Statistics of Volumes, Swept by Small Spheroidal Particles in a Turbulent Flow.
Abstract
Collisions between nonspherical particles (ice crystals) give rise to formation of aggregates; collision of non spherical crystals with cloud droplets is the main mechanism of graupel production. The rate of riming and that of iceice collisions is not well known even in a pure gravity case. Often these collisions take place in the regions of enhanced turbulence in cumulus clouds. In spite of its high importance, the problem of collisions of such particles in a turbulent flow is not yet solved. In this work we present novel method of collision kernels calculation between small (less than 30 mic) spheroid particles of different aspect ratios (both prolate and oblate). The collision kernel between two spheroids is defined in terms of velocity fluxes of the particle of one type relative to the particle of another type. In this study hydrodynamic interaction between particles is not taken into account, so that the collision kernel is the swept volume (hereafter, SV) of colliding particles. Scale analysis indicates that spatial and time characteristic scales of Lagrangian acceleration and turbulent shears are much larger then the scales determining particles collisions. The results of this analysis allows one to consider turbulent flow as a combination of small regions in which Lagrangian accelerations and shears can be considered frozen during the particles' approach and collision. The consequence of collisions may be then regarded as taking place at different independent values of these parameters. A large set of turbulent field realizations (acceleration/shear pairs) was generated using generators of shears and accelerations, reproducing probability distribution functions (PDF) at high Reynolds numbers and dissipation rates, as they were obtained in recent laboratory and theoretical studies. There was obtained approximate analytical solution of spheroid motion, valid for small Stokes numbers. This solution allowed us to find approximate probability distribution functions (PDF) of spheroid velocities (translation and angular) and orientations for any given realization of a turbulent field. Having in hand these PDFs, we were able to calculate analytically time series of SV for a given set of turbulent field realizations. Finally, PDF (histogram) of SV and the mean value were calculated from the time series. These results were obtained for a vide range of turbulent flow intensity (different Reynolds numbers and energy dissipations), from that corresponding to stratiform clouds up to deep cumulus clouds. The estimations were performed also for different values of aspect ratio (from a platelike spheroid (aspect ratio 0.05) up to a needlelike one (aspect ratio 20)) and different particles sizes. The results manifest that:  PDF of SV differs significantly from Gaussian and the difference increases with turbulent flow intensity and particle nonsphericity;  turbulence magnifies SV up to several times comparing with the pure gravity case; the effect is enlarging with flow intensity and particle aspect ratio deviation from unity;  an influence of turbulence on SV becomes especially large for small particles (of order ) and particles of similar size.
 Publication:

AGU Fall Meeting Abstracts
 Pub Date:
 December 2007
 Bibcode:
 2007AGUFM.A53A0910G
 Keywords:

 1854 Precipitation (3354);
 3354 Precipitation (1854)