Author Affiliations
1Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China2University of Chinese Academy of Sciences, Beijing 100049, Chinashow less
Fig. 1. Computational model
Fig. 2. Grids of the computational domain
Fig. 3. Comparison results between the numerical computation and experimental tests
Fig. 4. Flow chart of the multi-objective optimization model
Fig. 5. Analysis of head significance
Fig. 6. Pareto optimal solution set
Fig. 7. Comparison of blade geometry (a) Original model and molten salt optimization model, (b) Original model and water optimization model
Fig. 8. Parameters of the optimized models (a) Impeller inlet diameter, (b) Impeller outlet width, (c) Blade outlet placement angle, (d) Blade wrap angle, (e) Diffuser throat plane width
Fig. 9. Turbulence kinetic energy distribution of blade surfaces (a) , (b) , (c) , (d)
Fig. 10. Pressure distribution of diffuser (a) , (b) , (c) , (d)
网格数量 Mesh number | 扬程 Head / m |
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2 490 507 | 5.668 5 | 4 786 291 | 5.647 6 | 5 520 867 | 5.621 4 | 6 061 679 | 5.626 5 |
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Table 1. Mesh independence test
参数Parameters | 低水平(-1)Low level (-1) | 高水平(1)High level (1) |
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叶轮进口直径Impeller inlet diameter D1 / mm | 115 | 145 | 叶轮出口宽度Impeller outlet width b2 / mm | 10 | 16 | 叶片进口边位置 Blade leading edge position l / mm | 0 | 15 | 叶片进口冲角 Blade incidence angle β1 / (º) | 0 | 10 | 叶片包角 Blade wrap angle / (º) | 115 | 150 | 叶片出口安放角 Blade outlet placement angle / (º) | 20 | 40 | 导叶喉部平面宽度 Diffuser throat plane width / mm | 15 | 25 | 导叶出口平面宽度 Diffuser outlet plane width / mm | 26 | 36 | 导叶进口轴向宽度 Diffuser inlet axial width / mm | 25 | 35 |
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Table 2. Parameters and levels
编号 Number | 参数Parameters | 熔盐Molten salt | 水Water |
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| | | | | | | | | / m | / % | / m | / % |
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1 | -1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 3.070 1 | 44.91 | 3.246 0 | 47.27 | 2 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | 5.427 3 | 58.60 | 5.461 0 | 58.97 | 3 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | 4.820 2 | 56.59 | 4.856 9 | 57.20 | 4 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | 4.027 6 | 51.38 | 4.146 9 | 52.97 | 5 | 1 | -1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | 4.394 4 | 56.41 | 4.487 1 | 57.70 | 6 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | -1 | 4.047 2 | 51.51 | 4.190 7 | 53.23 | 7 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 5.367 1 | 56.87 | 5.420 5 | 57.63 | 8 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | 1.137 9 | 25.47 | 1.345 8 | 30.03 | 9 | 1 | -1 | 1 | -1 | -1 | -1 | 1 | 1 | 1 | 3.325 5 | 52.75 | 3.395 3 | 54.16 | 10 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | -1 | 5.418 6 | 58.41 | 5.450 0 | 58.87 | 11 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 3.835 2 | 50.16 | 3.873 3 | 51.12 | 12 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 3.433 7 | 49.65 | 3.539 4 | 51.05 |
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Table 3. Plackett-Burman design parameters and results
编号 Number | 参数Parameters | 熔盐Molten salt | 水Water |
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| | | | | / m | / % | / m | / % |
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1 | 0 | -1 | 0 | 1 | 0 | 5.107 0 | 59.55 | 5.133 3 | 60.07 | 2 | 0 | 0 | -1 | 0 | -1 | 4.747 9 | 58.96 | 4.801 3 | 59.87 | 3 | 0 | 0 | 1 | -1 | 0 | 5.261 9 | 57.38 | 5.336 6 | 58.23 | 4 | 0 | -1 | 0 | 0 | 1 | 5.465 2 | 60.27 | 5.478 3 | 60.76 | 5 | 1 | 1 | 0 | 0 | 0 | 5.347 5 | 58.04 | 5.396 8 | 58.85 | 6 | 0 | 0 | -1 | 0 | 1 | 4.906 7 | 60.34 | 4.988 5 | 60.85 | 7 | -1 | 0 | 0 | -1 | 0 | 4.239 1 | 54.39 | 4.283 2 | 55.22 | 8 | 0 | 1 | 0 | -1 | 0 | 4.796 4 | 55.91 | 4.878 3 | 56.96 | 9 | -1 | 0 | 0 | 0 | -1 | 4.025 3 | 54.41 | 4.108 4 | 55.65 | 10 | 0 | 1 | -1 | 0 | 0 | 4.520 0 | 58.25 | 4.585 5 | 59.34 | 11 | 1 | 0 | 0 | -1 | 0 | 5.677 9 | 58.24 | 5.700 6 | 58.86 | 12 | 0 | -1 | -1 | 0 | 0 | 5.156 1 | 60.60 | 5.182 5 | 61.16 | 13 | 0 | 1 | 0 | 1 | 0 | 4.493 1 | 56.81 | 4.561 7 | 57.73 | 14 | 0 | 1 | 0 | 0 | -1 | 4.507 9 | 55.67 | 4.606 4 | 56.94 | 15 | 0 | 0 | 0 | 1 | -1 | 4.688 2 | 57.20 | 4.752 0 | 58.06 | 16 | 0 | 0 | -1 | -1 | 0 | 4.908 9 | 57.87 | 4.943 2 | 58.61 | 17 | 1 | 0 | 1 | 0 | 0 | 5.641 6 | 58.24 | 5.667 4 | 58.82 | 18 | 0 | 0 | 0 | 0 | 0 | 5.150 5 | 59.49 | 5.190 3 | 60.25 | 19 | 0 | -1 | 1 | 0 | 0 | 5.463 6 | 59.33 | 5.487 0 | 59.86 | 20 | 0 | 0 | 1 | 0 | -1 | 5.060 1 | 57.43 | 5.125 7 | 58.36 | 21 | 0 | 0 | 0 | 0 | 0 | 5.150 5 | 59.49 | 5.190 3 | 60.25 | 22 | 0 | 0 | 0 | 0 | 0 | 5.150 5 | 59.49 | 5.190 3 | 60.25 | 23 | 0 | 0 | 0 | 0 | 0 | 5.150 5 | 59.49 | 5.190 3 | 60.25 | 24 | 0 | 0 | 0 | 0 | 0 | 5.150 5 | 59.49 | 5.190 3 | 60.25 | 25 | 0 | 0 | 0 | 0 | 0 | 5.150 5 | 59.49 | 5.190 3 | 60.25 | 26 | 0 | 0 | 0 | 1 | 1 | 4.999 3 | 59.56 | 5.031 1 | 60.14 | 27 | -1 | 0 | 0 | 1 | 0 | 4.146 0 | 56.68 | 4.255 9 | 57.85 | 28 | -1 | 0 | 0 | 0 | 1 | 4.538 0 | 58.58 | 4.585 2 | 59.42 | 29 | 1 | 0 | 0 | 0 | 1 | 5.631 6 | 59.28 | 5.656 2 | 59.81 | 30 | 0 | 0 | 0 | -1 | 1 | 5.310 7 | 58.78 | 5.330 8 | 59.27 | 31 | 0 | -1 | 0 | 0 | -1 | 5.314 6 | 59.76 | 5.347 7 | 60.42 | 32 | 0 | -1 | 0 | -1 | 0 | 5.469 7 | 58.91 | 5.502 8 | 59.44 | 33 | 0 | 0 | 1 | 1 | 0 | 4.893 1 | 58.14 | 5.020 2 | 58.79 | 34 | -1 | 0 | -1 | 0 | 0 | 3.922 5 | 56.79 | 3.974 9 | 57.92 | 35 | 1 | -1 | 0 | 0 | 0 | 5.707 4 | 58.45 | 5.692 1 | 58.40 | 36 | 0 | 1 | 1 | 0 | 0 | 4.838 1 | 56.92 | 4.923 5 | 58.04 | 37 | 1 | 0 | 0 | 0 | -1 | 5.553 6 | 58.86 | 5.580 2 | 59.41 | 38 | 0 | 0 | 0 | -1 | -1 | 5.057 4 | 56.93 | 5.104 9 | 57.62 | 39 | -1 | 0 | 1 | 0 | 0 | 4.484 0 | 57.18 | 4.559 8 | 58.22 | 40 | 0 | 1 | 0 | 0 | 1 | 4.929 3 | 58.66 | 4.987 8 | 59.57 | 41 | 1 | 0 | -1 | 0 | 0 | 5.423 4 | 59.39 | 5.444 8 | 59.89 | 42 | -1 | 1 | 0 | 0 | 0 | 3.881 3 | 55.56 | 3.872 5 | 55.06 | 43 | 0 | 0 | -1 | 1 | 0 | 4.691 2 | 59.41 | 4.728 2 | 60.14 | 44 | 0 | 0 | 1 | 0 | 1 | 5.362 4 | 59.31 | 5.388 6 | 59.89 | 45 | -1 | -1 | 0 | 0 | 0 | 4.802 9 | 60.57 | 4.857 9 | 61.73 | 46 | 1 | 0 | 0 | 1 | 0 | 5.347 9 | 58.56 | 5.385 7 | 59.16 |
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Table 4. Box-Behnken design parameters and results
模型 Models | |
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| 0.992 8 | | 0.886 9 | | 0.993 6 | | 0.904 6 |
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Table 5. Adjusted coefficients of determination
| | | | |
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H / m | RSM | — | 5.657 0 | — | 5.570 2 | CFD | 5.591 0 | 5.669 2 | 5.621 4 | 5.585 5 | Η / % | RSM | — | 59.96 | — | 60.62 | CFD | 59.30 | 60.05 | 59.91 | 60.46 |
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Table 6. Comparison of optimization results