Direct Numerical Simulation of Particles-Bubbles Collisions Kernel in Homogeneous Isotropic Turbulence

Particles and bubbles suspended in homogeneous isotropic turbulence are tracked and their collisions frequency is determined as a function of particle Stokes number. The carrier phase velocity fluctuations are determined by Direct Numerical Simulations (DNS). The effects of the dispersed phases on the carrier phase are neglected. Particles and bubbles of sizes on the order of Kolmogorov length scale are treated as point masses. In addition to Stokes drag, the pressure gradient in the carrier phase and added-mass forces are also included. Equations of motion of dispersed phases are integrated simultaneously with the equations of the carrier phase using the same time stepping scheme. The collision model used here allows overlap of particles and bubbles. Simulations for three turbulence Reynolds numbers Re Λ = 57, 77, and 96 have been performed. Collisions kernel, radial relative velocity, and radial distribution function found by DNS are compared to theoretical models over a range of particle Stokes number. Comparisons are made with Zaichik et al. [22] model, which is applicable to heavy particles, and Zaichik et al. [23] model which is valid for an arbitrary Stokes number. Zaichik et al. [23] is essentially a model for the radial relative velocity, and for the purpose of computing the collision kernel, it assumes the radial distribution function to be one. In general, good agreement between DNS and Zaichik et al. models is obtained for radial relative velocity for both particle-particle and particle-bubble collisions. The DNS results show that around Stokes number of unity particles of the same group undergo expected preferential concentration while particles and bubbles are segregated. The segregation behavior of particles and bubbles leads to a radial distribution function that is less than one. Existing theoretical models do not account for effects of this segregation behavior of particles and bubbles on the radial distribution function.