ALBERT

Description: Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations, we show that the turbulent fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. Based on this, we propose a Lagrangian stochastic model for condensation and evaporation of small droplets in turbulent flows. It consists of a set of stochastic integro-differential equations for the joint evolution of the squared radius and the supersaturation along the droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral time scale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterized by an exponential tail in the droplet mass distribution. These results reconcile those of earlier numerical studies, once these various regimes are considered. © 2016 Cambridge University Press.

Description: This study deals with the comparison of numerically and experimentally determined collision kernels of water drops in air turbulence. The numerical and experimental setups are matched as closely as possible. However, due to the individual numerical and experimental restrictions, it could not be avoided that the turbulent kinetic energy dissipation rate of the measurement and the simulations differ. Direct numerical simulations (DNS) are performed resulting in a very large database concerning geometric collision kernels with 1470 individual entries. Based on this database a fit function for the turbulent enhancement of the collision kernel is developed. In the experiments, the collision rates of large drops (radius 〉 7.5 µm) are measured. These collision rates are compared with the developed fit, evaluated at the measurement conditions. Since the total collision rates match well for all occurring dissipation rates the distribution information of the fit could be used to enhance the statistical reliability and for the first time an experimental collision kernel could be constructed. In addition to the collision rates, the drop size distributions at three consecutive streamwise positions are measured. The drop size distributions contain mainly small drops (radius 〈 7.5 µm). The measured evolution of the drop size distribution is confronted with model calculations based on the newly derived fit of the collision kernel. It turns out that the observed fast evolution of the drop size distribution can only be modeled if the collision kernel for small drops is drastically increased. A physical argument for this amplification is missing since for such small drops, neither DNSs nor experiments have been performed. For large drops, for which a good agreement of the collision rates was found in the DNS and the experiment, the time for the evolution of the spectrum in the wind tunnel is too short to draw any conclusion. Hence, the long-time evolution of the drop size distribution is presented in Riechelmann et al. 2015 (doi:10.1127/metz/2015/0608).