-
铅铋堆换热器主要分为套管式和螺管式换热器[7-8]两大类,本文以中国科学院核能安全技术研究所设计的双层套管式换热器进行数值计算模型构建,其简图如图1所示,其相关设计参数可见表1[9-10]。在模型构建时,对换热器的管道进行了简化处理,即将142根管道等效为单管通道,同时,将其中的一次侧、管壁和二次侧以一维通道的形式表示,二次侧则采用开式通道。一次侧铅铋和二次侧高压过冷水互为逆向流动,且均与外界绝热,如图2所示。一回路的高温铅铋冷却剂在换热器套管的壳程(一次侧)内流动,将热量传递给套管管程(二次侧)内的二回路高压过冷水,即实现一次侧与二次侧间的传热耦合。其中,二次侧采用压力为4 MPa的加压过冷水,入口温度为488.15 K,出口温度为503.15 K。一次侧铅铋的入口设计温度为673 K,出口的设计温度为573 K。
表 1 铅铋堆套管式换热器的设计参数
名称 单位 壳程 管程 入口温度 K 673 488.15 出口温度 K 573 503.15 流量 kg·s−1 158.844 40.21 压降 Pa 863.33 17 503 传热面积 m 25.86 / 换热管数量 根 142 / 换热管规格 mm 外管:∅30 × 2.5 / mm 内管:∅25 × 2.5 / 换热管有效换热长度 mm 1932 / -
换热器套管流动换热的控制方程仅考虑能量守恒方程,一次侧、二次侧及管壁的控制方程分别如下所示:
$$ \frac{{\partial {\rho _1}{C_{p,\,1}}{T_1}}}{{\partial t}} + \frac{{\partial {\rho _1}{C_{p,\,1}}{T_1}{v_1}}}{{\partial z}} = {\lambda _1}\frac{{{\partial ^2}{T_1}}}{{\partial {z^2}}} - {q_{V,\,1 \to w}}\text{,} $$ (1) $$ \frac{{\partial {\rho _2}{C_{p,\,2}}{T_2}}}{{\partial t}} + \frac{{\partial {\rho _2}{C_{p,\,2}}{T_2}{v_2}}}{{\partial z}} = {\lambda _2}\frac{{{\partial ^2}{T_2}}}{{\partial {z^2}}} + {q_{V,\,w \to 2}}\text{,} $$ (2) $$ \frac{{\partial {\rho _w}{C_{p,\,w}}{T_w}}}{{\partial t}} = {\lambda _w}\frac{{{\partial ^2}{T_w}}}{{\partial {z^2}}}{\text{ + }}{q_{V,\,1 \to w}} - {q_{V,\, w \to 2}}\text{,} $$ (3) 式中:ρ为密度,单位为kg/m3;Cp为比热容,J/(kg·K);T为温度;z为单位结点长度,单位为m;v为流体流动速度,单位为kg/m;λ为热导率,单位为J/(m·K);t为时间;q为对流换热项(下标1、w和2分别对应换热器一次侧铅铋、管壁和二次侧高压过冷水)。
-
在套管式换热器中有两个对流换热模型,分别为一次侧与管壁之间的对流换热模型式(4)及管壁与二次侧之间的对流换热模型式(5)[11]:
$$ q_{V,\, 1 \rightarrow w}=h_{1} S_{1,\,w}\left(T_{1}-T_{w}\right) , $$ (4) $$ q_{V,\, w \rightarrow 2}=h_{1} S_{2,\,w}\left(T_{w}-T_{2}\right) 。 $$ (5) 其中:铅铋与管壁之间的努塞尔数关系式表示如下[12-15]:
$$ N{u_1} = 4.5 + 0.018 \times P{e_1}^{0.8} \text{。} $$ (6) $$ N{u_2} = 0.023 \times R{e_2}^{0.8}P{r_2}^{0.4} \text{,} $$ (7) 式中:h为对流换热系数;Nu为努塞尔数;Re为雷诺数;Pe为贝克莱数;Pr为普朗特数。
-
液态铅铋的密度、动力粘度及热导率等物性参数均来自公开发布的拟合公式[21],依次表示如下:
$$ {\rho _1}{\text{ = }}11113.6 - 1.34{T_1}\text{,} $$ (8) $$ {\mu _1} = 4.94 \times {10^{ - 4}} \times {\rm{exp}}\left( {\frac{{757.1}}{{{T_1}}}} \right)\text{,} $$ (9) $$ {\lambda _1} = 4.21 + 1.2 \times {10^{ - 2}} \times {T_1}\text{,} $$ (10) $$ {C_{p,1}} = 143.919。 $$ (11) 管壁材质为不锈钢,二次侧过冷水和管壁的相关物性参数均为常数,分别如表2和表3所列[7-8]。
表 2 二次侧水的物性参数
参数 数值 ρ2 /(g·m−3) 1 000 Cp,2 /J·(kg·K)−1 4.2×103 λ2 /W·(m·K)−1 0.645 μ2 /(Pa·s) 124.6×10−6 表 3 管壁材料的物性参数
参数 数值 ρw /(g·m−3) 7.93×103 Cp,w /[J·(kg·K)−1] 4.6×103 λw /[W·(m·K)−1] 21.5 -
从前述方程(1)、(2)及(3)中可看出,一次侧液态铅铋、管壁和二次侧水三者温度是相互耦合关联的,对此本文采用了显式耦合、隐式耦合两种方案。显式耦合和隐式耦合在算法上的不同主要表现在三个能量守恒方程中对流换热项离散化的形式不同,且在同一时间步长下显式耦合算法是一次侧、管壁和二次侧依次单独迭代计算求解,如图3所示。而隐式耦合则是将三个能量守恒方程同时进行迭代计算求解,因此隐式耦合算法比显式耦合算法更复杂,但计算结果更准确,算法步骤如图4所示。
Development of a Heat Exchanger Module for a Transient Safety Analysis MPC_LBE Program for Lead-bismuth Reactors
-
摘要: 铅铋堆作为第四代先进核能系统之一,具有优良的中子经济性、固有安全性。为提高其紧凑性、安全性,铅铋堆主冷却剂系统倾向于采用一体化池式结构设计理念,但该设计理念同时也造成了复杂的热工水力问题。铅铋堆多物理耦合瞬态安全分析程序MPC_LBE在此背景下开发,但该程序的换热器模块采用了定温简化模型,无法模拟换热器一、二次侧之间的换热过程,事故瞬态模拟过于保守,偏离实际工况。为此,开展了铅铋堆换热器模块数值模拟方法研究,换热器一次侧、管壁以及二次侧均采用了一维通道等效处理手段,构建了其数值传热模型,编制了程序代码,并与MPC_LBE实现了外部显式耦合。对于该数值传热模型,单独进行了稳态验证及时间步长敏感性分析,结果显示,显式耦合策略的时间步长敏感性较大,而隐式耦合策略时间步长设置对模拟结果几乎无影响。对耦合了该数值传热模型的新MPC_LBE程序,开展了自然循环铅铋反应堆稳态模拟应用,同时添加了以一次侧出口段的设计温度为基准的二次侧冷却剂流量调节系统。Abstract: As one of the fourth-generation advanced nuclear energy systems, Lead-Bismuth Eutectic(LBE) cooled reactor has excellent neutron economy and inherent safety. To improve its compactness and safety, the main coolant system of LBE-cooled reactor tends to adopt the integrated pool structure design concept, but this design concept also introduces complex thermal hydraulic problems. To solve the above issues, the multi-physics coupling transient safety analysis code for LBE-cooled reactor MPC_LBE was developed, but this code uses a constant temperature simplified model which are not able to simulate the heat exchange process between the first and second circuits, and the accident transient simulation is rather conservative which deviating from the actual condition. To solve this problem, the numerical simulation method of the heat exchanger module for LBE-cooled reactor was carried out in this paper. A one-dimensional numerical calculation models were employed for the primary side, pipe wall and secondary side of heat exchanger, and the numerical heat transfer model was constructed. Finally, the heat exchanger module was coupled with the MPC_LBE code by external explicit means. For the heat exchanger numerical calculation module, steady-state verification and time step sensitivity analysis were performed separately, and the results show that the time step sensitivity of the explicit coupling strategy is large, while the time step setting of the implicit coupling strategy has almost no effect on the simulation results. For the new MPC_LBE program coupled with the numerical calculation module of the heat exchanger, the steady-state simulation application of the natural cycle lead-bismuth reactor was carried out.
-
Key words:
- lead–bismuth reactors /
- MPC_LBE /
- heat exchanger model /
- multi-physics coupling.
-
表 1 铅铋堆套管式换热器的设计参数
名称 单位 壳程 管程 入口温度 K 673 488.15 出口温度 K 573 503.15 流量 kg·s−1 158.844 40.21 压降 Pa 863.33 17 503 传热面积 m 25.86 / 换热管数量 根 142 / 换热管规格 mm 外管:∅30 × 2.5 / mm 内管:∅25 × 2.5 / 换热管有效换热长度 mm 1932 / 表 2 二次侧水的物性参数
参数 数值 ρ2 /(g·m−3) 1 000 Cp,2 /J·(kg·K)−1 4.2×103 λ2 /W·(m·K)−1 0.645 μ2 /(Pa·s) 124.6×10−6 表 3 管壁材料的物性参数
参数 数值 ρw /(g·m−3) 7.93×103 Cp,w /[J·(kg·K)−1] 4.6×103 λw /[W·(m·K)−1] 21.5 -
[1] WU Yican. Engineering, 2016, 2(1): 262. doi: 10.1016/J.ENG.2016.01.023 [2] 吴宜灿, 王明煌,黄群英,等. 核科学与工程, 2015, 35(2): 213. doi: 10.3969/j.issn.0258-0918.2015.02.004 WU Yican, WANG Minghuang, HUANG Qunying, et al. Nuclear Science and Engineering, 2015, 35(2): 213. (in Chinese) doi: 10.3969/j.issn.0258-0918.2015.02.004 [3] 吴宜灿, 柏云清, 宋勇, 等. 核科学与工程, 2014, 34(2): 201. doi: 10.3969/j.issn.0258-0918.2014.02.009 WU Yican, BAI Yunqing, SONG Yong, et al. Nuclear Science and Engineering, 2014, 34(2): 201. (in Chinese) doi: 10.3969/j.issn.0258-0918.2014.02.009 [4] GU Zhixing, ZHANG Qingxian, GU Yi, et al. Nuclear Science and Techniques, 2021, 32(5): 86. doi: 10.1007/s41365-021-00887-x [5] 张玲, 辜峙钘, 戴嘉宁, 等. 核技术, 2022, 45(10): 87. doi: 10.11889/j.0253-3219.2022.hjs.45.100602 ZHANG Ling, GU Zhixing, DAI Jianing, et al. Nuclear Techniques, 2022, 45(10): 87. (in Chinese) doi: 10.11889/j.0253-3219.2022.hjs.45.100602 [6] ZHANG L, SONG T, GU Z, et al. Kerntechnik, 2023, 88(2): 240. [7] 张巍, 李净松, 施慧烈. 核动力工程, 2022, 43(3): 38. ZHANG Wei, LI Jingsong, SHI Huilie. Nuclear Power Engineering, 2022, 43(3): 38. (in Chinese) [8] 丁雪友, 陈志强, 文青龙. 核动力工程, 2021, 42(4): 21. DING Xueyou, CHEN Zhiqiang, WEN Qinglong. Nuclear Power Engineering, 2021, 42(4): 21. (in Chinese) [9] 陈森. 加速器驱动铅铋冷却自然循环次临界堆无保护瞬态分析研究[D]. 合肥: 中国科学技术大学, 2014. CHEN Sen. Unprotected Transient Analysis of Accelerator Driven LBE-Cooled Natural Circulation Sub-critical Reactor [D]. Hefei: University of Science and Technology of China, 2014. (in Chinese) [10] 席文宣. 基于特殊介质的高效换热器流动传热特性研究[D]. 合肥: 中国科学院大学(中国科学院工程热物理研究所), 2018. XI Wenxua. Investigation on Flow and Heat Transfer Characteristics of High Efficiency Heat Exchangers Based on Special Medium [D]. University of Chinese Academy of Sciences(Institute of Engineering Thermophysics, Chinese Academy of Sciences), 2018. (in Chinese) [11] 丁雪友, 文青龙, 阮神辉. 铅铋快堆螺旋管直流蒸汽发生器热工水力模型研究[C]/第十六届全国反应堆热工流体学术会议暨中核核反应堆热工水力技术重点实验室 2019 年学术年会论文集. 2019: 196. DING Xueyou, WEN Qinglong, RUAN Shenhui. A thermal Hydraulic Model for a Helical Coiled Tube Once Through Steam Generator of Lead Cooled Fast Reactor[C]//Proceedings of the 16th National Conference on Reactor Thermal Fluids and the 2019 Annual Conference of the Key Laboratory of Thermal and Hydraulic Technology of Nuclear Nuclear Reactors. 2019: 196. (in Chinese) [12] 郭政, 阴继翔, 易文杰. 中国科技论文, 2021, 16(2): 217. doi: 10.3969/j.issn.2095-2783.2021.02.015 GUO Zheng, YIN Jixiang, YI Wenjie. China Sciencepaper, 2021, 16(2): 217. (in Chinese) doi: 10.3969/j.issn.2095-2783.2021.02.015 [13] 邢海坤. U型管蒸汽发生器仿真模型及动态特性研究[D]. 北京: 华北电力大学, 2014. XING Haikun. The Simulation Model and Research on the Dynamic Characteristics of U-tube Steam Generator[D]. Beijing: North China Electric Power University, 2014. (in Chinese) [14] 陈佳跃. 自然循环蒸汽发生器热工水力过程的数值仿真 [D]. 广州: 华南理工大学, 2013. CHEN Jiayue. Numerical Simulation of Natural Circulation Stam Generator’s Thermal-hydraulic Process[D]. Guangzhou: South China University of Technology, 2013. (in Chinese) [15] 张羽, 孙宝芝, 张国磊. 原子能科学技术, 2012, 46(1): 57. ZHANG Yu, SUN Baozhi, ZHANG Guolei. Atomic Energy Science and Technology, 2012, 46(1): 57. (in Chinese) [16] 刘乐, 陈文振, 黄文. 核科学与工程, 2020, 40(4): 596. doi: 10.3969/j.issn.0258-0918.2020.04.012 LIU Le, CHEN Wenzhen, HUANG Wen. Nuclear Science and Engineering, 2020, 40(4): 596. (in Chinese) doi: 10.3969/j.issn.0258-0918.2020.04.012 [17] 缠阿芳. 压水堆核电站U型管蒸汽发生器建模与仿真 [D]. 北京: 华北电力大学, 2012. CHAN Afang. Modeling and Simulation of U-Tube Steam Generator in PWR Nuclear Power Plant[D]. Beijing: North China Electric Power University, 2012. (in Chinese) [18] 程蔡阳. 山西化工, 1982(2): 53. CHENG Caiyang. Shanxi Chemical Industry, 1982(2): 53. (in Chinese) [19] 何啸峰, 阳小华, 何金桥. 南华大学学报(自然科学版), 2006, 20(2): 47. HE Xiaofeng, YANG Xiaohua, HE Jinqiao. Journal of the University of South China (Natural Science Edition), 2006, 20(2): 47. (in Chinese) [20] 杨瑞昌, 覃世伟, 刘若雷. 工程热物理学报, 2006(1): 130. doi: 10.3321/j.issn:0253-231X.2006.01.041 YANG Ruichang, QIN Shiwei, LIU Ruolei. Journal of Engineering Thermophysics, 2006(1): 130. (in Chinese) doi: 10.3321/j.issn:0253-231X.2006.01.041 [21] 苏子威, 周涛, 刘梦影, 等. 核技术, 2013, 36(9): 090205. doi: 10.11889/j.0253-3219.2013.hjs.36.090205 SU Ziwei, ZHOU Tao, LIU Mengying, et al. Nuclear Techniques, 2013, 36(9): 090205. (in Chinese) doi: 10.11889/j.0253-3219.2013.hjs.36.090205 [22] GU Zhixing, LI Fei, GE Liangquan, et al. Annals of Nuclear Energy, 2019, 133: 491. doi: 10.1016/j.anucene.2019.05.053 [23] XIAO Yulong, GU Zhixing, ZHANG Qingxian, et al. Annals of Nuclaer Energy, 2020, 141: 107308. doi: 10.1016/j.anucene.2020.107308