Particle-resolved Simulations Research Articles

Analysis of Particle-Resolved CFD Results for Dispersion in Packed Beds

Dispersion is the spreading of a solute while it is moved by a flowing medium. The study of dispersion in catalytic chemical reactors is fundamental to their design, since dispersion influences the reactant and product transport within the bed. In this paper, longitudinal and transverse dispersion of an inert tracer in slender packed beds of spheres and spherocylinders is studied using Computational Fluid Dynamics simulations. The focus is on the analysis of dispersion from full field data. The purpose is to develop a methodology that can later also be used to characterize dispersion from full field experimental data such as MRI measurements. Results obtained by means of particle-resolved CFD simulations are discussed. Spatial distributions and residence times are analyzed and the results are interpreted by comparison to results obtained from 1D and 2D convection-diffusion equations.

Particle-resolved CFD simulations of local bubble behaviors in a mini-packed bed with gas–liquid concurrent flow

• Particle-resolved CFD method is established with good model reliability. • The local bubble behaviors in packed bed are numerically investigated. • Gas residence time can be adjusted by controlling flow rate and packing wettability. • Gas phase is more evenly distributed in the packed bed with hydrophobic particles. The controlling of residence time and gas–liquid interface distribution is critical issue in operating packed bed reactors with gas–liquid concurrent upflow. Herein, gas–liquid interface in the particle-resolved packed bed is calculated with the Volume of Fluid (VOF) method. The influences of flow rate, bed supporting wire, packing wettability and surface tension on gas–liquid upflow in a mini-packed bed are studied. The periodic bubble flow behavior at bed bottom is observed due to bubble coalescence. Increasing superficial liquid and gas velocity can shorten the time needed for bubble traveling through the bed and increase the pressure drop. The supporting wires aggravate the degree of bubbles coalescence and slightly increase the residence time of the gas phase. The hydrophobic packing can promote the uniform distribution of the gas–liquid interface and greatly increase the gas–liquid interface area. The bubble behavior in the packed bed can be changed by manipulating liquid surface tension.

Particle-resolved simulations of local liquid spreading in packed beds: Effect of wettability at varying particle size

Packed beds are widely used to perform solid-catalyzed gas–liquid reactions, e.g., hydrodesulfurization, oxidation, and hydrogenation. The overall performance of packed beds is often governed by local liquid spreading. In the present work, the dynamics of liquid spreading through a randomly packed three-dimensional bed is investigated using particle-resolved volume-of-fluid simulations. The effect of particle surface-wettability (θ) at varying particle diameter (dp) on the relative contributions of forces governing the dynamics of liquid spreading is analyzed using the Ohnesorge (OhI), Weber (WeI), and ABI (proposed in the present work) numbers. With the help of simulated liquid spreading and these numbers, we show that the contribution of inertial force is significant at the beginning of liquid spreading irrespective of θ as well as dp and promotes lateral liquid spreading (ABI >1, WeI >1). Once the dominance of inertial force diminishes, the capillary force leads to a substantial increase in the lateral spreading (ABI > 1, WeI < 1). In the final stages, the gravitational force dominates restricting the lateral liquid spreading (ABI < 1). Furthermore, we have proposed a regime map constructed using ABI and WeI, which provides a relationship between different forces and the resultant liquid spreading at breakthrough. We also show that the dominance of capillary force (ABI >1, WeI <1) results in the highest lateral spreading, whereas the flow dominated by inertial (ABI >1, WeI >1) and gravitational force (ABI ≪ 1) leads to intermediate and least lateral liquid spreading, respectively.

Thermal radiation effects on heat transfer in slender packed-bed reactors: Particle-resolved CFD simulations and 2D modeling

Radial heat management is crucial for a safe and stable operation of fixed-bed reactors with small tube-to-particle diameter ratios (N). Under high temperature conditions, thermal radiation can contribute substantially to the overall heat transfer. In the present work, the influence of radiation is studied with particle resolved computational fluid dynamics (PRCFD) in a fixed-bed reactor consisting of 1000 spheres and rings with N = 5.1 over 300 < Rep< 2000 and for three different temperature levels (300–800 ∘C). Two heat transfer parameters, i.e., the wall Nusselt number Nuw and the effective radial thermal conductivity of the bed keff, r, are derived directly from PRCFD. While the radiation effect is minor in keff, r, it is substantial for Nuw, which is not captured adequately in the current correlations presented in literature. Depending on the temperature level and flow conditions, thermal radiation between the hot wall and the packed bed intensifies the radial heat transfer represented by an increase of up to 170 % in Nuw and 65% in keff, r. A 2D axisymmetric pseudo-homogeneous model including the derived heat transfer parameters can predict the radial temperature profile of the PRCFD with reasonable accuracy also with radiation except for the near-wall region.

Characterization of lift force and torque in prolate ellipsoid suspensions

The paper derives correlations for lift force and fluid torques acting on stationary prolate ellipsoid suspensions of aspect ratio (AR) 2.5, 5, and 10 subjected to uniform flow. Particle Resolved Simulations (PRS) are conducted on a suspension of infinite extent in two directions for Reynolds number 10 ≤ Re ≤ 200 and solid fractions (φ) between 0.1 ≤ φ ≤ 0.3.The suspension-mean lift-to-drag ratio varies between 7% to 14% at Re=10 which increases to 14% ~ 22% at Re=200. The torque-induced tip rotational acceleration can reach 38% ~ 85% of drag-induced translational acceleration at Re = 200. Single particle lift force and torque correlations of (Fröhlich et al., 2020) are modified and adapted to predict current angular-mean lift and torque data. The resulting lift correlation captures the PRS data within an average deviation below 7%. Torque exhibits a somewhat more complex dependency at AR = 10 than the assumed sinθ ∙ cosθ variation but nevertheless the correlations predict angular-mean values with mean relative deviations of 16.6% at AR = 10.

Particle Scale Investigation of Influencing Factors on Heat Transfer in Nonspherical Particle–Fluid System

Abstract Heat transfer characteristics of random suspensions of 0.25 aspect ratio (AR) cylinders are investigated for Reynolds numbers (Re) between 10 and 300 and solid fraction (φ) ranging from 0.1 to 0.3 using particle resolved simulations. The effect of particle inclination with respect to flow and particle clustering on heat transfer is investigated. The Nusselt number decreases with an increase in inclination angle and the dependence becomes stronger as φ and Re increase. On the other hand, while prolate ellipsoid suspensions of AR 2.5 follow the same trend, the Nusselt number increases with inclination angle as AR increases to 5 and 10 and as φ increases. Local particle clustering nominally decreases the Nusselt number because of the dominance of thermal wakes. At low φ, this effect is felt only at low Re, but as φ increases, the effect spreads to higher Re. Similar but weaker trends are also found in suspensions of prolate ellipsoids of AR 2.5, 5, and 10. High AR, low Re prolate ellipsoids exhibit the greatest dependence of Nusselt number on local solid fraction. Implementation of two independent definitions of reference length, i.e., volume equivalent sphere diameter deq for ellipsoids and diameter dp of the cylindrical particle in the correlation of Tavassoli et al. (2015, “Direct Numerical Simulation of Fluid-Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles,” Chem. Eng. Sci., 129, pp. 42–48) provides good estimates of the respective suspension mean Nusselt numbers.

The rheology of confined colloidal hard disks.

Colloids may be treated as "big atoms" so that they are good models for atomic and molecular systems. Colloidal hard disks are, therefore, good models for 2d materials, and although their phase behavior is well characterized, rheology has received relatively little attention. Here, we exploit a novel, particle-resolved, experimental setup and complementary computer simulations to measure the shear rheology of quasi-hard-disk colloids in extreme confinement. In particular, we confine quasi-2d hard disks in a circular "corral" comprised of 27 particles held in optical traps. Confinement and shear suppress hexagonal ordering that would occur in the bulk and create a layered fluid. We measure the rheology of our system by balancing drag and driving forces on each layer. Given the extreme confinement, it is remarkable that our system exhibits rheological behavior very similar to unconfined 2d and 3d hard particle systems, characterized by a dynamic yield stress and shear-thinning of comparable magnitude. By quantifying particle motion perpendicular to shear, we show that particles become more tightly confined to their layers with no concomitant increase in density upon increasing the shear rate. Shear thinning is, therefore, a consequence of a reduction in dissipation due to weakening in interactions between layers as the shear rate increases. We reproduce our experiments with Brownian dynamics simulations with Hydrodynamic Interactions (HI) included at the level of the Rotne-Prager tensor. That the inclusion of HI is necessary to reproduce our experiments is evidence of their importance in transmission of momentum through the system.

Mach and Reynolds number dependency of the unsteady shock-induced drag force on a sphere

Shock–particle interaction is an important phenomenon in a wide range of technological applications and natural phenomena, and the development of accurate models for this interaction is therefore of interest. This study investigates the transient forces during shock–particle interaction at particle Reynolds numbers between 100 and 1000, and incident shock wave Mach numbers between 1.22 and 2.51. This is achieved with the aid of particle-resolved large-eddy simulations. The simulation results show that shock–particle interaction differs qualitatively for subcritical and supercritical incident flow conditions. By decomposing the total force, the inviscid and viscous unsteady forces are estimated. The inviscid unsteady component is significantly larger than the viscous contribution, but the magnitude of the viscous component is comparable to steady-state drag. The predictions of current state of the art force models are compared to the computed particle forces. For subcritical flows, the models are quite successful in predicting the drag. For these conditions, the magnitudes of both the inviscid and viscous unsteady force models agree well with the simulation results, but the transient nature of the viscous unsteady force history is not well captured. For supercritical flows, the inviscid unsteady force model is not able to capture the force dynamics. This highlights the need for the development of unsteady force models for supercritical flow conditions.

Particle resolved simulation of sediment transport by a hybrid parallel approach

Sediment transport over an erodible sediment bed is studied by particle resolved simulations with a hybrid parallel approach. To overcome the challenges of load imbalance in the traditional domain decomposition method when encountering highly uneven distributions of particles in sediment transport, the parallel approach of Darmana et al. (2006) originally developed for point particle simulations is modified and implemented into particle resolved simulations. A novel memory optimization technique is proposed to reduce the memory requirement of the hybrid approach for spherical particles with equal size. The present hybrid parallel approach shows good scalability and high parallel efficiency in a challenging sediment transport test case with more than a million spherical particles. Our code is validated by several benchmark cases, and the results show good agreement with experimental and computational data in the literature. Furthermore, a turbulent flow over an erodible sediment bed is simulated. An extraction method is proposed to distinguish the saltating and rolling particles and extract impact and rebound information of the particle–mobile bed interaction. The probability distribution functions (PDF) of several saltation parameters such as velocity, angle, and spanwise angular velocity of impact and rebound events are presented. Splash functions are established for the particle–mobile bed interaction in the turbulent flow, which was rarely investigated in the experiments and is helpful to model the complex particle–bed interactions in turbulent flow.

Physics-inspired architecture for neural network modeling of forces and torques in particle-laden flows

We present a physics-inspired neural network (PINN) model for direct prediction of hydrodynamic forces and torques experienced by individual particles in stationary arrays of randomly distributed spheres. In line with our findings, it has recently been demonstrated that conventional fully connected neural networks (FCNN) are incapable of making accurate predictions of force variations in a stationary random array of spheres. The problem arises due to the large number of input variables (i.e., the locations of individual neighboring particles) leading to an overwhelmingly large number of training parameters in a fully connected architecture. Given the typically limited size of training datasets that can be generated by particle-resolved simulations, the NN becomes prone to missing true patterns in the data, ultimately leading to overfitting. Inspired by our observations in developing the microstructure-informed probability-driven point-particle (MPP) model in a previous work, we incorporate two main features in the architecture of the present PINN model: (1) superposition of pairwise hydrodynamic interactions between particles, and (2) sharing training parameters between NN blocks that model neighbor influences. These strategies helps to substantially reduce the number of free parameters and thereby control the model complexity without compromising accuracy. We demonstrate that direct force and torque prediction using NNs is indeed possible, provided that the model structure corresponds to the underlying physics of the problem. For a Reynolds number range of 2⩽Re⩽150 and solid volume fractions of 0.1⩽ϕ⩽0.4, the PINN’s predictions prove to be as accurate as those of other currently available microstructure-informed models.

Deep learning methods for predicting fluid forces in dense particle suspensions

Two deep learning methods, Multi-Layer Perceptron (MLP) network and Convolution Neural Network (CNN) are evaluated to predict drag forces in dense suspensions of ellipsoidal particles using data from Particle Resolved Simulations (PRS). The MLP is trained on the mean flow Reynolds number, solid fraction of the suspension, the aspect ratio of the particle, and orientation to flow direction. The CNN is given an additional 3D spatial map of the particle of interest and its immediate neighborhood via a distance function. The prediction capability of the trained networks is tested at different levels of complexity: on an unseen particle arrangement (Level 1), to all arrangements of an unseen numerical experiment (Level 2), and finally to all experiments of an unseen Reynolds number, solid fraction or aspect ratio (Level 3). The CNN is shown to perform better than the MLP for all testing levels except when testing on an unseen aspect ratio.

Shock interacting with a random array of stationary particles underwater

In this paper, particle-resolved inviscid simulations of shock propagation over randomly distributed beds are performed, with the goal of quantifying the force on individual particles. An important observation was that the inviscid drag force on some particles remained consistently positive, while others consistently negative, even long after the passage of the shock. These persistent forces are inviscid quasi-steady contributions which, with the viscous counterpart, will play an essential role in the particle's long-term dispersion if allowed to move in response to the force.

Particle-Resolved CFD Simulations of Isobutane and 2-Butene Alkylation over Complex-Shaped Zeolite Catalysts in Fixed Bed Reactors

Liquid alkylation of isobutane and 2-butene in zeolite catalysts is impeded by severe internal diffusion influences, which are reduced by optimizing the catalyst shape in this paper. We simulate this reaction in fixed beds filled with catalyst shapes of sphere, cylinder, quadrilobe, trilobe, and ring using the particle-resolved computational fluid dynamics (CFD) approach to address the effects of catalyst shape on voidage, bulk flow, pressure drop, heat transfer, reaction, and internal diffusion effectiveness factor. Among them, trilobes in beds have the highest 2-butene conversion under the same volumetric space velocity because of their advantages such as more even velocity profile, larger external surface area compared with cylinders, spheres, and quadrilobes, and larger catalyst volume compared with rings, which show the highest conversion under the same weight hourly space velocity (WHSV) due to their highest external surface area per volume. The 2-butene conversion indicator increases with the increase of the catalyst porosity. Our research will benefit the catalyst design for this reaction.

Dataset for the Heat-Up and Heat Transfer towards Single Particles and Synthetic Particle Clusters from Particle-Resolved CFD Simulations

Heat transfer to particles is a key aspect of thermo-chemical conversion of pulverized fuels. These fuels tend to agglomerate in some areas of turbulent flow and to form particle clusters. Heat transfer and drag of such clusters are significantly different from single-particle approximations commonly used in Euler–Lagrange models. This fact prompted a direct numerical investigation of the heat transfer and drag behavior of synthetic particle clusters consisting of 44 spheres of uniform diameter (60 μm). Particle-resolved computational fluid dynamic simulations were carried out to investigate the heat fluxes, the forces acting upon the particle cluster, and the heat-up times of particle clusters with multiple void fractions (0.477–0.999) and varying relative velocities (0.5–25 m/s). The integral heat fluxes and exact particle positions for each particle in the cluster, integral heat fluxes, and the total acting force, derived from steady-state simulations, are reported for 85 different cases. The heat-up times of individual particles and the particle clusters are provided for six cases (three cluster void fractions and two relative velocities each). Furthermore, the heat-up times of single particles with different commonly used representative particle diameters are presented. Depending on the case, the particle Reynolds number, the cluster void fraction, the Nusselt number, and the cluster drag coefficient are included in the secondary data.

Modeling high-speed gas–particle flows relevant to spacecraft landings

The interactions between rocket exhaust plumes and the surface of extraterrestrial bodies during spacecraft landings involve complex multiphase flow dynamics that pose significant risk to space exploration missions. The two-phase flow is characterized by high Reynolds and Mach number conditions with particle concentrations ranging from dilute to close-packing. Low atmospheric pressure and gravity typically encountered in landing environments combined with reduced optical access by the granular material pose significant challenges for experimental investigations. Consequently, numerical modeling is expected to play an increasingly important role for future missions. This article presents a review and perspectives on modeling high-speed disperse two-phase flows relevant to plume–surface interactions (PSI). We present an overview of existing drag laws, with origins from 18th-century cannon fire experiments and new insights from particle-resolved numerical simulations. While the focus here is on multiphase flows relevant to PSI, much of the same physics are shared by other compressible gas–particle flows, such as coal-dust explosions, volcanic eruptions, and detonation of solid material.

Heat Transfer Models for Dense Pulverized Particle Jets

Heat transfer is a crucial aspect of thermochemical conversion of pulverized fuels. Over-predicting the heat transfer during heat-up leads to under-estimation of the ignition time, while under-predicting the heat loss during the char conversion leads to an over-estimation of the burnout rates. This effect is relevant for dense particle jets injected from dense-phase pneumatic conveying. Heat fluxes characteristic of such dense jets can significantly differ from single particles, although a single, representative particle commonly models them in Euler–Lagrange models. Particle-resolved direct numerical simulations revealed that common representative particles approaches fail to reproduce the dense-jet characteristics. They also confirm that dense clusters behave similar to larger, porous particles, while the single particle characteristic prevails for sparse clusters. Hydrodynamics causes this effect for convective heat transfer since dense clusters deflect the inflowing fluid and shield the center. Reduced view factors cause reduced radiative heat fluxes for dense clusters. Furthermore, convection is less sensitive to cluster shape than radiative heat transfer. New heat transfer models were derived from particle resolved simulations of particle clusters. Heat transfer increases at higher void fractions and vice versa, which is contrary to most existing models. Although derived from regular particle clusters, the new convective heat transfer models reasonably handle random clusters. Contrary, the developed correction for the radiative heat flux over-predicts shading effects for random clusters because of the used cluster shape. In unresolved Euler–Lagrange models, the new heat transfer models can significantly improve dense particle jets’ heat-up or thermochemical conversion modeling.

Impact of dipole-dipole interactions on motility-induced phase separation.

We present a hydrodynamic theory for systems of dipolar active Brownian particles which, in the regime of weak dipolar coupling, predicts the onset of motility-induced phase separation (MIPS), consistent with Brownian dynamics (BD) simulations. The hydrodynamic equations are derived by explicitly coarse-graining the microscopic Langevin dynamics, thus allowing for a mapping of the coarse-grained model and particle-resolved simulations. Performing BD simulations at fixed density, we find that dipolar interactions tend to hinder MIPS, as first reported in [Liao et al., Soft Matter, 2020, 16, 2208]. Here we demonstrate that the theoretical approach indeed captures the suppression of MIPS. Moreover, the analysis of the numerically obtained, angle-dependent correlation functions sheds light into the underlying microscopic mechanisms leading to the destabilization of the homogeneous phase.

Geometric percolation of hard-sphere dispersions in shear flow.

We combine a heuristic theory of geometric percolation and the Smoluchowski theory of colloid dynamics to predict the impact of shear flow on the percolation threshold of hard spherical colloidal particles, and verify our findings by means of molecular dynamics simulations. It appears that the impact of shear flow is subtle and highly non-trivial, even in the absence of hydrodynamic interactions between the particles. The presence of shear flow can both increase and decrease the percolation threshold, depending on the criterion used for determining whether or not two particles are connected and on the Péclet number. Our approach opens up a route to quantitatively predict the percolation threshold in nanocomposite materials that, as a rule, are produced under non-equilibrium conditions, making comparison with equilibrium percolation theory tenuous. Our theory can be adapted straightforwardly for application in other types of flow field, and particles of different shape or interacting via other than hard-core potentials.

Modeling of shock-induced force on an isolated particle in water and air

The prediction of force on an isolated particle, while a shock is passing over it, is an important problem in many natural and industrial applications. Although the flow monotonically changes from the pre-shock to the post-shock state, the particle's force has been observed to behave nonmonotonically with a sharp peak when the shock is located halfway across the particle. This nonmonotonic behavior is due to the unsteady nature of the compression and rarefaction waves that radiate as the shock diffracts around the particle and, therefore, cannot be predicted by a quasi-steady model. An accurate force model must account for the unsteady nature of the flow and the sharp discontinues in the flow properties across the shock. In this work, we test four different inviscid models and observe that the compressible Maxey–Riley–Gatignol (C-MRG) model is the most accurate based on comparison with results from particle-resolved inviscid simulations at two different Mach numbers for both water and air as the medium. The C-MRG model is first demonstrated to predict the force on a stationary particle accurately and then extended to capture the force on a moving particle. Numerical complexities regarding the implementation of the C-MRG model are also discussed.

Accelerating particle-resolved CFD simulations of catalytic fixed-bed reactors with DUO

Simulation of fixed-bed catalytic reactors is important for engineering industrial technologies. The large number of catalytically active surface faces makes the application of microkinetic models too time consuming for large 3D simulations that include fully resolved particle structures (e.g., ≫ 10′s of particles). Such simulations, though, are often required for small tube-to-particle diameter ratio configurations, where local flow effects are difficult to capture with 1D or 2D simulations. A common solution for speeding up reactive computational fluid dynamics (CFD) involves the use of chemistry acceleration methods, including In-Situ Adaptive Tabulation (ISAT) and Cell Agglomeration (CA). In the present contribution, DUO (DETCHEMTM + OpenFOAM coupling) CFD software has been extended to include ISAT and CA methods for surface reactions, in particular, using a CA method that is simpler than other implementations of this acceleration technique. Speedup factors and errors were tabulated for an 86 spherical particle 3D resolved fixed-bed reactor, considering the exothermic methane catalytic partial oxidation (CPOX) and the endothermic dry reforming of methane (DRM) chemistries. For CPOX, a speedup factor of ∼ 7x was achieved, while for DRM, a speedup of ∼ 35x was obtained, with both cases achieving an acceptable error in the solution. Although a tighter error tolerance with ISAT and CA is shown to reduce the overall calculation error, for some engineering situations this tradeoff in speedup and accuracy will be acceptable. Achieving usable results in around 0.5 – 2 h instead of around 20-hours (for these chemistries on this particular grid, run on a 400-core cluster) can vastly improve the feasibility of computational fluid dynamics for the analysis of fixed-bed catalytic reactors including microkinetics mechanisms.