Effect of interstitial fluid on particle-particle interactions in kinetic theory approach of dilute turbulent fluid-particle flow

A new two-fluid model for fluid-particle turbulent flow is developed in the present study. The model, which employs kinetic theory of dense gas concepts in describing momentum and kinetic energy transfer between colliding particles, incorporates the influence of the interstitial fluid on the random motions of the particles by introducing two distinct particle coefficients of restitution, e_f and e_s, to characterize the inelasticity of particles colliding in a fluid and in a vacuum, respectively. When two particles collide in a fluid, a fraction of the particles' fluctuating kinetic energy is dissipated as heat as a result of inelastic collisions and another fraction is dissipated into the fluid fluctuations, as the particles must exert work on the fluid to displace the interstitial fluid between the two particle surfaces. The values for e_f have been shown experimentally to depend on the impact Stokes number, St, which characterizes the ratio of the particle inertia to the viscous force. The predictions of the model are compared with data from several experiments on dilute turbulent fluid-particle flow in a vertical pipe for a wide range of impact Stokes numbers (40-1600), including both gas-particle and liquid-particle flows. In general, good agreement is found between the model predictions and the experimental data for both the fluid and particle phases at the level of the mean and fluctuating velocity.