Bulletin of the American Physical Society
73rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 65, Number 13
Sunday–Tuesday, November 22–24, 2020; Virtual, CT (Chicago time)
Session R12: ParticleLaden Flows: Clustering (5:00pm  5:45pm CST)Interactive On Demand

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R12.00001: Toward improved heat transfer models for stronglycoupled particleladen flows Sarah Beetham, Aaron Lattanzi, Jesse Capecelatro At sufficient mass loading, gassolid flows exhibit the development of largescale, coherent structures (clusters) due to interphase momentum coupling. This behavior is particularly prevalent in the context of circulating fluidized bed reactors, commonly used in the upgrading of feedstock into fuel. In this talk, we demonstrate that heterogeneity caused by particle clustering degrades gassolid contact and ultimately impedes heat transfer between the phases. Here, we employ high resolution EulerianLagrangian (EL) simulations to quantify the role of clustering on heat transfer. This is accomplished via a twostep approach, in which fullydeveloped particle clustering is first established under isothermal conditions and then fed into a secondary simulation with prescribed temperature difference between the phases. The secondary simulation develops a thermal length scale in the flow direction as the phases tend to equilibrium, thereby allowing us to quantify the effect of clustering on heat transfer. Additionally, models will be proposed for the unclosed terms appearing in the averaged twofluid equations that account for solids heterogeneity. [Preview Abstract] 

R12.00002: On Understanding Preferential Concentration for ParticleLaden Isotropic Turbulent Flows using Combined Theoretical and DataDriven Techniques Kyle Pietrzyk, Fady Najjar, Jeremy Horwitz, Roger Minich A consistent observation in particleladen turbulence is the tendency of inertial particles to sample particular regions of a flow, known as preferential concentration. As the Stokes number increases from zero, particle trajectories become misaligned with the flow field and particle concentration gradients form. Previous investigations found that regions of high stainrate and low vorticity promote the accumulation of particles for a low Stokes number. As the Stokes number increases, however, the mechanisms behind particle behaviors become more complex. In this work, a theoretical understanding of preferential concentration is motivated by a datadriven analysis to identify clustered particles in isotropic turbulence. Features that promote and demote particle accumulation are identified through theoretical means and verified using simulation data of particleladen, isotropic turbulence for multiple Stokes numbers. [Preview Abstract] 

R12.00003: Analysis of divergence and rotation of the intertial particle velocity in high Reynolds number turbulence Thibault Oujia, Keigo Matsuda, Kai Schneider Inertial particle data from threedimensional direct numerical simulations of particleladen homogeneous isotropic turbulence at high Reynolds number are analyzed using Voronoi tessellation of the particle positions and considering different Stokes numbers. A finitetime measure to quantify divergence and the rotation of the particle velocity by determining respectively the volume change rate of the Voronoi cells and their rotation is proposed. For inertial particles the probability distribution functions (PDF) of the divergence and of the curl deviate from that for fluid particles. Joint PDFs of the divergence and the Voronoi volume illustrate that the divergence is most prominent in cluster regions and less pronounced in void regions. For larger volumes the results show negative divergence values which represent cluster formation and for small volumes the results show positive divergence values which represents cluster destruction/void formation. Moreover, when the Stokes number increases the divergence takes larger values, which gives some evidence why fine clusters are less observed for large Stokes numbers. Finally, the PDFs of the particle vorticity have much heavier tails compared to the fluid vorticity, and the extreme values increase significantly with the Stokes number. [Preview Abstract] 

R12.00004: Experimental analysis of clustering in particle risers Kee Onn Fong, Filippo Coletti In particle risers, where the dispersed phase fall against a rising fluid, clusters are observed to form near the walls. These have sizes of order of the riser diameter and alters the bulk mass and heat transfer properties of the device. Previous experimental studies focused on clusters in risers are either limited to quasitwodimensional configurations, report only the bulk properties, or observe only the nearwall dynamics. Here we present experimental observations on the velocities and spatial distribution of particles in a threedimensional, gassolid riser with particle volume fractions approaching 1{\%}. The setup consists of a vertical square duct in which air flows upwards against falling 212 $\mu $m glass spheres. We use a backlighting technique and a highspeed camera to image and quantify the spatial and temporally resolved particle concentration and velocity fields. By controlling the particle feed rate and the flow rate of the fluidizing air, volume fractions and bulk flow Reynolds number are adjusted independently. Results show that, in the present range of parameters, clustering of particles appear beyond a critical volume fraction regardless of fluidization velocities. The findings are discussed in the context of collective particle behaviour, the influence of clusters on the mean statistics, and modelling strategies for dense particleladen flows. [Preview Abstract] 

R12.00005: Falling snow behaves as inertial particles in turbulence Filippo Coletti, Cheng Li, Kaeul Lim, Tim Berk, Aliza Abraham, Michael Heisel, Michele Guala, Jiarong Hong The effect of turbulence on snow precipitation is not incorporated in present weather forecasting models. Here we show that turbulence is in fact key to determine both fall speed and spatial distribution of settling snow. We consider three snow fall events under vastly different levels of atmospheric turbulence. We characterize the size and morphology of the snow particles, and we simultaneously image their velocity, acceleration, and concentration over vertical planes about 30 square meters in area. We find that turbulencedriven settling enhancement explains otherwise contradictory trends between the particle size and velocity. The estimates of the Stokes number and the correlation between vertical velocity and local concentration indicate that the enhanced settling is rooted in the preferential sweeping mechanism. When the snow fall speed is large compared to the characteristic turbulence velocity, the crossing trajectories effect results in strong accelerations. When the conditions of preferential sweeping are met, the concentration field is highly nonuniform and clustering appears over a wide range of scales. These clusters display the signature features seen in canonical settings: powerlaw size distribution, fractallike shape, vertical elongation, and large fall speed that increases with the cluster size. These findings demonstrate that the fundamental phenomenology of particleladen turbulence can be leveraged towards a more predictive understanding of snow precipitation. [Preview Abstract] 

R12.00006: The effect of particle to fluid density ratio on the clustering of inertial particles in turbulence Anirban Bhattacharjee, Mahdi Esmaily Inertial particles show negligible clustering in turbulence when the Stokes number (St) is either large or small but show substantial clustering at St $=$ O(1). This nonmonotonic trend has been analytically proven and numerically verified in the past with the assumption that the particle to fluid density ratio is infinitely large. In this work, we investigate the more physically realistic case of particle clustering in flows where the particle to fluid density ratio is finite. The Lyapunov exponent which characterizes the amount of clustering (negative values) or dispersion (positive values) has been analytically derived as a function of Stokes number and particle to fluid density ratio. At infinite density ratio, it has been shown that much of the behavior of particles in 3D turbulence can be explained using a 1D canonical flow that oscillates at a single frequency. We employ this canonical flow to show that a decrease in particle to fluid density ratio leads to less clustering and more dispersion when the flow is hyperbolic, whereas in elliptical flows, there is no clustering and the dispersion decreases with a decrease in density ratio. [Preview Abstract] 

R12.00007: On largescale clustering in particle laden turbulence Keigo Matsuda, Kai Schneider, Katsunori Yoshimatsu The nonlinear dynamics of inertial particles in high Reynolds number turbulence, and in particular clustering and void formation, are important fundamental processes in multiphase flow. Here we study particle data from threedimensional direct numerical simulations of particleladen homogeneous isotropic turbulence at high Reynolds number, up to $Re_\lambda=678$ and with up to $3.2 \times 10^9$ particles, computed at resolution $4096^3$. The analyzed flow data show that for sufficiently high Reynolds number the particle density spectra exhibit two well pronounced bumps. The secondary bump at larger scale is attributed to large scale clustering of inertial particles. We found that this behavior is generic and independent of the forcing scheme used to maintain a statistically stationary flow. Possible explanations for this largescale organization of the particles will be presented. [Preview Abstract] 

R12.00008: Topological and temporal analysis of particle clusters in turbulent flows using densitybased clustering algorithms. Alvaro Tomas, Laura Villafane A novel method for the identification and temporal tracking of particle clusters in turbulent particleladen flows is presented. It makes use of densitybased clustering algorithms such as DBSCAN and OPTICS in order to discern regions of high particle concentrations, labeled as clusters, from those with lesser particles. The key features of the proposed methodology are its ability for identification and tracking of particle clusters in 3D and 2D, its robustness to particle number density, the absence of independent user defined parameters, and its computational efficiency for large data sets. The flexibility on the data dimensionality, and in part the reduced computational cost, are rooted on the treatment of 3D particle positions as multiple 2D projections into equidistant parallel planes. Clustering algorithms are used on each plane to identify clouds of particles conforming independent clusters, and the topology of each cluster is then condensed into boundary particles and a limited set of representative internal particles that define the 2D skeleton. This reduced set of particles is used to reconstruct 3D topologies and to track the cluster evolution in time at consecutive time steps. Cluster volume statistics are in good agreement with those obtained using more traditional Voronoi based analysis, with the new proposed method showing a significant reduction in computational cost. [Preview Abstract] 

R12.00009: Forcing in DNS of Isotropic Turbulence and its Effects on Closure Model for the Diffusion Current of HighInertia Particle Pairs Sarma Rani, Donald Koch We developed a closure approximation for the phasespace diffusion current in the probability density function kinetic equation for monodisperse, highStokesnumber particle pairs. We investigate the effects of the nature of forcing on the Eulerian twotime correlations of fluid relative velocities computed through DNS of isotropic turbulence. Two forcing schemes, deterministic and stochastic, were employed in the DNS runs. In the stochastic scheme, one also needs to specify the correlation time scale $T_f$ of the UhlenbeckOrnstein (UO) processes that constitute the forcing. DNS runs based on the stochastic forcing were undertaken for five values of $T_f = T_E/4,~T_E/2,~T_E,~2T_E$, and $4T_E$, where $T_E$ is the largeeddy time scale obtained from the DNS run with deterministic forcing. At $Re_\lambda \approx 80$ and $210$, the Eulerian twotime correlation of fluid relative velocities seen by the stationary particles were computed. It is seen that the correlations obtained from the deterministicforcing DNS runs were higher than those from the stochasticforcing runs, the differences being substantially more pronounced at larger separations and for higher $Re_\lambda$. [Preview Abstract] 

R12.00010: Mechanisms governing the settling velocities of inertial particles in wallbounded turbulence David Richter, Andrew Bragg, Guiquan Wang In isotropic, homogeneous turbulence, it is wellrecognized that inertial particles settle at a rate which can exceed their terminal velocity, due to the socalled preferential sweeping mechanism. At the same time, it is also known that inertialess particles subject to gravitational settling in the logarithmic layer near a wall distribute in such a way as to exhibit a powerlaw profile in mean concentration. In this study, direct numerical simulations with Lagrangian particle tracking are used to explore the effects of particle inertia on settling through wallbounded turbulence. As in the case of isotropic turbulence, inertia leads to clustering and an enhanced settling rate as compared to the particle terminal velocity, but the inhomogeneous nature of wall turbulence gives rise to multiple underlying mechanisms and regimes of inertial effects. In this work, we explore these phenomena from a PDFbased description of the dispersed phase, discuss the prospects of applying perturbation theory to account for particle inertia, and explore the possibility of correcting simple theory in order to predict mean settling rates and connect vertical fluxes with average concentration profiles. [Preview Abstract] 

R12.00011: Predicting particle concentration enhancement due to preferential concentration in a mechanicallydriven regime using the twofluid equations Sara Nasab, Pascale Garaud Using Direct Numerical Simulations (DNSs), we find that particle concentration enhancement follows a simple scaling law, derived from arguments of dominant balance. We consider a twophase system characterized by a dilute collection of small inertial particles in a turbulent carrier flow driven by an imposed body force. We use the twofluid equations, in which we apply a continuum treatment to the particles and solve for the particles and fluid separately. We find that when the system reaches a statistically steady state, the maximum particle concentration enhancement over the mean scales with the rms fluid velocity, the particle stopping time, and the "assumed" particle diffusivity. This recovers previous results obtained in the context of the particleinduced RayleighTaylor instability (Nasab & Garaud, arXiv:2001.05588, 2020). [Preview Abstract] 

R12.00012: Experimental measurements of diatom trajectories and distributions in a smallscale turbulence tank Nimish Pujara, Kevin Du Clos, Stephanie Ayres, Lee KarpBoss, Evan Variano Interactions of phytoplankton (aquatic photosynthetic microorganisms) with ambient turbulence has important consequences for life in the ocean since their vertical transport affects primary production at the base of the ocean food web. To understand this vertical transport, we use an experimental setup where the motion of live Cosinodiscus diatom cells is measured in a 3D volume using a Volumetric Particle Imager (VoPI) in a smallscale turbulence tank. The tank is small enough to allow use of labgrown cultures in sea water and produces a turbulent flow with homogeneous statistics and a low mean flow in the tank centre. The VoPI is be able to measure 3D positions of individual cells that can be tracked to obtain cell trajectories, cell velocities, and spatial distributions of cells. Experimental data from tracer particles and phytoplankton cells show that the rootmeansquared velocities of diatom cells in turbulence are similar to those of tracer particles, but diatom cells show increased clustering at small scales relative to tracer particles. Moreover, this clustering does not show a simple Stokes number scaling leading us to postulate that the flow Reynolds number also plays an important role for diatomturbulence interactions at small scales. [Preview Abstract] 

R12.00013: Clustering of Inertial Particles in Turbulent Flow Through a FaceCentered Cubic Cell Xiaoliang He, Thibault Oujia, Benjamin Kadoch, Keigo Matsuda, Kai Schneider, Sourabh Apte Fine inertial particle migration, transport and deposition is of importance in several applications such as hyporheic exchange of river beds, gravel packs in enhanced oil recovery, among others. Specifically, how turbulence within confined geometries of a porous bed affects migration, clustering, and deposition of fine particles is of importance. Direct numerical simulation is performed to investigate effect of turbulent flow in a face centered cubic porous unit cell on the transport of inertial particles at different Stokes numbers ($St_p = 0.01, 0.1, 0.5, 1$, and $2$) and at a pore Reynolds number of 500. Particles are advanced using oneway coupling and collision of particles with pore walls is modeled as perfectly elastic specular reflection. The pattern of clustering is investigated using multiscale wavelet analysis and area of Voronoi tessellation cells. The results are compared with preferential concentration in forced isotropic turbulence to investigate the effect of geometric confinement on particle clustering. It is shown that the general features of cluster and void formation and higher order statistics of number density of particles are modified by the wall collision creating very fine scale clusters. [Preview Abstract] 
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