Computational investigation of complex-shaped snow particle aerodynamics: drag prediction and wake characteristics

Abstract

Snow crystal shapes and falling behavior play a paramount role in snow precipitation. The knowledge of snow precipitation microstructure is fundamental for many applications such as precipitation remote sensing, polarimetric measurements, and climate model parametrization. Moreover, snowfalls influence snow distribution on the ground, which plays a pivotal role in Earth’s climate regulation due to its high albedo. Therefore, understanding snow particles falling behavior is crucial. The irregular shape of snowflakes makes their falling attitudes elaborate, gives rise to convoluted trajectories, and may trigger meandering and turbulent wakes. This complex interaction between snowflake shape and the surrounding air impacts the particle drag coefficient and its settling velocity, but it is far from being fully understood. In the first part of this study, a Delayed-Detached Eddy Simulation model is developed to predict the drag coefficient of snowflakes falling at Reynolds number (Re) between 50 and 2200. The model results are then compared against laboratory experiments using 3D-printed snowflake analogs of the same shape, falling at the same Reynolds number. The first objective is to assess the capability of the numerical model to predict the drag coefficient of complex-shaped particles when their orientation is known a posteriori. Close agreement in the drag coefficient value is found in cases where the particles fall steadily, while a more complex behavior is observed in cases where the flow is unsteady. Secondly, a method to estimate the drag coefficient when the orientation of the particle is not known a posteriori is proposed. A suitable average of two orientations corresponding to the minimum and maximum eigenvalues of the inertia tensor provides a good estimate of the particle drag coefficient. Meanwhile, existing correlations for the drag of non-spherical particles produce large errors (≈ 50%). The same approach in then used to evaluate the snow particle terminal velocity. Subsequently, the previously validated Delayed-Detached Eddy Simulations (DDES), combined with experimental observations of free-falling, 3D-printed snowflakes analogs, are employed to analyze the wake topology and momentum flux and investigate the influence of shape and wake flow on the drag coefficient, together with its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is related to particle porosity and increased drag coefficient. With regard to the momentum flux, the contribution of the mean velocity term in the wake momentum deficit is the largest for all particles. At moderate flow regimes, the particle roundness impacts the shear layers separation and the momentum loss in the wake, with increasing contribution by the fluctuating velocity term. At high Re, even though the drag coefficient does not change much among the different geometries, although the contribution of the fluctuating velocity term in momentum flux differs significantly. Finally, to cross-validate and assess the limitation of the numerical and experimental approaches used in this thesis for snowflake wake characterization, 4D-Particle Tracking Velocimetry experiments of free-falling, 3D-printed snowflakes analogs and Delayed-Detached Eddy Simulations of fixed snow particles are compared analyzing time- and space-averaged flow quantities in the snowflake wake. Firstly, the two approaches are cross-validated for low Re cases where close agreement is found and, secondly, we investigate how strongly the wake of freely falling particles deviates from a fixed particle wake at high Re. At low Reynolds numbers (steady falling behavior), the fixed-particle model can properly represent the wake of freely falling particles, while at moderate/high flow regimes (unsteady falling motion), the comparison highlights much larger differences. Accounting for the movement of the particle by applying a co-moving frame to the laboratory data or filtering the numerical data on larger grids partially reduces these differences, implying that an unsteady fall significantly alters the average wake structure as compared to a fixed particle model.