Filtered volume fraction fluctuations: a measure to model clustering in dilute, non-collisional particle-laden flow

Turbulent particle-laden flows are known to give rise to spatial heterogeneity (e.g. clustering) characterized by two-point statistics. However, most coarse-grained models only solve for one-point moments, challenging their ability to accurately reproduce important two-phase flow statistics. In this talk, we present a new set of equations describing the evolution of these flows that include fluctuating components of filtered fields that describe the level of clustering present in these flows. We demonstrate that for dilute heavy particles settling in homogeneous isotropic turbulence, the averaged filtered drag and filtered Reynolds-stress like term that dictates enhanced settling is correlated to this description of volume fraction fluctuation. A data-driven approach that efficiently traverses parameter space in direct numerical simulations to inform closures is proposed, providing both descriptive insights and directions for future modeling. The evolution of the fluctuation of filtered volume fraction is shown to be valuable in that it may enable better fits for unclosed quantities related to particle drag and particle-phase momentum flux in coarse-grained simulations.