Computational Particle Mechanics

, Volume 4, Issue 3, pp 345–356 | Cite as

Air demand estimation in bottom outlets with the particle finite element method

Susqueda Dam case study
  • Fernando SalazarEmail author
  • Javier San-Mauro
  • Miguel Ángel Celigueta
  • Eugenio Oñate


Dam bottom outlets play a vital role in dam operation and safety, as they allow controlling the water surface elevation below the spillway level. For partial openings, water flows under the gate lip at high velocity and drags the air downstream of the gate, which may cause damages due to cavitation and vibration. The convenience of installing air vents in dam bottom outlets is well known by practitioners. The design of this element depends basically on the maximum air flow through the air vent, which in turn is a function of the specific geometry and the boundary conditions. The intrinsic features of this phenomenon makes it hard to analyse either on site or in full scaled experimental facilities. As a consequence, empirical formulas are frequently employed, which offer a conservative estimate of the maximum air flow. In this work, the particle finite element method was used to model the air–water interaction in Susqueda Dam bottom outlet, with different gate openings. Specific enhancements of the formulation were developed to consider air–water interaction. The results were analysed as compared to the conventional design criteria and to information gathered on site during the gate operation tests. This analysis suggests that numerical modelling with the PFEM can be helpful for the design of this kind of hydraulic works.


Particle finite element method Two fluids Bottom outlets Air demand 



The authors thank Felipe Río and Francisco J. Conesa, from ENDESA GENERACION, for supplying the information about Susqueda Dam and Francisco Riquelme for promoting this research. It was carried out with the financial support received from the FLOODSAFE project funded by the Proof of Concept Program of the European Research Council.


  1. 1.
    ANSYS Inc (2011) Ansys Fluent theory guideGoogle Scholar
  2. 2.
    Aubry R, Idelsohn S, Oñate E (2005) Particle finite element method in fluid-mechanics including thermal convection-diffusion. Comput Struct 83(17–18):1459–1475CrossRefGoogle Scholar
  3. 3.
    Campbell F, Guyton B (1953) Air demand in gated conduits. In: IAHR Symposium, MinneapolisGoogle Scholar
  4. 4.
    Carbonell JM, Oñate E, Suárez B (2009) Modeling of ground excavation with the particle finite-element method. J Eng Mech 136(4):455–463CrossRefGoogle Scholar
  5. 5.
    Chanson H (2013) Hydraulics of aerated flows: qui pro quo? J Hydraul Res 51(3):223–243CrossRefGoogle Scholar
  6. 6.
    Cheng SW, Dey TK, Shewchuk J (2012) Delaunay mesh generation. CRC Press, Boca RatonzbMATHGoogle Scholar
  7. 7.
    Edelsbrunner H, Mücke EP (1994) Three-dimensional alpha shapes. ACM Trans Gr 13(1):43–72CrossRefzbMATHGoogle Scholar
  8. 8.
    Erbisti PC (2014) Design of hydraulic gates. CRC Press, Boca ratonCrossRefGoogle Scholar
  9. 9.
    FEMA (2010) Outlet works energy dissipators. Tech. Rep. P–679Google Scholar
  10. 10.
    Frizell K (2004) Hydraulic model studies of aeration enhancements at the folsom dam outlet works: reducing cavitation damage potential. Water Oper Maint Bull 185:11–24Google Scholar
  11. 11.
    Hirt CW (2003) Modeling turbulent entrainment of air at a free surface. Flow Science Inc, LelandGoogle Scholar
  12. 12.
    Idelsohn S, Mier-Torrecilla M, Oñate E (2009) Multi-fluid flows with the particle finite element method. Comput Methods Appl Mech Eng 198(33):2750–2767CrossRefzbMATHGoogle Scholar
  13. 13.
    Idelsohn S, Nigro N, Limache A, Oñate E (2012) Large time-step explicit integration method for solving problems with dominant convection. Comput Methods Appl Mech Eng 217:168–185MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Idelsohn S, Oñate E, Del Pin F (2003) A Lagrangian meshless finite element method applied to fluid-structure interaction problems. Comput Struct 81(8):655–671CrossRefGoogle Scholar
  15. 15.
    Idelsohn S, Oñate E, Pin FD (2004) The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61(7):964–989MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Idelsohn SR, Marti J, Becker P, Oñate E (2014) Analysis of multifluid flows with large time steps using the particle finite element method. Int J Numer Methods Fluids 75(9):621–644MathSciNetCrossRefGoogle Scholar
  17. 17.
    Larese A, Rossi R, Oñate E, Idelsohn SR (2008) Validation of the particle finite element method (PFEM) for simulation of free surface flows. Eng Comput 25(4):385–425CrossRefzbMATHGoogle Scholar
  18. 18.
    Liu T, Yang J (2014) Three-dimensional computations of water-air flow in a bottom spillway during gate opening. Eng Appl Comput Fluid Mech 8(1):104–115Google Scholar
  19. 19.
    Oñate E, Idelsohn SR, Celigueta MA, Rossi R (2008) Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows. Comput Methods Appl Mech Eng 197(19):1777–1800MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Oñate E, Rossi R, Idelsohn SR, Butler KM (2010) Melting and spread of polymers in fire with the particle finite element method. Int J Numer Methods Eng 81(8):1046–1072zbMATHGoogle Scholar
  21. 21.
    Oñate E, Celigueta MA, Idelsohn SR (2006) Modeling bed erosion in free surface flows by the particle finite element method. Acta Geotech 1(4):237–252CrossRefGoogle Scholar
  22. 22.
    Oñate E, Celigueta MA, Idelsohn SR, Salazar F, Suárez B (2011) Possibilities of the particle finite element method for fluid-soil-structure interaction problems. Comput Mech 48(3):307–318MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Oñate E, Franci A, Carbonell JM (2014) Lagrangian formulation for finite element analysis of quasi-incompressible fluids with reduced mass losses. Int J Numer Methods Fluids 74(10):699–731MathSciNetCrossRefGoogle Scholar
  24. 24.
    Oñate E, Franci A, Carbonell JM (2014) A particle finite element method for analysis of industrial forming processes. Comput Mech 54(1):85–107MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Oñate E, Idelsohn S (2004) The particle finite element method. an overview. Int J Comput Methods 1:267–307CrossRefzbMATHGoogle Scholar
  26. 26.
    Pozo D, Salazar F, Toledo M (2014) Modeling the hydraulic performance of the aeration system in dam bottom outlets using the particle finite element method. Rev Int Métodos Numér para Cálc Diseño Ing 30(1): 51–59 (in Spanish)Google Scholar
  27. 27.
    Ribó R, Pasenau M, Escolano E, Ronda J, González L (1998) GiD reference manual. CIMNE, BarcelonaGoogle Scholar
  28. 28.
    Riquelme F, Morán R, Salazar F, Celigueta M, Oñate E (2011) Flat-seat round-section valves: design criteria and performance analysis via numerical modelling. In: Dam maintenance and rehabilitation II, CRC Press, pp. 609–615 (in Spanish)Google Scholar
  29. 29.
    Safavi K, Zarrati A, Attari J (2008) Experimental study of air demand in high head gated tunnels. In: Proceedings of the Institution of Civil Engineers-Water Management, vol 161. Thomas Telford Ltd, pp. 105–111Google Scholar
  30. 30.
    Sagar B (1995) Asce hydrogates task committee design guidelines for high-head gates. J Hydraul Eng 121(12):845–852CrossRefGoogle Scholar
  31. 31.
    Salazar F, Irazábal J, Larese A, Oñate E (2015) Numerical modelling of landslide-generated waves with the particle finite element method (PFEM) and a non-Newtonian flow model. Int J Numer Anal Methods Geomech 40:809–826CrossRefGoogle Scholar
  32. 32.
    Salazar F, Oñate E, Morán R (2012) Numerical modelling of landslides in reservoirs via the particle finite element method (PFEM). Rev Int Métodos Numér para Cál Diseño Ing 28(2):112–123 (in Spanish)Google Scholar
  33. 33.
    Sharma HR (1976) Air-entrainment in high head gated conduits. J Hydraul Div 102(11):1629–1646Google Scholar
  34. 34.
    Spanish National Comittee on Large Dams (SPANCOLD) (1997) Dam safety technical guide n. 5 spillways and bottom outlets. Colegio de Ingenieros de Caminos, Canales y Puertos (in Spanish)Google Scholar
  35. 35.
    The particle finite element method—PFEM.
  36. 36.
    Toombes L, Chanson H (2007) Free-surface aeration and momentum exchange at a bottom outlet. J Hydraul Res 45(1):100–110CrossRefGoogle Scholar
  37. 37.
    Tullis BP, Larchar J (2011) Determining air demand for small-to medium-sized embankment dam low-level outlet works. J Irrig Drain Eng 137(12):793–800CrossRefGoogle Scholar
  38. 38.
    USACE (1964) Hydraulic design criteria, air demand, regulated outlet works. US Army Corps of Engineer, Washington DCGoogle Scholar
  39. 39.
    Valero D, García-Bartual R (2016) Calibration of an air entrainment model for cfd spillway applications. In: Gourbesville P, Cunge J, Caignaert G (eds) Advances in hydroinformatics. Springer, Singapore, pp 571–582CrossRefGoogle Scholar
  40. 40.
    Vischer D, Hager WH, Cischer D (1998) Dam hydraulics. Wiley, ChichesterGoogle Scholar
  41. 41.
    Wright N, Tullis B (2014) Prototype and laboratory low-level outlet air demand comparison for small-to-medium-sized embankment dams. J Irrig Drain Eng 140(6):04014013CrossRefGoogle Scholar
  42. 42.
    Zienkiewicz OC, Taylor RL (2005) The finite element method for solid and structural mechanics. Butterworth-Heinemann, BostonzbMATHGoogle Scholar

Copyright information

© OWZ 2016

Authors and Affiliations

  • Fernando Salazar
    • 1
    Email author
  • Javier San-Mauro
    • 1
  • Miguel Ángel Celigueta
    • 1
  • Eugenio Oñate
    • 1
  1. 1.Centre International de Mètodes Numèrics en Enginyeria (CIMNE)Universitat Politècnica de Catalunya (UPC)BarcelonaSpain

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