一种非连续介质中热传导过程的数值模拟方法

A NUMERICAL SIMULATION METHOD FOR HEAT CONDUCTION IN DISCONTINUOUS MEDIA

传统热传导的分析基于连续模型,无法刻画热量在两个接触体之间的传递。该文提出了一种非连续介质中热传导过程的数值计算方法,并编制了相应的C++计算程序。该方法首先将计算域离散为一系列的块体,块体内部划分若干连续介质单元,块体边界设定为潜在接触界面,并利用半弹簧-半棱联合接触模型进行接触对的快速检索及标记。每个块体内部的热传导采用传统连续模型进行计算(该文采用有限体积法),每个接触界面采用点面接触型及棱棱接触型热传导模型进行描述。通过调整接触界面热传导系数中的刚度因子,可以实现接触界面对热传导过程不同的抵抗效应。数值算例表明,该文所述方法可以较为准确地模拟热量在非连续介质中的传递过程;接触界面上的刚度因子越大,界面对热传导过程的抵抗效应越小;当刚度因子大于100,界面抵抗效应基本消失,非连续介质的计算结果与连续介质的计算结果完全一致;此外,接触界面上的刚度因子仅影响热传导的瞬态过程,而不影响其稳态解。

Conventional heat conduction analysis is based on continuous model, so it cannot describe heat transport between two bodies with contact. A numerical simulation method for heat conduction in discontinuous media is proposed, and a C＋＋ computing code is developed. When simulating such problems, the domain is discretized as a series of blocks, and then each block is divided into several continuous elements. The boundaries of blocks are considered as potential contact interfaces, and the contact pairs are detected and marked efficiently according to the semi-spring semi-edge combined contact model. In this method, a traditional continuous model is adopted for heat conduction inside each block（the Finite Volume Method is used in this paper）, and a point-face type, edge-edge type heat conduction model is introduced for each contact interface. By modifying the stiffness factor of thermal conductivity for each contact interface, different heat transfer resistance effects can be realized. Numerical cases show that the method proposed in this paper can simulate heat conduction effects in discontinuous media well; the larger the stiffness factor on the contact interface, the smaller the heat conducting resistance effect of the contact interface; when the stiffness factor is larger than 100, interface resistance effects mostly disappear, and the results of discontinuous media and continuous media are more or less the same; finally, the interface stiffness factor only affects the transient process of heat conduction, but has no influence on steady state solution.