Hydraulic Optimization of Double Chamber Surge Tank Using NSGA-II
Abstract
:1. Introduction
2. Material and Methods
2.1. Governing Equations
2.2. Method of Characteristics
2.3. Boundary Conditions
2.3.1. Surge Tank
2.3.2. Valve in Line
2.4. Modeling
2.5. Objective Functions
2.5.1. Upsurge
2.5.2. Downsurge
2.5.3. Damping
2.6. Variables and Constraints
2.7. NSGA-II
3. Results and Discussions
3.1. Surge Analysis
3.2. Sensitivity Analysis
3.3. Optimization
3.4. Operational Stage
4. Conclusions
- Steady state water level and safety criteria governed the location of the lower chamber and the upper chamber. The surge shaft was provided with a minimum possible area required by Thoma criteria for the economic design of the chamber surge tank. Thus, diameter of orifice (), diameter of upper chamber (), and length of lower chamber (L) were taken as the variables for optimization of the double chamber surge tank;
- Sensitivity analysis of these variables shows that did not have any effect in downsurge, and L did not have any effect in upsurge. Water level in the surge tank and damping of surge waves during downsurge and upsurge had conflicting behaviors for and L, whereas the lower value of was favorable. Further, the calculation of sensitivity indicated the was more sensitive on objectives functions. However, at the time of the worst upsurge, to maintain the maximum piezometric head in the bottom tunnel at the orifice and the maximum water level in the upper chamber of the surge tank at nearly equal levels, and had to be optimized to find the optimum ratio between the pressure amplitudes from the water hammer and the mass oscillations;
- The NSGA-II optimized the values of , , and L with a notable improvement in maximum and minimum water levels in the double chamber surge tank with viable damping of surge waves. The double chamber surge tank served as an effective limiter of maximum amplitudes of oscillation. Further, the total volume of the optimized double chamber surge tank was only 44.53% of the total volume of the simple surge tank. Hence, by providing effective throttling with an optimum volume of chambers, damping could be improved, and a huge amount of volume of surge tank could be decreased;
- In the hydropower system with multiple units, controlling the water level oscillation in surge tank is a major issue. The most effective operation mode should be adopted to limit the amplitude of surge in the surge tank. Surge can be killed by acceptance of load in multiple stages.
Author Contributions
Funding
Conflicts of Interest
References
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Pipe Segment | Diameter (m) | Length (m) | No. of Segment (Nj) | Δx (m) |
---|---|---|---|---|
L01 | 5.5 | 236.0 | 23 | 10.26 |
L02 | 5.5 | 3850.7 | 385 | 10.00 |
L03 | 4.8 | 119.8 | 11 | 10.89 |
L04 | 2.5 | 47.4 | 4 | 11.85 |
L05 | 4.0 | 11.0 | 1 | 11.00 |
L06 | 2.5 | 40.3 | 4 | 10.08 |
L07 | 3.3 | 11.0 | 1 | 11.00 |
L08 | 2.5 | 37.4 | 3 | 12.47 |
L09 | 2.8 | 11.9 | 1 | 11.90 |
L10 | 4.0 | 108.6 | 10 | 10.86 |
L11 | 4.0 | 107.8 | 10 | 10.78 |
L12 | 4.0 | 107.0 | 10 | 10.70 |
Water Level (m) | Area of Surge Tank (m2) |
---|---|
70.88 | |
70.88 | |
Variable | Upsurge | Downsurge | ||
---|---|---|---|---|
7.3 | 0.0006 | 4 | 0.0007 | |
−3.6 | 0.0001 | 0 | 0 | |
L | 0 | 0 | −0.36 | 0.0001 |
Opt. | Pop. No. | Variable | Objective Function | Gen | |||||
---|---|---|---|---|---|---|---|---|---|
Upsurge | Downsurge | ||||||||
L (m) | |||||||||
30 | 2.81 | 12.30 | 249.374 | 0.002648 | 135 | ||||
I | 40 | 2.80 | 12.26 | 249.400 | 0.002656 | 105 | |||
50 | 2.80 | 12.23 | 249.419 | 0.002657 | 115 | ||||
30 | 20.04 | 183.254 | 0.002372 | 120 | |||||
II | 40 | 20.00 | 183.245 | 0.002375 | 109 | ||||
50 | 20.17 | 183.275 | 0.002365 | 165 |
Objective Function | SST | DCST |
---|---|---|
Upsurge (m) | 248.427 | 249.400 |
Downsurge (m) | 183.245 | 183.245 |
Volume (m3) | 16208.9 | 7219.1 |
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Dhakal, R.; Zhou, J.; Palikhe, S.; Bhattarai, K.P. Hydraulic Optimization of Double Chamber Surge Tank Using NSGA-II. Water 2020, 12, 455. https://doi.org/10.3390/w12020455
Dhakal R, Zhou J, Palikhe S, Bhattarai KP. Hydraulic Optimization of Double Chamber Surge Tank Using NSGA-II. Water. 2020; 12(2):455. https://doi.org/10.3390/w12020455
Chicago/Turabian StyleDhakal, Resham, Jianxu Zhou, Sunit Palikhe, and Khem Prasad Bhattarai. 2020. "Hydraulic Optimization of Double Chamber Surge Tank Using NSGA-II" Water 12, no. 2: 455. https://doi.org/10.3390/w12020455
APA StyleDhakal, R., Zhou, J., Palikhe, S., & Bhattarai, K. P. (2020). Hydraulic Optimization of Double Chamber Surge Tank Using NSGA-II. Water, 12(2), 455. https://doi.org/10.3390/w12020455