OpenFOAM® pp 491-508 | Cite as

Two-Way Coupled Eulerian–Eulerian Simulations of a Viscous Snow Phase with Turbulent Drag

  • Ziad BoutaniosEmail author
  • Hrvoje Jasak


A novel two-way coupled Eulerian–Eulerian CFD formulation was developed to simulate drifting snow based on turbulent drag and a new viscous treatment of the drifting snow phase, derived from first principles. This approach allowed explicit resolution of the saltation layer without resorting to empiricism, unlike other Eulerian–Eulerian models based on mixture formulations and one-way coupling. Initial validations were carried out against detailed snow flux, airflow velocity, and turbulent kinetic energy measurements in a controlled experimental simulation of drifting snow in a wind tunnel using actual snow particles. The two-way coupled approach was found capable of simulating drifting snow fluxes in both saltation and suspension layers with reasonable accuracy. Recommendations were made to improve the accuracy of the method for air velocity and turbulent kinetic energy, and to allow simulating a drifting snow phase with a particle size distribution.


Drifting snow Eulerian–Eulerian Viscosity Turbulent drag Snow flux 



The authors warmly thank Profs. Akashi Mochida, Tsubasa Okaze, and Yoshihide Tominaga for sharing their experimental results. In particular, the patience and dedication of Prof. Okaze to answering our numerous questions are gratefully acknowledged. Many thanks!


  1. 1.
    R. Bagnold, The physics of blown sand and desert dunes. London, Methuen, 1941.Google Scholar
  2. 2.
    B. Lee, J. Tu, and C. Fletcher, “On numerical modeling of particle-wall impaction in relation to erosion prediction: Eulerian versus Lagrangian method,” Wear, vol. 252, pp. 179–188, 2002.CrossRefGoogle Scholar
  3. 3.
    T. Uematsu, T. Nakata, K. Takeuchi, Y. Arisawa, and Y. Kaneda, “Three-dimensional numerical simulation of snowdrift,” Cold Regions Science and Technology, vol. 20, pp. 65–73, 1991.CrossRefGoogle Scholar
  4. 4.
    M. Naaim, F. Naaim-Bouvet, and H. Martinez, “Numerical simulation of drifting snow: erosion and deposition model,” Annals of Glaciology, vol. 26, pp. 191–196, 1998.CrossRefGoogle Scholar
  5. 5.
    Y. Tominaga and A. Mochida, “CFD prediction of flowfield and snowdrift around a building complex in a snowy region,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 81, no. 13, pp. 273 – 282, 1999.CrossRefGoogle Scholar
  6. 6.
    J. Pomeroy and D. Gray, “Saltation of snow,” Water Resources Research, vol. 26, no. 7, pp. 1583–1594, 1990.CrossRefGoogle Scholar
  7. 7.
    T. Okaze, A. Mochida, Y. Tominaga, M. Nemoto, Y. Ito, and T. Shida, “Modeling of drifting snow development in a boundary layer and its effect on windfield,” in The Sixth Snow Engineering Conference, Whistler, B.C., Canada, June 1–5 2008.Google Scholar
  8. 8.
    Y. Tominaga, T. Okaze, and A. Mochida, “CFD modeling of snowdrift around a building: overview of models and evaluation of a new approach,” Building and Environment, vol. 46, pp. 899–910, 2011.CrossRefGoogle Scholar
  9. 9.
    B. Bang, A. Nielsen, P. Sundsbø, and T. Wiik, “Computer simulation of wind speed, wind pressure and snow accumulation around buildings (SNOW-SIM),” Energy and Buildings, vol. 21, no. 3, pp. 235–243, 1994.CrossRefGoogle Scholar
  10. 10.
    J. Beyers, “Numerical modeling of the snowdrift characteristics surrounding the SANAE IV research station,” Ph.D. Dissertation, Department of Mechanical Engineering, University of Stellenbosch, 2004.Google Scholar
  11. 11.
    J. Beyers and B. Waechter, “Modeling transient snowdrift development around complex three-dimensional structures,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 96, pp. 1603–1615, 2008.CrossRefGoogle Scholar
  12. 12.
    P. Sundsbø, “Numerical simulations of wind deflection fins to control snow accumulation in building steps,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 74–76, pp. 543–552, 1998.Google Scholar
  13. 13.
    P. Gauer, “Blowing and drifting snow in alpine terrain: A physically-based numerical model and related field measurements,” Ph.D. dissertation, ETH Zurich, 1999.Google Scholar
  14. 14.
    OpenFOAM Documentation, Extended Code Guide, 2018.Google Scholar
  15. 15.
    A. Gosman, R. Issa, C. Lekakou, S. Politis, and M. Looney, “Multidimensional modeling of turbulent two-phase flows in stirred vessels,” AIChE Journal, vol. 38, no. 12, pp. 1946–1956, 1992.CrossRefGoogle Scholar
  16. 16.
    D. Gidaspow, “Hydrodynamics of fluidization and heat transfer: supercomputer modelling,” Appl. Mech. Rev., vol. 39, pp. 1–22, 1986.CrossRefGoogle Scholar
  17. 17.
    L. Schiller and Z. Naumann, “A drag coefficient correlation,” Z. Ver. Deutsch. Ing., vol. 77, 1935.Google Scholar
  18. 18.
    H. Enwald, E. Peirano, and A.-E. Almstedt, “Eulerian two-phase flow theory applied to fluidization,” Int. J. of Multiphase Flow, vol. 22, pp. 21–66, 1996.CrossRefGoogle Scholar
  19. 19.
    H. Weller, “Derivation, modelling and solution of the conditionally averaged two-phase flow equations,” OpenCFD Ltd, Report TR/HGW/02, 2005.Google Scholar
  20. 20.
    H. Teufelsbauer, “A two-dimensional snow creep model for alpine terrain,” Natural Hazards, vol. 56, pp. 481–497, 2011.CrossRefGoogle Scholar
  21. 21.
    R. Kind, Handbook of Snow, Principles, Processes, Management and Use. Pergamon Press, 1981, ch. Snowdrifting, pp. 338–359.Google Scholar
  22. 22.
    T. Okaze, A. Mochida, Y. Tominaga, M. Nemoto, T. Sato, Y. Sasaki, and K. Ichinohe, “Wind tunnel investigation of drifting snow development in a boundary layer,” J. Wind Eng. Ind. Aerodyn., vol. 104-106, pp. 532–539, 2012.CrossRefGoogle Scholar
  23. 23.
    Z. Boutanios and H. Jasak, “Viscous treatment of the snow phase in Eulerian-Eulerian simulations of drifting snow,” in The 14th International Conference on Wind Engineering, Porto Alegre, Brazil, June 21-26 2015.Google Scholar
  24. 24.
    W. Budd, “The drifting of nonuniform snow particles,” in Studies in Antarctic meteorology, M. Rubin, Ed. American Geophysical Union, 1966.Google Scholar
  25. 25.
    R. Schmidt, “Vertical profiles of wind speed, snow concentration and humidity in blowing snow,” Boundary-Layer Meteorology, vol. 23, no. 2, pp. 223–246, 1982.MathSciNetCrossRefGoogle Scholar
  26. 26.
    W. Strahle, “Stagnation point flows with freestream turbulence – the matching condition,” AIAAJ, vol. 23, pp. 1822–1824, 1985.CrossRefGoogle Scholar
  27. 27.
    B. Launder and M. Kato, “Modeling flow-induced oscillations in turbulent flow around square cylinder,” in ASME Fluid Eng. Conference, 1993, p. 20.Google Scholar
  28. 28.
    P. Durbin, “Separated flow computations with the k–epsilon-v2 model,” AIAA Journal, vol. 33, pp. 659–664, 1995.CrossRefGoogle Scholar
  29. 29.
    T. Okaze, Y. Takano, A. Mochida, and Y. Tominaga, “Development of a new \( k-\epsilon \) model to reproduce the aerodynamic effects of snow particles on a flow field,” J. Wind Eng. Ind. Aerodyn., vol. 144, pp. 118–124, 2015.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Binkz IncLavalCanada
  2. 2.Faculty of Mechanical Engineering and Naval ArchitectureUniversity of ZagrebZagrebCroatia

Personalised recommendations