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

Giorgia Tagliavini,Mark Mccorquodale,Chris Westbrook,Markus Holzner

doi:10.1063/5.0064902

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 also has 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 model of airflow around a fixed snowflake, combined with experimental observations of free-falling, 3D-printed snowflake 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 in the drag coefficient. At moderate flow regimes, the particle flatness impacts the shear layer 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 toward a deeper understanding the drag of complex-shaped particles.

Highlights

An accurate prediction of snow precipitation is crucial to constrain climate models parametrization
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
For large snow particles (Dmax > 100 μm), the CD − Re relation becomes non-linear, resulting from a complex interaction between the particle and the surrounding air (Re 1, where Re = ut Dmax/ν is the particle Reynolds number, Dmax is the particle maximum extension orthogonal to the flow direction [m], ut the snowflake terminal velocity [m/s] and ν the kinematic viscosity of air [m2/s]), and one cannot rely on Stokesian dynamics [Happel and Brenner 1983; Westbrook 2008; Zeugin et al 2020]

Summary

Introduction

An accurate prediction of snow precipitation is crucial to constrain climate models parametrization. The study discussed and improved the parametrization proposed by Heymsfield and Westbrook 2010 to predict snow particles terminal velocity, which includes parameters to quantify the particle shape (i.e., area ratio) and building on the work of Khvorostyanov and Curry 2005 and Mitchell and Heymsfield 2005 The accuracy of these parametrized models are generally dependent on the measurements resolution and on the chosen parameters and empirical constants, often leading to large error in the prediction of the terminal velocity, as shown by McCorquodale and Westbrook 2021b. Various numerical models of free-falling non-spherical particles, such as disks and plate-like geometries [Auguste et al 2013; Yang et al 2014; Cheng et al 2015; Nettesheim and Wang 2018], or columnar crystals and hexagonal plates [Hashino et al 2016], were employed to predict the drag coefficient and to investigate the particle falling attitude They focus mainly on investigating geometric shapes representative of "pristine" ice crystals, with falling trajectories limited to Re 1000 and a simpler wake than the one of irregular particles, such snowflakes

Objectives

Methods

Results

Discussion

Conclusion