A Numerical Investigation of the Efficiency with which Simple Columnar Ice Crystals Collide with Supercooled Water Drops

View More View Less
  • 1 Department of Meteorology, University of California, Los Angeles 90024
  • | 2 Department of Chemical Engineering, McMaster University, Hamilton, Canada
© Get Permissions
Full access

Abstract

The Navier-Stokes equation of motion for two-dimensional, viscous, steady-state incompressible flow past an infinitely long circular cylinder was solved by numerical techniques for Reynolds numbers between 0.1 and 50. From the streamfunction and vorticity fields the pressure at the cylinder surface, the pressure drag, and the frictional drag were computed, and from the latter two the total drag on the cylinder was derived. The values found for the drag compared well with the best theoretical and experimental values reported in literature, suggesting that our flow fields were sufficiently accurate. These flow fields were used to determine the hydrodynamic interaction between simple columnar ice crystals idealized as circular cylinders of finite length L′, of radius aL′, and of Reynolds number NRe,L (67.1≤L′≤2440 µm; 23.5≤ aL′≤146.4 µm;0.2≤NRe,L <20) and spherical water drops of radius aS′ varying between 2 and 134µm. The flow fields used to describe the flow past drops were numerically computed by a method analogous to that given by LeClair et al. (1970). For atmospheric conditions of −8°C and 800 mb numerical methods were used to determine the trajectory of the drops relative to the cylinder by means of a semi-empirically modified version of the “superposition” model. The model was semi-empirical in that the flow fields used were those determined theoretically by us, while the drag on the columnar crystals was that determined by Jayaweera and Cottis (1969) and by Kajikawa (1971), and the dimensional relationships between the diameter and length of the columnar crystal were those given by the observational relations of Auer and Veal (1970). From the trajectories of the water drops relative to the columnar ice crystals collision efficiencies were computed. Our computations predict that riming on a columnar ice crystal will not commence until the crystal has a diameter which is larger than about 50 µm. This result is in good agreement with field observations reported in literature.

Abstract

The Navier-Stokes equation of motion for two-dimensional, viscous, steady-state incompressible flow past an infinitely long circular cylinder was solved by numerical techniques for Reynolds numbers between 0.1 and 50. From the streamfunction and vorticity fields the pressure at the cylinder surface, the pressure drag, and the frictional drag were computed, and from the latter two the total drag on the cylinder was derived. The values found for the drag compared well with the best theoretical and experimental values reported in literature, suggesting that our flow fields were sufficiently accurate. These flow fields were used to determine the hydrodynamic interaction between simple columnar ice crystals idealized as circular cylinders of finite length L′, of radius aL′, and of Reynolds number NRe,L (67.1≤L′≤2440 µm; 23.5≤ aL′≤146.4 µm;0.2≤NRe,L <20) and spherical water drops of radius aS′ varying between 2 and 134µm. The flow fields used to describe the flow past drops were numerically computed by a method analogous to that given by LeClair et al. (1970). For atmospheric conditions of −8°C and 800 mb numerical methods were used to determine the trajectory of the drops relative to the cylinder by means of a semi-empirically modified version of the “superposition” model. The model was semi-empirical in that the flow fields used were those determined theoretically by us, while the drag on the columnar crystals was that determined by Jayaweera and Cottis (1969) and by Kajikawa (1971), and the dimensional relationships between the diameter and length of the columnar crystal were those given by the observational relations of Auer and Veal (1970). From the trajectories of the water drops relative to the columnar ice crystals collision efficiencies were computed. Our computations predict that riming on a columnar ice crystal will not commence until the crystal has a diameter which is larger than about 50 µm. This result is in good agreement with field observations reported in literature.

Save