POD-RBF Based ROM Method to Calculate Temporal-Spatial Temperature Distribution under DLOFC Accident for VHTR
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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。
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关键词:
- 超高温气冷堆（VHTR） /
- 本征正交分解（POD） /
- 径向基函数（RBF）插值 /
- 降阶模型（ROM）
Abstract: Very High-Temperature Gas-cooled Reactor (VHTR) has a wide range of applications such as hydrogen production by nuclear energy. Depressurized Loss of Forced Cooling (DLOFC) accident is one of the most serious design basis accidents of VHTR. It may cause large computational cost to analyze the DLOFC accident with large amount of different input parameters using the Full Order Model (FOM). Based on Reduced Order Model (ROM), it is of great demand and significance to calculate DLOFC accidents quickly and accurately for different schemes within the design parameters. In this paper, the FOM of VHTR is established by the code TINTE, and a ROM for fast calculation of the DLOFC accident of VHTR is realized based on Proper Orthogonal Decomposition-Radial Basis Function Interpolation (POD-RBF) method. Two methods are given to realize the transient process calculation of ROM. Method 1 equates time with input parameters such as inlet temperature; Method 2 calculates the coefficients of different time steps under the same parameter as a whole. The results show that the maximum relative error of both ROM methods is less than 1%, and the computation efficiency of ROMs is much higher than that of FOM. Furthermore, the computational efficiency of Method 2 is 40 times that of Method 1. Therefore, the ROM proposed in this paper can provide a fast calculation code for the optimization of design parameters of VHTR. -
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 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 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 10 FOM温度、ROM温度及温度绝对误差的空间分布
r、z—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 n和m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 
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