PARTICLE SWARM OPTIMIZATION-BASED DETERMINATION OF HYDRAULIC JUMP LOCATION IN SLUICE GATE FLOWS

Year 2025, Volume: 13 Issue: 3, 766 - 782, 01.09.2025

Ali Yıldız , Volkan Yılmaz

https://doi.org/10.36306/konjes.1652389

Abstract

The hydraulic jump is a critical phenomenon in open channel hydraulics, and understanding its behavior is essential for the design and safety of hydraulic structures. In this study, 96 experiments were conducted using five different gate openings to model the location of hydraulic jumps in an open channel. The Particle Swarm Optimization (PSO) algorithm, a metaheuristic optimization technique, was employed to develop both linear and nonlinear predictive models. Experimental data from gate openings (e) of 2.5 cm, 3.5 cm, 4 cm, and 5 cm were used to train the models, while data from a e=6 cm gate opening were used for testing. The results demonstrated that the PSO algorithm effectively modeled the hydraulic jump location, yielding high accuracy and consistency with experimental observations. Model performance was evaluated using the Coefficient of Determination (R²), Nash-Sutcliffe Efficiency (NSE), and Mean Squared Error (MSE). The linear model outperformed the nonlinear model, achieving NSE = 0.954, R² = 0.983, and MSE = 0.022. Furthermore, the upstream total head (H) and gate opening (e) were identified as the most influential parameters affecting the hydraulic jump location.

Keywords

Open Channel Hydraulics , Sluice Gate , Hydraulic Jump , Particle Swarm Optimization (PSO)

Ethical Statement

The authors declare that all ethical guidelines including authorship, citation, data reporting, and publishing original research are followed.

Supporting Institution

No Funding is received by authors

References

• K. Safranez, “Researches relating to the hydraulic jump,” English translation by DP Barnes, Bureau of Reclamation Files, Denver, CO, USA, File no. 37, 1929.
• A. J. Peterka, “Hydraulic Design of Stilling Basins and Energy Dissipators,” 8th ed., Engineering Monograph No. 25, United States Department of the Interior, Bureau of Reclamation, Denver, CO, USA, 1984.
• J. N. Bradley and A. J. Peterka, “Hydraulic Design of Stilling Basins: Hydraulic Jumps on a Horizontal Apron (Basin I),” Journal of the Hydraulics Division, vol. 83, no. 5, pp. 1401–1, Oct. 1957, doi: 10.1061/JYCEAJ.0000126.
• W. H. Hager, Energy Dissipators and Hydraulic Jump, Water Science and Technology Library, vol. 8. Dordrecht, Netherlands: Springer, 1992.
• U.S. Bureau of Reclamation, Design of Small Dams, 2nd ed. Washington, DC, USA: U.S. Government Printing Office, 1977.
• B. A. Bakhmeteff and A. E. Matzke, “The Hydraulic Jump in Terms of Dynamic Similarity,” Transactions of the American Society of Civil Engineers, vol. 101, no. 1, pp. 630–647, Jan. 1936, doi: 10.1061/TACEAT.0004708.
• M. Cihan Aydın and A. E. Ulu, “Journal of Science and Technology Numerical modelling of sluice gates with different baffle types under submerged flow conditions,” Bitlis Eren University Journal of Science and Technology, vol. 7, no. 1, pp. 1–6, 2017.
• G. Bidone, “Observations sur la hauteur du ressaut hydraulique en 1818,” report presented to the Academy of Sciences of Turin (in French), Turin, Italy, 1819.
• J.-B. Bélanger, Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes. Paris, France: École Royale des Ponts et Chaussées, 1828.
• A. G. Levy, J. W. Ellms, W. Gore, ve A. L. Fales, “The hydraulic jump as a mixing device,” Journal of the American Water Works Association, cilt 17, sayı 1, s. 1–26, 1927, doi:10.1002/j.1551-8833.1927.tb12673.x.
• H. Rouse, T. T. Siao, and S. Nagaratnam, “Turbulence Characteristics of the Hydraulic Jump,” Transactions of the American Society of Civil Engineers, vol. 124, no. 1, pp. 926–950, Jan. 1959, doi: 10.1061/TACEAT.0007738.
• R. Silvester, “Hydraulic Jump in All Shapes of Horizontal Channels,” Journal of the Hydraulics Division, vol. 90, no. 1, pp. 23–55, Jan. 1964, doi: 10.1061/JYCEAJ.0000977.
• N. Rajaratnam and K. Subramanya, “Profile of the Hydraulic Jump,” Journal of the Hydraulics Division, vol. 94, no. 3, pp. 663–674, May 1968, doi: 10.1061/JYCEAJ.0001810.
• W. H. Hager and R. Wanoschek, “Hydraulic jump in triangular channel,” Journal of Hydraulic Research, vol. 25, no. 5, pp. 549–564, 1987, doi: 10.1080/00221688709499255.
• B. M. Araz Gharangik and M. Hanif Chaudhry, “Numerical Simulation of Hydraulic Jump,” Journal of Hydraulic Engineering, vol. 117, no. 9, pp. 1195–1211, Sep. 1991, doi: 10.1061/(ASCE)0733-9429(1991)117:9(1195).
• S. A. Ead, M. Asce, N. Rajaratnam, and F. Asce, “Hydraulic Jumps on Corrugated Beds,” Journal of Hydraulic Engineering, vol. 128, no. 7, pp. 656–663, Jul. 2002, doi: 10.1061/(ASCE)0733-9429(2002)128:7(656).
• A. Habibzadeh, A. R. Vatankhah, and N. Rajaratnam, “Role of Energy Loss on Discharge Characteristics of Sluice Gates,” Journal of Hydraulic Engineering, vol. 137, no. 9, pp. 1079–1084, Sep. 2011, doi: 10.1061/(ASCE)HY.1943-7900.0000406
• Y. Kim, G. Choi, H. Park, and S. Byeon, “Hydraulic Jump and Energy Dissipation with Sluice Gate,” Water 2015, Vol. 7, Pages 5115-5133, vol. 7, no. 9, pp. 5115–5133, Sep. 2015, doi: 10.3390/W7095115.
• S. A. M. Movahed, J. Mozaffari, D. Davoodmaghami, and M. Akbari, “A Semi-Analytical Equation to Estimate Hydraulic Jump Length,” Periodica Polytechnica Civil Engineering, vol. 62, no. 4, pp. 1001–1006, Sep. 2018, doi: 10.3311/PPCI.11257.
• O. Simsek, M. S. Akoz, and N. G. S. Oksal, “Experimental analysis of hydraulic jump at high froude numbers,” Sadhana - Academy Proceedings in Engineering Sciences, vol. 48, no. 2, pp. 1–16, Jun. 2023, doi: 10.1007/S12046-023-02081-8/FIGURES/19.
• M. Naseri and F. Othman, “Determination of the length of hydraulic jumps using artificial neural networks,” Advances in Engineering Software, vol. 48, no. 1, pp. 27–31, Jun. 2012, doi: 10.1016/J.ADVENGSOFT.2012.01.003.
• M. H. Omid, M. Omid, and M. E. Varaki, “Modelling hydraulic jumps with artificial neural networks,” https://doi.org/10.1680/wama.2005.158.2.65, vol. 158, no. 2, pp. 65–70, May 2015, doi: 10.1680/WAMA.2005.158.2.65.
• M. Karbasi and H. M. Azamathulla, “GEP to predict characteristics of a hydraulic jump over a rough bed,” KSCE Journal of Civil Engineering, vol. 20, no. 7, pp. 3006–3011, Nov. 2016, doi: 10.1007/S12205-016-0821-X/METRICS.
• M. Karbasi, “Estimation of classical hydraulic jump length using teaching–learning based optimization algorithm,” Journal of Materials and Environmental Science, vol. 7, no. 8, pp. 2947–2954, 2016.
• E. Gul, O. F. Dursun, and A. Mohammadian, “Experimental study and modeling of hydraulic jump for a suddenly expanding stilling basin using different hybrid algorithms,” Water Supply, vol. 21, no. 7, pp. 3752–3771, Nov. 2021, doi: 10.2166/WS.2021.139.
• A. Yıldız, “Bent Kapağı Altından Geçen Akımın Oluşturduğu Hidrolik Sıçramanın Konumunun Deneysel ve Nümerik Olarak Belirlenmesi,” Black Sea Journal of Engineering and Science, vol. 7, no. 5, pp. 988–1000, Sep. 2024, doi: 10.34248/BSENGINEERING.1463296.
• P. K. Swamee, “SluiceGate Discharge Equations,” Journal of Irrigation and Drainage Engineering, vol. 118, no. 1, pp. 56–60, Jan. 1992, doi: 10.1061/(ASCE)0733-9437(1992)118:1(56).
• E. Kubrak, J. Kubrak, A. Kiczko, and M. Kubrak, “Flow Measurements Using a Sluice Gate; Analysis of Applicability,” Water 2020, Vol. 12, Page 819, vol. 12, no. 3, p. 819, Mar. 2020, doi: 10.3390/W12030819.
• J. Kennedy and R. Eberhart, “Particle swarm optimization,” Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4, pp. 1942–1948, 1995, doi: 10.1109/ICNN.1995.488968.
• X. Li and S. Li, “An adaptive surrogate-assisted particle swarm optimization for expensive problems,” Soft comput, vol. 25, no. 24, pp. 15051–15065, Dec. 2021, doi: 10.1007/S00500-021-06348-2/TABLES/6.
• Y. Shi and R. C. Eberhart, “Empirical study of particle swarm optimization,” Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 3, pp. 1945–1950, 1999, doi: 10.1109/CEC.1999.785511.
• E. Ozcan and C. K. Mohan, “Particle swarm optimization: Surfing the waves,” Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 3, pp. 1939–1944, 1999, doi: 10.1109/CEC.1999.785510.
• R. C. Eberhart and Y. Shi, “Particle swarm optimization: Developments, applications and resources,” Proceedings of the IEEE Conference on Evolutionary Computation, ICEC, vol. 1, pp. 81–86, 2001, doi: 10.1109/CEC.2001.934374.
• D. N. Moriasi, J. G. Arnold, M. W. Van Liew, R. L. Bingner, R. D. Harmel, and T. L. Veith, “Model Evaluation Guidelines for Systematic Quantification of Accuracy in Watershed Simulations,” Trans ASABE, vol. 50, no. 3, pp. 885–900, 2007, doi: 10.13031/2013.23153.