Abstract

A new nonstationary three-dimensional mathematical model of an aluminum reduction cell which makes it possible to perform coupled thermoelectric and magneto-hydrodynamic calculation while taking into account sideledge formation is presented. The model takes into account the nonlinear dependence of the coefficients of electrical conductivity and thermal conductivity of materials on temperature, as well as, for ferromagnetic materials, the nonlinear dependence of magnetization on the magnetic field strength. The heat-transfer coefficients on the outer surfaces include radiant and convective components of heat transfer and are functions of the ambient temperature and the local surface temperature. In the energy equation, internal sources of heat are taken into account due to the flow of electric current, exothermic reactions, and additional thermal effects associated with the raw material loading and phase transitions. To obtain a numerical solution, the control volume method is applied. Experimental testing of the developed mathematical model is performed on the S8BME aluminum reduction cell. This paper presents the calculated and experimental data of magnetic, electric, thermal, and hydrodynamic fields. A comparison of the calculation results with the results of industrial experiments shows that the model reflects the physical processes taking place in the aluminum reduction cell with accuracy sufficient for engineering calculations. The calculated values of electrical voltage, magnetic induction, and temperature practically coincide with the measured ones. Values obtained from calculating the direction of velocity in the metal pad and the shape of the sideledge profile differ insignificantly from the experimental values. This model can be used to estimate the performance and design parameters of the operation of new and modernized aluminum electrolysis cells. Further studies will be aimed at clarifying the calculated results by improving the mathematical model.

中文翻译：

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铝还原池中磁流体动力学和传热的数学模型

摘要

提出了铝还原池的一种新的非稳态三维数学模型，该模型可以在考虑侧缘形成的情况下进行热电和磁流体动力耦合计算。该模型考虑了材料的电导率和热导率系数对温度的非线性依赖性，对于铁磁材料，还考虑了磁化强度对磁场强度的非线性依赖性。外表面上的热传递系数包括热传递的辐射和对流分量，并且是环境温度和局部表面温度的函数。在能量方程中，由于电流，放热反应，以及与原料负载和相变有关的其他热效应。为了获得数值解，应用了控制体积法。在S8BME铝还原池上进行了开发的数学模型的实验测试。本文介绍了磁场，电场，热力和流体动力场的计算和实验数据。计算结果与工业实验结果的比较表明，该模型反映了铝还原池中发生的物理过程，其精度足以进行工程计算。电压，磁感应强度和温度的计算值实际上与测量值一致。通过计算金属垫中的速度方向和侧板轮廓的形状获得的值与实验值相差不大。该模型可用于估算新型和现代化的铝电解槽的性能和设计参数。进一步的研究旨在通过改进数学模型来澄清计算结果。