Statistical modeling of particles relative motion in a turbulent gas flow

On the base of modern probability approach the theoretical model of turbulent relative motion of particles in the turbulent flow is developed. Closed equation for probability density function of coordinates and velocities of two particles in turbulent flow is obtained. The system of equations for balance of mass, averaged velocities and intensities of turbulent chaotic motion of particles with account of correlated motion of particles are deduced. The closed expressions for intensity of relative chaotic motion between particles are obtained on the base of probability density function of particles displacement with correlation effects. The correlation functions, intensity of relative turbulent motion and relative diffusion coefficients of particles are numerically investigated. The calculation results are compared with data of large eddy simulations. The results of calculation intensity of droplets relative motion in atmospheric conditions are presented.