Prediction of preferential concentration statistics from Eulerian two-point correlations

Non-local statistics of preferential concentration in the inertial range of turbulence are studied by considering the size distribution of high number density regions of particles, "clusters," and low number density regions, "voids". Direct Numerical Simulation is used to compute particle and fluid phase statistics in particle-laden isotropic turbulence and turbulent square duct flow, including the size distributions of clusters and voids. It is found, in agreement with the literature, that clusters are correlated with low enstrophy flow structures and voids with high enstrophy flow structures. Statistical topography is used to predict the size distributions of clusters and voids, which are in good agreement with those computed from the isotropic turbulence simulations. This suggests that the underlying carrier phase turbulence can be used to quantitatively model more complicated statistics of the particle phase in homogeneous and isotropic turbulence. However, the statistical topography methods poorly predict preferential concentration in an anisotropic turbulent square duct flow. The model shortcomings are discussed.