Sharp depletion of radial distribution function of particles due to collision and coagulation inside turbulent flow

Abstract

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 large ones). 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, the RDF do not decrease indefinitely but approach a finite value in the limit of $r\to d$. We study how the characteristics of this "depletion zone" relate 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 collisions-coagulation. In the region where ${\gamma }_c(r)$ is a quasi-power-law, the corresponding power-law exponent ${\tilde{c}}_1$ only depends weakly on $St$. The overall trend of ${\tilde{c}}_1$ with respect to $St$ is similar to that of the classical power-law exponent $c_1$ appearing in the RDF of non-colliding particles, i.e., the exponent increase at small $St$, peak around $St\approx 0.7$, and decrease thereafter. The same qualitative trend is also observed for the limiting values of ${\gamma }_c$ at $r\to d$. A complementary investigation on the Stokes number trend of the full RDF in the depletion zone is conducted. The slope of RDF appears constant for $St\ll 1$ but is changing when $St$ is getting large. The position where the RDF starts to decrease is found to be $St$-dependent. The depletion zone is insensitive to the flow Reynolds number and ${\gamma }_c$ of different $R{e}_{\lambda }$ overlap. With changing particle diameter $d$, the reduction of RDF occurs at scales that shift accordingly and always starts at around $2.4d-3d$. The shape of ${\gamma }_c(r)$ is independent of changes in $d$.