• PLK 方法和计算流体力学 •

### 三维方腔介电液体电对流的数值模拟研究1)

1. *哈尔滨工业大学能源科学与工程学院，哈尔滨 150001;
†新加坡国立大学机械工程学院流体力学系，新加坡 119260;
**新南威尔士大学工程与信息技术学院，澳大利亚堪培拉ACT 2600
• 收稿日期:2018-09-09 修回日期:2018-09-09 出版日期:2018-11-18 发布日期:2018-12-04
• 作者简介: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
• 基金资助:
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.

### NUMERICAL ANALYSIS OF THREE-DIMENSIONAL ELECTRO-CONVECTION OF DIELECTRIC LIQUIDS IN A CUBICAL CAVITY1)

Wu Jian*, Zhang Mengqi, Tian Fang-Bao**,2)

1. *School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China;
†Department of Mechanical Engineering,National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore;
**School of Engineering and Information Technology, University of New South Wales,Canberra, ACT 2600 Australia
• Received:2018-09-09 Revised:2018-09-09 Online:2018-11-18 Published:2018-12-04

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.

• O351.2