Calculation of probability density function of particle velocity in turbulent flow

Abstract

The random motion of inertial particles in uniform isotropic turbulence is considered. Fluctuations of the gas velocity at the particle trajectory are modelled as a random Gauss process with a finite decay time of the autocorrelation function. A closed equation for the probability density function (PDF) of the random particle velocity is derived. An analytical solution of the equation for the PDF is found. The equation for the PDF is solved by two numerical methods. The first method of solution is based on the finite-difference approximation of the equation for the PDF. The second method is based on the calculation of empirical PDF, which is obtained by averaging over an ensemble of random trajectories of particles. The results of the comparison of analytical numerical solutions are presented.