Journal of Hydrodynamics

, Volume 29, Issue 2, pp 322–331 | Cite as

The effects of step inclination and air injection on the water flow in a stepped spillway: A numerical study

  • Khadidja KherbacheEmail author
  • Xavier Chesneau
  • Belkacem Zeghmati
  • Stéphane Abide
  • Saâdia Benmamar


In this work, we perform a numerical study of a water flow over a stepped spillway. This flow is described by the Reynolds averaged Navier-Stokes equation (RANS) associated with the turbulence k-ε model. These equations are solved using a commercial software based on the finite volume scheme and an unstructured mesh. The air-water flow was modeled using volume of fluid (VOF) and multiphasic methods. The characteristics of the flow were investigated including the total pressure, the velocity profile, etc.. We analyze the effects on the flow structure of the steps and countermarch inclination, the air injection through the countermarch into the water flow and the dynamics water discharges. Results show that the inclination of the countermarch relative to the vertical and the air injection into the water flow increase the total pressure in the neighbourhood of the steps.

Key words

Stepped spillway turbulence air-water air injection volume of fluid (VOF) method multiphasic method 


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  1. [1]
    Chen Q., Dai G., Liu H. Volume of fluid model for turbulence numerical simulation of stepped spillway overflow [J]. Journal of Hydraulic Engineering, ASCE, 2002, 128(7): 683–688.CrossRefGoogle Scholar
  2. [2]
    Sánchez-Juny M. Hydraulic behavior of stepped spillway in compacted concrete dams. Analysis of the pressure field [D]. Doctoral Thesis, Barcelona, Spain: Universitat Politècnica de Catalunya, 2001 (in Spainish).Google Scholar
  3. [3]
    Felder S., Chanson H. Energy dissipation down a stepped spillway with non-uniform step heights [J]. Journal of Hydraulic Engineering, ASCE, 2011, 137(11): 1543–1548.CrossRefGoogle Scholar
  4. [4]
    Felder S., Chanson H. Energy dissipation and air entrainment on stepped spillway with Non-uniform cavity sizes [C]. 34th IAHR world congress-Balance and uncertainty, 33rd Hydrology et water resources symposium, 10th Hydraulics conference. Brisbane, Australia, 2011, 2412–2419.Google Scholar
  5. [5]
    Dermawan V., Anwar N. Hydraulic model of flow conditions on stepped spillway due to number of steps [J]. International Journal of Academic Research, 2010, 2(5): 200–205.Google Scholar
  6. [6]
    Pfister M., Chanson H. Two-phase air-water flows: Scale effects in physical modeling [J]. Journal of Hydrodynamics, 2014, 26(2): 291–298.CrossRefGoogle Scholar
  7. [7]
    Pfister M., Hager W. H. History and significance of the Morton number in hydraulic engineering [J]. Journal of Hydraulic Engineering, ASCE, 2014, 140(2): 02514001.Google Scholar
  8. [8]
    Cheng X. J., Cheng Y. C., Luo L. Numerical simulation of air-water two-phase flow over stepped spillways [J]. Science in China Series E: Technological Sciences, 2016, 49(6): 674–684.CrossRefGoogle Scholar
  9. [9]
    Qian Z. D., Hu X. Q., Huai W. X. et al. Numerical simulation and analysis of water flow over stepped spillways [J]. Science in China Series E: Technological Sciences, 2009, 52(7): 1958–1965.CrossRefGoogle Scholar
  10. [10]
    Meireles I., Bombardelli F., Matos J. Experimental testing and numerical simulation of the non-aerated skimming flow over steeply sloping stepped spillways [C]. 33rd IAHR Congress. Vancouver, Canada, 2009, 1972–1979.Google Scholar
  11. [11]
    Bombardelli F. A., Meireles I., Matos J. Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways [J]. Environmental Fluid Mechanics, 2011, 11(3): 263–288.CrossRefGoogle Scholar
  12. [12]
    Chinnarasri C., Kositgittiwong D., Julien P. Model of flow over spillways by computational fluid dynamics [J]. Proceedings of the Institute of Civil Engineers-Water Management, 2014, 167(3): 164–175.CrossRefGoogle Scholar
  13. [13]
    Sabbagh-Yazdi S. R., Safahieh R., Mastorakis N. E. Postprocessing of air entrainment on nasir flow solver results for skimming flow over stepped chutes [C]. 9th WSEAS International Conference on Automatic Control, Modeling and Simulation (ACMOS’07). Istanbul, Turkey, 2007.Google Scholar
  14. [14]
    Ahadian J., Aghamajidi R. Investigation of geometric effect of steps on energy dissipation on stepped spillway [J]. Applied mathematics in Engineering, Management and Technology, 2014, 2(2): 491–503.Google Scholar
  15. [15]
    Chen Q., Dai G. Q., Zhu F. Q. et al. Three-dimensional turbulence numerical simulation of a stepped spillway overflow [J]. Journal of Hydrodynamics, Ser. B, 2002, 14(3): 70–75.Google Scholar
  16. [16]
    Chen Q., Dai G. Q., Liu H. Numerical simulation for the stepped spillway overflow with turbulence model [J]. Journal of Hydrodynamics, Ser. B, 2002, 14(2): 58–63.Google Scholar
  17. [17]
    Fratino U., Amador A., Valenzano B. et al. Air inception and pressure fields over a stepped spillway in transition flow regime [C]. XXX IAHR Congress, AUTh. Thessaloniki, Greece, 2003, 711–718.Google Scholar
  18. [18]
    Chanson H. Hydraulic design of stepped spillways and downstream energy dissipaters [J]. Dam Engineering, 2001, 11(4): 205–242.Google Scholar
  19. [19]
    Amador A., Sánchez-Juny M., Dolz J. Characterization of the non-aerated flow region in a stepped spillway by PIV [J]. Journal of Fluids Engineering, 2006, 128(6): 1266–1273.CrossRefGoogle Scholar
  20. [20]
    Bung Daniel B. Developing flow in skimming flow regime on embankment stepped spillways [J]. Journal of Hydraulic Research, 2011, 49(5): 639–648.CrossRefGoogle Scholar
  21. [21]
    Guenther F., Felder S., Chanson H. Flow aeration, cavity processes and energy dissipation on flat and pooled stepped spillways for embankments [J]. Environmental Fluid Mechanics, 2013, 13(5): 503–525.CrossRefGoogle Scholar
  22. [22]
    Wei W. R., Deng J., Zhang F. X. et al. A numerical model for air concentration distribution in self-aerated open channel flows [J]. Journal of Hydrodynamics, 2015, 27(3): 394–402.CrossRefGoogle Scholar
  23. [23]
    Dong Z. Y., Lee J. H. W. Numerical simulation of skimming flow over mild stepped channel [J]. Journal of Hydrodynamics, Ser. B, 2006, 18(3): 367–371.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Chen Q., Dai G. Q., Zhu F. Q. Influencing factors for the energy dissipation ratio of stepped spillways [J]. Journal of Hydrodynamics, Ser. B, 2005, 17(1): 50–57.Google Scholar
  25. [25]
    Eghbalzadeh A., Javan M. Comparaison of mixture and VOF model for numerical simulation of air entrainment in skimming flow over stepped spillwas [J]. Procedia Engineering, 2012, 28: 657–660.CrossRefGoogle Scholar
  26. [26]
    Kherbache K. Contribution to the study of water flow on a stepped spillway [D]. Doctoral Thesis, Perpignan, France: Université de Perpignan Via Domitia, 2014 (in France).Google Scholar

Copyright information

© China Ship Scientific Research Center 2017

Authors and Affiliations

  • Khadidja Kherbache
    • 1
    • 2
    Email author
  • Xavier Chesneau
    • 1
  • Belkacem Zeghmati
    • 1
  • Stéphane Abide
    • 1
  • Saâdia Benmamar
    • 2
  1. 1.LAboratoire de Mathématiques et de PhySique (LAMPS) EA4217Université de Perpignan Via Domitia (UPVD)PerpignanFrance
  2. 2.Ecole Nationale PolytechniqueLaboratoire de Recherche des Sciences de l’eauAlgerAlgérie

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