| 基于Monte-Carlo随机有限元方法的随机边界条件下自然对流换热不确定性研究 |
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| 引用本文： | 何贻海,姜昌伟,姚鸣,张炳晴,朱炎鹤,张钟庆.基于Monte-Carlo随机有限元方法的随机边界条件下自然对流换热不确定性研究[J].应用数学和力学,2017,38(5):581-593. |
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| 作者姓名： | 何贻海 姜昌伟 姚鸣 张炳晴 朱炎鹤 张钟庆 |
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| 作者单位： | 长沙理工大学 能源与动力工程学院, 长沙 410114 |
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| 基金项目： | 国家自然科学基金(11572056)，湖南省研究生科研创新项目(CX2016B409)，湖南省教育厅重点项目(15A006)The National Natural Science Foundation of China(11572056) |
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| 摘 要： | 为分析边界条件不确定性对方腔内自然对流换热的影响，发展了一种求解随机边界条件下自然对流换热不确定性传播的Monte-Carlo随机有限元方法.通过对输入参数场随机边界条件进行Karhunen-Loeve展开及基于Latin(拉丁)抽样法生成边界条件随机样本，数值计算了不同边界条件随机样本下方腔内自然对流换热流场与温度场，并用采样统计方法计算了随机输出场的平均值与标准偏差.根据计算框架编写了求解随机边界条件下方腔内自然对流换热不确定性的MATLAB随机有限元程序，分析了随机边界条件相关长度与方差对自然对流不确定性的影响.结果表明:平均温度场及流场与确定性温度场及流场分布基本相同；随机边界条件下Nu数概率分布基本呈现正态分布，平均Nu数随着相关长度和方差增加而增大；方差对自然对流换热的影响强于相关长度的影响.
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| 关 键 词： | Monte-Carlo方法 随机有限元 随机边界条件 自然对流 不确定性 |
| 收稿时间： | 2016-07-21 |
Uncertainty Research of Natural Convection Heat Transfer Under Stochastic Boundary Condition Based on the Monte-Carlo Stochastic Finite Element Method |
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| HE Yi-hai,JIANG Chang-wei,YAO Ming,ZHANG Bing-qing,ZHU Yan-he,ZHANG Zhong-qing.Uncertainty Research of Natural Convection Heat Transfer Under Stochastic Boundary Condition Based on the Monte-Carlo Stochastic Finite Element Method[J].Applied Mathematics and Mechanics,2017,38(5):581-593. |
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| Authors: | HE Yi-hai JIANG Chang-wei YAO Ming ZHANG Bing-qing ZHU Yan-he ZHANG Zhong-qing |
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| Affiliation: | School of Energy and Power Engineering, Changsha University of Science and Technology,Changsha 410114, P.R.China |
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| Abstract: | In order to study the effects of stochastic boundary conditions on natural convection heat transfer in square cavities,a Monte-Carlo stochastic finite element method was developed to solve uncertainty propagation of natural convection heat transfer under stochastic boundary condition.The input random parameters were expanded through the Karhunen-Loeve expansion and the random samples of boundary condition were generated with the Latin sampling method.The flow field and temperature field in the square cavity for different random samples of boundary condition were calculated numerically.The mathematical expectations and variances of stochastic output fields were calculated with the sampling statistical method.The stochastic finite element program with the MATLAB language was coded to solve the uncertainty propagation of natural convection heat transfer in cavity under stochastic boundary condition based on the computational framework.The effects of the correlation length and the variance of stochastic boundary condition on natural convection uncertainty were analyzed.The results show that the mean temperature field and flow field are basically the same as the deterministic temperature field and flow field,respectively.The probability distribution of the Nusselt number under stochastic boundary condition is a normal distribution.The mean Nusselt number increases with the correlation length and the variance,the variance has a greater influence on natural convection heat transfer than the correlation length. |
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| Keywords: | Monte-Carlo method stochastic finite element stochastic boundary condition natural convection uncertainty |
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