Physics, 2017, 338: 21-67. DOI:10.1016/j.jcp.2017.02.048

DONG S. Multiphase flows of N immiscible incompressible fluids: a reduction-consistent and thermodynamically-consistent formulation and associated algorithm[J]. Journal of Computational Physics, 2018, 361: 1-49. DOI:10.1016/j.jcp.2018.01.041

YUE P T, ZHOU C F, FENG J J. Spontaneous shrinkage of drops and mass conservation in phase-field simulations[J]. Journal of Computational Physics, 2007, 223(1): 1-9. DOI:10.1016/j.jcp.2006.11.020

KIM J, LOWENGRUB J. Phase field modeling and simulation of three-phase flows[J]. Interfaces and Free Boundaries, 2005: 435-466. DOI:10.4171/ifb/132

WANG Y, SHU C, HUANG H B, et al. Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio[J]. Journal of Computational Physics, 2015, 280: 404-423. DOI:10.1016/j.jcp.2014.09.035

CHAI Z H, SHI B C, GUO Z L. A multiple-relaxation-time lattice boltzmann model for general nonlinear anisotropic convection-diffusion equations[J]. Journal of Scientific Computing, 2016, 69(1): 355-390. DOI:10.1007/s10915-016-0198-5

WANG L, ZHAO Y, YANG X G, et al. A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder[J]. Applied Mathematical Modelling, 2019, 71: 31-44. DOI:10.1016/j.apm.2019.02.012

LIANG H, SHI B C, CHAI Z H. Lattice Boltzmann modeling of three-phase incompressible flows[J]. Physical Review E, 2016, 93(1): 013308. DOI:10.1103/physreve.93.013308

HAGHANI HASSAN ABADI R, FAKHARI A, RAHIMIAN M H. Numerical simulation of three-component multiphase flows at high density and viscosity ratios using lattice Boltzmann methods[J]. Physical Review E, 2018, 97(3): 033312. DOI:10.1103/physreve.97.033312

HAGHANI HASSAN ABADI R, RAHIMIAN M H, FAKHARI A. Conservative phase-field lattice-Boltzmann model for ternary fluids[J]. Journal of Computational Physics, 2018, 374: 668-691. DOI:10.1016/j.jcp.2018.07.045

ZHENG L, ZHENG S, ZHAI Q L. Reduction-consistent phase-field lattice Boltzmann equation for N immiscible incompressible fluids[J]. Physical Review E, 2020, 101(4): 043302. DOI:10.1103/physreve.101.043302

HU Y, LI D C, HE Q. Generalized conservative phase field model and its lattice Boltzmann scheme for multicomponent multiphase flows[J]. International Journal of Multiphase Flow, 2020, 132: 103432. DOI:10.1016/j.ijmultiphaseflow.2020.103432

LI Q Z, LU Z L, ZHOU D, et al. Unified simplified multiphase lattice Boltzmann method for ferrofluid flows and its application[J]. Physics of Fluids, 2020, 32(9): 093302. DOI:10.1063/5.0021463

KHAN A, NIU X D, LI Q Z, et al. Dynamic study of ferrodroplet and bubbles merging in ferrofluid by a simplified multiphase lattice Boltzmann method[J]. Journal of Magnetism and Magnetic Materials, 2020, 495: 165869. DOI:10.1016/j.jmmm.2019.165869

CHEN Z, SHU C, LIU Y Y, et al. Ternary phase-field simplified multiphase lattice Boltzmann method and its application to compound droplet dynamics on solid surface in shear flow[J]. Physical Review Fluids, 2021, 6(9): 094304. DOI:10.1103/physrevfluids.6.094304

DING H, SPELT P D M, SHU C. Diffuse interface model for incompressible two-phase flows with large density ratios[J]. Journal of Computational Physics, 2007, 226(2): 2078-2095. DOI:10.1016/j.jcp.2007.06.028

ZU Y Q, HE S. Phase-field-based lattice Boltzmann model for incompressible binary fluid systems with density and viscosity contrasts[J]. Physical Review E, 2013, 87(4): 043301. DOI:10.1103/physreve.87.043301

LIANG H, XU J, CHEN J, et al. Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows[J]. Physical Review E, 2018, 97(3-1): 033309. DOI:10.1103/physreve.97.033309

KALANTARPOUR R, EBADI A, HOSSEINALIPOUR S M, et al. Three-component phase-field Lattice Boltzmann method with high density ratio and ability to simulate total spreading states[J]. Computers Fluids, 2020, 204: 104480. DOI:10.1016/j.compfluid.2020.104480

RAWLINSON J S, WIDOM B. The molecular theory of capillarity[M]. Oxford University Press, 1982.

REN F, SONG B, SUKOP M C, et al. Improved lattice Boltzmann modeling of binary flow based on the conservative Allen-Cahn equation[J]. Physical Review E, 2016, 94(2-1): 023311. DOI:10.1103/physreve.94.023311

DING H, SPELT P D M. Wetting condition in diffuse interface simulations of contact line motion[J]. Physical Review E, 2007, 75(4): 046708. DOI:10.1103/physreve.75.046708

ZHANG C Y, DING H, GAO P, et al. Diffuse interface simulation of ternary fluids in contact with solid[J]. Journal of Computational Physics, 2016, 309: 37-51. DOI:10.1016/j.jcp.2015.12.054

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

旋翼跨介质飞行气动特性与机理仿真分析

一种改进的浸入运动边界算法

声激励下的剪切流稳定性

大密度比双气泡在孔板结构微通道内上升行为的格子Boltzmann方法模拟

单个中性球形颗粒在三维方腔中的运动