Using Numerical Analysis to Design and Optimize River Hydrokinetic Turbines’ Capacity Factor to Address Seasonal Velocity Variations
Abstract
:1. Introduction
1.1. Capacity Factor
1.2. Power Performance Coefficient
1.3. Flow Velocity
1.4. Shroud
1.5. Computational Approaches
2. Materials and Methods
- Design inputs;
- Geometry development;
- Numerical analysis;
- 3.1.
- Preprocessing;
- 3.2.
- Solver;
- 3.3.
- Post-processing and validation;
- Material selection and structural analysis.
2.1. Design Inputs
2.2. Geometry Development
2.3. Numerical Analysis and Blade Optimization
2.3.1. Preprocessing
2.3.2. Solver
2.3.3. Post-Processing
2.4. FEA Mechanical Analysis
2.4.1. Material Selection
2.4.2. Preprocessing
3. Results and Discussions
3.1. CFD Results
3.1.1. Efficiency
3.1.2. Capacity Factor
3.2. FEA Mechanical Analysis Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Design Inputs | Value | Comment |
---|---|---|
Rated generator power output [kW] | 5 | Design goal |
Generator efficiency [-] | 0.96 | Assumption |
Turbine mechanical efficiency [-] | 0.97 | Assumption |
Turbine hydraulic efficiency [-] | 0.40 | Design goal |
V free stream [m/s] | 2.8 | Rotor 1 |
2.2 | Rotor 2 | |
1.6 | Rotor 3 | |
TSR initial [-] | 4 | Assumption |
Rhub [m] | 0.125 | Rotor 1 |
0.125 | Rotor 2 | |
0.125 | Rotor 2 | |
Span for tip [-] | 0.98 | Blade tips needed |
Blades spinning direction | Count clockwise seen from upstream | Same as for Smart Hydro |
Number of blades | 2 | Required |
Rotor | Velocity (m/s) | Frontal Area (m2) | Turbine Radius (m) | Shroud Simulation Domain R (m) |
---|---|---|---|---|
1 | 2.8 | 1.223 | 0.624 | 0.634 |
2 | 2.2 | 2.522 | 0.896 | 0.911 |
3 | 1.6 | 6.555 | 1.445 | 1.469 |
Rotor | Section | r (m) | u (m/s) | Cm (m/s) | Cu (m/s) | Beta_LE (Deg) | Beta_TE (Deg) |
---|---|---|---|---|---|---|---|
Rotor 1 | 1 | 0.125 | 2.25 | 2.24 | 0.87 | 31.65 | 45.15 |
2 | 0.252 | 4.54 | 2.24 | 0.43 | 61.43 | 63.76 | |
3 | 0.380 | 6.84 | 2.24 | 0.29 | 71.12 | 71.86 | |
4 | 0.507 | 9.13 | 2.24 | 0.21 | 75.90 | 76.21 | |
5 | 0.634 | 11.42 | 2.24 | 0.17 | 78.74 | 78.91 | |
Rotor 2 | 1 | 0.180 | 1.77 | 1.76 | 1.11 | 20.72 | 45.19 |
2 | 0.363 | 3.57 | 1.76 | 0.55 | 59.77 | 63.76 | |
3 | 0.545 | 5.37 | 1.76 | 0.37 | 70.62 | 71.85 | |
4 | 0.728 | 7.17 | 1.76 | 0.27 | 75.68 | 76.20 | |
5 | 0.911 | 8.96 | 1.76 | 0.22 | 78.62 | 78.89 | |
Rotor 3 | 1 | 0.250 | 1.13 | 1.28 | 1.74 | 154.32 | 41.33 |
2 | 0.555 | 2.50 | 1.28 | 0.78 | 53.25 | 62.87 | |
3 | 0.860 | 3.87 | 1.28 | 0.51 | 69.17 | 71.70 | |
4 | 1.165 | 5.24 | 1.28 | 0.37 | 75.27 | 76.28 | |
5 | 1.469 | 6.62 | 1.28 | 0.30 | 78.55 | 79.05 |
Parameters | Rotor 1 | Rotor 2 | Rotor 3 |
---|---|---|---|
Blockage ratio | 0.03 | 0.03 | 0.03 |
distance turbine tip—water surface w1-w (m) | 1 | 1 | 1 |
Distance tip to river bottom B1-B (m) | 1 | 1 | 1 |
River/channel sectional area (m2) | 40.77 | 84.05 | 218.51 |
Channel depth C1-C3 (m) | 3.2480 | 3.7920 | 4.8900 |
Channel width C1-C2 (m) | 12.5526 | 22.1660 | 44.6842 |
Section | Time Step Size (s) | Mesh Size | Number of Iterations | Number of Nodes | Efficiency % |
---|---|---|---|---|---|
Mesh 1 | 4.05–1.54 | 441 | 1,579,000 | 42.37 | |
Mesh 2 | 3.52–1.02 | 392 | 1,500,000 | 42.57 | |
Mesh 3 | 3.57–1.09 | 528 | 1,345,000 | 42.28 | |
Mesh 4 | 2.5–1.02 | 392 | 1,336,300 | 42.61 | |
Mesh 5 | 1.00–1.2 | 401 | 1,124,000 | 43.00 | |
Mesh 6 | 0.8–1.06 | 566 | 1,086,000 | 42.44 | |
Mesh 7 | 1.00–1.2 | Residual value > 10−4 | 1,087,000 | 41.23 | |
Mesh 8 | 1.00–1.2 | Residual value > 10−4 | 1,000,000 | 40.10 |
Rotor | Type | X | Y | Z |
---|---|---|---|---|
Rotor 1 | Pressure force (N) | 0.295 | −0.011 | 4275.20 |
Viscous force (N) | 0.008 | −0.052 | 10.07 | |
Total force (N) | 0.304 | −0.159 | 4285.30 | |
Pressure torque (N-m) | 0.037 | −0.314 | −362.85 | |
Viscous torque (N-m) | −0.003 | 0.007 | 26.97 | |
Total torque (N-m) | 0.037 | −0.307 | −335.88 | |
Rotor 2 | Pressure force (N) | −72.235 | 46.309 | 5768.60 |
Viscous force (N) | −0.356 | −0.548 | 12.08 | |
Total force (N) | −72.591 | 45.761 | 5780.70 | |
Pressure torque (N-m) | −111.050 | 148.630 | −612.42 | |
Viscous torque (N-m) | −0.049 | 0.114 | 48.12 | |
Total torque (N-m) | −111.10 | 148.750 | −564.29 | |
Rotor 3 | Pressure force (N) | 0.469 | −0.059 | 8156.60 |
Viscous force (N) | −0.002 | 0.005 | 17.77 | |
Total force (N) | 0.467 | −0.055 | 8174.40 | |
Pressure torque (N-m) | 1.612 | −1.931 | −1351.30 | |
Viscous torque (N-m) | 0.0002 | −0.0007 | 111.77 | |
Total torque (N-m) | 1.613 | −1.932 | −1239.50 |
Rotor | Section | r (m) | Beta_LE (Deg) | Beta_TE (Deg) | Efficiency |
---|---|---|---|---|---|
Rotor 1 | 1 | 0.125 | 19.53 | 74.16 | 45.10% |
2 | 0.252 | 42.10 | 80.91 | ||
3 | 0.380 | 52.74 | 83.47 | ||
4 | 0.507 | 54.44 | 85.16 | ||
5 | 0.634 | 57.82 | 88.31 | ||
Rotor 2 | 1 | 0.180 | 22.36 | 77.40 | 43.27% |
2 | 0.363 | 44.91 | 83.73 | ||
3 | 0.545 | 54.29 | 85.10 | ||
4 | 0.728 | 55.35 | 86.10 | ||
5 | 0.911 | 57.83 | 88.31 | ||
Rotor 3 | 1 | 0.25 | 26.37 | 73.80 | 43.42% |
2 | 0.555 | 45.92 | 82.26 | ||
3 | 0.860 | 54.44 | 86.19 | ||
4 | 1.165 | 55.54 | 86.26 | ||
5 | 1.469 | 58.19 | 88.67 |
Rotor 1 | Rotor 2 | Rotor 3 | |
---|---|---|---|
Number of blades | 2 | 2 | 2 |
Turbine radius | 0.624 m | 0.896 m | 1.445 m |
Hub radius | 0.125 m | 0.180 m | 0.250 m |
Free stream velocity | 2.8 m/s | 2.2 m/s | 1.6 m/s |
TSR | 4 | 4 | 4 |
RPM | 172 | 94 | 43 |
45.10 | 43.27 | 43.42 |
Month | Velocity (m/s) | Radius (m) | Area (m2) | Cp | kW | kWh |
---|---|---|---|---|---|---|
Jan | 1.5 | 0.6240 | 1.2233 | 0.451 | 0.9 | 680.1 |
Feb | 1.6 | 0.6240 | 1.2233 | 0.451 | 1.1 | 825.4 |
Mar | 1.8 | 0.6240 | 1.2233 | 0.451 | 1.6 | 1175.2 |
Apr | 2.2 | 0.6240 | 1.2233 | 0.451 | 2.9 | 2145.7 |
May | 2.2 | 0.6240 | 1.2233 | 0.451 | 2.9 | 2145.7 |
Jun | 2.8 | 0.6240 | 1.2233 | 0.451 | 6.0 | 4423.7 |
12 months | 22,791.7 | |||||
Average kW | 3.11 | |||||
CF | 0.52 |
Month | Velocity (m/s) | Radius (m) | Area (m2) | Cp | kW | kWh |
---|---|---|---|---|---|---|
Jan | 1.5 | 1.4450 | 6.5597 | 0.434 | 4.8 | 3511.2 |
Feb | 1.6 | 1.4450 | 6.5597 | 0.434 | 5.8 | 4261.3 |
Mar | 2.0 | 0.8960 | 2.5221 | 0.432 | 4.4 | 3189.0 |
Apr | 2.2 | 0.8960 | 2.5221 | 0.432 | 5.8 | 4244.6 |
May | 2.6 | 0.6240 | 1.2233 | 0.451 | 4.8 | 3541.8 |
Jun | 2.8 | 0.6240 | 1.2233 | 0.451 | 6.0 | 4423.7 |
12 months | 43,445.6 | |||||
Average kW | 4.96 | |||||
CF | 0.92 |
Rotor | Material | Maximum Deformation (mm) | Maximum Equivalent Stress (MPa) |
---|---|---|---|
Rotor 1 | Stainless steel | 0.84 | 52.72 |
PEEK–carbon fiber 40% | 4.63 | 55.53 | |
PEEK–carbon fiber 30% | 6.21 | 55.47 | |
PEEK–carbon fiber 20% | 7.97 | 55.52 | |
PEEK–carbon fiber 10% | 13.6 | 55.52 | |
PEEK–glass fiber 40% | 14.39 | 56.17 | |
PEEK–glass fiber 30% | 18.61 | 56.14 | |
PEEK–glass fiber 20% | 24.32 | 56.10 | |
PEEK–glass fiber 10% | 35.11 | 56.02 | |
Rotor 2 | Stainless steel | 0.94 | 55.89 |
PEEK–carbon fiber 40% | 5.2 | 56.85 | |
PEEK–carbon fiber 30% | 6.99 | 56.66 | |
PEEK–carbon fiber 20% | 8.95 | 56.83 | |
PEEK–carbon fiber 10% | 15.27 | 56.83 | |
PEEK–glass fiber 40% | 11.82 | 56.89 | |
PEEK–glass fiber 30% | 15.28 | 56.88 | |
PEEK–glass fiber 20% | 19.98 | 56.85 | |
PEEK–glass fiber 10% | 28.85 | 56.84 | |
Rotor 3 | Stainless steel | 0.97 | 45.9 |
PEEK–carbon fiber 40% | 5.31 | 47.89 | |
PEEK–carbon fiber 30% | 7.15 | 47.89 | |
PEEK–carbon fiber 20% | 9.15 | 47.89 | |
PEEK–carbon fiber 10% | 15.61 | 47.89 | |
PEEK–glass fiber 40% | 12.08 | 47.89 | |
PEEK–glass fiber 30% | 15.62 | 47.89 | |
PEEK–glass fiber 20% | 20.42 | 47.89 | |
PEEK–glass fiber 10% | 29.49 | 47.89 |
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Shaabani, B.; Chatoorgoon, V.; Bibeau, E.L. Using Numerical Analysis to Design and Optimize River Hydrokinetic Turbines’ Capacity Factor to Address Seasonal Velocity Variations. Energies 2025, 18, 477. https://doi.org/10.3390/en18030477
Shaabani B, Chatoorgoon V, Bibeau EL. Using Numerical Analysis to Design and Optimize River Hydrokinetic Turbines’ Capacity Factor to Address Seasonal Velocity Variations. Energies. 2025; 18(3):477. https://doi.org/10.3390/en18030477
Chicago/Turabian StyleShaabani, Bahador, Vijay Chatoorgoon, and Eric Louis Bibeau. 2025. "Using Numerical Analysis to Design and Optimize River Hydrokinetic Turbines’ Capacity Factor to Address Seasonal Velocity Variations" Energies 18, no. 3: 477. https://doi.org/10.3390/en18030477
APA StyleShaabani, B., Chatoorgoon, V., & Bibeau, E. L. (2025). Using Numerical Analysis to Design and Optimize River Hydrokinetic Turbines’ Capacity Factor to Address Seasonal Velocity Variations. Energies, 18(3), 477. https://doi.org/10.3390/en18030477