﻿ PWR栅元流固共轭传热CFD计算方案研究
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (4): 716-720  DOI: 10.11990/jheu.201612110 0

### 引用本文

CHEN Guangliang, XU Junying, ZHANG Zhijian, et al. Research on the CFD scheme of liquid-solid conjugate heat transfer in PWR fuel cells[J]. Journal of Harbin Engineering University, 2018, 39(4), 716-720. DOI: 10.11990/jheu.201612110.

### 文章历史

PWR栅元流固共轭传热CFD计算方案研究

1. 哈尔滨工程大学 核安全与仿真技术国防重点学科实验室, 黑龙江 哈尔滨 150001;
2. 中广核研究院有限公司, 深圳 广东 518000

Research on the CFD scheme of liquid-solid conjugate heat transfer in PWR fuel cells
CHEN Guangliang1, XU Junying2, ZHANG Zhijian1, TIAN Zhaofei1, LI Lei1
1. Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, Harbin Engineering University, Harbin 150001, China;
2. China Nuclear Power Research Institute Co., Ltd., CGN, Shenzhen 518000, China
Abstract: To accurately predict the thermal hydraulic status of a PWR core and improve the economy and safety of the reactor operation, a study was conducted to reflect the strong coupling relationship between the heat release process of a fuel lattice cell and the flowing heat transfer process of a coolant and to improve the efficiency of the engineering application. Based on equivalence principle and geometry, mass and energy balance, and heat transfer in the liquid-solid area in the fuel lattice cell, a calculation scheme on liquid-solid conjugate heat transfer with equivalent gas gap was designed. A variable property calculation software was developed to realize an extensive calculation of the steady-state and transient conjugate heat transfer. The variable properties include fuel pellet, gas gap, cladding, and equivalent domain. By comparing various schemes, it was verified that the calculation on the purely liquid area may result in a wrong estimate of the circumferential heat transfer of the lattice cell. Comparing the calculation of liquid-solid conjugate heat transfer with equivalent gas gap and the calculation of non-simplified liquid-solid conjugate heat transfer, the maximum error is 0.1%, the minimum optimization on storage resources was 24.7%, and the minimum optimization on computing efficiency was 14.3%.
Key words: PWR    liquid-solid conjugate heat transfer    gas gap    CFD    reactor operation    fuel cell

1 气隙CFD计算优化方案

1.1 气隙等效方案

1.1.1 等效区的质量守恒原则

 $\rho '{\rm{ \mathsf{ π} }}\frac{{\left( {d_{{\rm{co}}}^2 - d_{\rm{f}}^2} \right)}}{4} = {\rho _{\rm{g}}}{\rm{ \mathsf{ π} }}\frac{{\left( {d_{{\rm{ci}}}^2 - d_{\rm{f}}^2} \right)}}{4} + {\rho _{\rm{c}}}{\rm{ \mathsf{ π} }}\frac{{\left( {d_{{\rm{co}}}^2 - d_{{\rm{ci}}}^2} \right)}}{4}$ (1)

 $\rho ' = \frac{{{\rho _{\rm{g}}}\left( {d_{{\rm{ci}}}^2 - d_{\rm{f}}^2} \right) + {\rho _{\rm{c}}}\left( {d_{{\rm{co}}}^2 - d_{{\rm{ci}}}^2} \right)}}{{\left( {d_{{\rm{co}}}^2 - d_{\rm{f}}^2} \right)}}$ (2)

1.1.2 等效区的能量守恒原则

 $\begin{array}{*{20}{c}} {\rho 'c'\frac{{{\rm{ \mathsf{ π} }}\left( {d_{{\rm{co}}}^2 - d_{\rm{f}}^2} \right)}}{4} = {\rho _{\rm{c}}}{c_{\rm{c}}}\frac{{{\rm{ \mathsf{ π} }}\left( {d_{{\rm{co}}}^2 - d_{{\rm{ci}}}^2} \right)}}{4} + }\\ {{\rho _{\rm{g}}}{c_{\rm{g}}}\frac{{{\rm{ \mathsf{ π} }}\left( {d_{{\rm{ci}}}^2 - d_{\rm{f}}^2} \right)}}{4}} \end{array}$ (3)

 $c' = \frac{{{\rho _{\rm{c}}}{c_{\rm{c}}}\left( {d_{{\rm{co}}}^2 - d_{{\rm{ci}}}^2} \right) + {\rho _{\rm{g}}}{c_{\rm{g}}}\left( {d_{{\rm{ci}}}^2 - d_{\rm{f}}^2} \right)}}{{\rho '\left( {d_{{\rm{co}}}^2 - d_{\rm{f}}^2} \right)}}$ (4)

1.1.3 等效区的热扩散能力一致原则

 $\frac{1}{{2{\rm{ \mathsf{ π} }}\lambda '}}\ln \frac{{{d_{{\rm{co}}}}}}{{{d_{\rm{f}}}}} = \frac{1}{{2{\rm{ \mathsf{ π} }}{\lambda _{\rm{g}}}}}\ln \frac{{{d_{{\rm{ci}}}}}}{{{d_{\rm{f}}}}} + \frac{1}{{2{\rm{ \mathsf{ π} }}{\lambda _{\rm{c}}}}}\ln \frac{{{d_{{\rm{co}}}}}}{{{d_{{\rm{ci}}}}}}$ (5)

 $\lambda ' = \left( {\ln \frac{{{d_{{\rm{co}}}}}}{{{d_{\rm{f}}}}}} \right)/\left( {\frac{1}{{{\lambda _{\rm{g}}}}}\ln \frac{{{d_{{\rm{ci}}}}}}{{{d_{\rm{f}}}}} + \frac{1}{{{\lambda _{\rm{c}}}}}\ln \frac{{{d_{{\rm{co}}}}}}{{{d_{{\rm{ci}}}}}}} \right)$ (6)

1.2 流固耦合仿真计算方案 1.2.1 研究对象

 Download: 图 1 单燃料栅元结构示意图 Fig. 1 Structure of single fuel cell
 Download: 图 2 有、无气隙的单栅元网格方案 Fig. 2 Mesh schemes with gas and no gas
1.2.2 材料及热物性

 ${\lambda _{{\rm{uo2}}}} = \frac{{3824}}{{402.55 + t}} + 4.788 \times {10^{ - 11}}{\left( {t + 273.15} \right)^3}$ (7)

 ${c_{{\rm{uo2}}}} = \left\{ \begin{array}{l} 304.38 + 2.51 \times {10^{ - 2}}t - 6 \times {10^6}/\\ \;\;\;\;{\left( {t + 273.15} \right)^2},\\ \;\;\;\;25{}^ \circ {\rm{C}} \le t \le 1226{}^ \circ {\rm{C}}\\ - 712.25 + 2.789t - 2.71 \times {10^{ - 3}}{t^2} + \\ \;\;\;\;\;1.12 \times {10^{ - 6}}{t^3} - 1.59 \times {10^{ - 10}}{t^4},\\ \;\;\;\;\;1~226{}^ \circ {\rm{C}} < t \le 2~800{}^ \circ {\rm{C}} \end{array} \right.$ (8)

 ${\lambda _{\rm{g}}} = 2.639 \times {10^{ - 3}}{\left( {t + 273.15} \right)^{0.7085}}$ (9)

 $\begin{array}{*{20}{c}} {{\lambda _{\rm{c}}} = 7.73 \times {{10}^{ - 2}} + 3.15 \times {{10}^{ - 4}}t - }\\ {2.87 \times {{10}^{ - 7}}{t^2} + 1.552 \times {{10}^{ - 10}}{t^3}} \end{array}$ (10)

 ${c_{\rm{c}}} = \left\{ \begin{array}{l} 286.5 + 0.1t,0 < t < 750{}^ \circ {\rm{C}}\\ 360,\;\;t > 750{}^ \circ {\rm{C}} \end{array} \right.$ (11)

1.2.3 程序实现

1.2.4 仿真计算边界及数值方案设置

2 优化方案性能分析

 Download: 图 3 表面热流密度的周向分布 Fig. 3 Heat flux along circumferential length

 Download: 图 4 稳态工况温度分布分析 Fig. 4 Temperature at steady condition
 Download: 图 5 瞬态工况下温度分析 Fig. 5 Maximum temperature at transient condition

3 结论

1) 研究实现了流固共轭传热的CFD计算，并研究了流固共轭传热计算方案与纯流体域计算方案的差异，证明前者的优势在于准确预测PWR燃料栅元周向的非均匀传热特性。

2) 通过研究几何、质能守恒、传热过程的等效原则，设计气隙等效方案，编写变物性计算程序，实现了气隙等效方案在流固共轭传热CFD计算中的成功应用。解决了PWR堆芯CFD分析中微米级厚气隙的几何建立、网格划分、数值计算所引起的效率问题。

3) 经稳态与瞬态工况下冷却剂与燃料区的热工性能分析，证明了流固共轭等效计算方案与非等效方案精度相同，但能够至少节省近1/4的硬件存储资源，至少提高14.3%计算效率。

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