Numerical Simulation of Three-Dimensional Unsteady Flow past Ice Crystals

Abstract

The unsteady flow fields around falling columnar ice crystals, hexagonal ice plates, and broad-branch crystals are simulated by numerically solving the time-dependent Navier–Stokes equations appropriate for these geometries in the primitive equation form. A predictor–corrector method and a quadratic interpolation for convective kinematics (QUICK) scheme are applied on nonuniform grids to determine the velocity fields. The ice crystals are held in fixed orientation but time-dependent behaviors such as eddy shedding are allowed to occur by imposing an initial perturbation with a magnitude 30% of the free-stream velocity. The computed flow fields cover a Reynolds number range from 0.1 to about 200, being slightly different for different crystal habits. Examples of velocity fields are illustrated. The computed drag coefficients for cylinders agree with experimental values to within a few percent, while those for hexagonal plates agree with experimental values and previous calculations by Pitter et al. to less than 15% even though the aspect ratios are different. The drag coefficients for broad-branch crystals are higher than those for hexagonal plates at the same Reynolds numbers. Special features of flow passing through the branch gaps of broad-branch crystals suggest that it may be possible to use a creeping flow assumption to treat flow passing through spaces in complicated dendritic crystals.