基于气液相界面捕捉的统一气体动理学格式

王昭; 严红

doi:10.6052/0459-1879-17-364

基于气液相界面捕捉的统一气体动理学格式

doi: 10.6052/0459-1879-17-364

王昭¹,
严红^1,2,3,*, ,

1西北工业大学动力与能源学院, 西安 710072
2西北工业大学陕西省航空发动机内流动力学重点实验室, 西安 710072
3先进航空发动机协同创新中心, 北京 100191;

基金项目: 国防基础科研科学挑战计划资助项目(TZ2016001).

详细信息

作者简介:
^*严红, 教授, 主要研究方向: 超声速流动. E-mail:yanhong@nwpu.edu.cn

通讯作者:
严红

中图分类号: O359;
计量
- 文章访问数: 1230
- HTML全文浏览量: 84
- PDF下载量: 425
- 被引次数: 0
出版历程
- 刊出日期: 2018-07-18

UNIFIED GAS-KINETIC SCHEME FOR TWO PHASE INTERFACE CAPTURING

Wang Zhao¹,
Yan Hong^{1,2,3,*
, ,}

1School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China

摘要

摘要: 气液相界面运动的研究无论是在科学还是工程领域都是非常重要的. 其中, 非平衡流动的计算尤其受到关注. 基于此, 我们构造了捕捉气液相界面的统一气体动理学格式. 由于统一气体动理学格式将自由输运和粒子碰撞耦合起来更新宏观物理量和微观分布函数, 故而可以求解非平衡流动. 具体思路是, 通过将范德瓦尔斯状态方程所表达的非理想气体效应引入统一气体动理学格式之中来捕捉气液相界面, 两相的分离与共存通过范德瓦尔斯状态方程描述. 由于流体在椭圆区域是不稳定的, 因此气液相界面可以通过蒸发和凝结过程自动捕捉. 如此, 一个锋锐的相界面便可以通过数值耗散和相变而得到. 利用该方法得到麦克斯韦等面积律(Maxwell construction)对应的数值解, 并与其相应的理论解相比较, 二者符合良好. 而后, 通过对范德瓦尔斯状态方程所描述的液滴表面张力进行数值计算, 验证了Laplace定理. 此外, 通过模拟两个液滴的碰撞融合过程, 进一步证明了该格式的有效性. 但是, 由于范德瓦尔斯状态方程的特性, 其所构造的格式仅适用于液/气两相密度比小于5的情况.
- 统一气体动理学格式 /
- 范德瓦尔斯状态方程 /
- 相界面捕捉 /
- 麦克斯韦等面积律 /
- 液滴表面张力
Abstract: The study of interfacial motion of gas-liquid phase is very important in science and engineering. Considering the non-equilibrium flow calculation, a unified gas-kinetic scheme for gas-liquid two phase interface capturing is presented in this paper. Since the free transport and particle collision are coupled to update the macroscopic variables and microscopic distribution functions, the unified gas-kinetic scheme can solve the non-equilibrium flow. The van der Waals (vdW) equation of state (EOS) is included to describe the coexistence of gas and liquid and the phase transition between them. Because of the characteristics of vdW EOS, the interface between gas and liquid can be captured naturally through condensation and evaporation processes. As a result, the new scheme can solve the gas-liquid two phase problems. Finally, the proposed method is used to obtain the numerical solution of Maxwell construction, which agrees well with the corresponding theoretical solution. Then, the Laplace’s theorem is verified by numerical calculation of the surface tension of the droplet corresponding to the van der Waals state equation. In addition, the collision of the two droplets is simulated, which proves the validity of the scheme further. However, due to the characteristics of the van der Waals equation of state, the constructed scheme is only applicable to the case where the liquid/gas two-phase density ratio is less than 5.
- unified gas-kinetic scheme /
- van der Waals equation of state /
- interface capturing /
- Maxwell construction /
- surface tension

HTML全文

参考文献(1)

[1]	刘文超, 刘曰武. 低渗透煤层气藏中气?水两相不稳定渗流动态分析. 力学学报, 2017, 49(4): 828-835
[1]	(Liu Wenchao, Liu Yuewu.Dynamic analysis on gas-water two-phase unsteady seepage flow in low-permeable coalbed gas reservoirs.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(4): 828-835 (in Chinese))
[2]	李康, 刘娜, 何志伟等. 一种基于双界面函数的界面捕捉方法. 力学学报, 2017, 49(6): 1290-1300
[2]	(Li Kang, Liu Na, He Zhiwei, et al.A new interface capturing method based on double interface functions.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1290-1300 (in Chinese))
[3]	Hirt CW, Nichols BD.Volume of fluid (VOF) method for the dynamics of free boundaries.J Comput Phys, 1981, 39(1): 201-225
[4]	张洋, 陈科, 尤云祥等. 壁面约束对裙带气泡动力学的影响. 力学学报, 2017, 49(5): 1050-1058
[4]	(Zhang Yang, Chen Ke, You Yunxiang, et al.Confinement effect on the rising dynamics of a skirted bubble.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1050-1058 (in Chinese))
[5]	Sussman M, Smereka P, Osher S.A level set approach for computing solutions to incompressible two-phase flow.J Comput Phys, 1994, 114(1): 146-159
[6]	郭照立, 郑楚光. 格子Boltzmann 方法的原理及应用. 北京: 科学出版社, 2009
[6]	(Guo Zhaoli, Zheng Chuguang.Principle and Application of Lattice Boltzmann Method. Beijing: Science Press, 2009 (in Chinese))
[7]	Shan X, Chen H.Lattice Boltzmann model for simulating flows with multiple phases and components.Phys Rev E, 1993, 47(3): 1815-1819
[8]	Shan X, Chen H.Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation.Phys Rev E, 1994, 49(4): 2941-2948
[9]	Gunstensen AK, Rothman DH, aleski SZ, et al. Lattice Boltzmann model of immiscible fluids.Phys Rev A, 1991, 43(8): 4320-4327
[10]	Swift MR, Osborn WR, Yeomans JM.Lattice Boltzmann simulation of nonideal fluids.Phys Rev Lett, 1995, 75(5): 830-833
[11]	Zhang R, Chen H.Lattice Boltzmann method for simulations of liquid-vapor thermal flows.Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 2003, 67(6): 66711
[12]	Yuan, P, Schaefer L. Equations of state in a lattice Boltzmann model.Phys Fluids, 2006, 18(4): 42101
[13]	Kupershtokh AL, Karpov DI, Medvedev DA, et al.Stochastic models of partial discharge activity in solid and liquid dielectrics.IET Science, Measurement & Technology, 2007, 1(6): 303-311
[14]	胡安杰. 多相流动格子Boltzmann 方法研究. [博士论文]. 重庆: 重庆大学, 2015
[14]	(Hu Anjie.Study on lattice Boltzmann method for multiphase flow. [PhD Thesis]. Chongqing: Chongqing University, 2015 (in Chinese))
[15]	Li Q, Luo KH, Kang QJ, et al.Lattice Boltzmann methods for multiphase flow and phase-change heat transfer.Progress in Energy and Combustion Science, 2016, 52: 62-105
[16]	Chikatamarla SS, Karlin IV.Entropic lattice Boltzmann method for multiphase flows.Physical Review Letters, 2015, 114(17): 174502
[17]	Wang Y, Shu C, Huang HB, et al.Multiphase lattice Boltzmann flux solver for incompressible multiphase flows with large density ratio.Journal of Computational Physics, 2015, 280: 404-423
[18]	Liu H, Kang Q, Leonardi CR, et al.Multiphase lattice Boltzmann simulations for porous media applications.Computational Geosciences, 2016, 20(4): 777-805
[19]	Lycett-Brown D, Luo KH.Improved forcing scheme in pseudopotential lattice Boltzmann methods for multiphase flow at arbitrarily high density ratios.Physical Review E, 2015, 91(2): 023305
[20]	Shao JY, Shu C.A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast.International Journal for Numerical Methods in Fluids, 2015, 77(9): 526-543
[21]	郭宇隆. 基于格子Boltzmann 方法的气液混合流体模拟. [硕士论文]. 广州: 华南理工大学, 2015
[21]	(Guo Yulong.Study on gas-liquid mixed fluid simulation based on lattice Boltzmann method [Master Thesis]. Guangzhou: South China University of Technology, 2015 (in Chinese))
[22]	史冬岩, 王志凯, 张阿漫. 一种模拟气液两相流的格子波尔兹曼改进模型. 力学学报, 2013, 46(2): 224-233
[22]	(Shi Dongyan, Wang Zhikai, Zhang Aman.Improved model of simulating gas-liquid two-phase flow by lattice Boltzmann.Chinese Journal of Theoretical and Applied Mechanics, 2013, 46(2): 224-233 (in Chinese))
[23]	曾建邦, 李隆键, 廖全等. 格子Boltzmann 方法在相变过程中的应用. 物理学报, 2010, 59(1): 178-185
[23]	(Zeng Jianbang, Li Longjian, Liao Quan, et al.Application of lattice Boltzmann method in phase transition process.Acta Physica Sinica, 2010, 59(1): 178-185 (in Chinese))
[24]	Gong S, Cheng P.A lattice Boltzmann method for simulation of liquid-vapor phase-change heat transfer.International Journal of Heat and Mass Transfer, 2012, 55(17-18): 4923-4927
[25]	Dong L, Gong S, Cheng P.Direct numerical simulations of film boiling heat transfer by a phase-change lattice Boltzmann method.International Communications in Heat and Mass Transfer, 2018, 91: 109-116
[26]	Guo Z, Zhao T S, Shi Y.Physical symmetry, spatial accuracy, and relaxation time of the lattice Boltzmann equation for micro gas flows.Journal of Applied Physics, 2006, 99(7): 074903
[27]	Zhang Y, Qin R, Emerson DR.Lattice Boltzmann simulation of rarefied gas flows in microchannels.Physical Review E, 2005, 71(4): 047702
[28]	Guo Z, Zheng C, Shi B.Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow.Physical Review E, 2008, 77(3): 036707
[29]	Shan X, Yuan XF, Chen H.Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation.Journal of Fluid Mechanics, 2006, 550(1): 413-441
[30]	Xu K, Huang JC.A unified gas-kinetic scheme for continuum and rarefied flows.Journal of Computational Physics, 2010, 229(20): 7747-7764
[31]	毛枚良, 江定武, 李锦等. 气体动理学统一算法的隐式方法研究. 力学学报, 2015, 47(5): 822-829
[31]	(Mao Meiliang, Jiang Dingwu, Li Jin, et al.Study on implicit implementation of the unified gas kinetic scheme.Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 822-829 (in Chinese))
[32]	江定武, 毛枚良, 李锦等. 气体动理学统一算法中相容性条件不满足引起的数值误差及其影响研究. 力学学报, 2015, 47(1):163-168
[32]	(Jiang Dingwu, Mao Meiliang, Li Jin, et al.Study on the numerical error introduced by dissatisfying the conservation constraint in UGKS and its effects .Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1): 163-168 (in Chinese))
[33]	Xu K.A kinetic method for hyperbolic-elliptic equations and its application in two-phase flow.Journal of Computational Physics, 2001, 166(2): 383-399
[34]	Wang Z, Yan H, Li Q, et al.Unified gas-kinetic scheme for diatomic molecular flow with translational, rotational, and vibrational modes.Journal of Computational Physics, 2017, 350: 237-259
[35]	Huang H, Sukop M, Lu X.Multiphase Lattice Boltzmann Methods: Theory and Application. Beijing: John Wiley & Sons, 2015
[36]	Hu A, Li L, Chen S, et al.On equations of state in pseudo-potential multiphase lattice Boltzmann model with large density ratio.International Journal of Heat and Mass Transfer, 2013, 67: 159-163
[37]	Hu A, Li L, Uddin R.Force method in a pseudo-potential lattice Boltzmann model.Journal of Computational Physics, 2015, 294: 78-89
[38]	Shan X.Pressure tensor calculation in a class of nonideal gas lattice Boltzmann models.Physical Review E, 2008, 77(6): 066702
[39]	强洪夫, 陈福振, 高巍然. 基于SPH 方法的低韦伯数下三维液滴碰撞聚合与反弹数值模拟研究. 工程力学, 2012, 29(2): 21-28
[39]	(Qiang Hongfu, Chen Fuzhen, Gao Weiran.Simulation of coalescence and bouncing of three-dimensional droplet collisions with low weber numbers based on SPH method.Journal of Engineering Mechanics, 2012, 29(2): 21-28 (in Chinese))
[40]	Nugent S, Posch HA.Liquid drops and surface tension with smoothed particle applied mechanics.Physical Review E, 2000, 62: 4968-4975
[41]	Meleán Y, Sigalotti LDG.Coalescence of colliding van der Waals liquid drops.International Journal of Heat and Mass Transfer, 2005, 48: 4041-4061
[42]	夏盛勇. 三氧化二铝液滴碰撞机理及模型研究. [博士论文]. 西安: 西北工业大学, 2015
[42]	(Xia Shengyong.Physics and model of alumina droplet collisions. [PhD Thesis]. Xi’an: Northwestern Polytechnical University, 2015 (in Chinese))