基于CFD的铅铋快堆上腔室降阶热分层模型开发

杨涛; 赵鹏程; 赵亚楠; 于涛

doi:10.13832/j.jnpe.2023.02.0048

基于CFD的铅铋快堆上腔室降阶热分层模型开发

doi: 10.13832/j.jnpe.2023.02.0048

杨涛^{1, 2,},
赵鹏程^{1, 2, ,},
赵亚楠^{1, 2},
于涛^{1, 2}

1.
南华大学核科学技术学院，湖南衡阳，421001
2.
南华大学湖南省数字化反应堆工程技术研究中心，湖南衡阳，421001

基金项目: 国家自然科学基金项目（11905101）；湖南省研究生科研创新项目（CX20220992）

详细信息

作者简介:
杨　涛（1994—），男，博士研究生，现从事反应堆热工水力方向研究，E-mail: yangtao@stu.usc.edu.cn

通讯作者:
赵鹏程，E-mail: pengcheng.zhao@usc.edu.cn

中图分类号: TL33
计量
- 文章访问数: 155
- HTML全文浏览量: 118
- PDF下载量: 47
- 被引次数: 0
出版历程
- 收稿日期: 2022-05-30
- 修回日期: 2023-01-19
- 刊出日期: 2023-04-15

Development of Reduced-Order Thermal Stratification Model for Upper Plenum of Lead-Bismuth Fast Reactor Based on CFD

Yang Tao^{1, 2
,},
Zhao Pengcheng^{1, 2
, ,},
Zhao Yanan^{1, 2},
Yu Tao^{1, 2}

1.
School of Nuclear Science and Technology, University of South China, Hengyang, Hunan, 421001, China
2.
Hunan Engineering and Technology Research Center for Virtual Nuclear Reactor, University of South China, Hengyang, Hunan, 421001, China

摘要

摘要: 在铅铋快堆紧急停堆后，上腔室发生热分层现象对堆内结构完整性和自然循环余热排出能力产生重要影响，需要重点关注。为克服传统热分层分析方法的缺陷，基于计算流体动力学（CFD）程序Fluent得到高精度的全阶快照，通过特征正交基分解（POD）与Galerkin投影结合的方法构建降阶热分层模型。通过与CFD全阶热分层模型对热分层现象进行对比分析，研究结果表明所开发的降阶热分层模型能很好地模拟上腔室温度分布，能快速地开展铅铋快堆事故下的热分层界面特性研究。本文研究对热分层现象产生机理、有效遏制热分层现象产生提供了重要分析工具。
- 铅铋快堆上腔室 /
- 热分层 /
- 计算流体动力学（CFD） /
- 特征正交基分解（POD） /
- Galerkin
Abstract: After the emergency shutdown of the lead-bismuth fast reactor, the thermal stratification in the upper plenum has an important impact on the integrity of the reactor structure and the residual heat removal capacity of the natural circulation, which requires special attention. In order to overcome the defects of traditional thermal stratification analysis method, a high-precision full-order snapshot is obtained based on computational fluid dynamics (CFD) code, and a reduced-order thermal stratification model is built by combining proper orthogonal decomposition (POD) with Galerkin projection. After conducting a comparative analysis of thermal stratification with the full-order model of CFD, the results show that the reduced-order thermal stratification model developed can effectively simulate the temperature distribution in the upper plenum and carry out a quick research on the thermal stratification interface characteristics in case of the lead-bismuth fast reactor accident. The research in this paper provides an important analytical tool for studying the thermal stratification mechanism and effectively curbing the thermal stratification.
- Upper plenum of lead-bismuth fast reactor /
- Thermal stratification /
- Computational fluid dynamics (CFD) /
- Proper orthogonal decomposition (POD) /
- Galerkin

HTML全文

图 1 结构模型和网格划分

Figure 1. Structural Model and Meshing

下载: 全尺寸图片幻灯片

图 2 网格独立性验证

Figure 2. Mesh Independence Verification

下载: 全尺寸图片幻灯片

图 3 1~45 s上腔室温度分布云图

Figure 3. Temperature Distribution Nephogram of Upper Plenum at 1~45 s

下载: 全尺寸图片幻灯片

图 4 不同时间点温度随轴向高度变化

Figure 4. Variation of Temperature with Axial Height at Different Time Points

下载: 全尺寸图片幻灯片

图 5 不同轴向高度上温度随时间变化

Figure 5. Variation of Temperature with Time at Different Axial Heights

下载: 全尺寸图片幻灯片

图 6 不同POD基函数个数降阶模型轴向温度误差

Figure 6. Axial Temperature Error of Reduced-Order Model with Different Numbers of POD Basis Functions

下载: 全尺寸图片幻灯片

图 7 不同时刻轴向温度分布重构

Figure 7. Axial Temperature Distribution Reconstruction at Different Times

下载: 全尺寸图片幻灯片

表 1 结构参数和实验数据

Table 1. Structural Parameters and Experimental Parameters

实验参数	实验设计数据	ABTR数据	比值
腔室高度H_pool/m	1.2	8.02	0.15
出口高度H_out/m	0.8	5.347	0.15
腔室直径D_pool/m	0.3147	4.91	0.065
中间构建直径D_UIS/m	0.1455	2.27	0.065
入口直径D_inlet/m	0.0127(×3)	0.371(×3)	0.009
出口直径D_outlet/m	0.016(×2)
非保护性事故流量Q_ULOF/(m³·s⁻¹)	0.001429	0.3775	0.0038
堆芯冷却剂流速V_core/(m·s⁻¹)	3.759	0.296	12.7
腔室热流体温度T_hot/℃	300	575	0.52
腔室冷流体温度T_cold/℃	250	525	0.48
佩克莱数（Pe）	1616	12520	0.13
Re	28349	788237	0.04
Ri	1616	1616	1

下载: 导出CSV

表 2 铅铋流体热物性关系式

Table 2. Thermophysical Relationship of Lead-Bismuth Fluid

物性	实验关系式
$ \rho \text{/}(\text{kg}·{\text{m}}^{-3}) $	$ 11096 - 1.3236T $
λ/[W·(m·K)⁻¹]	$ 4.94 \times {10^{ - 4}}{{\text{e}}^{754.1/T}} $
动力黏度$\mu { {/({\rm{Pa}} \cdot {\rm{s}}} })$	$ 3.61 + 1.517 \times {10^{ - 2}}T - 1.741 \times {10^{ - 6}}{T^2} $
${c_p}{\text{/} }\left[ { { {{\rm{J}} \cdot ({\rm{kg}} \cdot {\rm{K}}} }{)^{ - 1} } } \right]$	$ 159 + 2.72 \times {10^{ - 2}}T + 7.12 \times {10^{ - 6}}{T^2} $

下载: 导出CSV

参考文献(18)

[1]	薛秀丽,杨红义,冯预恒. 日本文殊快堆紧急停堆后堆芯出口腔室瞬态工况模拟研究[J]. 原子能科学技术,2017, 51(10): 1827-1833. doi: 10.7538/yzk.2017.51.10.1827
[2]	MORIYA S, TANAKA N, KATANO N, et al. Effects of Reynolds number and Richardson number on thermal stratification in hot plenum[J]. Nuclear Engineering and Design, 1987, 99: 441-451. doi: 10.1016/0029-5493(87)90140-3
[3]	SCHNEIDER J A, ANDERSON M H. Thermal stratification in a pool-type geometry: DOE-UWM-10268-3[R]. Madison: University of Wisconsin Madison, 2019.
[4]	BANDINI G, POLIDORI M, GERSCHENFELD A, et al. Assessment of systems codes and their coupling with CFD codes in thermal–hydraulic applications to innovative reactors[J]. Nuclear Engineering and Design, 2015, 281: 22-38. doi: 10.1016/j.nucengdes.2014.11.003
[5]	YUE N N, MA Z Y, CAI R, et al. Thermal-hydraulic analysis of EBR-II shutdown heat removal tests SHRT-17 and SHRT-45R[J]. Progress in Nuclear Energy, 2015, 85: 682-693. doi: 10.1016/j.pnucene.2015.09.002
[6]	LU C H, WU Z Y, MORGAN S, et al. An efficient 1-D thermal stratification model for pool-type sodium-cooled fast reactors[J]. Nuclear Technology, 2020, 206(10): 1465-1480. doi: 10.1080/00295450.2020.1719799
[7]	DONG Z Y, QIU H R, WANG M J, et al. Numerical simulation on the thermal stratification in the lead pool of lead-cooled fast reactor (LFR)[J]. Annals of Nuclear Energy, 2022, 174: 109176. doi: 10.1016/j.anucene.2022.109176
[8]	HE S P, WANG M J, ZHANG J, et al. Numerical simulation of three-dimensional flow and heat transfer characteristics of liquid lead–bismuth[J]. Nuclear Engineering and Technology, 2021, 53(6): 1834-1845. doi: 10.1016/j.net.2020.12.025
[9]	WANG M J, WANG Y J, TIAN W X, et al. Recent progress of CFD applications in PWR thermal hydraulics study and future directions[J]. Annals of Nuclear Energy, 2021, 150: 107836. doi: 10.1016/j.anucene.2020.107836
[10]	SHIBAHARA M, TAKATA T, YAMAGUCHI A. Numerical study on thermal stratification phenomena in upper plenum of LMFBR “MONJU”[J]. Nuclear Engineering and Design, 2013, 258: 226-234. doi: 10.1016/j.nucengdes.2013.02.007
[11]	SCHNEIDER J, ANDERSON M, BAGLIETTO E, et al. Thermal stratification analysis for sodium fast reactors [C]//Proceedings of 2018 International Congress on Advances in Nuclear Power Plants. Charlotte, 2018.
[12]	ABE K, KONDOH T, NAGANO Y. A two-equation heat transfer model reflecting second-moment closures for wall and free turbulent flows[J]. International Journal of Heat and Fluid Flow, 1996, 17(3): 228-237. doi: 10.1016/0142-727X(96)00037-9
[13]	ABE K, KONDOH T, NAGANO Y. A new turbulence model for predicting fluid flow and heat transfer in separating and reattaching flows—I. Flow field calculations[J]. International Journal of Heat and Mass Transfer, 1994, 37(1): 139-151. doi: 10.1016/0017-9310(94)90168-6
[14]	FAZIO Concetta. Handbook on lead-bismuth eutectic alloy and lead properties, materials compatibility, thermal-hydraulics and technologies-2015 edition-Introduction [M]. Paris: OECD, 2016: 17-27.
[15]	丁鹏,陶文铨. 建立低阶模型的POD方法[J]. 工程热物理学报,2009, 30(6): 1019-1021.
[16]	ROWLEY C W, COLONIUS T, MURRAY R M. Model reduction for compressible flows using POD and Galerkin projection[J]. Physica D:Nonlinear Phenomena, 2004, 189(1-2): 115-129. doi: 10.1016/j.physd.2003.03.001
[17]	VOLKWEIN S. Model reduction using proper orthogonal decomposition [EB/OL]. (2011-12-07). [2022-05-01]. http://www.uni-graz.at/imawww/volkwein/POD.pdf.
[18]	李航. 统计学习方法[M]. 北京: 清华大学出版社, 2012: 271-290.