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基于POD-RBF降阶模型的超高温气冷堆DLOFC事故温度时空分布计算方法

丁永旺 张汉 彭杵真 邬颖杰 郭炯 彭威 张平 李富

丁永旺, 张汉, 彭杵真, 邬颖杰, 郭炯, 彭威, 张平, 李富. 基于POD-RBF降阶模型的超高温气冷堆DLOFC事故温度时空分布计算方法[J]. 核动力工程, 2025, 46(2): 107-118. doi: 10.13832/j.jnpe.2024.10.0056
引用本文: 丁永旺, 张汉, 彭杵真, 邬颖杰, 郭炯, 彭威, 张平, 李富. 基于POD-RBF降阶模型的超高温气冷堆DLOFC事故温度时空分布计算方法[J]. 核动力工程, 2025, 46(2): 107-118. doi: 10.13832/j.jnpe.2024.10.0056
Ding Yongwang, Zhang Han, Peng Chuzhen, Wu Yingjie, Guo Jiong, Peng Wei, Zhang Ping, Li Fu. POD-RBF Based ROM Method to Calculate Temporal-Spatial Temperature Distribution under DLOFC Accident for VHTR[J]. Nuclear Power Engineering, 2025, 46(2): 107-118. doi: 10.13832/j.jnpe.2024.10.0056
Citation: Ding Yongwang, Zhang Han, Peng Chuzhen, Wu Yingjie, Guo Jiong, Peng Wei, Zhang Ping, Li Fu. POD-RBF Based ROM Method to Calculate Temporal-Spatial Temperature Distribution under DLOFC Accident for VHTR[J]. Nuclear Power Engineering, 2025, 46(2): 107-118. doi: 10.13832/j.jnpe.2024.10.0056

基于POD-RBF降阶模型的超高温气冷堆DLOFC事故温度时空分布计算方法

doi: 10.13832/j.jnpe.2024.10.0056
基金项目: 国家重点研发项目(2022YFB1903000);国家自然科学基金面上项目(12275150)
详细信息
    作者简介:

    丁永旺(1998—),男,博士研究生,现主要从事反应堆降阶方法方面研究,E-mail: dingyw22@mails.tsinghua.edu.cn

    通讯作者:

    张 汉,E-mail: han-zhang@tsinghua.edu.cn

  • 中图分类号: TL33

POD-RBF Based ROM Method to Calculate Temporal-Spatial Temperature Distribution under DLOFC Accident for VHTR

  • 摘要: 超高温气冷堆(VHTR)具有核能制氢等广泛的应用领域,失冷失压(DLOFC)事故是VHTR后果最严重的设计基准事故之一,而利用全阶模型(FOM)进行大量不同参数下的DLOFC事故特性分析需要消耗大量的计算资源。对设计参数范围内的不同方案进行基于降阶模型(ROM)的DLOFC事故的快速、准确计算具有重要需求和意义。本文利用TINTE程序建立了VHTR的FOM,基于本征正交分解-径向基函数插值(POD-RBF)方法实现了一个快速计算VHTR-DLOFC事故的ROM,并给出了两种方法来实现ROM的瞬态过程计算,方法1将时间等同于入口温度等输入参数;方法2对于同一参数下的不同时间步的系数整体进行计算。结果表明,两种ROM方法的计算结果最大相对误差均低于1%,且ROM计算效率远高于FOM;同时方法2的计算效率是方法1的40倍。因此,ROM可以为VHTR设计参数的优化工作提供快速计算程序。

     

  • 图  1  计算模型

    Figure  1.  Calculation Model

    图  2  算例设置

    Figure  2.  Case Setting

    图  3  ROM原理

    N—全阶模型的总自由度;M—快照数量;n—保留的基向量阶数,通过保留n阶基向量,问题总自由度将由N变为n

    Figure  3.  Principle of ROM

    图  4  两种方法直接投影法对比

    Figure  4.  Comparison of Direct Projection for the Two Methods  

    图  5  两种方法原解、投影和插值保留的解空间信息的关系

    Figure  5.  Relation among Sloution, Projection and Interpolation Space for the Two Methods

    图  6  奇异值分解结果

    Figure  6.  Results of Singular Value Decomposition

    图  7  样本点数量敏感性分析

    Figure  7.  Sensitivity Analysis of Number of Sample Points

    图  8  不同算例(算例序号对应于图2)利用不同方法计算得到的最大二范数误差与截断项以及基向量个数的关系

    Figure  8.  Relation between the Max Norm Error of Different Cases Calculated by Different Methods and the Trunction Term

    图  9  FOM与ROM结果对比

    Figure  9.  Comparison of FOM and ROM Results

    图  10  FOM温度、ROM温度及温度绝对误差的空间分布

    rz—二维几何位置

    Figure  10.  FOM Temperature, ROM Temperature and Space Distribution of Absolute Temperature Error

    图  11  不同阶基向量系数与时间的关系

    Figure  11.  Relation between Coefficients of Base Vector of Different Orders and Time

    表  1  两种方法计算时间和误差对比

    Table  1.   Comparison of Calculation Time and Error between Two Methods

    方法 POD-RBF方法1 POD-RBF方法2 投影方法1 投影方法2
    nm取值 $ n = 51 $ $ n=51,\ m=6 $ $ n = 51 $ $ n=51,\ m=6 $
    计算时间/s 0.0674 0.0016
    加速比 4.2×105 1.8×107
    温度最大绝对误差/℃ 3.625 3.799 0.938 1.068
    温度最大相对误差/% 0.774 0.789 0.369 0.461
    $ {\text{Err}}_{\text{M,n}}$/℃ 0.643 0.649 0.160 0.172
    $ {\text{Err}}_{\text{r,M,n}}$/% 0.124 0.125 0.0339 0.0366
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-10-12
  • 录用日期:  2024-11-13
  • 修回日期:  2024-11-12
  • 网络出版日期:  2025-01-15
  • 刊出日期:  2025-04-02

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