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The Effects of Entrainment and Mixing on Droplet Size Distributions: Bridging the DNS-LES Gap 

The fundamental difficulty that large-eddy simulation (LES) faces when attempting to represent the effects of entrainment and mixing on droplet microphysics is representing the subgrid-scale variability of subsaturation and its impact on the droplet size distribution (DSD). 

Direct numerical simulation (DNS) resolves the smallest scales of fluid motion, but is restricted to domains of about one meter in extent. This limits the range of Damkohler (Da) numbers (ratio of a flow time scale to a droplet evaporation time scale) to values ~1. The limits, Da << 1 and Da >> 1, correspond to homogeneous and inhomogeneous mixing, respectively. 

The EMPM (Explicit Mixing Parcel Model) predicts the evolving internal variability due to entrainment and finite-rate turbulent mixing using a 1D representation of a parcel. It calculates the growth of thousands of individual cloud droplets based on each droplet's local environment. The 1D formulation allows the model to resolve variability down to the smallest turbulent scales (about 1 mm) in large domains (20 to 200 m), thereby bridging the DNS-LES gap, and allowing large Da to be achieved. 

Kumar, Schumacher, and Shaw (2014, 2015) performed several DNSs of the response of a droplet population to entrainment and mixing that are ideally suited for evaluating the EMPM. We compared EMPM results to their DNS results for identical configurations, and obtained excellent agreement for the evolution of the DSDs and the droplet subsaturation PDFs. I will present these results and related EMPM results for scenarios that DNS is not presently capable of simulating.   

We are currently developing and testing a version of the EMPM that is suitable for simulating turbulent clouds in the Pi Cloud Chamber at Michigan Tech. I will present the status of this effort.