Large-Eddy Simulation of Particles and Bubbles Collisions in Homogeneous Isotropic Turbulence

Abstract

Particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as function of particle Stokes number. The effects of the dispersed phases on the carrier phase are neglected (one-way coupling). Particles and bubbles of sizes on the order of Kolmogorov length scales are treated as point masses. The equations of motion of dispersed phases are integrated simultaneously in time with the carrier phase equations using a 3rd-order Runge-Kutta method. The carrier phase large-scale velocity fluctuations are determined by a Large-Eddy Simulation (LES) at Reλ = 96 on a coarse grid of N = 32. Collision kernel, radial relative velocity and radial distribution function using LES are compared to Direct Numerical Simulation(DNS) data obtained by Fayed and Ragab [6] at the same Reλ and a fine grid 256 . It is found that around Stokes number of unity solid particles of the same group undergo the well known preferential concentration while particles and bubbles are segregated. This segregative behavior of particles and bubbles leads to a radial distribution function less than one. Collisions statistics obtained by neglecting the effects of the subgrid velocity fluctuations on the particles motion are in good agreement with DNS data for mono-disperse at high Stokes number. Small scales fluctuations are needed to accurately track particles and bubbles at small Stokes number. A multifractal approach is proposed to synthesis the SGS scales from the resolved enstrophy field. ∗Graduate Research Assistant, email: hehady@vt.edu †Professor, email: ragab@vt.edu, AIAA Member