Probabilistic model of dispersed turbulent flow in channels with rough walls

An equation for the probability density function (PDF) for particle velocity and coordinates in a gas turbulent flow is derived. The system of equations for the first and second moments of particle velocity fluctuations is obtained. Using a method similar to Grad's method, an approximate solution of the PDF equation was found. Based on this approximate solution, the system of equations for the averaged concentration, velocity, and second moments of particle velocity fluctuations was closed. Also, using an approximate solution, the boundary conditions on the rough wall of the channel were obtained. The boundary conditions self-consistently take into account the direction of the velocity vector of particles colliding with the surface, as well as the direction of the normal to a random plane that simulates the roughness. The fundamental difference between the mechanisms of generation of random motion of particles in channels with smooth and rough walls is shown. Copyright (c) 2020 American Association for Aerosol Research