Numerical Study on Convective Heat Transfer at Low Flow and Spacer Effects in Lead-bismuth Eutectic
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摘要: 铅冷快堆的冷却剂铅铋合金（LBE）的传热特性相较于水等常规介质不同，为此本文对LBE在低流量下的流动传热特性及其格架效应进行了数值研究。通过和已有实验数据对比并结合先前研究确定了合适的湍流普朗特数模型和湍流模型，基于此采用计算流体动力学（CFD）方法进行了LBE低流量对流传热计算，结果表明随着浮升力效应的增强，上升流传热先弱化后强化，下降流则一直表现为强化，此规律同水类似；但由于LBE普朗特数极低的特性，其整体的传热强、弱化程度相较于水大幅降低。在带有格架的管内CFD计算中发现在格架下游出现传热局部强化，该强化程度随浮升力效应增加而降低并逐渐消失，且格架下游死区强度和长度均随浮升力效应增加而呈现先增加后减少的趋势，转折点大致位于传热弱化区上升段和传热强化区的分界点。此外，在传热强化区并未出现传热振荡现象，此规律与水不同。Abstract: The heat transfer characteristics of lead-bismuth eutectic (LBE), the coolant of LFR, are different from conventional fluid such as water. Therefore, the flow and heat transfer characteristics of LBE at low flow rate and its spacer effect are numerically studied in this paper. By comparing with existing experimental data and combining with previous studies, appropriate turbulence Prandtl number model and turbulence model were chosen. Based on this, the LBE low-flow convective heat transfer was calculated by computational fluid dynamics (CFD). The results show that with the enhancement of buoyancy effect, the heat transfer in upflow is firstly weakened and then strengthened, while in downflow, the heat transfer is always being strengthened, which is similar to water; However, due to the extremely low Prandtl number of LBE, its overall heat transfer strengthening and weakening degree are greatly smaller than water. In the CFD calculation of a tube with a spacer, it is found that local heat transfer enhancement occurs downstream of the spacer, and the degree of enhancement decreases and gradually disappears with the increase of the buoyancy effect. The strength and length of the stagnation zone downstream of the spacer increased first and then decreased with the increase of the buoyancy effect, and the turning point was roughly located at the boundary point between the heat transfer weakening zone rising section and the heat transfer strengthening zone. In addition, there is no heat transfer oscillation in the heat transfer enhancement zone, which is different from water.
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图 3 湍流模型和湍流普朗特数模型验证
Nu—努塞尔数
Figure 3. Validation of Turbulence Models and Turbulence Prandtl Number Models
图 4 LBE后台阶流计算结果与DNS对比
Ri—理查德森数，Ri=Gr*/Re2；Gr—格拉晓夫数
Figure 4. Comparison of LBE in Backward-Facing Step Flow Calculation Results with DNS
图 7 上升流动时浮升力效应在水和LBE中表现对比
Figure 7. Comparison of Buoyancy Effect between Water and LBE in Upflow
图 8 浮升力对LBE上升流场影响分析
纵坐标为当地速度v与主流速度v0比值或湍动能（Tk）与主流速度v0平方的比值；横坐标为无量纲离壁高度，0表示壁面，1.0表示管道轴线
Figure 8. Analysis of the Influence of Buoyancy on LBE Upflow
图 9 LBE与水在湍流传热中分子导热所占比重对比
Figure 9. Comparison of the Proportion of Molecular Heat Conduction Between LBE and Water in Turbulent Heat Transfer
图 10 格架下游LBE传热能力分析
Figure 10. Analysis of LBE Heat Transfer Capacity Downstream of Spacer
图 11 Bo*=1.11×10−5工况LBE与水对比
Figure 11. Comparison of LBE and Water in Bo* =1.11×10−5 Case
图 12 Bo*=1.11×10−5工况速度分布云图
Figure 12. Velocity Distribution Nephogram in Bo*=1.11×10−5 Case
表 1 LBE热物性
Table 1. Thermophysical Properties of LBE
热物性 实验关联式 密度ρ/(kg·m−3) $\rho = 11{\text{113}}{\text{.6}} - 1.3{\text{4}} \cdot T$ 比热容cp/(J·kg−1·K−1) $ c_p^{} = 156.2 - 1.6 \times {10^{ - 2}} \cdot T $ 动力粘度μ/(Pa·s) $ \mu =4.94\times {10}^{-4}\cdot \mathrm{exp}\left(\dfrac{757.1}{T}\right) $ 热导率λ/(W·m−1·K−1) $\lambda = 4.21 + 1.2 \times {10^{ - 2}} \cdot T$ T—流体当地温度 
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表 2 湍流普朗特数模型
Table 2. Turbulent Prandtl Number Models
湍流普朗特数模型 表达式 Aoki(1963) ${Pr _{\text{t}}}^{ - 1} = 0.014{{Re} ^{0.45}}{Pr ^{0.2}}\left[ {1 - {\text{exp}}\left( { - \dfrac{1}{{0.014{{{Re} }^{0.45}}{{Pr }^{0.2}}}}} \right)} \right]$ Reynolds(1975) $ {{Pr}}_{\text{t}}=（1+100P{\text{e}}^{-0.5}）\left(\dfrac{1}{1+120{{Re}}^{-0.5}}-0.15\right) $ Jischa-Rieke(1979) ${Pr _{\text{t}}} = 0.9 + \dfrac{{182.4}}{{ Pr {{{Re} }^{0.888}}}}$ Kays(1994) ${ Pr _{\text{t}}} = 0.85 + \dfrac{{0.7}}{{\dfrac{{{\nu _{\text{t}}}}}{\nu } \cdot Pr }}$ Cheng-Tak(2006) $ {{Pr}}_{\text{t}}=\left\{\begin{array}{c}4.12\begin{array}{ccc}\begin{array}{cc}\begin{array}{cc}{}_{}^{}& \end{array}& \end{array}& & \end{array}\begin{array}{cc}\begin{array}{cc}\begin{array}{l}\\ \end{array}& \end{array}& \end{array}0 < Pe\le 1000\\ \dfrac{0.01Pe}{(0.018P{e}^{0.8}-0.0009P\text{e}-\text{1}\text{.6})^{1.25}}\begin{array}{cc}& 1000 < Pe\le 2000\end{array}\\ \dfrac{0.01Pe}{(0.018P{e}^{0.8}-3.4)^{1.25}}\begin{array}{cc}& \end{array}\begin{array}{cccc}& & & 2000 < Pe\le 6000\end{array}\end{array}\right. $ ν—运动粘度，m2/s；νt—湍流运动粘度，m2/s；Re—雷诺数；Pr—普朗特数；Prt—湍流普朗特数；Pe—贝克莱数，Pe=Pr·Re
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