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基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化

姜昌伟 谢云峰 石尔 刘代飞 李杰 胡章茂

姜昌伟, 谢云峰, 石尔, 刘代飞, 李杰, 胡章茂. 基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化. 力学学报, 2022, 54(1): 1-13 doi: 10.6052/0459-1879-21-427
引用本文: 姜昌伟, 谢云峰, 石尔, 刘代飞, 李杰, 胡章茂. 基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化. 力学学报, 2022, 54(1): 1-13 doi: 10.6052/0459-1879-21-427
Jiang Changwei, Xie Yunfeng, Shi Er, Liu Daifei, Li Jie, Hu Zhangmao. Uncertainty quantification for thermomagnetic convection of paramagnetic fluid in random porous media based on intrusive polynomial chaos method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 1-13 doi: 10.6052/0459-1879-21-427
Citation: Jiang Changwei, Xie Yunfeng, Shi Er, Liu Daifei, Li Jie, Hu Zhangmao. Uncertainty quantification for thermomagnetic convection of paramagnetic fluid in random porous media based on intrusive polynomial chaos method. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(1): 1-13 doi: 10.6052/0459-1879-21-427

基于侵入混沌多项式法的随机多孔介质内顺磁性流体热磁对流不确定度量化

doi: 10.6052/0459-1879-21-427
基金项目: 国家自然科学基金资助项目(11572056, 51674042)
详细信息
    作者简介:

    姜昌伟, 教授, 主要研究方向: 多场耦合仿真及其优化. E-mail: jiangcw@csust.edu.cn

  • 中图分类号: O361.3

UNCERTAINTY QUANTIFICATION FOR THERMOMAGNETIC CONVECTION OF PARAMAGNETIC FLUID IN RANDOM POROUS MEDIA BASED ON INTRUSIVE POLYNOMIAL CHAOS METHOD

Funds: The project was supported by the (12345678) and (9876543)
  • 摘要: 目前流体流动与传热问题的研究大都基于确定性工况条件, 而现实流体流动与传热问题中存在着大量不确定性因素, 计算流体力学的不确定性量化提供了一种理解流体物性、边界条件与初始条件等不确定性因素对模拟结果影响的能力. 为揭示随机多孔介质内顺磁性流体热磁对流的传播规律与演化特征, 本文发展了一种基于侵入式多项式混沌展开法的热磁对流不确定性量化数理模型与算法程序. 该方法分别利用Karhunen-Loeve展开与多项式混沌展开表达输入随机参数与输出响应量, 同时利用伽辽金投影方法将随机热磁对流控制方程解耦为一组可以应用有限元修正方法求解的确定性控制方程, 并对输出响应量多项式混沌进行求解, 最后采用随机投影法求解相应的确定性控制方程中的混沌系数, 得到输出响应量的统计特征与混沌效应. 热磁对流不确定性量化表明多孔介质孔隙率不确定性通过控制方程演化, 进而影响着多孔介质方腔内顺磁性流体热磁对流, 顺磁性流体热磁对流呈现出显著的混沌效应. 与蒙特卡罗法预测结果相比, 两者计算结果吻合良好, 但侵入式混沌多项式展开法计算量显著减少.

     

  • 图  1  热磁对流物理模型

    Figure  1.  Physical model of thermomagnetic convection

    图  2  不确定性量化流程图

    Figure  2.  Flowchart of uncertainty quantification

    图  3  孔隙率KL展开中协方差核特征值

    Figure  3.  Eigenvalues of covariance kernel used in the KL expansion of porosity

    4  孔隙率KL展开中协方差核特征函数

    4.  Eigenfunction of covariance kennel used in the KL expansion of porosity

    图  4  孔隙率KL展开中协方差核特征函数(续)

    Figure  4.  Eigenfunction of covariance kennel used in the KL expansion of porosity (continued)

    图  5  不同不确定性量化方法下流函数与温度场均值

    Figure  5.  Mean value of stream function and temperature field with different uncertainty quantification methods

    图  6  不同不确定性量化方法下流函数与温度场标准偏差

    Figure  6.  Standard deviation of stream function and temperature field with different uncertainty quantification methods

    图  7  不同不确定性量化方法下热壁面局部Nusselt数分布

    Figure  7.  Distribution of local Nusselt number at the hot wall with different uncertainty quantification methods

    图  8  不同不确定性量化方法下热壁面平均Nusselt数概率密度函数和累积分布函数

    Figure  8.  Probability density function and cumulative distribution function of average Nusselt number at hot wall with different uncertainty quantification methods

    9  流函数一阶模式

    9.  First-order modes of stream function

    图  9  流函数一阶模式(续)

    Figure  9.  First-order modes of stream function (continued)

    图  10  温度场一阶模式

    Figure  10.  First-order modes of temperature field

    图  11  流函数与温度场二阶模式

    Figure  11.  Second-order modes of stream function and temperature field

    表  1  多项式混沌展开阶数对平均Nusselt数均值与标准偏差的影响

    Table  1.   Influence of order of polynomial chaos expansion on mean value and standard deviation of average Nusselt number

    Order of polynomial chaos expansionMean value of average
    Nusselt number
    Standard deviation of average Nusselt number
    PCEMCrelative error/%PCEMCrelative error/%
    n = 1 3.3074 3.2161 2.84 0.4286 0.4187 2.36
    n = 2 3.2029 3.2161 −0.41 0.4136 0.4187 −1.23
    PCE: polynomial chaos expansion; MC: Monte Carlo
    下载: 导出CSV
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  • 收稿日期:  2021-08-21
  • 录用日期:  2021-11-04
  • 网络出版日期:  2021-11-05

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