1. Determining Optimal Discharge and Optimal Penstock Diameter in Water Turbines Arturo S. Leon, Ph.D., P.E., D.WRE School of Civil and Construction Engineering, Oregon State University 6th International Symposium on Hydraulic Structures Portland, OR, June 27-30, 2016 Starting on 09/01/2016, I will be at Department of Civil and Environmental Engineering, University of Houston

2. Acknowledgements: Financial support of the Bonneville Power Administration of the U.S. Department of Energy (DOE) under award number TIP#258.

3. Outline Background/Motivation Dimensional analysis Application Conclusions

4. Background/Motivation Three Gorges hydropower plant, China www.water-technology.net Hoover Dam, US www.hdrinc.com 16% of global electricity production came from hydropower in 2007

5. Background/Motivation (Cont.) Hydropower can provide flexibility and reliability for energy production in integrated systems. In combination with hydropower, diffuse sources (wind, wave, solar) can play a larger role in providing electrical power of commercial quality. http://www.lexisnexis.com/

6. Background/Motivation (Cont.) Theoretical framework for determining optimal design flow and penstock diameter for impulse and reaction turbines is NOT available in literature. https://upload.wikimedia.org/wikipe dia/commons/2/27/Gonbo_hydroele ctric_power_station_penstock.jpg https://upload.wikimedia.org/wiki pedia/commons/6/61/Tarraleah_ hydroelectric_penstocks.jpg

7. Electrical power (P) in water turbines 7

8. Electrical power (P) of impulse and reaction turbines (Cont.)

9. Dimensionless relationship between power and flow discharge (Cont.) Define reference power (P r ) P r is defined as maximum P with fixed C L and 100% effic.

10. Dimensionless relationship between power and flow discharge (Cont.)

11. 11 Impulse turbines (η = 0.8) Dimensionless discharge versus Power

12. Reaction turbines (η = 0.8) Dimensionless discharge versus Power

13. 13 Impulse turbines (η = 0.8) ΔP + /ΔQ + is small in [0, 0.8η] Dimensionless discharge versus Power

14. Determine optimal Q and optimal D 2 (Cont.) Minimizing water consumption Achieving large ΔP + with small ΔQ + Maximize ΔP + / ΔQ +

15. Determine optimal Q and optimal D 2 (Cont.) Optimal head loss h L+ (= h L / H g ) ≤ 15.6%

16. P is specified Q is specified Turbine design when P or Q is specified Max Min

17. Example: Impulse Turbine design

18. Impulse Turbine design (Cont.) Case 1: Design an impulse turbine with Q = 0.6 m 3 /s

19. Impulse Turbine design (Cont.)

20. MATLAB Toolbox for turbine design http://web.engr.oregonstate.edu/~le ona/Codes.html

21. CONCLUSIONS Various dimensionless relationships were derived for determining optimal design flow and penstock diameter when designing impulse and reaction turbines It was found that for minimizing water consumption, the ratio of head loss to gross head (h L /H g ) should not exceed 15%. To facilitate the calculations, a MATLAB hydropower toolbox was developed.

22. Arturo S. Leon Many thanks for your attention! Contact: https://upload.wikimedia.org/wikipedia/commons/7/73/Penstocks.jpg Starting on 09/01/2016, I will be at Department of Civil and Environmental Engineering, University of Houston