Evidence of Caustics From Inertial Particle Relative Velocity Statistics in Isotropic Turbulence

Monday, November 8, 2010: 2:00 PM
Alpine Ballroom East (Hilton)
Juan P. L. C. Salazar, Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY and Lance R. Collins, Department of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY

As a consequence of their inertia, solid or liquid particles in a turbulent gas have trajectories that differ substantially from those of the equivalent fluid particle. In particular, in the absence of collisions (herein neglected for convenience), inertia allows two particles with uncorrelated flow histories to occupy the same spatial position. Historically this has been referred to as "crossing trajectories," "random uncorrelated motion" (RUM), the "sling effect," and more recently "caustics." We investigate this phenomenon using direct numerical simulations (DNS) by studying the relative velocity statistics of inertial particles in the dissipation range of simulated Navier-Stokes turbulence. We observe evidence of caustics for particles with Stokes numbers that lie in the range 0.2-0.5. The magnitude of the caustic is well represented by the Arrhenius-like expression put forth by Wilkinson et al. (2006) and Falkovich & Pumir (2007), which suggests they arise from an activated process. Over the limited range available to us in the DNS, we observe a relatively strong and somewhat counterintuitive dependence of the caustic strength on the Reynolds number. We show how their existence impacts the collision kernel for droplets in a turbulent flow.

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See more of this Session: Turbulent Flows
See more of this Group/Topical: Engineering Sciences and Fundamentals