热动力学问题的数值计算

Numerical Simulation of Thermodynamics Problem

对含热传导的流体动力学方程组 ,用有限元方法进行数值求解。采用傅里叶热传导计算热流、用热流连续条件计算单元间接触面的温度、用三角形传热法计算体单元表面的热流 ,考虑各向同性弹塑性流体材料模型、三项式物态方程和导热系数与状态的相关性 ,给出了傅里叶热传导、接触传热、热应力应变效应、以及混合物冲击压缩特性等算例。对混合物冲击温度的数值模拟表明 ,小颗粒混合物在冲击压缩过程中 ,颗粒间的温度有差别、稍有波动 ,并随时间趋向于一致 ,以至热平衡。

The equations of hydrodynamics including conduction of heat are solved numerically by using the finite element method. The heat flow is calculated according to the Fourier's heat conduction. The temperature on the contact side elements is calculated by the continuity condition of heat flow. According to triangular partitions divided from a quadrangle side of body element, convection heat flow is calculated. Considering the isotropic-elastic-plastic-hydrodynamic material model, the equation of state with three contributions, and the correlation between thermal conductivity and temperature, some computational examples, including the Fourier's heat conduction, contact heat transfer, deformation effects of heat, and shock compression of mixture, are given by the finite element code. The numerical simulation of shock temperature of mixture indicates that the temperatures among minute gains fluctuate, and tend to reach a thermal equilibrium during the shock propagation.