Stochastic Lagrangian Simulation of Particle Deposition in Turbulent Channel Flows

We develop a new method for the derivation of stochastic normalized Langevin models for particle dispersion in non-homogeneous turbulent flows. Using the near-equilibrium assumptions we utilize the Chapman-Enskog expansion for the solution of corresponding Fokker-Planck equation to obtain the diffusion matrix and drift vector. To derive the drift vector we use the Furutsu-Novikov approach to obtain the exact asymptotic expression for the drift velocity, which provides the consistency of the proposed model with passive scalar modelling. We show the validity of the near-equilibrium assumptions for so-called diffusional particles in the viscous sublayer, which velocities are comparable to the local fluid velocities, despite the strong inhomogeneity of particle statistics near the wall. This justifies the suitability of proposed approach for the modelling of particle transport in wall-bounded turbulent flows. The results of simulation of particle concentration, second moments of particle velocity and deposition rates in particle-laden channel and pipe flows obtained with the proposed model demonstrate the good agreement with both experimental and DNS/Lagrangian tracking data in a wide range of particle Stokes number.