Environmental Fluid Mechanics

, Volume 12, Issue 6, pp 495–513 | Cite as

Numerical simulation of particle-driven gravity currents

  • Sangdo An
  • Pierre Y. Julien
  • Subhas K. Venayagamoorthy
Original Article

Abstract

Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG) \({k-\epsilon}\) scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG \({k-\epsilon}\) and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration Co/Ci by the gravity current varies as a function of the particle diameter ds. We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (ds is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm < ds<40 μm) where deposition rates significantly change the flow dynamics; and (3) a deposition regime (ds > 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG \({k-\epsilon}\) turbulence closure scheme for field scale investigation of particle-driven gravity currents.

Keywords

Gravity currents Density currents Buoyant forces Computational fluid dynamics (CFD) Lock-exchange flows Particle settling Environmental fluid mechanics 

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References

  1. 1.
    Altinakar MS, Graf WH, Hopfinger EJ (1990) Weakly depositing turbidity current on a small slope. J Hydraul Res 28(1): 55–80CrossRefGoogle Scholar
  2. 2.
    An SD (2011) Interflow dynamics and three-dimensional modeling of turbid density currents in Imha Reservoir, South Korea. Ph.D. dissertation in Department of Civil and Environmental Engineering, Colorado State UniversityGoogle Scholar
  3. 3.
    Benjamin TB (1968) Gravity currents and related phenomena. J Fluid Mech 31: 209–248CrossRefGoogle Scholar
  4. 4.
    Britter RE, Simpson JE (1981) A note on the structure of the head of an intrusive gravity current. J Fluid Mech 112: 459–466CrossRefGoogle Scholar
  5. 5.
    Cantero MI, Balachandar S, García MH (2008) An Eulerian-Eulerian model for gravity currents driven by inertial particles. Int J Multiphase Flow 34: 484–501CrossRefGoogle Scholar
  6. 6.
    Cheong HB, Kuenen JJ, Linden PF (2006) The front speed of intrusive gravity currents. J Fluid Mech 552: 1–11CrossRefGoogle Scholar
  7. 7.
    Choi SU, García MH (2002) \({k-\epsilon}\) turbulence modeling of density currents developing two dimensionally on a slope. J Hydraul Eng ASCE 128(1): 55–63CrossRefGoogle Scholar
  8. 8.
    Chung SW, Gu R (1998) Two-dimensional simulations of contaminant currents in stratified reservoir. J Hydraul Eng ASCE 124(7): 704–711CrossRefGoogle Scholar
  9. 9.
    De Cesare G, Schleiss A, Hermann F (2001) Impact of turbidity currents on reservoir sedimentation. J Hydraul Eng ASCE 127(1): 6–16CrossRefGoogle Scholar
  10. 10.
    De Cesare G, Boillat G, Schleiss A (2006) Circulation in stratified lake due to flood-induced turbidity currents. J Environ Eng ASCE 132(11): 1508–1517CrossRefGoogle Scholar
  11. 11.
    Faust KM, Plate EJ (1984) Experimental investigation of intrusive gravity currents entering stably stratified fluids. J Hydraul Res 22: 315–325CrossRefGoogle Scholar
  12. 12.
    FLOW-3D release 9.3: (2007) User guide and manual. Flow Science Inc, Santa FeGoogle Scholar
  13. 13.
    Fringer OB, Gerritsen MG, Street RL (2006) An unstructured-grid, finite-volume, nonhydrostatic, parallel coastal ocean simulator. Ocean Modell 14: 139–173CrossRefGoogle Scholar
  14. 14.
    Georgoulas A, Angelidis B, Panagiotidis T, Kotsovinos N (2010) 3D numerical modelling of turbidity currents. J Environ Fluid Mech 10: 603–635CrossRefGoogle Scholar
  15. 15.
    Gill AE (1982) Atmosphere-ocean dynamics. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. Academic Press, New YorkGoogle Scholar
  16. 16.
    Gladstone C, Phillips JC, Sparks RSJ (1998) Experiments on bidisperse, constant-volume gravity currents: propagation and sediment deposition. Sedimentology 45(5): 833–843CrossRefGoogle Scholar
  17. 17.
    Hallworth MA, Huppert HE (1998) Abrupt transitions in high-concentration, particle-driven gravity currents. Phys Fluids 10(5): 1083–1087CrossRefGoogle Scholar
  18. 18.
    Härtel C, Meiburg E, Necker F (2000) Analysis and direct numerical simulation of the flow at a gravity-current head, Part I, Flow topology and front speed for slip and no-slip boundaries. J Fluid Mech 418: 189–212CrossRefGoogle Scholar
  19. 19.
    Heimsund S (2007) Numerical simulation of turbidity currents: a new perspective for small- and large scale sedimentological experiments. Master thesis in Sedimentology/Petroleum Geology Department of Earth Science University of BergenGoogle Scholar
  20. 20.
    Hirt CW (1993) Volume-fraction techniques: powerful tools for wind engineering. J Wind Eng Ind Aerodyn 46&47: 327–338CrossRefGoogle Scholar
  21. 21.
    Hirt CW, Nichols BD (1981) Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys 39: 1–11CrossRefGoogle Scholar
  22. 22.
    Holyer JY, Huppert HE (1980) Gravity currents entering a two-layer fluid. J Fluid Mech 100(04): 739–767CrossRefGoogle Scholar
  23. 23.
    Huppert HE (2006) Gravity currents: a personal perspective. J Fluid Mech 554: 299–322CrossRefGoogle Scholar
  24. 24.
    Keulegan GH (1957) Thirteenth progress report on model laws for density currents an experimental study of the motion of saline water from locks into fresh water channels. U.S. Natl Bur Standards Rept 5168Google Scholar
  25. 25.
    Lesieur M, Metais O, Comte P (2005) Large-eddy simulations of turbulence. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  26. 26.
    Lowe RJ, Linden PF, Rottman JW (2002) A laboratory study of the velocity structure in an intrusive gravity current. J Fluid Mech 456: 33–48CrossRefGoogle Scholar
  27. 27.
    McCaffrey WD, ChouxCM Baas JH, Haughton P (2003) Spatio-temporal evolution of velocity structure, concentration and grain size stratification within experimental particulate gravity currents. Mar Petrol Geol 20: 851–860CrossRefGoogle Scholar
  28. 28.
    Middleton GV (1966) Experiments on density and turbidity currents: I. Motion of the head. Can J Earth Sci NRC Research Press 3(5): 627–637CrossRefGoogle Scholar
  29. 29.
    Necker F., Hartel C., Kleiser L., Meiburg E. (2002) High-resolution simulations of particle-driven gravity currents. Int J Multiphase Flow 28: 279–300CrossRefGoogle Scholar
  30. 30.
    Ooi SK, Constantinescu G, Weber L (2007) A numerical study of intrusive compositional gravity currents. Phys Fluids 19: 076602. doi:10.1063/1.2750672 CrossRefGoogle Scholar
  31. 31.
    Parker G, Fukushima Y, Pantin HM (1986) Self accelerating turbidity currents. J Fluid Mech 171: 145–181CrossRefGoogle Scholar
  32. 32.
    Pope SB (2000) Turbulent flows. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  33. 33.
    Rodi W (1980) Turbulence models and their application in hydraulics-A state of the art review. Int Assoc Hydraul Res Public, 2nd edn. BalkemaGoogle Scholar
  34. 34.
    Rooij F, Linden PF, Dalziel SB (1999) Saline and particle-driven interfacial intrusions. J Fluid Mech 389: 303–334CrossRefGoogle Scholar
  35. 35.
    Schmitt FG (2007) About Boussiness turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. Comptes Rendus Mécanique 335(9&10): 617–627CrossRefGoogle Scholar
  36. 36.
    Shin JO, Dalziel SB, Linden PF (2004) Gravity currents produced by lock exchange. J Fluid Mech 521: 1–34CrossRefGoogle Scholar
  37. 37.
    Simpson JE (1987) Gravity currents: in the environment and the laboratory. Cambridge University Press, CambridgeGoogle Scholar
  38. 38.
    Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Wea Rev 91: 99–164CrossRefGoogle Scholar
  39. 39.
    Sutherland BR, Kyba PJ, Flynn MR (2004) Intrusive gravity currents in two-layer fluids. J Fluid Mech 514: 327–353CrossRefGoogle Scholar
  40. 40.
    Turner JS (1979) Buoyancy effects in fluids. Cambridge University Press, CambridgeGoogle Scholar
  41. 41.
    Ungarish M (2009) An introduction to gravity currents and intrusions. CRC Press, Boca RatonCrossRefGoogle Scholar
  42. 42.
    Ungarish M, Huppert HE (2004) On gravity currents propagating at the base of a stratified ambient: effects of geometrical constraints and rotation. J Fluid Mech 521: 69–104CrossRefGoogle Scholar
  43. 43.
    Von Kármán T (1940) The engineer grapples with nonlinear problems. Bull Am Math Soc 46(8): 615–684CrossRefGoogle Scholar
  44. 44.
    Yakhot V, Orszag SA (1986) Renormalization group analysis of turbulence. I. Basic theory. J Sci Comput 1(1): 3–51CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Sangdo An
    • 1
  • Pierre Y. Julien
    • 1
  • Subhas K. Venayagamoorthy
    • 1
  1. 1.Department of Civil and Environmental EngineeringColorado State UniversityFort CollinsUSA

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