Experimental Fitting of Efficiency Hill Chart for Kaplan Hydraulic Turbine
Abstract
:1. Introduction: The Characteristic Curves of Hydraulic Turbines
2. The Operational Parameters
- Specific speed;
- Flow coefficient ;
- Load coefficient .
- -
- Model-specific flow rate: ;
- -
- Model-specific speed: .
3. The Prototype Tests
Determination of Efficiency Contour Map
4. Stator/Rotor Setup
- -
- = diameter of the passing sphere [m];
- -
- = number of distributor blades;
- -
- = pitch diameter [m];
- -
- = specific opening degree [m].
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Model Type | Turbine Characteristics | ||
---|---|---|---|
Optimal flow coefficient | ϕopt | 0.20 | [-] |
Optimal load coefficient | ψopt | 0.36 | [-] |
Model optimum efficiency | ηopt | 0.915 | [-] |
Specific speed | Ns | 554 | [-] |
Flow coefficient max at ψopt | ϕopt | 0.34 | [-] |
Hn = 13.5 m | Hn = 10 m | ||||||||
---|---|---|---|---|---|---|---|---|---|
Q | Hn | ψ | φ | η | Q | Hn | ψ | φ | η |
[m3/s] | [m] | [-] | [-] | [%] | [m3/s] | [m] | [-] | [-] | [%] |
1.35 | 13.5 | 0.387 | 0.029 | 72.9 | 1.35 | 10 | 0.287 | 0.029 | 62 |
2.7 | 13.5 | 0.387 | 0.058 | 80.5 | 2.7 | 10 | 0.287 | 0.058 | 74 |
4.05 | 13.5 | 0.387 | 0.087 | 88.9 | 4.05 | 10 | 0.287 | 0.088 | 82 |
5.4 | 13.5 | 0.387 | 0.116 | 90.9 | 5.4 | 10 | 0.287 | 0.117 | 87 |
6.75 | 13.5 | 0.387 | 0.146 | 92.4 | 6.75 | 10 | 0.287 | 0.146 | 90.7 |
8.1 | 13.5 | 0.387 | 0.175 | 92.9 | 8.1 | 10 | 0.287 | 0.175 | 91.9 |
9.45 | 13.5 | 0.387 | 0.204 | 93 | 9.45 | 10 | 0.287 | 0.204 | 92 |
10.8 | 13.5 | 0.387 | 0.233 | 93 | 10.8 | 10 | 0.287 | 0.234 | 91.9 |
12.15 | 13.5 | 0.387 | 0.262 | 92.4 | 12.15 | 10 | 0.287 | 0.263 | 91.4 |
13.5 | 13.5 | 0.387 | 0.292 | 91.9 | 13.5 | 10 | 0.287 | 0.292 | 90.5 |
Parameter | Turbomachinery | |||
---|---|---|---|---|
Radial (Francis) | Diagonal (Mixed Flow) | Axial (Kaplan, Bulb) | Impulse (Pelton) | |
Reynolds number Re | 4 × 106 | 4 × 106 | 4 × 106 | 2 × 106 |
Specific hydraulic energy E [J/kg] | 100 | 50 | 30 | 500 |
Reference diameter D [m] | 0.25 | 0.3 | 0.3 | ----- |
Bucket width [m] | ----- | ----- | ----- | 0.08 |
Runner | Distributor | Hn | P | ψ | φ | ηprototype | ηmodel | |
---|---|---|---|---|---|---|---|---|
[%] | [%] | [m3/s] | [m] | [kW] | [-] | [-] | [%] | [%] |
5.5 | 45 | 2.86 | 11.35 | 260 | 0.326 | 0.062 | 79.6 | 77.8 |
8.7 | 47 | 3.08 | 11.19 | 285 | 0.321 | 0.067 | 81.3 | 79.4 |
11 | 48 | 3.23 | 11.05 | 310 | 0.317 | 0.070 | 84.4 | 82.5 |
20 | 50 | 4.38 | 10.87 | 470 | 0.312 | 0.095 | 88.4 | 86.6 |
27 | 58 | 5.4 | 10.71 | 590 | 0.307 | 0.117 | 90.4 | 88.5 |
35 | 65 | 6.62 | 10.52 | 725 | 0.302 | 0.143 | 91.2 | 89.3 |
40 | 67 | 7.04 | 10.42 | 780 | 0.299 | 0.152 | 92.2 | 90.4 |
50 | 75 | 8.7 | 10.19 | 955 | 0.292 | 0.188 | 92.7 | 90.8 |
56 | 80 | 9.65 | 10.03 | 1050 | 0.288 | 0.209 | 93.0 | 91.1 |
65 | 82 | 10.7 | 9.83 | 1150 | 0.282 | 0.232 | 93.1 | 91.3 |
72 | 85 | 11.8 | 9.62 | 1240 | 0.276 | 0.255 | 92.5 | 90.6 |
78 | 87 | 12.5 | 9.44 | 1290 | 0.271 | 0.270 | 91.9 | 90.0 |
80 | 90 | 13.3 | 9.39 | 1340 | 0.269 | 0.288 | 90.8 | 89.0 |
90 | 97 | 14.3 | 9 | 1410 | 0.258 | 0.309 | 90.3 | 88.4 |
Plant | Solution | D | n | H | Q | φ | ψ |
---|---|---|---|---|---|---|---|
[mm] | [rpm] | [m] | [m3/s] | [-] | [-] | ||
1 | 1 | 1500 | 333 | 333 | 11.05 | 0.317 | 0.292 |
2 | 2 | 950 | 300 | 300 | 4.6 | 0.405 | 0.284 |
3 | 3 | 1500 | 250 | 250 | 6.7 | 0.341 | 0.317 |
4 | 4 | 700 | 750 | 750 | 11.9 | 0.309 | 0.227 |
5 | 5 | 900 | 428 | 428 | 6.9 | 0.333 | 0.281 |
6 | 975 | 375 | 375 | 6.9 | 0.369 | 0.252 | |
7 | 850 | 428 | 428 | 6.9 | 0.373 | 0.278 | |
6 | 8 | 680 | 500 | 500 | 6.3 | 0.390 | 0.309 |
9 | 700 | 500 | 500 | 6.3 | 0.368 | 0.284 | |
7 | 10 | 1150 | 375 | 375 | 9.7 | 0.373 | 0.298 |
8 | 11 | 3500 | 75 | 75 | 3.7 | 0.384 | 0.302 |
9 | 12 | 1400 | 175 | 175 | 3.4 | 0.405 | 0.304 |
10 | 13 | 800 | 600 | 600 | 12.2 | 0.379 | 0.237 |
11 | 14 | 1800 | 231 | 231 | 7.5 | 0.310 | 0.271 |
12 | 15 | 1000 | 500 | 500 | 10.8 | 0.309 | 0.292 |
13 | 16 | 1450 | 250 | 250 | 6.2 | 0.338 | 0.319 |
14 | 17 | 1150 | 375 | 375 | 7.7 | 0.296 | 0.277 |
15 | 18 | 1600 | 250 | 250 | 6.6 | 0.295 | 0.285 |
16 | 19 | 1900 | 200 | 200 | 6.15 | 0.305 | 0.319 |
17 | 20 | 2100 | 187 | 187 | 5.9 | 0.274 | 0.329 |
18 | 21 | 2560 | 167 | 167 | 7 | 0.274 | 0.295 |
19 | 22 | 2950 | 136 | 136 | 7.8 | 0.347 | 0.258 |
23 | 2950 | 136 | 136 | 7.7 | 0.342 | 0.258 | |
24 | 2950 | 136 | 136 | 9.2 | 0.409 | 0.258 | |
25 | 2950 | 136 | 136 | 7.4 | 0.329 | 0.258 | |
26 | 2950 | 136 | 136 | 7.3 | 0.325 | 0.258 | |
27 | 2950 | 136 | 136 | 9.1 | 0.405 | 0.258 | |
28 | 2600 | 200 | 220 | 17.5 | 0.383 | 0.233 | |
20 | 29 | 950 | 375 | 375 | 6 | 0.338 | 0.310 |
21 | 30 | 740 | 375 | 375 | 4.25 | 0.395 | 0.280 |
22 | 31 | 920 | 333 | 333 | 4.6 | 0.351 | 0.281 |
23 | 32 | 3500 | 75 | 82 | 4.2 | 0.365 | 0.277 |
24 | 33 | 1250 | 428 | 428 | 14.1 | 0.353 | 0.291 |
34 | 1250 | 428 | 428 | 15 | 0.375 | 0.291 | |
35 | 1250 | 428 | 428 | 16.12 | 0.403 | 0.291 | |
25 | 36 | 540 | 600 | 600 | 5.5 | 0.375 | 0.257 |
37 | 540 | 600 | 600 | 5.5 | 0.375 | 0.257 | |
26 | 38 | 743 | 300 | 300 | 2.65 | 0.382 | 0.267 |
27 | 39 | 2747 | 187.5 | 187.5 | 12.5 | 0.337 | 0.288 |
28 | 40 | 1350 | 300 | 300 | 7.5 | 0.327 | 0.297 |
41 | 1550 | 250 | 250 | 7.5 | 0.357 | 0.235 | |
29 | 42 | 2550 | 120 | 140 | 5.9 | 0.331 | 0.241 |
30 | 43 | 670 | 500 | 500 | 5.3 | 0.338 | 0.323 |
31 | 44 | 550 | 750 | 750 | 9 | 0.379 | 0.292 |
32 | 45 | 850 | 500 | 500 | 10.3 | 0.408 | 0.277 |
33 | 46 | 5000 | 100 | 100 | 10.3 | 0.295 | 0.324 |
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Capata, R.; Calabria, A.; Baralis, G.M.; Piras, G. Experimental Fitting of Efficiency Hill Chart for Kaplan Hydraulic Turbine. Designs 2024, 8, 80. https://doi.org/10.3390/designs8040080
Capata R, Calabria A, Baralis GM, Piras G. Experimental Fitting of Efficiency Hill Chart for Kaplan Hydraulic Turbine. Designs. 2024; 8(4):80. https://doi.org/10.3390/designs8040080
Chicago/Turabian StyleCapata, Roberto, Alfonso Calabria, Gian Marco Baralis, and Giuseppe Piras. 2024. "Experimental Fitting of Efficiency Hill Chart for Kaplan Hydraulic Turbine" Designs 8, no. 4: 80. https://doi.org/10.3390/designs8040080