土体冻结过程中相变导热的光滑粒子法分析

Analysis of smoothed particle hydrodynamics of heat conduction with phase change during the soil freezing process

相变导热在矿山工程、城市地铁、河底隧道等领域有着广泛的应用.由于该问题模型方程独特的数学性质及网格背景数值方法的局限性,引入光滑粒子算法求解相变导热问题.给出基于Fortran语言开发的数值分析程序,并通过推导得到的半无限域凝固问题的解析解验证了其精度和可靠性.最后针对低温冻结管作用下土体冻结过程进行了分析,计算结果表明:土体冻结过程中冻结锋面的移动速度随时间逐渐减小,温度场曲线上的"折线"变化是相变时潜热释放引起的;冻结温度对土层冻结的发展影响显著,冻结管的温度越低冻结锋面的移动速度越快;冻土导热系数k_s的取值大小对冻结锋面的移动速度没有显著影响;然而未冻土导热系数k_l取值越大,土层中冻结锋面的移动速度越快.

Heat conduction with phase change is widely applied in the field of mine engineering, urban subway, tunnel under river and so on. Due to the unique mathematical properties of the model equations and limitations of the grid numerical methods, Smoothed Particle Hydrodynamics(SPH)is presented for trying to solve heat conduction with phase change. The numerical analysis program based on Fortran language is given, of which the accuracy and reliability are verified by the analytical solution of solidification problem in semi-infinite domain. Then, the freezing process of soil under the influence of freezing pipe is analyzed. The results show that the moving speed of frozen front gradually decreases with time during the soil freezing process, the "broken line" change on the temperature curve is caused by latent heat release during phase change. The temperature of freezing pipe has a significant influence on the development of soil freezing, the lower the temperature of freezing pipe is, the faster frozen front moves. The thermal conductivity of frozen soil k_s has no significant effect on the moving speed of frozen front. However, the larger the value of thermal conductivity k_l is, the faster the speed of frozen front is.