Numerical Study on Laminar Mixed Convective Heat Transfer of Molten Salt along Helical Cruciform Single-Rod
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摘要: 西安交通大学提出的小型氟盐冷却高温堆（FuSTAR）概念设计采用了螺旋十字型燃料组件。为研究熔盐在螺旋十字型燃料组件的混合对流传热特性，建立了螺旋十字型单棒通道模型。采用计算流体力学（CFD）方法，以实验数据验证数值计算模型，94%壁温数据点的数值计算值与实验测量值之差在±5℃的范围内，94%平均传热系数数据点的数值计算值与实验测量值相对误差范围是−15%~15%。熔盐沿螺旋十字型棒混合对流传热的结果表明，自然对流在整体混合对流传热的影响程度与入口温度、热流密度有关；Φ/Gz（Φ为自然对流无量纲数的组合变量，Gz为格雷兹数）能更合理地评估自然对流在整体对流传热中的影响程度。此外，拟合了在30≤Re≤500，6≤Pr≤26，600≤Gr≤42000（Re为雷诺数，Pr为普朗特数，Gr为格拉晓夫数）时熔盐沿螺旋十字型单棒的层流混合对流传热关系式。Abstract: The concept for FuSTAR, a small fluoride salt-cooled high-temperature reactor, was proposed by Xi'an Jiaotong University, and the helical cruciform fuel assembly is adopted for FuSTAR. In order to study the mixed convection heat transfer characteristics of molten salt in the helical cruciform fuel assembly, a helical cruciform single-rod channel model is established. The computational fluid dynamics (CFD) method is used to verify the numerical calculation model with experimental data. The difference between the numerical calculation value and the experimental measurement value of 94% wall temperature data point is within ±5℃, and the relative error between the numerical calculation value and the experimental measurement value of 94% average heat transfer coefficient data point is −15%~15%. The results of mixed convection heat transfer of molten salt along helical cruciform single-rod show that the influence of natural convection on the whole mixed convection heat transfer is related to inlet temperature and heat flux. The effect of natural convection on overall convective heat transfer can be more accurately evaluated by Φ/Gz (Φ is the combination variable of dimensionless number of natural convection, and Gz is Graetz number). In addition, the correlations of laminar mixed convection heat transfer of molten salt along helical cruciform single-rod at 30≤Re≤500, 6≤Pr≤26, 600≤Gr≤42000 are fitted(Re is Reynolds number, Pr is Prandtl number, and Gr is Grashof number).
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Key words:
- Fluoride-salt-cooled high-temperature reactor /
- FuSTAR /
- Helical cruciform fuel /
- Laminar flow /
- Mixed convection /
- CFD
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图 1 螺旋十字型单棒通道的几何形状
D—圆管内径；R1—叶谷半径，R1=0.5 mm；R2—叶峰半径，R2=3.5 mm；H—螺旋十字型棒长度；S—螺距；x、y、z、o—笛卡尔坐标系
Figure 1. Geometry of Helical Cruciform Single-Rod Channel
图 2 不同网格尺寸下对流传热系数沿流动方向的变化
Figure 2. Change of Convective Heat Transfer Coefficient along the Flow Direction under Different Mesh Sizes
图 5 实验段的温度测量截面和壁面温度测点位置
Figure 5. Temperature Measuring Cross-Section and Wall Temperature Measuring Points of Test Section
图 6 实验条件下（直流加热）壁温实验值与模拟值差值
Figure 6. Difference of Wall Temperature between Experimental and Numerical Values under Experimental Conditions (Direct Current Heating)
图 7 恒定均匀热流密度条件下平均表面传热系数实验值和模拟值相对误差
Figure 7. Relative Error between Experimental Value and Simulated Value of Average Surface Heat Transfer Coefficient under Constant Uniform Heat Flux
图 9 Ra1/4/NuF随Re的变化规律
实心数据点为混合对流传热计算结果，空心数据点为强迫对流计算结果，下同
Figure 9. Fig. 9 Change Law of Ra1/4/NuF with Re
图 10 Ri与Φ/Gz、Ra1/4/NuF的关系
Figure 10. Relationship between Ra1/4/NuF and Ri, Φ/Gz and Ri
表 1 数值计算的工况
Table 1. Conditions for Numerical Calculation
工况编号 q/(kW·m−2) Tin/℃ Re Case 1-1 14.9 500 35 Case 1-2 40 Case 1-3 50 Case 1-4 55 Case 1-5 70 Case 1-6 600 50 Case 1-7 70 Case 1-8 100 Case 1-9 130 Case 1-10 700 130 Case 1-11 350 Case 1-12 1000 Case 1-13 2000 Case 2-1 24.9 500 60 Case 2-2 70 Case 2-3 100 Case 2-4 600 100 Case 2-5 140 Case 2-6 300 Case 2-7 700 140 Case 2-8 300 Case 2-9 500 Case 3-1 149.4 500 330 Case 3-2 340 Case 3-3 350 Case 3-4 450 Case 3-5 800 Case 3-6 1000 Case 3-7 600 500 Case 3-8 1000 Case 3-9 2000 Case 3-10 4000 Case 3-11 5000 Case 3-12 6000 Case 3-13 700 1000 Case 3-14 2000 Case 3-15 4000 Case 3-16 5000 
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表 2 Dowtherm A、316不锈钢和熔盐FLiBe的物理性质
Table 2. Physical Properties of Dowtherm A, 316 Stainless Steel and FLiBe
物理量 Dowtherm A (T/℃) 316 不锈钢 (T/℃) 氟盐FLiBe (T/℃) 密度ρ/(kg·m−3) $\rho = 1078 - 0.85T{\text{ }}$ 8000 $ \rho=2330.0-0.42\left(T+273.15\right) $ 动力粘度μ/(Pa·s−1) $\mu = \dfrac{{0.130}}{{{T^{1.072}}}}$ $ \mu=0.000116\mathrm{exp}{\left(3760\mathord{\left/\vphantom{3760T}\right.}T\right)} $ 比热容cp/(J·kg−1·℃−1) ${c_p} = 1518 + 2.82T$ 500 2380.6 热导率λ/(W·m−1·K−1) $k = 0.142 - 0.00016T$ 16.3 1.1 电导率/(S·m−1) $ \dfrac{100}{7.4\times10^{-5}\times\left(1+9.4\times10^{-4}T\right)} $ 热膨胀率β/K−1 $\dfrac{1}{{995.1 - T}}$ $\dfrac{1}{{5557.1 - T}}$
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表 3 网格参数
Table 3. Mesh Parameters
网格编号 最小网格尺寸/mm 基础网格尺寸/mm 网格数量/万 #1 0.8 0.8 22.7 #2 0.7 0.7 42.5 #3 0.5 0.5 115.0 #4 0.3 0.4 299.2 #5 0.2 0.3 580.1 #6 0.15 0.25 1431.1
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表 4 本文验证的实验数据
Table 4. Experimental Data Verified in this Paper
工况编号 Tin/℃ q/(W·m−2) Re 电流/A Tw/℃ h/(W·m−2·K−1) 测点1 测点2 A-A截面 B-B截面 工况1 90 9682.5 1693 223 134.9 141.7 340 327 工况2 90 22988.3 2455 263 143.7 154.2 544 514 工况3 70 23760.6 3518 351 126.6 135.8 557 530 工况4 70 40793.6 5897 459 134.9 144.1 733 693 工况5 95 8685.7 3152 212 122.2 127.8 467 446 工况6 95 12112.5 4422 250 123.1 127.5 563 535 工况7 80 25095.9 4016 359 136.3 145.6 572 542 工况8 80 29546.9 4761 389 138.1 147.6 621 588
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