Eulerian, continuum two-phase modelling

This type of modelling is based on treating fluid flows after continuum theory based on an Eulerian description. The two phases, hence air and snow, may be considered by two equivalent sets of equations for the conservation of mass and momentum. Additional modelling of phase interaction effects is required. This two-fluid modelling is rather expensive in the sense of large computational costs. However, it is possible to simplify the two-fluid modelling by assuming the snow phase to be coupled to the air flow and thereby reducing the total number of governing equations.

One such approach is to consider the mixture of air and snow by full conservation of mass and momentum and allowing the snow phase to drift with respect to this mixture. For snow drift it may be assumed that the drift-velocity between the two phases is too small to contribute to any significant transport of momentum for the snow phase.

Another simplification of the two-fluid model can be achieved by treating only the air phase by the mentioned conservation laws and consider snow transport mainly governed by the airflow. Since the snow phase is allowed to drift with respect to the airflow, this modelling may be referred to as a homogeneous model with slip.

1. Numerical simulations of snowdrift can, described simply, be performed by the following procedure:
   Calculation of the airflow (Navier Stokes/Turbulence model)
2. Calculation of snow transport based
3. Evaluation of the quantity of formation and erosion on the snow surface

This procedure is repeated for each time step in the numerical simulations.

Results from 3D numerical simulations of snowdrift around buildings in Norway, using the Eulerian, continuum snow transport modelling concept.

Results from 2D simulation of snowdrift leeward a building, without and with a wind deflector, respectively.

• Beyers, J.H.M., Sundsbø, P.A. and Harms, T.M., 2004, Numerical simulation of three­dimensional, transient snow drifting around a cube, Journal of Wind Engineering and Industrial Aerodynamics, Volume 92, 725-747.
• Beyers, J.H.M, Harms, T.M. and Sundsbø, P.A., 2004, Numerical simulation of snow drifting around an elevated obstacle, Snow Engineering V, Balkema, ISBN 90-5809-634-3, Proceedings of the 5th international conference on snow engineering, Davos, Switzerland, 185-191.
• Beyers, J.H.M., Sundsbø, P.A. and Harms, T.M., 2003, Numerical simulation and verification of drifting snow around a cube, Proceedings of the 11th international conference on wind engineering, Texas Tech University, Lubbock, Texas, USA, 1886-1893.
• Sundsbø, P.A. and Bang, B., 1998, Calculation of snowdrift around roadside safety barriers, Proceedings of the International Snow Science Workshop, Sept, Sunriver, Oregon, USA, 279-283.
• Sundsbø, P.A., 1998, Numerical simulations of wind deflection fins to control snow accumulation in building steps, Journal of Wind Engineering and Industrial Aerodynamics, Volumes 74-76, 543-552.
• Sundsbø, P.A., 1997, Numerical modelling and simulation of snow drift – Application to snow engineering, Doctoral Thesis, ISBN 82-471-0047-9, Norwegian University of Science and Technology, Trondheim.

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