Steady State Thermal Surrogate Model of TOPAZ-II Reactor Core
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摘要: TOPAZ-Ⅱ反应堆是前苏联设计的空间核反应堆电源，以钠钾合金（NaK-78）为冷却剂，采用热离子转换发电原理为负载提供电力。为了快速准确地计算出堆芯的稳态热工参数，建立了高精度的堆芯稳态热工代理模型。本文首先使用Fluent开展堆芯稳态热工计算，选择中心纵截面网格节点温度为样本数据。然后使用本征正交分解（POD）方法提取样本数据中的主要特征，根据99.999%的能量占比保留前10阶模态完成模型降阶，最后基于反向传播（BP）神经网络建立堆芯的稳态热工代理模型，并将代理模型与Fluent进行对比验证，结果表明代理模型对网格节点温度的计算最大误差为9.95 K，相对误差小于1%，计算时间小于1 s。以冷却剂最热通道出口温度为参考，通过代理模型计算得到冷却剂保持单相工作状态的流量-功率百分值之比应大于0.35。因此，本文建立的稳态热工代理模型可以快速准确地计算得到堆芯的稳态热工参数，实现了对堆芯的仿真预测，并为堆芯热工安全分析提供了一定的参考。
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关键词:
- TOPAZ-Ⅱ反应堆 /
- 热工代理模型 /
- 本征正交分解（POD） /
- 反向传播（BP）神经网络
Abstract: The TOPAZ-Ⅱ reactor, a space nuclear reactor power designed by the former Soviet Union, uses sodium-potassium alloy (NaK-78) as coolant and adopts thermionic conversion power generation principle to provide power for the load. To quickly and accurately calculate the steady state thermal parameters of the core, a steady state high-precision thermal surrogate model of the core was established. This study firstly used Fluent to carry out thermal calculation of core steady state, with grid node temperatures along the central longitudinal cross-section selected as sample data. Then the main features in samples were extracted by Proper Orthogonal Decomposition (POD) method, and the top 10 modes were retained based on 99.999% energy proportion for model order reduction. Finally, through Back Propagation (BP) neural network, the steady state thermal surrogate model of core was established and was compared and validated with Fluent. The results show that the maximum error of the surrogate model in calculating the temperature at grid nodes is 9.95 K, the relative error is less than 1% and the calculation time is less than 1 s. Taking the outlet temperature of the hottest coolant channel as a reference, the flow-power percentage ratio of the coolant to maintain the single-phase working state should be greater than 0.35 calculated by the thermal surrogate model. Therefore, the thermal surrogate model established in this paper can quickly and accurately calculate the steady state thermal parameters of the core, achieve simulation prediction of the core, and provide certain reference for the thermal safety analysis of the core. -
图 13 堆芯中心纵截面温度分布
Figure 13. Temperature Distribution in the Longitudinal Section of the Core Center
图 15 由前10阶模态还原的温度分布
Figure 15. Temperature Distribution Reconstructed from the First 10 Modes
图 16 由前10阶模态还原的温度误差分布
Figure 16. Error Distribution Reconstructed from the First 10 Modes
图 18 代理模型对冷却剂沸腾工况的预测
Figure 18. Prediction of Coolant Boiling Conditions by Surrogate Model
表 1 TOPAZ-Ⅱ系统主要参数
Table 1. Main Parameters of TOPAZ-Ⅱ System
参数 数值 热功率/kW 115 电功率/kW 4.5~5.5 UO2富集度/% 96 热离子燃料元件数量 37 冷却剂流量/(kg·s−1) 1.3 冷却剂进口温度/K 743 冷却剂出口温度/K 843 堆芯活性区高度/cm 37.5 堆芯直径/cm 26 
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表 2 代理模型对5组验证工况的计算误差
Table 2. Calculation Error of Surrogate Model for 5 Validation Conditions
验证工况 堆芯功率/kW 堆芯流量/(kg·s–1) 所有节点温度
最大绝对误差/K所有节点温度
最大相对误差/%最热通道出口节点温度
最大绝对误差/K最热通道出口节点温度
最大相对误差/%1 50.6 1.144 3.17 0.397 3.17 0.397 2 101.2 1.144 2.05 0.231 0.50 0.058 3 101.2 0.741 2.95 0.126 0.43 0.047 4 101.2 0.572 5.63 0.317 1.28 0.133 5 101.2 0.455 9.95 0.565 2.56 0.252
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表 3 Fluent计算验证结果
Table 3. Calculation Verification Results by Fluent
验证
工况堆芯
功率/kW堆芯流量/
(kg·s–1)流量-功率
百分值之比最热通道
出口温度/K1 23.0 0.104 0.40 996.3 2 57.5 0.260 1008.4 3 92.0 0.416 1012.2 4 23.0 0.078 0.30 1073.3 5 57.5 0.195 1090.8 6 92.0 0.312 1096.9
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