磁场作用下复杂几何腔体内液态金属混合对流稳定性的数值研究

The flow and heat and mass transfers of the electrically conductive fluids, which can be widely found in new energy, new materials and other emerging industries, is a multi-physical field coupling nonlinear problem covering the flow field, magnetic field, temperature field and concentration field. The studies for the flow and heat and mass transfer in the complex geometrical enclosure under the magnetic field are the advanced topics for non-equilibrium dynamics, magnetohydrodynamics (MHD) and their application fields, which have attracted the interest of an increasing number of researchers in view of their wide applications in many emerging industries. In this project, an accurate, efficient and robust compact difference solver will be firstly established and developed for simulating the governing equations in an arbitrary curvilinear coordinates. Then, using the high-order accurate solver proposed in the project, direct numerical simulations mixtures binary convection of liquid metal in the difference geometrical enclosures with and without an external magnetic field are carried out. Instabilities, bifurcation, nonlinear evolutions of the flow field, and the characteristics of heat and mass transfer are investigated. The mechanisms of different convective states and its dependency on the parameters are also analyzed. This project will contribute to extend and enrich the research contents of self-organization pattern formation and stability of many nonlinear dissipative systems. Moreover, this study will help to reveal the pattern formation and dynamic characteristics of binary mixtures convection of the liquid metal, and also develop necessary theoretical basis for effectively predicting and controlling the convective process of fluid mixtures in industry productions and engineering applications, in which non-equilibrium phenomena are involved.

磁场作用下导电流体流动与热质传递问题广泛存在于新能源、新材料等新兴工业产业中，其主要特征是流场、磁场、温度场和浓度场等多物理、强非线性耦合，对该问题中自组织时空结构形成及其稳定性的深入研究，是非平衡动力学及其应用领域中的前沿性课题。本项目拟采用发展的任意曲线坐标系下高效、鲁棒的高精度求解器，针对外磁场作用下不同几何形状腔体中液态金属混合对流系统进行数值模拟，研究对流的不稳定性，分岔以及流场的非线性演化和对流传热传质特性，分析流动状态的形成和稳定机理以及参数依赖性等。本项目的实施，有利于深刻揭示混合流体对流系统斑图形成及其动力学特性、准确模拟磁场作用下复杂几何腔体内液态金属混合对流过程，为预测和控制涉及非平衡现象的工业生产中混合对流过程提供必要的理论依据。

外磁场作用下电流体混合对流问题广泛存在于新能源、新材料等新兴工业产业和前沿科学研究领域中，其涉及了热磁流体流动特性、传热传质特性以及流体力学稳定性等基础理论问题，对其中自组织时空结构形成及其稳定性的深入研究，是非平衡动力学及其应用领域中的前沿性课题。因此，针对外磁场作用下复杂几何外形腔体内导电流体混合对流的稳定性问题开展基础理论研究具有重要的科学意义和应用价值。本项目基于纯流函数或流函数-速度形式Navier-Stokes(N-S)方程，研发了求解磁场作用下复杂几何外形腔体中液态金属混合对流问题的高效、鲁棒的高精度求解器，并在此基础上实现了外磁场作用下复杂几何外形腔内混合流体对流的稳定性与非线性动力学特性的数值模拟研究。. 通过本项目支持，课题组已完成与项目研究内容相关的学术论文18篇（包括成果中列出的12篇发表论文），完成研究生学位论文3篇。本项目取得的主要研究成果如下: 1)针对一类高阶迎风紧致差分格式，提出了一种新的子域边界逼近格式的并行化策略，使其保持了内点处与紧致格式一致的精度和色散特性；2)提出了构造低成本且不损失精度的耗散可调格式的新思路，构造了一种3点4阶耗散可调迎风格式。3)发展了求解二维纯流函数N-S方程整体达到三阶精度的迎风紧致差分算法；建立了任意曲线坐标系下二维流函数-速度形式N-S方程的4阶紧致格式，并成功地求解了复杂几何区域的定常、非定常流动问题。4)建立了三维不可压N-S方程的保物理纯流函数（矢量势）公式，构造了鲁棒的高分辨率四阶紧致格式，并推广发展了任意曲线坐标系下三维流函数公式高阶紧致差分格式。5)数值研究了磁场作用下导电流体流动与传热传质系统中几何外形效应、流动稳定性以及传热传质特性与无量纲参数或物性参数的依赖关系。完成项目及后续进一步取得的成果可为预测和控制涉及非平衡现象的工业生产中混合对流过程提供必要的理论依据。

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