Numerical Evaluation of Turbulence Models for Velocity Distribution Simulation in Hydraulic Jumps

Öz

Hydraulic jumps in stilling basins are critical for dissipating the high kinetic energy of flows downstream of ogee spillways, mitigating risks of riverbed scouring and structural damage. This study employs computational fluid dynamics (CFD) using Flow-3D to simulate the velocity distribution of hydraulic jumps in a stilling basin with a smooth bed, under flow rates of 33–60 L/s and Froude numbers of 3–10. Four turbulence models—RNG, k-ε, k-ω, and LES—were evaluated to determine the most accurate model by comparing numerical results with experimental data from a 10 m long, 0.51 m wide laboratory flume. A mesh convergence study identified an optimal mesh size of 0.011 m, balancing accuracy and computational efficiency. The RNG turbulence model demonstrated superior performance, with the lowest relative error (RE = 5.41%) and absolute error (AE = 0.0065 m) for hydraulic head predictions, attributed to its robustness in capturing high-shear flows. These findings enhance the application of CFD in optimizing stilling basin designs for hydraulic structures.

Anahtar Kelimeler

• Hydraulic Jump
• ; Stilling Basin
• Turbulence Models
• Flow-3D
• RNG Model
• Energy Dissipation
• Velocity Distribution

Kaynakça

1. [1] Rajaratnam, N. (1965). The hydraulic jump as a well jet. Journal of the Hydraulics Division, 91(5) 107-132.
2. [2] Chanson, H. ed. Energy dissipation in hydraulic structures. CRC Press (2015).
3. [3] Vischer, D. and Hager, W.H. (1998). Dam hydraulics (Vol. 2). Chichester, UK: Wiley.
4. [4] Peterka, A.J. (1978). Hydraulic design of stilling basins and energy dissipators (No. 25). United States. Department of the Interior, Bureau of Reclamation. Engineering Monograph No. 25.
5. [5] Chaudhry, M.H. (2008). Open-channel flow. Boston, MA. Springer US.
6. [6] Mousavi, S.N., Júnior, R.S. and Teixeira, E.D. (2020). Predictive modeling the free hydraulic jumps pressure through advanced statistical methods. Mathematics, 8 1–18.
7. [7] Novak, P., Moffat, A.I.B., Nalluri, C. and Narayanan, R.A.I.B. (2017). Hydraulic structures. CRC Press.
8. [8] Chachereau, Y. and Chanson, H. (2011). Free-surface fluctuations and turbulence in hydraulic jumps. Experimental Thermal and Fluid Science, 35(6) 896-909.

9. [9] Bayon, A., Valero, D., García-Bartual, R. and López-Jiménez, P.A. (2016). Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environmental modelling & software, 80 322-335.
10. [10] Hirt, C.W. and Nichols, B.D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of computational physics, 39(1) 201-225.
11. [11] Bayon, A. and Lopez-Jimenez, P.A. (2015). Numerical analysis of hydraulic jumps using OpenFOAM. Journal of Hydroinformatics, 17(4) 662-678.
12. [12] Valero, D., Viti, N. and Gualtieri, C. (2019). Numerical simulation of hydraulic jumps. Part 1: Experimental data for modelling performance assessment. Water, 11(1) 36.
13. [13] Yakhot, V. and Orszag, S.A. (1986). Renormalization group analysis of turbulence. I. Basic theory. Journal of scientific computing, 1(1) 3-51.
14. [14] Wilcox, D.C. (1998). Turbulence modeling for CFD (Vol. 2, 103-217). La Canada, CA: DCW industries.
15. [15] Sagaut, P. (2006). Large eddy simulation for incompressible flows: An introduction (3rd ed.). Berlin, Heidelberg: Springer Berlin Heidelberg.
16. [16] Viti, N., Valero, D. and Gualtieri, C. (2019). Numerical simulation of hydraulic jumps. Part 2: Recent results and future outlook. Water, 11(1) 28.
17. [17] Daneshfaraz, R., Norouzi, R., Abbaszadeh, H., Kuriqi, A. and Di Francesco, S. (2022). Influence of sill on the hydraulic regime in sluice gates: an experimental and numerical analysis. Fluids, 7(7) 244.
18. [18] Abbaszadeh, H., Daneshfaraz, R. and Norouzi, R. (2023). Experimental investigation of hydraulic jump parameters in sill application mode with various synthesis. Journal of Hydraulic Structures, 1(1) 18-42.
19. [19] Daneshfaraz, R., Ghahramanzadeh, A., Ghaderi, A., Joudi, A.R. and Abraham, J. (2016). Investigation of the effect of edge shape on characteristics of flow under vertical gates. Journal‐American Water Works Association, 108(8) 425-432.
20. [20] Mousavi, S.N., Farsadizadeh, D., Salmasi, F., Dalir, A.H. and Bocchiola, D. (2020). Analysis of minimal and maximal pressures, uncertainty and spectral density of fluctuating pressures beneath classical hydraulic jumps. Water Supply, 20(5) 1909-1921.
21. [21] Mousavi, S.N., Farsadizadeh, D., Salmasi, F. and Hosseinzadeh Dalir, A. (2022). Evaluation of pressure fluctuations coefficient along the USBR Type II stilling basin using experimental results and AI models. ISH Journal of Hydraulic Engineering, 28 207-214.
22. [22] Mousavi, S.N., Apaydin, H., Sattari, M.T. and Abraham, J.P. (2024). Extreme pressure coefficients: modelling a hydraulic jump using deep-learning based methods. Sādhanā, 49(2) 151.
23. [23] Carvalho, R.F., Lemos, C.M. and Ramos, C.M. (2008). Numerical computation of the flow in hydraulic jump stilling basins. Journal of Hydraulic Research, 46(6) 739-752.
24. [24] Dasineh, M., Ghaderi, A., Bagherzadeh, M., Ahmadi, M. and Kuriqi, A. (2021). Prediction of hydraulic jumps on a triangular bed roughness using numerical modeling and soft computing methods. Mathematics, 9(23) 3135.
25. [25] Viti, N., Valero, D. and Gualtieri, C. (2019). Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water, 11(1) 28.
26. [26] Bayon, A., Macián-Pérez, J.F., Vallés-Morán, F.J. and López-Jiménez, P.A. (2019). Effect of RANS turbulence model in hydraulic jump CFD simulations. In Proceedings of the 38th IAHR World Congress, Panama City, Panama, September.1-6 (pp. 1-10).
27. [27] Bryant, D.J.E. and Ng, K.C. (2022). Numerical modelling of hydraulic jump using mesh-based CFD method and its comparison with Lagrangian moving-grid approach. Journal of Advanced Research in Micro and Nano Engineering, 10(1) 1-6.
28. [28] Macián-Pérez, J.F., García-Bartual, R., López-Jiménez, P.A. and Vallés-Morán, F.J., 2023. Numerical modeling of hydraulic jumps at negative steps to improve energy dissipation in stilling basins. Applied Water Science, 13(10), p.203.
29. [29] López Castaño, S. and Van Hoydonck, W. (2024). On the numerical resolution of hydraulic jumps: Algorithms, boundary conditions, and turbulence models. FH reports.
30. [30] Ghaderi, A., Daneshfaraz, R. and Abbasi, S. (2020). Numerical investigation of flow over spillways using Flow-3D. Journal of Hydraulic Structures, 6(3) 45-60.
31. [31] Roache, P.J. (1998). Verification and validation in computational science and engineering. Hermosa Publishers, Albuquerque, NM.
32. [32] Flow Science Inc. (2016). FLOW-3D V 11.2 User’s Manual; Flow Science: Santa Fe, NM, USA.
33. [33] Versteeg, H.K. and Malalasekera, W. (2007). An Introduction to computational fluid dynamics: The finite volume method. Pearson Education.
34. [34] Daneshfaraz, R., Aminvash, E., Esmaeli, R., Sadeghfam, S. and Abraham, J. (2020). Experimental and numerical investigation for energy dissipation of supercritical flow in sudden contractions. Journal of groundwater science and engineering, 8(4) 396-406.
35. [35] Daneshfaraz, R., Norouzi, R., & Ebadzadeh, P. (2022). Experimental and numerical study of sluice gate flow pattern with non-suppressed sill and its effect on discharge coefficient in free-flow conditions. Journal of Hydraulic Structures, 8(1), 1-20.
36. [36] Daneshfaraz, R., Sadeghfam, S., Adami, R., & Abbaszadeh, H. (2023). Numerical analysis of seepage in steady and transient flow state by the radial basis function method. Numerical Methods in Civil Engineering, 8(1), 58-68.
37. [37] Daneshfaraz, R., Norouzi, R., & Abbaszadeh, H. (2022). Experimental investigation of hydraulic parameters of flow in sluice gates with different openings. Environment and Water Engineering, 8(4), 923-939.
38. [38] Daneshfaraz, R., Norouzi, R., & Abbaszadeh, H. (2021). Numerical investigation on effective parameters on hydraulic flows in chimney proportional weirs. Iranian Journal of Soil and Water Research, 52(6), 1599-1616.
39. [39] Hassanzadeh, Y., Abbaszadeh, H., Abedi, A., & Abraham, J. (2024). Numerical simulation of the effect of downstream material on scouring-sediment profile of combined spillway-gate. AQUA—Water Infrastructure, Ecosystems and Society, 73(12), 2322-2343.
40. [40] Abbaszadeh, H., & Tarinejad, R. (2025). Soft Computing and Predicting Labyrinth Gates Discharge Coefficient. Water Resources, 52(4), 701-714.
41. [41] Ebadzadeh, P., Abbaszadeh, H., Daneshfaraz, R., & Abraham, J. (2025). Enhancing energy dissipation in stepped weirs: numerical analysis and machine learning of ANN, SVM and non-linear regression predictions. Multiscale and Multidisciplinary Modeling, Experiments and Design, 8(8), 345.
42. [42] Norouzi, R., Ebadzadeh, P., Sume, V., & Daneshfaraz, R. (2023). Upstream vortices of a sluice gate: An experimental and numerical study. AQUA—Water Infrastructure, Ecosystems and Society, 72(10), 1906-1919. [43] Abbaszadeh, H., Daneshfaraz, R., Sume, V., & Abraham, J. (2024). Experimental investigation and application of soft computing models for predicting flow energy loss in arc-shaped constrictions. AQUA—Water Infrastructure, Ecosystems and Society, 73(3), 637-661.
43. [44] Abbaszadeh, H., Ebadzadeh, P., Daneshfaraz, R., & Norouzi, R. (2024). Investigating and predicting hydraulic jump energy loss with threshold (Experimental and regression analysis). Journal of Hydraulic Structures, 10(2), 46-54.
44. [45] Daneshfaraz, R., Norouzi, R., Abbaszadeh, H., & Azamathulla, H. M. (2022). Theoretical and experimental analysis of applicability of sill with different widths on the gate discharge coefficients. Water Supply, 22(10), 7767-7781.
45. [46] Hassanzadeh, Y., & Abbaszadeh, H. (2023). Investigating discharge coefficient of slide gate-sill combination using expert soft computing models. Journal of Hydraulic Structures, 9(1), 63-80.
46. [47] Daneshfaraz, R., Abbaszadeh, H., & Aminvash, E. (2022). Theoretical and Numerical Analysis of Applicability‏ of Elliptical Cross-Section on Energy Dissipation of Hydraulic Jump. Türk Hidrolik Dergisi, 6(2), 22-35.
47. [48] Roushangar, K., Amanzadeh Aboueshagh, F., & Abbaszadeh, H. (2023). Numerical investigation of the influence of the combined seepage reduction scenarios on the hydraulic performance of the Alborz dam body. Iranian Journal of Soil and Water Research, 54(10), 1467-1483.
48. [49] Hager, W.H. and Li, D. (1992). Sill-controlled energy dissipator. Journal of Hydraulic Research, 30(2) 165-181.