The interaction of inertial droplets with turbulence as a mechanism for accelerated droplet size spectrum broadening: laboratory studies of preferential accumulation, enhanced settling and turbulence-induced collisions of small inertial droplets

Warm rain formation presents a long standing open question in cloud microphysics that has important implications for the overall understanding of this phenomenon and the accuracy of weather and climate model predictions. The broadening of the droplet size spectrum that follows condensation growth and necessarily precedes gravitationally-induced collision/coalescence has been the subject of intense investigation, but still remains poorly explained. Numerous hypotheses have been formulated relating this intermediate growth mechanism to the cloud turbulence state. This relationship, however, has not been fully verified and quantitative models of the turbulence-induced collision/coalescence process have not been fully validated (Vaillancourt and Yau 2000).

Inertial droplets have been shown to accumulate in the high strain region between vortices in a turbulent field, and this accumulation is associated with an enhanced settling velocity (Aliseda et al. 2002). Both the increased droplet concentration and the enhanced relative velocity associated with the turbulence-induced settling contribute to droplet collisions that can potentially lead to accelerated droplet growth and size spectrum broadening (Xue et al. 2008; Wang et al. 2005). When the growth of droplets in an intermediate regime (r=5-50 µm) is modeled using a simplistic approach that neglects droplet inertia and therefore assumes both a random spatial distribution of droplets and relative velocities equal to the fluctuations of the surrounding air motion, the collision rate is extremely slow and consistently overpredicts the time needed for precipitation. These predictions are on the order of hours for normal cumulus cloud conditions (Jonas 1996), whereas Doppler measurements made on similar clouds have shown precipitation forming in a little as 15-20 minutes (Szumowski et al. 1997). Considering droplet inertia is therefore necessary since, under typical cloud conditions, droplets in this size range (5-50µm) have Stokes numbers of order unity. This research project studies the effects of coupling droplet inertia and turbulence on the collision-coalescence of water droplets on a parameter range scale relevant to rain formation.

We have performed carefully controlled laboratory experiments of small inertial droplets interacting with homogeneous isotropic turbulence. The turbulence dissipation rate is approximately 10^(-2)-1 m^2 /s^3 and the Reynolds number based on the Taylor microscale is Re_λ = 200-400. The droplet volume fraction is kept between 10^(-5) and 10^(-4) , which provides a higher water content than found in clouds, while maintaining conditions where the droplets do not significantly influence the turbulence dynamics. These conditions are necessary to perform experiments with high droplet data rates, required for converged statistics, and higher probability of droplet collisions in the short residence times of droplets in the wind tunnel. Droplets between 1 and 50 µm in radius are immersed in a wind tunnel through an array of atomizers located at the nodes of a uniformly spaced turbulence-inducing grid that covers the tunnel's cross section. Measurements were made at sufficient distance downstream from the injectors (≈25M, where M is the grid spacing) that the droplets lose memory of the injection conditions, and the turbulence is slowly decaying, homogeneous, and isotropic, representing a good model of conditions in cloud cores. The droplet size distribution, concentration, and settling velocity are measured using a Phase Doppler Particle Analysis (PDPA) system. These PDPA measurements are processed to generate 1-D droplet radial distribution functions (RDF), while 2-D RDFs are obtained from planar high speed visualizations. The radial distribution function measures the concentration of droplets as a function of distance from each droplet. It can be used to analyze the spatial distribution of droplets and, by comparing the experimentally measured RDF to that from the baseline random distribution of droplets, it can quantify how turbulence modifies the behaviour of inertial droplets inducing preferential accumulation. This phenomenon, and the enhanced settling associated with it, results in higher probability of droplet collisions. The evolution of the Droplet Size Distribution along the wind tunnel's test section, measured by PDPA can be related to the statistics of turbulence-induced droplet collisions by the population dynamics equation with a model for the turbulent collision kernel. The experimental data, 1D and 2D RDF, and droplet size evolution are analyzed in conjunction with the hybrid DNS performed by Lian Ping Wang's group at the University of Delaware, in order to develop and validate droplet collision kernel models. Finally, instantaneous realizations of droplet collisions can be observed from high speed flow visualizations. Statistics built from the analysis of collision images can then be used to support the modeling of the turbulent collision kernel and to develop models of coalescence efficiency.

References

A. Aliseda, F. Hainaux, A. Cartellier, and J.C. Lasheras. Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. J. Fluid Mech., 468:77–105, 2002.

P. Jonas. Turbulence and cloud microphysics. Atm. Res., 40:283–306, 1996. M. J. Szumowski, R. M. Rauber, H. T. Ochs III, and L. J. Miller. The microphysical structure and evolution of Hawaiian rainband clouds. Part I: Radar observations of rainbands containing high reflectivity cores. J. Atmospher. Sci., 54:369–385, 1997.

P. A. Vaillancourt and M. K. Yau. Review of particle-turbulence interactions and consequences for cloud physics. Bull. Am. Meteorol. Soc., 81:285–298, 2000.

L.P. Wang, O. Ayala, S.E. Kasprzak, and W.W. Grabowski. Theoretical formulation of collision rate and collision efficiency of hydrodynamically interacting cloud droplets in turbulent atmosphere. J. Atmospher. Sci., 62(7):2433–2450, 2005.

Y. Xue, L.P. Wang, and W.W. Grabowski. Growth of Cloud Droplets by Turbulent Collision-Coalescence. J. Atmospher. Sci., 65(2):331–356, 2008.