DIRECT NUMERICAL SIMULATIONS OF SMALL PARTICLES IN TURBULENT FLOWS OF LOW DISSIPATION RATES USING ASYMPTOTIC EXPANSION

Collisions of sedimenting droplets in a turbulent flow is of great importance in cloud physics. Collision efficiency and collision enhancement over gravitational collision by air turbulence govern the growth of the cloud droplets leading to warm rain initiation and precipitation dynamics. Due to the low flow dissipation rate in stratocumulus clouds, a related challenge is low droplet Stokes number. Here the Stokes number is the ratio of droplet inertial response time to the flow Kolmogorov time. A very low Stokes number implies that the numerical integration time step is now governed by the droplet inertial response time, rather than the time step necessary for the flow simulation. This situation makes a simulation very expensive to perform. With the motivation to speed up the simulations, we implement an asymptotic expansion approach for particle tracking as this method is suitable for low particle Stokes number and avoids the numerical integration of the stiff equation of motion of droplets. We first validate our implementation using the simpler 2-D cellular flow. Next, we compare the collision statistics of the newly implemented asymptotic approach with our existing approach of particle tracking as well as with published results from the literature. Finally, we provide the run time comparison for both methods. We report that for 10µm and 20µm particle radius, in a flow of dissipation rate = 10cm 2 /s 3 , asymptotic expansion approach achieves a speed-up by a factor of 25.2