Development and Validation of a Four-Parameter SST k-ω-kθ-εθ Model for LBE Flow and Heat Transfer
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摘要: 为解决极低普朗特数流体的数值传热计算问题，提高液态铅铋合金（LBE）流动换热数值计算精度，在OpenFOAM框架下，构建了雷诺应力和湍流热通量的SST k-ω-kθ-εθ四参数模型。使用四参数模型在垂直管内和带绕丝格架19棒束LBE流动换热基准实验的基础上，结合相应的努塞尔数与摩擦因子经验关联式，进行了与湍流普朗特数（Prt）模型的对比验证和传热分析。结果表明，SST k-ω-kθ-εθ四参数模型所预测的温度与实验数据吻合较好，对传热的预测性能优于Prt模型，适用于LBE流动换热数值计算。Abstract: In order to solve the problem of numerical heat transfer computation for extremely low-Prandtl-number fluids and to improve the computational accuracy of the numerical simulation of liquid lead-bismuth eutectic (LBE), a four-parameter SST k-ω-kθ-εθ model for the Reynolds stress and turbulent heat flux is developed under the framework of OpenFOAM. Based on benchmark flow and heat transfer experiments of LBE in a vertical pipe and wire-wrapped 19-rod bundle, a comparison and thermal-hydraulic analysis were conducted against the turbulent Prandtl number (Prt) model using relevant empirical Nusselt number and friction factor correlations. The results show that the temperature predicted by the four-parameter SST k-ω-kθ-εθ model agrees well with the experimental data, and the heat transfer prediction performance is better than that of the Prt model. The model is suitable for the numerical computation of LBE flow and heat transfer.
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Key words:
- Four-parameter model /
- OpenFOAM /
- Lead-bismuth eutectic (LBE) /
- Flow and heat transfer
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图 1 四参数模型整体框架
λ—热导率；η—黏度；p_rgh—动压，在OpenFOAM软件中该表示为p_rgh
Figure 1. Overall Framework of the Four-parameter Model
图 2 数值模型及关联式Nu计算值与实验数据对比
Figure 2. Comparison of Nu Values between Numerical Models and Empirical Correlations with Experimental Data
图 3 数值模型及关联式Nu值与实验值平均绝对误差
Figure 3. Mean Absolute Error of Nu Values between Numerical Models and Empirical Correlations with Experimental Data
图 5 棒束入口横截面示意图
P—棒束间距；W—边缘间距
Figure 5. Schematic Diagram of Cross-section of Rod Bundle Inlet
图 6 模拟与实验局部测点温度比对
Figure 6. Comparison of Simulated and Experimental Local Measurement Temperatures
图 9 截面z/Lh=15/6处中心1号棒周向壁面温度分布
Figure 9. Temperature Profile on Circumferential Wall of Central No.1 Rod at Cross-section z/Lh=15/6
表 1 LBE物性推荐关系式
Table 1. Recommended Relationships of LBE Physical Properties
物性参数 表达式 ρ/(kg·m−3) 11096−1.3236T λ/(W·m−1·K−1) 3.61+1.517×10−2T−1.741×10−6T2 cp/(J·kg−1·K−1) 159−2.72×10−2T+7.12×10−6T2 η/(kg·m−1·s−1) 4.94×10−4exp(754.1/T) 
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表 2 带绕丝格架19棒束几何参数
Table 2. Dimensions of Wire-wrapped 19-rod Bundle
参数 参数值 绕丝直径d/mm 2.20 棒束直径D/mm 8.20 Dh/mm 5.20 P/mm 10.49 W/mm 10.58 绕丝节距H/mm 328 加热总长Lh/mm 870
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