Analysis of tracer particle migration in inhomogeneous turbulence

Previous studies [J.M. Maclnnes, F.V. Bracco, Stochastic particle dispersion modeling and the tracer particle limit, Physics of Fluids A 4 (1992) 2809–2824; X.Q. Chen, Heavy particle dispersion in inhomogeneous, anisotropic, turbulence flows, International Journal of Multiphase Flow 26 (2000) 635–661; T.L. Bocksell, E. Loth, Random walk models for particle diffusion in free-shear flows, AIAA Journal 29 (2001) 1086–1096] have shown that the commonly applied stochastic separated flow (SSF) model predicts unphysical results when dealing with the dispersion of tracer particles in inhomogeneous flows. This problem is explored, with regards to the discontinuous random walk model, by considering an idealized flow with constant mean velocity with two regions of constant turbulent kinetic energy. Using the probability density functions (PDFs) for the turbulent velocities it is shown that there is a higher probability of particles traveling into the low kinetic energy region than there are traveling to the region of high kinetic energy, thus resulting in a net migration of particles to the region of low kinetic energy. Corrections that apply a correction velocity and/or adjust the fluctuating velocity based on the local value of the turbulent kinetic energy are analyzed and tested.