Numerical analysis of the wake of complex-shaped snow particles at moderate Reynolds number

Abstract

Climate model parametrization relies strongly on the prediction of snow precipitation, which in turn depends upon the snowflakes falling motion in air. The falling attitudes of such particles are elaborate because of the particles' irregular shapes, which produce meandering and turbulent wakes and give rise to convoluted trajectories. This has also an impact on the drag experienced by the particle. Especially for large snow particles falling close to the ground, Stokesian dynamics is not applicable and the dependency of drag coefficient on Reynolds number becomes non-linear. This trend arises from the complex interaction between snowflakes and the surrounding air. We investigate the wake of complex-shaped snow particles using a validated Delayed-Detached Eddy Simulation (DDES) model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflakes analogs. This novel approach allows us to analyze the wake topology and decompose its momentum flux to investigate the influence of shape and wake flow on the drag coefficient and its implications on falling attitudes by comparison with experiments. At low Re, the presence of separated vortex rings is connected to particle porosity and produces an increase of the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layers separation and the momentum loss in the wake, while at high Re the drag coefficient has almost the same value among the tested geometries, although the contribution of different momentum flux terms differs. These results represent a further step towards a deeper understanding the drag of complex-shaped particles.

Thin disks falling in air

“…Recently, advanced formulations for estimating (and the associated drag coefficient ) for realistic ice crystal shapes were proposed for fixed falling orientations (Tagliavini et al. 2021 a , b ). However, it is not trivial to determine the level of fluid inertia beyond which the wake becomes strongly coupled with the object motion (Auguste et al.…”

Modal analysis reveals imprint of snowflake shape on wake flow structures

“…As a consequence, alternative orientations are selected for particle CC and MR. In particular, we define two extreme orientations that represent two extreme positions that these geometries frequently adopt during free fall, as illustrated in Figure A1(b, c) (Tagliavini et al, 2021b). A full description of the wake flow and falling behavior of each snow particle is presented in Section 3.1 to assist the reader in fully understanding the results.…”

“…To appraise the influence of the particle shape on the wake flow, the same geometrical features as in Tagliavini et al (2021b), namely the particle's shape porosity and Corey's shape factor (Corey, 1949), are employed. Since only the porosity ǫ showed a consistent correlation to the quantities from the modal analysis, we report its definition here below:…”

“…To better understand and contextualize the results, we first describe the snow particle falling behavior, as observed during the experiments described in Section 2. In one of our former studies, we analyzed the wake flow configuration of the presented snowflake geometries (Tagliavini et al, 2021b) and we highlight below the main features in the wake flow for particle D1, CC, and MR at Re = 1500 to help in the comprehension of the results. D1's wake flow field displays a small recirculation zone attached to the center of the particle and small vortices that originate from the branches of the dendrite.…”

“…Eddy Simulations (DDES) on fixed snowflakes subjected to airflow. This approach, validated for the prediction of the particles' drag coefficients and fall speeds (Tagliavini et al, 2021a) against experimental data of 3D-printed snowflake analogs falling in a vertical water tank (McCorquodale and Westbrook, 2020b), was further extended by Tagliavini et al (2021b) through a comprehensive analysis of wake flow organization, momentum flux decomposition, and their relation with the drag acting on the snow particles. While the analysis highlighted vortex dynamics in the wake flow of complex-shaped snow particles, the question regarding the dominant flow structures in the particle wake, as well as their impact on the particle falling behavior, remained open.…”