基于蒙特卡罗随机有限元方法的随机多孔介质内流体自然对流不确定性研究

Uncertainty study of natural convection in random porous media based on Monte-Carlo stochastic finite element method

为分析孔隙率不确定性对多孔介质方腔内自然对流换热的影响,发展了一种基于KL(Karhunen-Loeve展开)-蒙特卡罗随机有限元算法的随机多孔介质内自然对流不确定性分析数理模型及有限元数值模拟程序框架。通过K-L展开及基于拉丁抽样法生成多孔介质孔隙率随机实现,并耦合多孔介质自然对流有限元程序,进行随机多孔介质内自然对流传热数值模拟,得出了多孔介质内流场与温度场平均值与标准偏差,并分析了孔隙率不确定性条件下Da数对Nu数的影响。结果表明,孔隙率不确定性对多孔介质方腔内自然对流有重要影响。随机多孔介质内流场及温度场与确定性条件下的流场及温度场存在一定偏差,Nu数标准偏差随着Da的增大先增大后减小。

In order to analyze the influence of porosity uncertainty on heat transfer and fluid flow in random porous media cavity,a Karhunen-Loeve-Monte-Carlo stochastic mathematical model and finite element framework of uncertainty quantification of natural convection in random porous media were developed based on stochastic theory and porous media heat transfer theory. The momentum equations and energy equations are solved by the Brinkmann-Forchheimer-Darcy model. The Karhunen-Loeve expansion and Latin sampling method were utilized to represent the input random field,so as to simulate the heat and mass transfer of natural convection in the porous media cavity with Matlab stochastic finite element program. The mathematical expectation and standard deviation of stochastic output field were attained. Furthermore,the influence of Darcy number on Nusselt number was analyzed. The results show that the porosity uncertainty has an important influence on the natural convection in porous cavity. The flow field and temperature field in random porous media and those in deterministic porous media under certain condition have some deviations,the standard deviation of Nusselt number increases firstly and then decreases with the increase of Darcy number.