(320e) Analysis of near-Contact Inertial Particle Pair Statistics in Turbulence

It is well known that turbulence can dramatically increase the collision frequency of a population of droplets or particles embedded in the flow. This has been used to partially explain the discrepancy between the observations of relatively rapidly evolving atmospheric clouds and the slower predictions of microphysical models that do not take turbulence into consideration (i.e., assume collisions are driven solely by gravitational settling).  Recently there has been a lot of effort to better understand and predict this so-called "acceleration" of the drop size distribution due to turbulence using direct numerical simulations (DNS), high-precision laser based experiments and theory.  What is known is that the enhancement, driven by the response of particles to the turbulence, is very sensitive to the droplet size, leading to a very complex cumulative effect on the size distribution.  However, we can decompose this behavior into the weighted sum of pairwise interactions, which in turn can be described in terms of the average number density and relative velocity statistics of particle pairs at contact.  For small drops this can be challenging to observe in DNS because it requires a huge population of particles.  This is also challenging to measure in experiments due to experimental errors.  In this talk, we describe an alternate simulation strategy we call satellite particle simulations (SPS).  With SPS, the flow around a primary particle is linearized and the motion of a neighboring cloud of satellite particles is computed.  In this way, the near-contact flow can be accurately represented.  We show there is very good agreement between SPS and DNS for these statistics over a broad range of particle Stokes numbers (particle sizes).  Moreover, these tools have proven extremely useful for analyzing two recent theories for the collision kernel in the literature.