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三维方腔介电液体电对流的数值模拟研究

吴健, 张蒙齐, 田方宝

吴健, 张蒙齐, 田方宝. 三维方腔介电液体电对流的数值模拟研究[J]. 力学学报, 2018, 50(6): 1458-1469. DOI: 10.6052/0459-1879-18-301
引用本文: 吴健, 张蒙齐, 田方宝. 三维方腔介电液体电对流的数值模拟研究[J]. 力学学报, 2018, 50(6): 1458-1469. DOI: 10.6052/0459-1879-18-301
Wu Jian, Zhang Mengqi, Tian Fang-Bao. NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1458-1469. DOI: 10.6052/0459-1879-18-301
Citation: Wu Jian, Zhang Mengqi, Tian Fang-Bao. NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1458-1469. DOI: 10.6052/0459-1879-18-301
吴健, 张蒙齐, 田方宝. 三维方腔介电液体电对流的数值模拟研究[J]. 力学学报, 2018, 50(6): 1458-1469. CSTR: 32045.14.0459-1879-18-301
引用本文: 吴健, 张蒙齐, 田方宝. 三维方腔介电液体电对流的数值模拟研究[J]. 力学学报, 2018, 50(6): 1458-1469. CSTR: 32045.14.0459-1879-18-301
Wu Jian, Zhang Mengqi, Tian Fang-Bao. NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1458-1469. CSTR: 32045.14.0459-1879-18-301
Citation: Wu Jian, Zhang Mengqi, Tian Fang-Bao. NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1458-1469. CSTR: 32045.14.0459-1879-18-301

三维方腔介电液体电对流的数值模拟研究

基金项目: 1) 国家自然科学基金(11802079),国家“千人计划”(青年项目) 和澳大利亚ARC DECRA (DE160101098) 资助项目.
详细信息
    作者简介:

    null

    2) 田方宝,高级讲师,主要研究方向:流固耦合和复杂流动数值方法及应用. E-mail:f.tian@adfa.edu.au

  • 中图分类号: O351.2;

NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY

  • 摘要: 本文对封闭方腔内介电液体电对流进行了三维数值模拟研究.方腔的6个边界为固壁;4个侧边界为电绝缘边界;上下界面为两个电极.直流电场作用在从底部电极注入的自由电荷上,从而对液体施加库伦体积力并驱动流体流动形成电对流.为了求解这一物理问题,发展了一种二阶精度的有限体积法来求解完整的控制方程,包括Navier-Stokes方程和一组简化的Maxwell方程.考虑到电荷密度方程的强对流占优特性,采用了全逆差递减格式来求解该方程,获得了准确有界的解.通过研究发现,该流动在有限振幅区内的分叉类型为亚临界,即系统存在一个线性和非线性临界值,分别对应流动的开始和终止.由于非线性临界值比线性值小,因此两个临界值之间有一个迟滞回线.与无限大域中的自由对流相比,侧壁施加的额外约束改变了流场结构,使这两个临界值均有所增大.此外,还讨论了电荷密度和速度场的空间分布特征,发现电荷密度分布中存在电荷空白区.最后对更小空间尺寸情况计算结果表明,流动的线性分叉类型为超临界.本文的结果拓展了已有的二维有限空间内电对流的研究,并为三维电对流的线性和弱非线性理论分析提供参考.
    Abstract: A full three-dimensional numerical study on the electro-convection of dielectric liquids contained in a cubical cavity is reported. All boundaries are solid walls. The four lateral sides are electrically insulating and the top and bottom walls are planar electrodes. The flow motion is driven by the volumetric Coulomb force exerting on the free charge carriers introduced by a strong unipolar injection from the bottom electrode. The charge injection takes place due to the electro-chemical reaction at the interface between liquid and electrode. The unsteady Navier-Stokes equations and a reduced set of Maxwell's equations in the limit of electroquasistatics are solved using an efficient finite volume method with 2$^{\rm nd}$ order accuracy in space and time. Considering the strong convection-dominating nature of the charge conservation equation, a total variation diminishing scheme is specially used to solve this equation in order to obtain physically-bounded and accurate solution. It is found that the flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one, which correspond respectively to the onset and stop of the flow motion, are numerically determined. Since the nonlinear criterion is smaller than the linear one, there exists a hysteresis loop. Compared to the free convection in the infinitely large domain case, the constraint imposed by the lateral walls dramatically changes the flow structure and increases the two criteria. In addition, the spatial features of charge density distribution and velocity field are discussed in details. A central region free of charges is observed. This void region is formed due to the competition between the fluid velocity and the drift velocity, and it is closely related to the subcritical bifurcation feature of the flow. In addition, computations are also performed with a case with smaller domain sizes, and the results show that the linear bifurcation of the flow is supercritical. Once the system losses its linear stability, a steady convection state without charge void region is reached. The present results extend previous research on the two-dimensional electro-convection in confined cavities, and they provide reference for the three-dimensional theoretical analysis of the linear and weakly nonlinear stability.
  • [1] Castellanos A.Electrohydrodynamics. Springer Vienna, 1998
    [2] 陈效鹏, 程久生, 尹协振. 电流体动力学研究进展及其应用. 科学通报, 2003, 48(7): 637-646
    [2] (Chen Xiaopeng, Cheng Jiusheng, Yin Xiezhen.Advances and applications of electrohydrodynamics. Chinese Science Bulletin, 2003, 48(7): 637-646(in Chinese))
    [3] Saville DA.Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annual Review of Fluid Mechanics, 2003, 29(29): 27-64
    [4] 张鑫, 黄勇, 阳鹏宇等. 多等离子体激励器诱导射流的湍流特性研究. 力学学报, 2018, 50(4): 776-786
    [4] (Zhang Xin, Huang Yong, Yang Pengyu, et al.Investigation on the turbulent characteristics of the jet induced by a plasma actuator. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 776-786 (in Chinese))
    [5] Paillat T, Touchard G.Electrical charges and liquids motion. Journal of Electrostatics, 2009, 67(2-3): 326-334
    [6] 罗惕乾. 荷电多相流理论及应用. 北京: 机械工业出版社, 2010
    [6] (Luo Tiqian.Theory and Applications of Charged Multiphase Flows. Beijing: China Machine Press, 2010 (in Chinese))
    [7] 李帅兵, 杨睿, 罗喜胜等. 气流作用下同轴带电射流的不稳定性研究. 力学学报, 2017, 49(5): 997-1007
    [7] (Li Shuaibing, Yang Rui, Luo Xisheng, et al.Instability study of an electrified coaxial jet in a coflowing gas stream. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 997-1007 (in Chinese))
    [8] Fylladitakis ED, Theodoridis MP, Moronis AX.Review on the history, research, and applications of electrohydrodynamics. IEEE Transactions on Plasma Science, 2014, 42(2): 358-375
    [9] 甘云华,江政纬,李海鸽. 锥射流模式下乙醇静电喷雾液滴速度特性分析. 力学学报, 2017, 49(6): 1272-1279
    [9] (Gan Yunhua, Jiang Zhengwei, Li Haige.A study on droplet velocity of ethanol during electrospraying process at cone-jet mode. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1272-1279 (in Chinese))
    [10] Atten P.Electrohydrodynamic instability and motion induced by injected space charge in insulating liquids. IEEE Transaction on Dielectrics and Electrical Insulation, 1996, 3(1): 1-17
    [11] Schneider JM, Waston PK.Electrohydrodynamic stability of space-charge-limited currents in dielectric liquids. I. Theoretical study. Physics of Fluids, 1970, 13(8): 1948-1954
    [12] Atten P, Moreau R.Stabilité electrohydrodynamique des liquides isolants soumis à une injection unipolaire. Journal de Mécanique, 1972, 11: 471-520 (in French)
    [13] Atten P, Lacroix JC.Non-linear hydrodynamic stability of liquids subjected to unipolar injection. Journal de Mécanique, 1979, 18: 469-510
    [14] Lacroix JC, Atten P, Hopfinger EJ.Electro-convection in a dielectric liquid layer subjected to unipolar injection. Journal of Fluid Mechanics, 1975, 69(3): 539-563
    [15] Atten P, Lacroix JC, Malraison B.Chaotic motion in a Coulomb force driven instability: Large aspect ratio experiments. Physics Letters A, 1980, 79(4): 255-258
    [16] Malraison B, Atten P.Chaotic behavior of instability due to unipolar ion injection in a dielectric liquid. Physical Review Letters, 1982, 49(10): 723-726
    [17] Zhang M, Martinelli F, Wu J, et al.Modal and non-modal stability analysis of electrohydrodynamic flow with and without cross-flow. Journal of Fluid Mechanics, 2015, 770: 319-349
    [18] Zhang M.Weakly nonlinear stability analysis of subcritical electrohydrodynamic flow subject to strong unipolar injection. Journal of Fluid Mechanics, 2016, 792: 328-363
    [19] Suh YK.Modeling and simulation of ion transport in dielectric liquids - Fundamentals and review. IEEE Transactions on Dielectrics and Electrical Insulation, 2012, 19(3): 831-848
    [20] Chicón R, Castellanos A, Martín E.Numerical modelling of Coulomb-driven convection in insulating liquids. Journal of Fluid Mechanics, 1997, 344: 43-66
    [21] Vázquez PA, Georghiou GE, Castellanos A.Numerical analysis of the stability of the electrohydrodynamic (EHD) electroconvection between two plates. Journal of Physics D$:$ Applied Physics, 2008, 41: 175303-175313
    [22] Traoré P, Pérez AT.Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection. Physics of Fluids, 2012, 24(3): 037102
    [23] Wu J, Philippe T, Christophe L.An efficient finite volume method for electric field-space charge coupled problems. Journal of Electrostatics, 2013, 71(3): 319-325
    [24] Vázquez PA, Castellanos A, Numerical simulation of EHD flows using discontinuous Galerkin finite element methods. Computers & Fluids, 2013, 84: 270-278
    [25] Luo K, Wu J, Yi H, et al.Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids. Physical Review E, 2016, 93(2): 023309
    [26] Wu J, Philippe T, Alberto TP, et al.On two-dimensional finite amplitude electro-convection in a dielectric liquid induced by a strong unipolar injection. Journal of Electrostatics, 2015, 74: 85-95
    [27] Kourmatzis A, Shrimpton JS.Turbulent three-dimensional dielectric electrohydrodynamic convection between two plates. Journal of Fluid Mechanics, 2012, 696: 228-262
    [28] Luo K, Wu J, Yi H, et al.Three-dimensional finite amplitude electroconvection in dielectric liquids. Physics of Fluids, 2018, 30(2): 023602
    [29] Luo K, Wu J, Yi H, et al.Hexagonal convection patterns and their evolutionary scenarios in electroconvection induced by a strong unipolar injection. Physical Review Fluids, 2018, 3(5): 053702
    [30] Malraison B, Atten P.Exponential decrease of fluctuation spectra for chaotic regime of EHD instability, a universal behavior. Comptes Rendus de l Academie des Sciences Serie II, 1981, 292(3): 267-270
    [31] Chicón R, Pérez AT, Castellanos A.Electroconvection in small cylindrical cavities//IEEE Conference on Electrical Insulation and Dielectric Phenomena, 2003: 710-713
    [32] Philippe T, Wu J.On the limitation of imposed velocity field strategy for Coulomb-driven electroconvection flow simulations. Journal of Fluid Mechanics, 2013, 727: R3
    [33] Wu J, Philippe T, Pedro AV, et al.Onset of convection in a finite two-dimensional container due to unipolar injection of ions. Physical Review E, 2013, 88(5): 053018
    [34] Alberto TP, Pedro AV, Wu J, et al.Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls. Journal of Fluid Mechanics, 2014, 758: 586-602
    [35] Pérez AT, Castellanos A.Role of charge diffusion in finite-amplitude electroconvection. Physical Review A, 1989, 40(10): 5844
    [36] Frey F, Atten P, Frey F.Solid spacer influence on the liquid motion induced by unipolar injection. Journal of Electrostatics, 1978, 5:145-155
    [37] Tobazeon R.Electrohydrodynamic instabilities and electroconvection in the transient and A.C. regime of unipolar injection in insulating liquids: A review. Journal of Electrostatics, 1984, 15(3): 359-384
    [38] Wu J, Philippe T.A finite-volume method for electro-thermoconvective phenomena in a plane layer of dielectric liquid. Numerical Heat Transfer Part A, 2015, 68(5): 471-500
    [39] Patankar SV, Spalding DB.A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 1972, 15(10): 1787-1806
    [40] Rhie CM, Chow WL.Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA Journal, 1983, 21(11): 1525-1532
    [41] Neimarlija N, Demird$\check{z}$i I, Muzaferija S. Finite volume method for calculation of electrostatic fields in electrostatic precipitators. Journal of Electrostatics, 2009, 67(1): 37-47
    [42] Sweby PK.High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis, 1984, 21(5): 995-1011
    [43] Waterson NP, Deconinck. Design principles for bounded higher-order convection schemes-a unified approach. Journal of Computational Physics, 2007, 224(1): 182-207
    [44] Gaskell PH, Lau AKC.Curvature compensated convective transport: SMART, A new boundedness preserving transport algorithm. International Journal for Numerical Methods in Fluids, 2010, 8(6): 617-641
    [45] Albensoeder S, Kuhlmann HC.Accurate three-dimensional lid-driven cavity flow. Journal of Computational Physics, 2005, 206(2): 536-558
    [46] Davis SH.Convection in a box: Linear theory. Journal of Fluid Mechanics, 1967, 30(3): 465-478
    [47] Pallares J, Grau FX, Giralt F.Flow transitions in laminar Rayleigh--Bénard convection in a cubical cavity at moderate Rayleigh numbers. International Journal of Heat and Mass Transfer, 1999, 42(4): 753-769
    [48] Shan X.Simulation of Rayleigh-Bénard convection using a lattice Boltzmann method. Physical Review E, 1997, 55(3): 2780
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出版历程
  • 收稿日期:  2018-09-08
  • 刊出日期:  2018-11-17

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