Sharp depletion of radial distribution function of particles due to collision and coagulation inside turbulent flow: A systematic study

The clustering (preferential concentration) and collision of particles in turbulent flows is a significant process in nature, such as in the precipitation process of atmospheric clouds. We perform direct numerical simulation (DNS) to study the clustering of small, heavy, monodisperse particles subject to collision-coagulation in turbulent flow [i.e., colliding particles always coagulate (coalesce) into larger ones]. The simulations do not include gravitational effects and hydrodynamic interactions among particles. We find that collision-coagulation causes the radial distribution function (RDF) of the particles to decrease strongly at particle separation distances r close to the particle diameter d. However, we observe that the RDF does not decrease indefinitely but approaches a finite value in the limit of r -> d. We study how the properties of this "depletion zone" relates to the particle Stokes number (St), particle diameter, and the Reynolds number of the turbulent flow. A collision-induced modulation factor gamma(c) is defined to represent the degree of RDF depletion due to collision-coagulation. In the region where gamma(c)(r) is a quasi-power-law, we find that the effective power-law exponent (c) over tilde (1) depends only weakly on St in the regime of St << 1, but increases significantly for larger St and peaks at around St approximate to 0.7. The same qualitative trend is also observed for the limiting values of gamma(c) at r -> d. We find that the overall trend of (c) over tilde (1) with respect to St is qualitatively similar to that of the classical power-law exponent c(1) appearing in the RDF of noncolliding particles, except that (c) over tilde (1) is barely changed at small St and the magnitude of the trend is much weaker. A complementary investigation on the Stokes number trend of the full RDF in the depletion zone is performed. The slope of the RDF appears to be constant for St << 1 but changes as St becomes large. The location of the RDF's peak is found to be St-dependent. We found that the depletion zone is insensitive to the flow Reynolds number and that gamma(c) of different Re-lambda overlap. As the particle diameter d changes, the reduction of the RDF occurs on scales that shift accordingly, and always starting at around 2.4d-3d. We also find that the shape of gamma(c)(r) is independent of changes in d.