Single-point closures for turbulent multiphase flow that incorporate two-point statistics through filtered fields

Turbulent multiphase flows exhibit rich patterns of particle clustering and preferential concentration that are characterized by two-point spatial (and temporal) correlations. However, tractable models of spatially inhomogeneous flows that are useful for large-scale simulation necessarily rely on single-point theories based on the average measure of fluid (or particle) volume in each geometric volume. Unfortunately, signatures of clustering that appear in the two-point measure of particle volume (or pair correlation) disappear in the single-point limit. Here a new result is presented which shows how filtering the instantaneous volume fraction field permits the signatures of clustering to be retained in the single-point limit, thereby opening the door to modeling the aforementioned phenomena through single-point closures.