NUCLEAR TECHNIQUES, Volume. 48, Issue 4, 040605(2025)
Reduced-order analysis model for thermal stratification in the upper plenum of lead-bismuth fast reactors based on improved DMD and LSTM
Figures & Tables(15)
Fig. 1. Flow chart of thermal stratification model reduction method
Fig. 2. Diagram of model structure (a) and meshing subdivision (b)
Fig. 4. The temperature distribution contours of the upper plenum in 1~200 s (color online)
Fig. 5. Temperature changes with time at different axial heights (color online)
Fig. 7. DMD eigenvalue distribution and characteristic spectrum (a) Eigenvalue distribution, (b) Characteristic spectrum
Fig. 8. Reconstruction error of improved DMD for the first 30 orders
Fig. 9. The 200 s temperature error contours (color online)(a) 26-order standard DMD, (b) 26-order improved DMD, (c) 26-order improved DMD-LSTM
Fig. 10. Temperature oscillation error curve at 10 cm above the outlet (standard DMD, improved DMD, improved DMD-LSTM)
Table 1. Structural parameters and experimental data
View tableView in ArticleTable 1. Structural parameters and experimental data
实验参数
Experimental parameters
实验设计数据
Experimental design data
ABTR数据
ABTR data
比值
Specific value
上腔室高度 Upper plenum height / m 1.2 8.02 0.15 出口高度 Outlet height / m 0.8 5.347 0.15 上腔室直径 Upper plenum diameter / m 0.314 7 4.91 0.065 中间构件直径 Intermediate member diameter / m 0.145 5 2.27 0.065 入口直径 Inlet diameter / m 0.012 7 (×3) 0.371 (×3) 0.009 出口直径 Outlet diameter / m 0.016 (×2) 非保护性事故流量
Unprotected loss-of-flow / m3·s-1
0.001 429 0.377 5 0.003 8 堆芯冷却剂流速
Core coolant flow rate / m·s-1
3.759 0.296 12.7 腔室热流体温度
Chamber thermal fluid temperature / ℃
300 575 0.52 腔室冷流体温度
Chamber cold fluid temperature / ℃
250 525 0.48 佩克莱数(Pe)Peclet number 1 616 12 520 0.13 Re 28 349 788 237 0.04 Ri 1 616 1 616 1
Table 2. Lead-bismuth physical properties relation
View tableView in ArticleTable 2. Lead-bismuth physical properties relation
物性
Physical properties
实验关系式
Experimental relationships
ρ / kg⋅m-3 11 096-1.323 6T λ / W⋅(m⋅K)-1 3.61+1.517×10-2T-1.741×10-6 T2 μ / Pa⋅s 4.94×10-4 e754.1/T cp / J⋅(kg⋅K)-1 159-2.72×10-2T+7.12×10-6T2
Table 3. LSTM neural network predicts root mean square error and training time.
View tableView in ArticleTable 3. LSTM neural network predicts root mean square error and training time.
特征个数
Characteristic
number
LSTM预测均方根误差
LSTM predicts the root
mean square error
LSTM训练时间
LSTM training
time / s
22 0.004 891 518.05 24 0.004 786 482.44 26 0.003 883 506.28 28 0.004 455 504.25
Table 4. Computation time comparison (standard DMD, improved DMD, improved DMD-LSTM)
View tableView in ArticleTable 4. Computation time comparison (standard DMD, improved DMD, improved DMD-LSTM)
降阶预测方法
Reduced-order prediction
methods
特征提取用时
Feature extraction time / s
预测用时
Projected time
/ s
总用时
Total duration
/ s
26阶标准DMD
26-order standard DMD
2 002（对前13 000个时间样本的标准DMD）
2 002 (Standard DMD for the first 13 000 time samples)
5 2 007 26阶改进DMD
26-order improved DMD
122（第一轮截断DMD）+6（第二轮截断DMD）=128
122 (The first round of truncation DMD) +
6 (The second round of truncation DMD) =128
133 26阶改进DMD-LSTM
26-order improved DMD-LSTM
506 634
Table 5. Performance comparison of thermal stratification model calculation methods
View tableView in ArticleTable 5. Performance comparison of thermal stratification model calculation methods
热分层模型计算方法
Thermal stratification model
calculation methods
计算用时computation time / s 热分层后70 s
均方根误差
Root mean square
error at 70 s after
thermal stratification
热分层0~130 s
Thermal
stratification
0~130 s
热分层130~200 s
Thermal
stratification
130~200 s
总用时
Total time
/ s
CFD全阶模型
CFD full-order model
25 200 14 400 39 600 26阶DMD降阶模型
26-order DMD reduced
order model
标准DMD
Standard DMD
2 007 27 207 0.007 272 改进DMD
Improved DMD
133 25 333 0.005 583 改进DMD-LSTM
Improved DMD-LSTM
634 25 834 0.003 883
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Congyi WEN, Junjie DENG, Zijing LIU, Wei LI, Pengcheng ZHAO. Reduced-order analysis model for thermal stratification in the upper plenum of lead-bismuth fast reactors based on improved DMD and LSTM[J]. NUCLEAR TECHNIQUES, 2025, 48(4): 040605
Paper Information
Category: NUCLEAR ENERGY SCIENCE AND ENGINEERING
Received: Apr. 22, 2024
Accepted: --
Published Online: Jun. 3, 2025
The Author Email: Pengcheng ZHAO (赵鹏程)
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