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Numerical simulation and analysis of water flow over stepped spillways. (English) Zbl 1422.76098
Summary: Numerical simulation of water flow over the stepped spillway is conducted using Mixture multiphase flow model. Different turbulence models are chosen to enclose the controlling equations. The turbulence models investigated are realizable \(k-\varepsilon \) model, SST \(k-\omega \) model, \(v ^{2}-f\) model and LES model. The computational results by the four turbulence models are compared with experimental ones in the following aspects: mean velocity, the spanwise vorticity and the growth of the turbulent boundary layer thickness in the streamwise direction. It is found from the comparison that the realizable \(k-\varepsilon \) model, in which the rotation tensor is included, shows good performance for simulation of flows involving rotation, boundary layer and recirculation. The realizable \(k-\varepsilon \) model is the most efficient in simulating flow over stepped spillways. Further, the characteristics of water flow on the stepped spillway are studied in terms of the mean velocity profile normal to the pseudo-bottom and the pressure field on the steps based on the simulation results using realizable \(k-\varepsilon \) model.

MSC:
76F60 \(k\)-\(\varepsilon\) modeling in turbulence
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[1] Essery I, Homer M. The hydraulic design of stepped spillways. 2nd ed. CIRIA Report No. 33, London, 1978
[2] Chanson H. Hydraulics of stepped spillways: Current status. J Hydraul Eng, 2000, 126(9): 636–637 · doi:10.1061/(ASCE)0733-9429(2000)126:9(636)
[3] Chanson H. The Hydraulics of Stepped Chutes and Spillways. Lisse: Swets & Zeitlinger, 2001
[4] Chanson H, Toombes L. Air water flows down stepped chutes: turbulence and flow structure observations. Int J Multiphase Flow, 2002, 28(11): 1737–1761 · Zbl 1137.76547 · doi:10.1016/S0301-9322(02)00089-7
[5] Chamani M R, Rajaratnam N. Characteristics of skimming flow over stepped spillways. J Hydraul Eng, 1999, 125(4): 361–368 · doi:10.1061/(ASCE)0733-9429(1999)125:4(361)
[6] Pfister M, Hager W H, Minor H E. Bottom aeration of stepped spillways. J Hydraul Eng, 2006, 132(8): 850–853 · doi:10.1061/(ASCE)0733-9429(2006)132:8(850)
[7] Baylar A, Emiroglu M E, Bagatur T. An experimental investigation of aeration performance in stepped spillways. Water Environ J, 2006, 20(1): 35–42 · doi:10.1111/j.1747-6593.2005.00009.x
[8] Matos J. Air Entrainment and Energy Dissipation on Flow Over Stepped Spillways (in Portuguese). Dissertation of Doctoral Degree. Lisbon: Technical University of Lisbon, 1999
[9] Chinnarasri C, Wongwises S. Flow patterns and energy dissipation over various stepped chutes. J Irrig Drain Eng, 2006, 132(1): 70–76 · doi:10.1061/(ASCE)0733-9437(2006)132:1(70)
[10] Ohtsu I, Yasuda Y, Takahashi M. Flow characteristics of skimming flows in stepped channels. J Hydraul Eng, 2004, 130(9): 860–869 · doi:10.1061/(ASCE)0733-9429(2004)130:9(860)
[11] Pfister M, Hager W H. Bottom aeration of stepped spillway. J Hydraul Eng, 2006, 132(8): 850–853 · doi:10.1061/(ASCE)0733-9429(2006)132:8(850)
[12] Pfister M, Hager W H. Stepped chutes: Pre-aeration and spray reduction. Int J Multiphase Flow, 2006, 32(2): 269–284 · Zbl 1135.76519 · doi:10.1016/j.ijmultiphaseflow.2005.10.004
[13] Juny M S, Bladé E, Dolz J. Pressures on a stepped spillway. J Hydraul Res, 2007, 45(4): 505–511 · doi:10.1080/00221686.2007.9521785
[14] Zamora A S, Pfister M, Hager W H. Hydraulic performance of step aerator. J Hydraul Eng, 2008, 134(2): 127–134 · doi:10.1061/(ASCE)0733-9429(2008)134:2(127)
[15] Boes R M, Minor H E. Guidelines for the hydraulic design of stepped spillways. In: Proceedings of International Workshop on Hydraulics of Stepped Spillways. Zurich: Balkema Publishers, 2000
[16] Boes R M, Hager W H. Two-phase flow characteristics of stepped spillways. J Hydraul Eng, 2003, 129(9): 661–670 · doi:10.1061/(ASCE)0733-9429(2003)129:9(661)
[17] Chen Q, Dai G Q, Liu H W. Numerical simulation of overflow in stepped spillway (in Chinese). J Hydraul Eng, 2002, 33(9): 20–26
[18] Cheng X J, Luo L, Zhao W Q, et al. Numerical simulation of characteristics of free-surface aeration on stepped spillway (in Chinese). J Hydrodynam Ser A, 2004, 19(2): 152–157
[19] Cheng X J, Chen Y C, Luo L. Numerical simulation of air-water two-phase flow over stepped spillways. Sci China Ser E-Tech Sci, 2006, 49(6): 674–684 · Zbl 1176.76133 · doi:10.1007/s10288-006-2029-2
[20] Shih T, Liou W, Shabbir A, et al. A new k- eddy-viscosity model for high reynolds number turbulent flows-model development and validation. Comput Fluids, 1995, 24(3): 227–238 · Zbl 0825.76304 · doi:10.1016/0045-7930(94)00032-T
[21] Menter F R. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J, 1994, 32(8): 269–289 · doi:10.2514/3.12149
[22] Rumsey C L. Apparent transition behavior of widely-used turbulence models. Int J Heat Fluid Flow, 2007, 28(6): 1460–1471 · doi:10.1016/j.ijheatfluidflow.2007.04.003
[23] Durbin P A. Separated flow computations with the k–v 2 model. AIAA J, 1995, 33(4): 659–664 · doi:10.2514/3.12628
[24] Smagorinsky J. General circulation experiments with the primitive equations. I. The basic experiment. Mon Weather Rev, 1963, 91(3): 99–164 · doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2
[25] Peterka A J. The effect of entrained air on cavitation pitting. In: the 5th IAHR Congress. Minneapolis: IAHR, 1953
[26] Amador A. Characterization of the nonaerated flow region in a stepped spillway by PIV. J Fluids Eng, 2006, 128(6): 1266–11273 · doi:10.1115/1.2354529
[27] Chen Q G, Xu Z H, Zhang Y J. Advances in numerical studies of turbulent impinging jet flow and heat transfer (in Chinese). Adv Mech, 2002, 32(1): 92–108
[28] Luo J, Razinsky E H. Conjugate heat transfer analysis of a cooled turbine vane using the V2F tuibulence model. J Turbomach, 2006, 129(4): 773–781 · doi:10.1115/1.2720483
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