Numerical Simulation of Flow over Stepped Spillways with Varying Step-Angle

Source:
By:Mohsen Nasrabadi, Younes Aminpour

DOI: https://doi.org/10.30564/hsme.v2i2.2341

Abstract:

In the present study, the flow over the stepped spillway was numerically investigated by using Flow3D model. The effect of step angle on different properties of Nappe flow regime such as the water surface profile, location of free-surface aeration inception, Froude number at the spillway’s toe, and pressure, flow velocity, air concentration and cavitation index were evaluated. The realizable k–ε was applied as the turbulence model, and Volume of Fluid (VOF) model was used to determine the free surface flow profiles of the spillway. The model was verified using experimental data. In order to investigate the different characteristics of Nappe flow regime, 17 numerical runs was designed, in which,four step angles, four flow discharge were considered to investigate the flow characteristics over the stepped spillway. The results indicated that the numerical model is well suited with the experimental data over the stepped spillway (RMSE = 0.147 and ARE = 6.9%). In addition, with increasing the step angles, the aeration inception point is generally moved downstream. By increasing the step angles from zero to 10 degrees, the Froude number does not change significantly, however, at the angle of 15 degrees, the Froude number decreases by about 42 percent.

References:

[1]Sorensen, R. M. Stepped spillway hydraulic model investigation. Journal of Hydraulic Engineering, 1985, 111(12): 1461-72. https://doi.org/10.1061/(ASCE)0733- 9429(1985)111:12(1461) [2]Chen, Q., Guangqing, D., Haowu, L. Volume of fluid model for turbulence numerical simulation of stepped spillway overflow. Journal of Hydraulic Engineering, 2002, 128(7): 683-688. https://doi.org/10.1061/(ASCE)0733- 9429(2002)128:7(683) [3]Amador, A. M. S. J., Josep, D. Characterization of the nonaerated flow region in a stepped spillway by PIV. J. Fluids Eng., 2006, 128(6): 1266-1273. https://doi.org/10.1115/1.2354529. [4]Bai, Z., Yurong, W., Jianmin, Z. Pressure distributions of stepped spillways with different horizontal face angles. the Proceedings of the Institution of Civil Engineers- Water Management, 2018, 171(6): 1-12. https://doi.org/10.1680/jwama.16.00093 [5]Christodoulou, G. C. Energy dissipation on stepped spillways. Journal of Hydraulic Engineering, 1993, 119(5): 644-650. https://doi.org/10.1061/(ASCE)0733- 9429(1993)119:5(644) [6]Chen, Q., Guang-Qing, D., Fen-Qin, Z. Influencing factors for the energy dissipation ratio of stepped spillways. Journal of Hydrodynamics, Series B, 2005, 17(1): 50-57. [7]Chinnarasri, C., Wongwises, S. Flow patterns and energy dissipation over various stepped chutes. Journal of irrigation and drainage engineering, 2006, 132(1): 70-76. https://doi.org/10.1061/(ASCE)0733- 9437(2006)132:1(70) [8]Gonzalez, C. A., Masayuki, T., Hubert, C. An experimental study of effects of step roughness in skimming flows on stepped chutes. Journal of Hydraulic Research, 2008, 46(sup1), 24-35. https://doi.org/10.1080/00221686.2008.9521937 [9]Felder, S., Hubert, C. Closure to “Energy Dissipation down a Stepped Spillway with Nonuniform Step Heights. by Stefan Felder and Hubert Chanson”, Journal of Hydraulic Engineering, 2012, 138(10): 921. h t t p s : / / d o i . o rg / 1 0 . 1 0 6 1 / ( A S C E ) H Y. 1 9 4 3 - 7900.0000611 [10]Zare, H. K., John, C. D. Energy dissipation and flow characteristics of baffles and sills on stepped spillways. Journal of Hydraulic Research, 2012, 50(2): 192-9. https://doi.org/10.1080/00221686.2012.659840 [11]Otun, J. A., Munta, S., Adie, D.B. Modelling flow over stepped spillway with varying chute geometry. Nigerian Journal of Technology, 2012, 31(2): 206-12. [12]Aras, E., Mehmet B. Effects of tailwater depth on spillway aeration. Water SA, 2012, 38(2): 307-12. https://doi.org/10.4314/wsa.v38i2.16 [13]Munta, S., Otun, J. A. Study of the Inception Length of Flow over Stepped Spillway Models. Nigerian Journal of Technology, 2014, 33(2): 176-83. https://doi.org/10.4314/njt.v33i2.6 [14]Falvey, H. T. Cavitation in chutes and spillways. US Department of the Interior, Bureau of Reclamation Denver, 1990. [15]Savage, B. M., Michael, J. Flow over ogee spillway: Physical and numerical model case study. Journal of Hydraulic Engineering, 2001, 127(8): 640-9. https://doi.org/10.1061/(ASCE)0733- 9429(2001)127:8(640) [16]Tabbara, M., Jean C., Rita A. Computational simulation of flow over stepped spillways. Computers & Structures, 2005, 83(27): 2215-24. https://doi.org/10.1016/j.compstruc.2005.04.005 [17]Kositgittiwong, D., Chinnarasr, C., Julien, P. Y. Numerical simulation of flow velocity profiles along a stepped spillway. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2013, 227(4): 327-35. https://doi.org/10.1177%2F0954408912472172 [18]Rafi, M., Akhtar, A., Ghulam, Q., Rafaquat, A. Modeling the Mangla dam spillway for cavitation and aerators optimization. Journal of Water Resource and Protection, 2012, 4(12): 1051. http://dx.doi.org/10.4236/jwarp.2012.412121 [19] Shahheydari, H., Jafari Nodoshan, E., Barati, R., Azhdary Moghadam, M. Discharge coefficient and energy dissipation over stepped spillway under skimming flow regime”, KSCE Journal of Civil Engineering, 2015, 19(4), 1174-82. doi 10.1007/s12205-013-0749-3 [20] Dursun, O. F., Ozturk, M. Determination of flow characteristics of stepped spillways. The Proceedings of the Institution of Civil Engineers-Water Management, 2016, 169(1): 30-42. https://doi.org/10.1680/wama.14.00120 [21] Chinnarasri, C., Kositgittiwong, D., Julien, P. Y. Model of flow over spillways by computational fluid dynamics. The Proceedings of the Institution of Civil Engineers-Water Management, 2014, 167(3): 164- 175. https://doi.org/10.1680/wama.12.00034 [22] Bayon, A., Toro, J. P., Bombardelli, F. A., Matos, J., and López-Jiménez, P. A. Influence of VOF technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated, skimming flow in stepped spillways. Journal of hydro-environment research, 2018, 19: 137-49. https://doi.org/10.1016/j.jher.2017.10.002 [23] Wan, H., Li, R., Gualtieri, C., Yang, H., Feng, J. Numerical simulation of hydrodynamics and reaeration over a stepped spillway by the SPH method. Water, 2017, 9(8): 565. https://doi.org/10.3390/w9080565 [24] Shih, T. H., Liou, W. W., Shabbir, A., Yang, Z., Zhu, J. A new k-epsilon eddy viscosity model for high Reynolds number turbulent flows: Model development and validation. Computers & Fluids, 1994, 24(3): 227-238. [25] Qian, Z. D., Hu X. Q., Huai W. X., Amador A. Numerical simulation and analysis of water flow over stepped spillways. Science in China Series E: Technological Sciences, 2009, 52(7): 1958-65. doi: 10.1007/s11431-009-0127-z [26] Essery, I. T. S., Horner, M. W. The hydraulic design of stepped spillways, Report 33 Constr. Industry Res. and Information Assoc., London, England, 1978.