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

Xiaohui MengEwe-Wei Saw
Dec 2022
We perform direct numerical simulation (DNS) to study the clustering ofsmall, heavy, monodisperse particles subject to collision-coagulation inturbulent flow (i.e., colliding particles always coagulate (coalesce) intolarge ones). We find that collision-coagulation causes the radial distributionfunction (RDF) of the particles to decrease strongly at particle separationdistances $r$ close to the particle diameter $d$. However, the RDF do notdecrease indefinitely but approach a finite value in the limit of $r\to d$. Westudy how the characteristics of this "depletion zone" relate to the particleStokes number (St), particle diameter, and the Reynolds number of the turbulentflow. A collision-induced modulation factor $\gamma_{c}$ is defined torepresent the degree of RDF depletion due to collisions-coagulation. In theregion where $\gamma_c(r)$ is a quasi-power-law, the corresponding power-lawexponent $\tilde{c}_1$ only depends weakly on $St$. The overall trend of$\tilde{c}_1$ with respect to $St$ is similar to that of the classicalpower-law exponent $c_{1}$ appearing in the RDF of non-colliding particles,i.e., the exponent increase at small $St$, peak around $St \approx 0.7$, anddecrease thereafter. The same qualitative trend is also observed for thelimiting values of $\gamma_c$ at $r\to d$. A complementary investigation on theStokes number trend of the full RDF in the depletion zone is conducted. Theslope of RDF appears constant for $St\ll1$ but is changing when $St$ is gettinglarge. The position where the RDF starts to decrease is found to be$St$-dependent. The depletion zone is insensitive to the flow Reynolds numberand $\gamma_c$ of different $Re_{\lambda}$ overlap. With changing particlediameter $d$, the reduction of RDF occurs at scales that shift accordingly andalways starts at around $2.4d-3d$. The shape of $\gamma_c(r)$ is independent ofchanges in $d$.