Numerical modeling of skimming flow in a stepped channel with vertical curves
DOI:
https://doi.org/10.24850/j-tyca-2025-02-02Keywords:
Skimming flow, stepped channel, stepped spillway, vertical curves, computational fluid dynamics (CFD), turbulence, turbulent dissipationAbstract
Stepped channels are frequently used for the discharge of water in reservoirs, however, there are few studies that consider the implementation of curves at their bottom. This article presents a quantitative evaluation, using numerical modeling with computational fluid dynamics (CFD), of the properties of skimming flow in steep stepped chutes with vertical curves. The stepped geometry was defined with a convex curve at the inlet, an intermediate straight chute, and a concave curve at the outlet. A comparative analysis was performed on the velocity, pressure, vorticity, and turbulence statistics fields in the three sections of the channel. It was concluded that the velocity profiles obtained with the RNG k-ε turbulence model presented a good agreement with experimental measurements in the non-aerated flow zone. However, the correlation decreased downstream since the numerical model did not capture the aeration phenomenon. When comparing the hydrodynamic behavior in both stepped curves, it was found that the separation zone covered a greater fraction of each step in the convex curve. In the latter, negative pressure values were observed at the height of the upper corner of the risers, which were not present in the concave curve. Finally, the turbulent dissipation maxima were found near the bottom in the final section of the treads, and on the border between the main stream and the recirculating flow of each step, being higher for the outlet curve.
References
Amador, A., Sánchez-Juny, M., & Dolz, J. (2006). Characterization of the nonaerated flow region in a stepped spillway by PIV. Journal of Fluids Engineering, 128(6), 1266. DOI: 10.1115/1.2354529
Ansys Inc. (2022). ANSYS Fluent User’s Guide (Vol. 2022 R2).
Arjenaki, M. O., & Sanayei, H. R. Z. (2020). Numerical investigation of energy dissipation rate in stepped spillways with lateral slopes using experimental model development approach. Modeling Earth Systems and Environment, 6(2), 605-616. DOI: 10.1007/S40808-020-00714-Z/METRICS
Ashoor, A., & Riazi, A. (2019). Stepped spillways and energy dissipation: A non-uniform step length approach. Applied Sciences, 9(23), 5071. DOI: 10.3390/app9235071
Attari, J., & Sarfaraz, M. (2012). Transitional steps zone in steeply sloping stepped spillways. 9th International Congress on Civil Engineering, 9. Recuperado de https://civilica.com/doc/165678/certificate/print/
Boes, R. M., & Hager, W. H. (2003). Two-phase flow characteristics of stepped spillways. Journal of Hydraulic Engineering, 129(9), 661-670. DOI: 10.1061/(ASCE)0733-9429(2003)129:9(661)
Bombardelli, F. A., Meireles, I., & Matos, J. (2011). Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways. Environmental Fluid Mechanics, 11(3), 263-288. DOI: 10.1007/S10652-010-9188-6/METRICS
Bureau of Reclamation. (1987). Design of small dams (3rd ed.). Washington, DC: US Government Printing Office. Recuperado de https://www.usbr.gov/tsc/techreferences/mands/mands-pdfs/SmallDams.pdf
Casa, E., Hidalgo, X., Castro, M., Ortega, P., & Vera, P. (2018). Modelación numérica del flujo rasante en una rápida escalonada aplicando la dinámica de fluidos computacional (CFD) mediante el uso de Flow-3D. Revista Politécnica, 41(2), 53-64. Recuperado de https://revistapolitecnica.epn.edu.ec/ojs2/index.php/revista_politecnica2/article/view/823
Chahed, J., Roig, V., & Masbernat, L. (2003). Eulerian-Eulerian two-fluid model for turbulent gas–liquid bubbly flows. International Journal of Multiphase Flow, 29(1), 23-49. DOI: 10.1016/S0301-9322(02)00123-4
Chanson, H. (1994). Hydraulics of skimming flows over stepped channels and spillways. Journal of Hydraulic Research, 32(3), 445-460. DOI: 10.1080/00221689409498745
Chanson, H. (2001). Hydraulic design of stepped spillways and downstream energy dissipators. Dam Engineering, 11(4), 205-242.
Chanson, H., & Toombes, L. (2004). Hydraulics of stepped chutes: The transition flow. Journal of Hydraulic Research, 42(1), 43-54.
Cheng, X., Luo, L., Zhao, W., & Li, R. (2004). Two-phase flow simulation of aeration on stepped spillway. Progress in Natural Science, 14(7), 626-630. DOI: 10.1080/10020070412331344051
Chinnarasri, C., & Wongwises, S. (2006). Flow patterns and energy dissipation over various stepped chutes. Journal of Irrigation and Drainage Engineering, 132(1), 70-76. DOI: 10.1061/(ASCE)0733-9437(2006)132:1(70)
Cifani, P., Michalek, W. R., Priems, G. J. M., Kuerten, J. G. M., van der Geld, C. W. M., & Geurts, B. J. (2016). A comparison between the surface compression method and an interface reconstruction method for the VOF approach. Computers & Fluids, 136, 421-435. DOI: 10.1016/J.COMPFLUID.2016.06.026
Dalili-Khanghah, K., & Kavianpour, M. R. (2020). Numerical investigation of the effect of CEDEX profile on the hydraulic parameters in the stepped spillway and the performance of this profile in various chute slopes. Iranian Journal of Science and Technology - Transactions of Civil Engineering, 44(4), 1247-1254. DOI: 10.1007/S40996-019-00313-8/FIGURES/8
Escue, A., & Cui, J. (2010). Comparison of turbulence models in simulating swirling pipe flows. Applied Mathematical Modelling, 34(10), 2840-2849. DOI: 10.1016/J.APM.2009.12.018
Gonzalez, C. A. (2005). An experimental study of free-surface aeration on embankment stepped chutes. Recuperado de https://espace.library.uq.edu.au/view/UQ:158019
Greenshields, C. (2022). OpenFOAM v10 User Guide. London, UK: The OpenFOAM Foundation. Recuperado de https://doc.cfd.direct/openfoam/user-guide-v10
Greenshields, C., & Weller, H. (2022). Notes on computational fluid dynamics: General principles. Reading, UK: CFD Direct Ltd. Recuperado de https://doc.cfd.direct/notes/cfd-general-principles/index/
Henrique-Povh, P., & Junji-Ota, J. (2019). Transition stretch of spillways with bevelled steps. 38th IAHR World Congress - ‘Water: Connecting the World’, 38, 1520-1528. DOI: 10.3850/38WC092019-1065
Hirt, C. W. (2003). Modeling turbulent entrainment of air at a free surface. Technical Note 61(FSi-03-TN61). Pasadena, USA: Flow Science Inc.
Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201-225. DOI: 10.1016/0021-9991(81)90145-5
Hunt, S., & Kadavy, K. (2010a). Energy dissipation on flat sloped stepped spillways: Part 1. Upstream of the inception point. Transactions of the American Society of Agricultural and Biological Engineers, 53(1), 103-109.
Hunt, S., & Kadavy, K. (2010b). Energy dissipation on flat sloped stepped spillways: Part 2. Downstream of the inception point. Transactions of the American Society of Agricultural and Biological Engineers, 53(1), 111-118.
Kundu, P. K., Cohen, I. M., & Dowling, D. R. (2012). Fluid Mechanics (5th ed.). Oxford, UK: Elsevier Inc. DOI: 10.1016/C2009-0-63410-3
Llano, S. (2003). Hydraulics of Stepped structures - importance of flow regimes on stepped chutes and practical application in developing countries. Delft, Netherlands: IHE Delft Institute for Water Education.
Matos, J., Frizell, K. H., André, S., & Frizell, K. W. (2002). On the performance of velocity measurement techniques in air-water flows. In: Hydraulic measurements and experimental methods 2002 (pp. 1-11). Reston, USA: American Society of Civil Engineers. DOI: 10.1061/40655(2002)58
Medhi, B. J., Singh, A., Thokchom, A. K., & Mahapatra, S. (2019). Experimental and computational study on flow over stepped spillway. Journal of Mechanical Science and Technology, 33(5), 2101-2112. DOI: 10.1007/S12206-019-0116-5/METRICS
Nikseresht, A. H., Talebbeydokhti, N., & Rezaei, M. J. (2013). Numerical simulation of two-phase flow on step-pool spillways. Scientia Iranica, 20(2), 222–230. DOI: 10.1016/j.scient.2012.11.013
Orszag, S. A., Yakhot, V., Flannery, W. S., & Boysan, F. (1993). Renormalization group modeling and turbulence simulations. On near-wall turbulent flows. Near-wall turbulent flows: Proceedings of the International Conference on Near-Wall Turbulent Flows, Tempe, Arizona, USA, 15-17 March 1993, Elsevier Publishing Company.
Saqib, N. U., Akbar, M., Pan, H., Ou, G., Mohsin, M., Ali, A., & Amin, A. (2022). Numerical analysis of pressure profiles and energy dissipation across stepped spillways having curved risers. Applied Sciences 2022, 12(1), 448. DOI: 10.3390/APP12010448
Sarkardeh, H., Marosi, M., & Roshan, R. (2015). Stepped spillway optimization through numerical and physical modeling. International Journal of Energy and Environment, 6(6), 597-606. Recuperado de https://www.ijee.ieefoundation.org/
Sotelo-Ávila, G. (2002). Hidráulica de Canales. México, DF, México: Facultad de Ingeniería, Universidad Nacional Autónoma de México.
Tabbara, M., Chatila, J., & Awwad, R. (2005). Computational simulation of flow over stepped spillways. Computers & Structures, 83(27), 2215-2224. DOI: 10.1016/j.compstruc.2005.04.005
Versteeg, H. K., & Malalasekera, W. (2007). An introduction to computational fluid dynamics: The finite volume method. Harlow, England: Pearson Education Ltd.
Wang, F. F., Wu, S. Q., & Zhu, S. L. (2019). Numerical simulation of flow separation over a backward-facing step with high Reynolds number. Water Science and Engineering, 12(2), 145-154. DOI: 10.1016/J.WSE.2019.05.003
Wilcox, D. C. (2006). Turbulence modeling for CFD (3rd ed.). La Cañada, California: DCW Industries, Inc.
Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B., & Speziale, C. G. (1992). Development of turbulence models for shear flows by a double expansion technique. Physics of Fluids A, 4(7), 1510-1520. DOI: 10.1063/1.858424
Zare, H. K., & Doering, J. C. (2012). Effect of rounding edges of stepped spillways on the flow characteristics. Canadian Journal of Civil Engineering, 39(2), 140-153. DOI: 10.1139/L11-121
Zhan, J., Zhang, J., & Gong, Y. (2016). Numerical investigation of air-entrainment in skimming flow over stepped spillways. Theoretical and Applied Mechanics Letters, 6(3), 139-142. DOI: 10.1016/J.TAML.2016.03.003
Zuhaira, A. A., Al-Hamd, R. K. S., Alzabeebee, S., & Cunningham, L. S. (2021). Numerical investigation of skimming flow characteristics over non-uniform gabion-stepped spillways. Innovative Infrastructure Solutions, 6(4). DOI: 10.1007/S41062-021-00579-W
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