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

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 $d$.

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