| A study of particle collision and concentration non-uniformity in turbulent flows is carried out. A correction to the classical result of Smoluchowski for the collision rate of monodisperse particles in a laminar shear flow has been made. A theoretical framework has been developed to evaluate the collision rate and collision velocity of very small particles in general turbulent flows. The present approach differs significantly from the classical approach of Saffman & Turner in that the ensemble average is taken after the collision rate for a given flow realization is calculated. This avoids the assumption of isotropy, as needed in the classical approach, and allows for the evaluation of the collision rate in general turbulent flows.; Direct numerical simulations and analytical studies on particle collisions in an isotropic, Gaussian turbulence have been carried out. Several different collision models (or post-collision treatments) are implemented in the simulations and the difference among various collision models is examined. The effects of particle inertia, size, gravity, and mean-concentration on the collision rate, collision velocity, and collision angle are investigated. Asymptotic analyses have been developed to predict the effects of small inertia on the increases in collision rate and collision velocity. Asymptotic prediction for the increased collision velocity agrees well with the results of both numerical simulation and PDF-based method. The increased collision velocity is found to contain terms of both {dollar}rm O((betatausb{lcub}k{rcub})sp{lcub}-1{rcub}){dollar} and {dollar}rm O((betatausb{lcub}k{rcub})sp{lcub}-2{rcub}),{dollar} where {dollar}betasp{lcub}-1{rcub}{dollar} is the particle response time and {dollar}rmtausb{lcub}k{rcub}{dollar} is the kolmogorov time scale. The increases in particle size, gravitational acceleration, and mean-concentration in general reduce the normalized particle collision rate in isotropic turbulence for monosized particles as opposed to very small particles in the very dilute limit.; A new method has been developed to quantify the concentration non-uniformity of particles in turbulent flows. The effects of particle size and inertia on the concentration non-uniformity are examined and elucidated. The concentration non-uniformity can be greatly overestimated if the effect of finite particle size is neglected. |
