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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。
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:
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)。
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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]:
其中:铅铋与管壁之间的努塞尔数关系式表示如下[12-15]:
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。
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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:
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]。
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 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
doi: 10.11804/NuclPhysRev.40.2022125
- Received Date: 2022-12-07
- Rev Recd Date: 2023-03-08
- Available Online: 2024-02-04
- Publish Date: 2023-12-20
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Key words:
- lead–bismuth reactors /
- MPC_LBE /
- heat exchanger model /
- multi-physics coupling.
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.
Citation: | Qiwen PAN, Wenlan OU, Zhixing GU, Zhengyu GONG, Jianing DAI. Development of a Heat Exchanger Module for a Transient Safety Analysis MPC_LBE Program for Lead-bismuth Reactors[J]. Nuclear Physics Review, 2023, 40(4): 660-667. doi: 10.11804/NuclPhysRev.40.2022125 |