Particle-resolved direct numerical simulation (PR-DNS) is used to quantify the drag force on clustered particle configurations over the solid phase volume fraction range of 0.1 ≤ φ ≤ 0.35 and the mean slip Reynolds number range of 0.01 ≤ Re m ≤ 50. The particle configurations and flow parameters correspond to gas-solid suspensions of Geldart A particles in which formation of clusters have been reported. In our PR-DNS, we use clustered particle configurations that match cluster statistics observed in experimental studies.To generate the particle configurations, we perform discrete element method (DEM) simulations of homogeneous cooling gas (HCG) systems with cohesive and inelastic particles in the absence interstitial fluid. Clustered particle subensembles are then extracted from HCG simulations to match the statistics of cluster size distributions observed in experiments. These sub-ensembles are used for PR-DNS. It is found that the mean drag on clustered configurations decreases when compared to the drag laws for uniform particle configura- * tions. The maximum drag reduction belongs to the configuration with low solid-phase volume fraction φ = 0.1 in Stokes flow, and is about 35%. The drag reduction reduces with increase in both φ and Re m . A clustering metric is introduced to explain the behavior of the drag reduction with respect to solid-phase volume fraction. Also the behavior of the drag reduction with mean slip Reynolds number is related to the Brinkman screening length. PR-DNS results are then used to propose a clustered drag model for the range of flow parameters considered in this study. This clustered drag model provides a smooth transition between the uniform and clustered states by means of a weighting function with two model parameters.

We treat the case of an undriven gas of inelastic hard-spheres with short-ranged attractive potentials via an extension of the pseudo-Liouville operator formalism. New evolution equations for the granular temperature and coordination number are obtained. The granular temperature exhibits deviation from both Haff's law and the case of long-ranged potentials. We verify this departure using soft-sphere discrete element method simulations. Excellent agreement is found for the duration of the simulation even beyond where exclusively binary collisions are expected. Simulations show the emergence of strong spatial-velocity correlations on the length scale of the last peak in the pair-correlation function but do not show strong correlations beyond this length scale. We argue that molecular chaos may remain an adequate approximation if the system is modelled as a Smoluchowski type equation with aggregation and break-up processes. C 2015 AIP Publishing LLC.

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An analytical framework for calculating the filtration efficiency of polydisperse aerosols in a granular bed is developed for cases where inertial impaction and interception are the principal filtration mechanisms. This framework is used to develop a model for the polydisperse single‐collector efficiency from monodisperse single‐collector efficiency correlations. Conceptually, the polydisperse model is developed by transforming the probability density of particle radius into a probability density of particle Stokes number that is then used to weight the monodisperse single‐collector efficiency at a given Stokes number. An extension of this polydisperse filtration concept results in an analytical solution for the axial variation of polydisperse particle flux in a random three‐dimensional granule configuration. In order to verify the analytical results for polydisperse particle filtration, a granule‐resolved direct numerical simulation approach is coupled with Lagrangian particle tracking to simulate filtration of polydisperse aerosols in a granular bed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3594–3606, 2015

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