Hydrodynamic Loads in a Stilling Basin of a Converging Stepped Spillway: An Experimental Study
Abstract
:1. Introduction
2. Methodology
2.1. Hydrodynamic Load Characterization
2.2. Dimensional Analysis
2.3. Scale Models
- small steps (s = 4.5 cm), labelled as “S”,
- large steps (s = 9 cm), labelled as “L”,
- no convergence cm, labelled as “0”,
- small convergence angle cm, labelled as “1”,
- medium convergence angle cm, labelled as “2”,
- large convergence angle cm, labelled as “3”,
2.4. Measurements
3. Results and Discussion
3.1. Pressure Distribution at the Bottom
3.2. Pressure Distribution on the Wall
3.3. Estimating Hydrodynamic Load
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Boes, R.M.; Hager, W.H. Hydraulic Design of Stepped Spillways. J. Hydraul. Eng. 2003, 129, 671–679. [Google Scholar] [CrossRef]
- Chanson, H. Hydraulics of Stepped Chutes and Spillways, 1st ed.; Balkema: Lisse, The Netherlands, 2002; p. 424. ISBN 9789058093523. [Google Scholar]
- Khatsuria, R.M. Hydraulics of Spillways and Energy Dissipators, 1st ed.; CRC Press: Boca Raton, FL, USA, 2004; p. 680. ISBN 9780824757892. [Google Scholar]
- Ljubicic, R.; Zindovic, B.; Vojt, P.; Pavlovic, D.; Kapor, R.; Savic, L. Hydraulic Jumps in Adverse-Slope Stilling Basins for Stepped Spillways. Water 2018, 10, 460. [Google Scholar] [CrossRef]
- Schleiss, A.J.; Erpicum, S.; Matos, J. Energy dissipation in stilling basins with side jets from highly convergent chutes. Water 2023, 12, 2161. [Google Scholar] [CrossRef]
- Stojnic, I. Stilling Basin Performance Downstream of Stepped Spillways. Ph.D. Thesis, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 2020. [Google Scholar]
- Ruff, J.F.; Ward, J.P. Hydraulic Design of Stepped Spillways; Report 99FC800156; U.S. Bureau of Reclamation: Denver, CO, USA, 2002; p. 245.
- Zindovic, B.; Vojt, P.; Kapor, R.; Savic, L. Converging stepped spillway flow. J. Hydraul. Res. 2016, 6, 699–707. [Google Scholar] [CrossRef]
- Moran, R.; Toledo, M.A.; Peraita, J.; Pellegrino, R. Energy dissipation in stilling basins with side jets from highly convergent chutes. Water 2021, 13, 1343. [Google Scholar] [CrossRef]
- Morera, L.; San Mauro, J.; Salazar, F.; Toledo, M.Á. Highly-converging chutes as an overtopping protection for concrete dams: Physical and numerical modelling. In Proceedings of the 1st International Seminar on Dam Protections against Overtopping and Accidental Leakage, Madrid, Spain, 24–25 November 2014; pp. 245–257. [Google Scholar]
- Toso, J.W.; Bowers, E. Extreme Pressures in Hydraulic-Jump Stilling Basins. J. Hydraul. Eng. 1988, 8, 829–843. [Google Scholar] [CrossRef]
- Melo, J.F.; Pinheiro, A.N.; Ramos, C.M. Forces on plunge pool slabs: Influence of joints location and width. J. Hydraul. Eng. 2006, 132, 49–60. [Google Scholar] [CrossRef]
- Peterka, A.J. Hydraulic Design of Stilling Basins and Energy Dissipators, 8th ed.; United States Bureau of Reclamation: Denver, CO, USA, 1984; p. 225.
- Sánchez-Juny, M.; Dolz, J. Experimental study of transition and skimming flows on stepped spillways in RCC dams: Qualitative analysis and pressure measurements. J. Hydraul. Res. 2005, 5, 540–548. [Google Scholar] [CrossRef]
- Bellin, A.; Fiorotto, V. Direct Dynamic Force Measurement on Slabs in Spillway Stilling Basins. J. Hydraul. Eng. 1995, 10, 686–693. [Google Scholar] [CrossRef]
- Fiorotto, V.; Rinaldo, A. Turbulent pressure fluctuations under hydraulic jumps. J. Hydraul. Res. 1992, 4, 499–520. [Google Scholar] [CrossRef]
- Farhoudi, J.; Narayanan, R. Force on Slab Beneath Hydraulic Jump. J. Hydraul. Eng. 1991, 1, 64–82. [Google Scholar] [CrossRef]
- Hajdin, G. Estimate of the fluctuating load on solid surfaces based on the pressure measurements in a finite number of gauging points. In Proceedings of the Yugoslav Society of Hydraulic Engineers, Portoroz, Yugoslavia, 2–4 December 1982. [Google Scholar]
- Vasiliev, O.F.; Bukreyev, V.I. Statistical Characteristics of Pressure Fluctuations in the Region of Hydraulic Jump. In Proceedings of the 12th IAHR Congress, Fort Collins, CO, USA, 11–14 September 1967. [Google Scholar]
- Castillo, L.G.; Carrillo, J.M. Pressure and Velocity Distributions in Plunge Pools. In Proceedings of the 2nd International Seminar on Dam Protection against Overtopping, Fort Collins, CO, USA, 7–9 September 2016. [Google Scholar]
- Stojnic, I.; Pfister, M.; Matos, J.; Schleiss, A.J. Plain Stilling Basin Performance below 30° and 50° Inclined Smooth and Stepped Chutes. Water 2022, 14, 3976. [Google Scholar] [CrossRef]
- Valentin, G.; Volkart, P.U.; Minor, H.E. Energy dissipation along stepped spillways. In Hydraulics of Dams and River Structures; Yazdandoost, F., Attari, J., Eds.; Taylor & Francis: Boca Raton, FL, USA, 2004; pp. 273–278. ISBN 9789058096326. [Google Scholar]
- Milovanovic, B. Hydrodynamic Loads on the Evacuation Facilities of Hydraulic Structures. Ph.D. Thesis, Faculty of Civil Engineering, University of Belgrade, Belgrade, Serbia, 2018. [Google Scholar]
- Ljubicic, R.; Vicanovic, I.; Zindovic, B.; Kapor, R.; Savic, L. Image processing for hydraulic jump free-surface detection: Coupled gradient/machine learning model. Meas. Sci. Technol. 2020, 31, 104003. [Google Scholar] [CrossRef]
- Novak, P.; Moffat, A.I.B.; Nalluri, C.; Narayanan, R. Hydraulic Structures, 4th ed.; Taylor & Francis: Abingdon, UK, 2006; p. 700. ISBN 9780415386265. [Google Scholar]
- Amador, A.; Sánchez-Juny, M.; Dolz, J. Developing Flow Region and Pressure Fluctuations on Steeply Sloping Stepped Spillways. J. Hydraul. Eng. 2009, 12, 1092–1100. [Google Scholar] [CrossRef]
(a) Entire Slab | (b) Upstream Slab | (c) Downstream Slab | |
---|---|---|---|
0.759 | 0.647 | 0.836 | |
0.134 | 0.179 | 0.1 | |
0.081 | 0.087 | 0.031 | |
0.837 | 0.523 | ||
0.406 | 0.929 | ||
0.478 | 0.617 | ||
m | |||
n | 0.25 | 0.25 | 0.2 |
(a) Entire Slab | (b) Upstream Slab | (c) Downstream Slab | |
---|---|---|---|
0.07 | 0.115 | 0.059 | |
0 | 0 | 0.04 | |
0.152 | 0.158 | ||
0.005 | 0.341 | 0.743 | |
0.437 | |||
9.007 | 9.434 | 5.33 | |
k |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Milovanovic, B.; Vojt, P.; Zindovic, B.; Kuzmanovic, V.; Savic, L. Hydrodynamic Loads in a Stilling Basin of a Converging Stepped Spillway: An Experimental Study. Water 2024, 16, 140. https://doi.org/10.3390/w16010140
Milovanovic B, Vojt P, Zindovic B, Kuzmanovic V, Savic L. Hydrodynamic Loads in a Stilling Basin of a Converging Stepped Spillway: An Experimental Study. Water. 2024; 16(1):140. https://doi.org/10.3390/w16010140
Chicago/Turabian StyleMilovanovic, Bojan, Predrag Vojt, Budo Zindovic, Vladan Kuzmanovic, and Ljubodrag Savic. 2024. "Hydrodynamic Loads in a Stilling Basin of a Converging Stepped Spillway: An Experimental Study" Water 16, no. 1: 140. https://doi.org/10.3390/w16010140
APA StyleMilovanovic, B., Vojt, P., Zindovic, B., Kuzmanovic, V., & Savic, L. (2024). Hydrodynamic Loads in a Stilling Basin of a Converging Stepped Spillway: An Experimental Study. Water, 16(1), 140. https://doi.org/10.3390/w16010140