Institut für Thermo- und Fluiddynamik, Technische Universität Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany.
Phys Rev E. 2017 May;95(5-1):053114. doi: 10.1103/PhysRevE.95.053114. Epub 2017 May 25.
The combined effects of buoyancy-driven Rayleigh-Bénard convection (RC) and surface tension-driven Marangoni convection (MC) are studied in a triple-layer configuration which serves as a simplified model for a liquid metal battery (LMB). The three-layer model consists of a liquid metal alloy cathode, a molten salt separation layer, and a liquid metal anode at the top. Convection is triggered by the temperature gradient between the hot electrolyte and the colder electrodes, which is a consequence of the release of resistive heat during operation. We present a linear stability analysis of the state of pure thermal conduction in combination with three-dimensional direct numerical simulations of the nonlinear turbulent evolution on the basis of a pseudospectral method. Five different modes of convection are identified in the configuration, which are partly coupled to each other: RC in the upper electrode, RC with internal heating in the molten salt layer, and MC at both interfaces between molten salt and electrode as well as anticonvection in the middle layer and lower electrode. The linear stability analysis confirms that the additional Marangoni effect in the present setup increases the growth rates of the linearly unstable modes, i.e., Marangoni and Rayleigh-Bénard instability act together in the molten salt layer. The critical Grashof and Marangoni numbers decrease with increasing middle layer thickness. The calculated thresholds for the onset of convection are found for realistic current densities of laboratory-sized LMBs. The global turbulent heat transfer follows scaling predictions for internally heated RC. The global turbulent momentum transfer is comparable with turbulent convection in the classical Rayleigh-Bénard case. In summary, our studies show that incorporating Marangoni effects generates smaller flow structures, alters the velocity magnitudes, and enhances the turbulent heat transfer across the triple-layer configuration.
双层结构中浮力驱动的瑞利-贝纳对流（RC）和表面张力驱动的马兰戈尼对流（MC）的综合效应在一种简化的液态金属电池（LMB）模型中进行了研究。三层模型由液态金属合金阴极、熔盐分离层和顶部的液态金属阳极组成。对流是由热电解质和较冷电极之间的温度梯度引发的，这是操作过程中电阻热释放的结果。我们提出了一种线性稳定性分析，结合基于伪谱法的非线性湍流演化的三维直接数值模拟，对纯热传导状态进行了分析。在该配置中确定了五种不同的对流模式，它们部分相互耦合：上部电极中的 RC、熔盐层中的内部加热 RC 和熔盐与电极之间的两个界面上的 MC 以及中间层和下部电极中的逆流。线性稳定性分析证实，在当前设置中增加的马兰戈尼效应增加了线性不稳定模式的增长率，即马兰戈尼和瑞利-贝纳不稳定性在熔盐层中共同作用。临界格拉肖夫和马兰戈尼数随中间层厚度的增加而减小。对于实验室规模的 LMB 的实际电流密度，计算出了对流开始的阈值。全局湍流传热符合内部加热 RC 的标度预测。全局湍流动量传递与经典瑞利-贝纳情况下的湍流对流相当。总之，我们的研究表明，考虑马兰戈尼效应会产生较小的流动结构，改变速度大小，并增强三层结构的湍流传热。
