Optimization and Performance Analysis of Francis Turbine Runner Based on Super-Transfer Approximate Method under Multi-Energy Complementary Conditions
Abstract
:1. Introduction
2. Establishment of Optimization Method
2.1. Blade Parameterization
2.2. Super-Transitive Approximate Method
2.3. Establishment of Optimization System
3. Numeric Calculation Method and Selection of Operating Point
Numerical Computation Model
4. Results and Comparative Analysis
Optimization Results
5. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Serial Number | x1 | x2 | x3 | x4 | … | x17 | x18 | x19 | x20 |
---|---|---|---|---|---|---|---|---|---|
Original blade | 40.35 | 18.08 | 25.86 | 49.71 | … | 49.02 | 40.36 | 68.60 | 77.55 |
1 | 37.10 | 17.63 | 24.24 | 54.21 | … | 49.02 | 40.36 | 68.60 | 77.55 |
2 | 42.38 | 16.37 | 23.31 | 45.56 | … | 51.20 | 43.05 | 67.60 | 75.42 |
3 | 42.75 | 16.64 | 27.06 | 51.18 | … | 44.83 | 38.73 | 73.09 | 78.36 |
4 | 42.79 | 19.08 | 27.40 | 46.65 | … | 49.83 | 42.00 | 63.07 | 85.26 |
5 | 42.83 | 19.75 | 26.67 | 51.92 | … | 53.90 | 41.55 | 65.20 | 80.30 |
6 | 42.87 | 17.16 | 27.89 | 53.86 | … | 45.61 | 41.96 | 71.51 | 75.96 |
7 | 42.91 | 16.68 | 25.85 | 47.40 | … | 53.36 | 38.81 | 74.87 | 73.71 |
8 | 42.95 | 19.82 | 24.79 | 50.13 | … | 53.75 | 44.30 | 74.74 | 70.53 |
… | … | … | … | … | … | … | … | … | … |
194 | 44.36 | 16.63 | 23.81 | 54.53 | … | 49.27 | 36.61 | 75.11 | 77.21 |
195 | 44.31 | 16.75 | 28.07 | 54.19 | … | 49.61 | 44.10 | 74.77 | 75.57 |
196 | 44.36 | 16.63 | 23.81 | 54.61 | … | 49.27 | 37.55 | 75.23 | 78.10 |
197 | 44.33 | 19.87 | 28.04 | 54.55 | … | 48.57 | 44.35 | 74.99 | 77.26 |
198 | 44.15 | 18.43 | 28.30 | 54.33 | … | 48.96 | 42.07 | 75.41 | 79.10 |
199 | 44.32 | 18.58 | 28.26 | 54.43 | … | 50.46 | 43.30 | 73.47 | 76.29 |
200 | 44.15 | 18.43 | 27.99 | 54.40 | … | 47.88 | 42.18 | 75.44 | 79.19 |
Algorithm Type | Parameter | Numerical Value |
---|---|---|
MOGA | Initial sample number | 10,000 |
Number of iteration samples | 4000 | |
Maximum Allowed Pareto Percentage | 95 | |
Convergence Stable Ratio | 0.5 | |
Maximum number of iterations | 1000 | |
number of candidate points | 5 |
Geometry Parameter Name | Parameter Value |
---|---|
Wheel diameter D1 (m) | 2.46 |
Relative guide vane height | 0.29 |
Rated speed nr (rpm) | 300 |
Rated water head (m) | 79.5 |
Number of runner blades | 14 |
Number of active guide vanes | 24 |
Number of fixed guide vanes | 24 |
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Zheng, X.; Zhao, Y.; Zhang, H.; Pu, Y.; Li, Z.; Guo, P. Optimization and Performance Analysis of Francis Turbine Runner Based on Super-Transfer Approximate Method under Multi-Energy Complementary Conditions. Sustainability 2022, 14, 10331. https://doi.org/10.3390/su141610331
Zheng X, Zhao Y, Zhang H, Pu Y, Li Z, Guo P. Optimization and Performance Analysis of Francis Turbine Runner Based on Super-Transfer Approximate Method under Multi-Energy Complementary Conditions. Sustainability. 2022; 14(16):10331. https://doi.org/10.3390/su141610331
Chicago/Turabian StyleZheng, Xiaobo, Yaping Zhao, Huan Zhang, Yongjian Pu, Zhihua Li, and Pengcheng Guo. 2022. "Optimization and Performance Analysis of Francis Turbine Runner Based on Super-Transfer Approximate Method under Multi-Energy Complementary Conditions" Sustainability 14, no. 16: 10331. https://doi.org/10.3390/su141610331