An Economical Model for Simulating Turbulence Enhancement of Droplet Collisions and Coalescence

Abstract

ClusColl, an economical simulation method for droplet motions and collisions in turbulent flows, has been developed, implemented, tested, and applied. In the Linear Eddy Model, permutations called triplet maps representing individual turbulent eddies implement turbulent advection of fluid in 1-D. This captures flow processes down to the smallest turbulent eddy (Kolmogorov microscale), but the inertial response of small Stokes number droplets to turbulence has important features at scales down to the droplet radius, notably sub-Kolmogorov-scale clustering of finite-inertia droplets that can increase collision rates significantly. Additionally, shear due to the smallest scales of turbulence increases collision rates of zero-inertia droplets. In ClusColl, a 3-D triplet map for droplets captures both effects. We implemented collision detection, enabling simulation of droplet collisions and coalescence, and a sedimentation treatment in ClusColl. Published direct numerical simulations (DNSs) of monodispersions were used to tune parameters. For sedimenting droplets in turbulence, ClusColl's turbulent enhancement of bidisperse collision kernels agrees reasonably well with published DNS results. We compared ClusColl and DNS coalescence growth results. For weak turbulence ( ≤ 100 cm 2 /s 3 ), ClusColl's turbulent enhancement of coalescence growth closely matches that of the DNS. For ≥ 200 cm 2 /s 3 , lack of accurate collision efficiencies precludes definitive quantitative evaluation of ClusColl's coalescence growth. In a comparison of coalescence growth dependence on the droplet size distribution width and on turbulent enhancement, ClusColl indicates that the latter dramatically accelerates cloud droplet conversion into raindrops, while the former has significantly less impact.Plain Language Summary A long-standing scientific challenge has been explaining the observed short time between initial cloud droplet formation and the development of raindrops in warm (liquid-water-only) cumulus clouds. Cloud droplets initially grow by condensation, but this process by itself is too slow to produce raindrops in the observed short times. Growth by collision and coalescence in nonturbulent air is rapid enough to do so once cloud droplets grow to a diameter of about 0.1 mm. How cloud droplets grow to this size in a short time has been the puzzle. During the last two decades, scientists have recognized that turbulence can accelerate droplet growth by collision and coalescence, but quantifying its impact has been theoretically difficult and computationally expensive.We developed a new, economical, and accurate method to simulate droplet growth by collision and coalescence in turbulent air. A simplified, yet physically based, representation of the smallest turbulent eddies-which predominantly influence droplet collision rates-and their interactions with droplet motions is the basis of the method, which captures the enhancement of collision rates due to the subtle phenomenon of turbulence-induced droplet clustering.

Scaling of Turbulence and Microphysics in a Convection–Cloud Chamber of Varying Height

“…The parameter space is multi‐dimensional and LES with microphysics is computationally expensive, so a thorough exploration will require a combination of more computational resources and more idealized and efficient analytical or computational methods. In particular, one‐dimensional turbulence approaches and collision models are likely to be beneficial (Chandrakar et al., 2020; Krueger & Kerstein, 2018). At this stage, it is clear that increasing the size of a convection–cloud chamber allows larger Da and smaller Rou and Kn to be explored, in addition to larger Ra and Nu .…”

Turbulence modulation in particle-laden stationary homogeneous isotropic turbulence using one-dimensional turbulence

“…This could reflect a variety of possible influences, ranging from the case parametrization issue that has been mentioned to increasing importance of particle clustering at high mass loading. (Triplet mapping of inertial particles is known to induce clustering that is consistent with physical and mathematical requirements [37,38]) In view of the limited evidence and the potentially complicated phenomenology at high mass loading, no interpretation of the φ = 2.0 results is attempted, but they serve as additional predictions that are subject to possible future validation by DNS or other means. downward trend with increasing φ, in contrast to the complicated dependence seen in Fig.…”

Detection of small drizzle droplets in a large cloud chamber using ultrahigh-resolution radar

“…4 and 5 may underestimate the drizzle occurrence probability with the collision-coalescence process being activated. ClusColl is a simulation method for describing droplet motions and collisions in turbulent flows (Krueger and Kerstein, 2018). ClusColl simulates the movement of individual droplets in a vertical column due to turbulence and gravitational sedimentation.…”