GPU accelerated MFiX-DEM simulations of granular and multiphase flows

In this research, a Graphical Processing Unit (GPU) accelerated Discrete Element Method (DEM) code was developed and coupled with the Computational Fluid Dynamic (CFD) software MFiX to simulate granular and multiphase flows with heat transfers and chemical reactions. The Fortran-based CFD solver was coupled with the CUDA/C++ based DEM solver through inter-process pipes. The speedup to the CPU version of MFiX-DEM is about 130–243 folds in the simulation of particle packings. In fluidized bed simulations, the DEM computation time is reduced from 91% to 17% with a speedup of 78 folds. The simulation of Geldart A particle fluidization revealed a similar level of importance of both fluid and particle coarse-graining. The filtered drag derived from the two-fluid model is suitable for Euler-Lagrangian simulations with both fluid and particle coarse-graining. It overcorrects the influence of sub-grid structures if used for simulations with only fluid coarse-graining.     

CFD–DEM study of effect of bed thickness for bubbling fluidized beds

The effect of bed thickness in rectangular fluidized beds is investigated through the CFD–DEM simulations of small-scale systems. Numerical results are compared for bubbling fluidized beds of various bed thicknesses with respect to particle packing, bed expansion, bubble behavior, solids velocities, and particle kinetic energy. Good two-dimensional (2D) flow behavior is observed in the bed having a thickness of up to 20 particle diameters. However, a strong three-dimensional (3D) flow behavior is observed in beds with a thickness of 40 particle diameters, indicating the transition from 2D flow to 3D flow within the range of 20–40 particle diameters. Comparison of velocity profiles near the walls and at the center of the bed shows significant impact of the front and back walls on the flow hydrodynamics of pseudo-2D fluidized beds. Hence, for quantitative comparison with experiments in pseudo-2D columns, the effect of walls has to be accounted for in numerical simulations.     

Two and three dimensional modeling of fluidized bed with multiple jets in a DEM-CFD framework

Fluidized beds with multiple jets have widespread industrial applications. The objective of this paper is to investigate the jet interactions and hydrodynamics of a fluidized bed with multiple jets. Discrete element modeling coupled with in-house CFD code GenlDLEST has been used to simulate a bed with nine jets. The results are compared with published experiments. Mono dispersed particles of size 550 ~m are used with 1.4 times the minimum fluidization velocity of the particles. Both two and three dimensional computations have been performed. To the best of our knowledge, the results presented in this paper are the first full 3D simulations of a fluidized bed performed with multiple jets. Discrepancies between the experiment and simulations are discussed in the context of the dimensionality of the simulations. The 2D solid fraction profile compares well with the experiment close to the distributor plate. At higher heights, the 2D simulation over-predicts the solid fraction profiles near the walls. The 3D simulation on the other hand is better able to capture the solid fraction profile higher up in the bed compared to that near the distributor plate. Similarly, the normalized particle velocities and the particle fluxes compare well with the experiment closer to the distributor plate for the 2D simulation and the freeboard for the 3D simulation, respectively. A lower expanded bed height is predicted in the 2D simulation compared to the 3D simulation and the experiment. The results obtained from DEM computations show that a 2D simulation can be used to capture essential jetting trends near the distributor plate regions, whereas a full scale 3D simulation is needed to capture the bubbles near the freeboard regions. These serve as validations for the experiment and help us understand the complex jet interaction and solid circulation patterns in a multiple jet fluidized bed system.     

Three-dimensional multi-phase simulation of the mixing and segregation of binary particle mixtures in a two-jet spout fluidized bed

This study presents a three-dimensional numerical study of the mixing and segregation of binary particle mixtures in a two-jet spout fluidized bed based on an Eulerian–Eulerian three-fluid model. Initially, the particle mixtures were premixed and packed in a rectangular fluidized bed. As the calculation began, the gas stream was injected into the bed from the distributor and jet nozzles. The model was validated by comparing the simulated jet penetration depths with corresponding experimental data. The main features of the complex gas–solid flow behaviors and the mechanism of mixing and segregation of the binary mixtures were analyzed. Moreover, further simulations were carried out to evaluate the effects of operating conditions on the mixing and segregation of binary particle mixtures. The results illustrate that mixing can be enhanced by increasing the jet velocity or enlarging the difference of initial proportions of binary particle mixtures.     

CFD-DEM simulation of spouting of corn-shaped particles

Three dimensionally coupled computational fluid dynamics (CFD) and discrete element method (DEM) were used to investigate the flow of corn-shaped particles in a cylindrical spouted bed with a conical base. The particle motion was modeled by the DEM, and the gas motion by the k-? two-equation turbulent model. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas–particle interactions in terms of momentum exchange. The corn-shaped particles were constructed by a multi-sphere method. Drag force, contact force, Saffman lift force, Magnus lift force, and gravitational force acting on each individual particle were considered in establishing the mathematical modeling. Calculations were carried out in a cylindrical spouted bed with an inside diameter of 200 mm, a height of 700 mm, and a conical base of 60°. Comparison of simulations with experiments showed the availability of the multi-sphere method in simulating spouting action with corn-shaped particles, but it depended strongly on the number and the arrangement of the spherical elements. Gas–solid flow patterns, pressure drop, particle velocity and particle concentration at various spouting gas velocity were discussed. The results showed that particle velocity reaches a maximum at the axis and then decreases gradually along the radial direction in the whole bed. Particle concentration increases along the radial direction in the spout region but decreases in the fountain region, while it is nearly constant in the annulus region. Increasing spouting gas velocity leads to larger pressure drop, remarkably increased speed of particle moving upward or downward, but decreased particle concentration.     

Two and three dimensional modeling of fluidized bed with multiple jets in a DEM–CFD framework

Fluidized beds with multiple jets have widespread industrial applications. The objective of this paper is to investigate the jet interactions and hydrodynamics of a fluidized bed with multiple jets. Discrete element modeling coupled with in-house CFD code GenIDLEST has been used to simulate a bed with nine jets. The results are compared with published experiments. Mono dispersed particles of size 550 μm are used with 1.4 times the minimum fluidization velocity of the particles. Both two and three dimensional computations have been performed. To the best of our knowledge, the results presented in this paper are the first full 3D simulations of a fluidized bed performed with multiple jets. Discrepancies between the experiment and simulations are discussed in the context of the dimensionality of the simulations. The 2D solid fraction profile compares well with the experiment close to the distributor plate. At higher heights, the 2D simulation over-predicts the solid fraction profiles near the walls. The 3D simulation on the other hand is better able to capture the solid fraction profile higher up in the bed compared to that near the distributor plate. Similarly, the normalized particle velocities and the particle fluxes compare well with the experiment closer to the distributor plate for the 2D simulation and the freeboard for the 3D simulation, respectively. A lower expanded bed height is predicted in the 2D simulation compared to the 3D simulation and the experiment. The results obtained from DEM computations show that a 2D simulation can be used to capture essential jetting trends near the distributor plate regions, whereas a full scale 3D simulation is needed to capture the bubbles near the freeboard regions. These serve as validations for the experiment and help us understand the complex jet interaction and solid circulation patterns in a multiple jet fluidized bed system.     

Improvement,validation and application of CFD/DEM model to dense gas–solid flow in a fluidized bed

Dense gas–solid flow with solid volume fraction greater than 10% and at moderate Reynolds number is important in many industrial facilities such as fluidized beds. In this work, the Euler–Lagrange approach in combination with a deterministic collision model is applied to a laboratory-scale fluidized bed. The fluid–particle interaction is studied using a new procedure called the offset method, which results in several numbers of spatial displacements of the fluid grid. The proposed method is highly precise in determining porosity and momentum transfer, thus improving simulation accuracy. A validation study was carried out to assess the results using this in-house CFD/DEM code against 5-s operation of a Plexiglas spouted-fluidized bed, showing good qualitative correlation of solid distribution in the bed and acceptable quantitative agreement of pressure drops at different positions in the bed. In view of high computing cost, special emphasis is placed on effective program design, such as application of advanced detection algorithm for particle–particle/wall collisions, the multi-grid method and parallel calculation. In this context, the influence of increasing the processor number, up to 36, on calculation efficiency was investigated.     

Diffusion-based coarse graining in hybrid continuum–discrete solvers: Theoretical formulation and a priori tests

Coarse graining is an important ingredient in many multi-scale continuum–discrete solvers such as CFD–DEM (computational fluid dynamics–discrete element method) solvers for dense particle-laden flows. Although CFD–DEM solvers have become a mature technique that is widely used in multiphase flow research and industrial flow simulations, a flexible and easy-to-implement coarse graining algorithm that can work with CFD solvers of arbitrary meshes is still lacking. In this work, we proposed a new coarse graining algorithm for continuum–discrete solvers for dense particle-laden flows based on solving a transient diffusion equation. Via theoretical analysis we demonstrated that the proposed method is equivalent to the statistical kernel method with a Gaussian kernel, but the current method is much more straightforward to implement in CFD–DEM solvers. A priori numerical tests were performed to obtain the solid volume fraction fields based on given particle distributions, the results obtained by using the proposed algorithm were compared with those from other coarse graining methods in the literature (e.g., the particle centroid method, the divided particle volume method, and the two-grid formulation). The numerical tests demonstrated that the proposed coarse graining procedure based on solving diffusion equations is theoretically sound, easy to implement and parallelize in general CFD solvers, and has improved mesh-convergence characteristics compared with existing coarse graining methods. The diffusion-based coarse graining method has been implemented into a CFD–DEM solver, the results of which are presented in a separate work.     

A LBM–DEM solver for fast discrete particle simulation of particle–fluid flows

The lattice Boltzmann method (LBM) for simulating fluid phases was coupled with the discrete element method (DEM) for studying solid phases to formulate a novel solver for fast discrete particle simulation (DPS) of particle–fluid flows. The fluid hydrodynamics was obtained by solving LBM equations instead of solving the Navier–Stokes equation by the finite volume method (FVM). Interparticle and particle–wall collisions were determined by DEM. The new DPS solver was validated by simulating a three-dimensional gas–solid bubbling fluidized bed. The new solver was found to yield results faster than its FVM–DEM counterpart, with the increase in the domain-averaged gas volume fraction. Additionally, the scalability of the LBM–DEM DPS solver was superior to that of the FVM–DEM DPS solver in parallel computing. Thus, the LBM–DEM DPS solver is highly suitable for use in simulating dilute and large-scale particle–fluid flows.     

Flow structures inside a large-scale turbulent fluidized bed of FCC particles:Eulerian simulation with an EMMS-based sub-grid scale model

Turbulent fluidized bed reactors are widely used in industry. However, CFD simulations of the hydrodynamic characteristics of these reactors are relatively sparse, despite the urgent demand from industry. To address this problem, Eulerian simulations with an EMMS-based sub-grid scale model, accounting for the effect of sub-grid scale structures on the inter-phase friction, are performed to study the hydrodynamics inside a large-scale turbulent fluidized bed of FCC particles. It is shown that the simulated a...     

Particle-scale and sub-grid drag models coupled CFD for simulating the CO methanation in a CFB riser

The diffusion and chemical reactions inside the catalyst particles and the heterogeneous flow structure in the computational cells are key factors to affect the accuracy of the coarse-grid simulation in circulating fluidized bed (CFB) methanation reactors. In this work, a particle-scale model is developed to calculate the effective reaction rate considering the transient diffusion and chemical reactions in the particle scale, i.e., the scale of the single catalyst particle. A modified sub-grid drag model is proposed to consider the effects of the meso-scale and chemical reactions on the heterogeneous gas-solid interaction, where the meso-scale is between the single particle and the whole reactor and featured with the particle cluster. Subsequently, a coupled model is developed by integrating the particle-scale and modified sub-grid drag models into CFD. Moreover, the coupled model is validated to achieve accurate predictions on the CO methanation process in a CFB riser. Notably, the coupled model can be performed with a coarse grid (∼58 times particle diameter) and a large time step (0.005 s) to accelerate the simulation. By simply changing the reaction kinetics, different gas-solid catalytic reaction systems can be simulated by using the coupled model.     

Effect of rolling friction on wall pressure,discharge velocity and outflow of granular material from a flat-bottomed bin

The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flat-bottomed bin. In the DEM model, the fixed mean values of the experimentally determined single particle data, such as the particle density, Young's modulus, Poisson's ratio as well as the sliding and rolling friction coefficients were incorporated to analyse their effects on the macroscale indicators, such as the wall pressure, discharge velocities and material outflow parameters. The effect of rolling friction was studied based on the experimentally measured single particle rolling friction coefficient. This analysis is aimed at the quantitative prediction of flow parameters as related to the identification of material parameters.     

Three-dimensional multi-phase simulation of the mixing and segregation of binary particle mixtures in a two-jet spout fluidized bed

This study presents a three-dimensional numerical study of the mixing and segregation of binary particle mixtures in a two-jet spout fluidized bed based on an Eulerian-Eulerian three-fluid model.Initially,the particle mixtures were premixed and packed in a rectangular fluidized bed.As the calculation began,the gas stream was injected into the bed from the distributor and jet nozzles.The model was validated by comparing the simulated jet penetration depths with corresponding experimental data.The main features of the complex gas-solid flow behaviors and the mechanism of mixing and segregation of the binary mixtures were analyzed.Moreover,further simulations were carried out to evaluate the effects of operating conditions on the mixing and segregation of binary particle mixtures.The results illustrate that mixing can be enhanced by increasing the jet velocity or enlarging the difference of initial proportions of binary particle mixtures.     

Investigation into improving the efficiency and accuracy of CFD/DEM simulations

The Euler-Lagrange approach combined with a discrete element method has frequently been applied to elucidate the hydrodynamic behavior of dense fluid-solid flows in fluidized beds. In this work, the efficiency and accuracy of this model are investigated. Parameter studies are performed; in these studies, the stiffness coefficient, the fluid time step and the processor number are varied under conditions with different numbers of particles and different particle diameters. The obtained results are compared with measurements to derive the optimum parameters for CFD/DEM simulations. The results suggest that the application of higher stiffness coefficients slightly improves the simulation accuracy. However, the average computing time increases exponentially. At larger fluid time steps, the results show that the average computation time is independent of the applied fluid time step whereas the simulation accuracy decreases greatly with increasing the fluid time step. The use of smaller time steps leads to negligible improvements in the simulation accuracy but results in an exponential rise in the average computing time. The parallelization accelerates the DEM simulations if the critical number for the domain decomposition is not reached. Above this number, the performance is no longer proportional to the number of processors. The critical number for the domain decomposition depends on the number of particles. An increase in solid contents results in a shift of the critical decomposition number to higher numbers of CPUs.     

Lagrangian–Eulerian simulation of slugging fluidized bed

This work studies gas–solid slugging fluidized beds with Type-D particles, using two-dimensional simulations based on discrete element model (DEM). DEM performance is quantitatively validated by two commonly accepted correlations for determining slugging behavior. The voidage profiles simulated with bed height corresponding to Baeyens and Geldart (1974) correlation for onset of slugging demonstrate a transitional flow pattern from free bubbling to slugging. The present calculated values for the maximum slugging bed height are in good agreement with the correlation from Matsen et al. (1969). Simulations show that fluidized beds with Type-D particles can operate in the round-nosed slugging regime and also shows that wall slugs and square-nosed slugs tend to be formed with increase in superficial gas velocity and in bed height, respectively.     

Development and assessment of algorithms for DEM-LES simulations of fluidized bed

The use of high-fidelity Discrete Element Method (DEM) coupled with Computational Fluid Dynamics (CFD) for particle-scale simulations demands extensive simulation times and restricts application to small particulate systems. DEM-CFD simulations require good performance and satisfactory scalability on high-performance computing platforms. A reliable parallel computing strategy must be developed to calculate the collision forces, since collisions can occur between particles that are not on the same processor, or even across processors whose domains are disjoint. The present paper describes a parallelization technique and a numerical verification study based on a number of tests that allow for the assessment of the numerical performance of DEM used in conjunction with Large-Eddy Simulation (LES) to model dense flows in fluidized beds. The fluid phase is computed through solving the volume-averaged four-way coupling Navier-Stokes equations, in which the Smagorinsky sub-grid scale tensor model is used. Furthermore, the performance of Sub-Grid Scale (SGS) turbulence models applied to Fluidized Bed Reactor (FBR) configurations has been assessed and compared. The developed numerical solver represents an interesting combination of techniques that work well for the present purpose of studying particle formation in fluidized beds.     

A coupled sliding and rolling friction model for DEM calibration

The accuracy of dense Discrete Element Method (DEM) simulations is sensitive to initial density, contact orientation, particle size and shape, and interparticle interaction parameters including contact stiffness, cohesion, coefficients of friction, and coefficients of restitution. Although studies have characterized the effects of individual particle interaction parameters on mechanical responses of loaded granular material, research combining DEM parameters for calibration is scarce. Robust DEM calibration methodology combining sliding and rolling friction coefficients was developed and validated to predict bulk residual soil strength of initially dense DEM particle assemblies.     

Calibration of granular material parameters for DEM modelling and numerical verification by blade-granular material interaction

The discrete element method (DEM) is a promising approach to model blade-granular material interactions. The accuracy of DEM models depends on the model parameters. In this study, a calibration process was developed to determine the parameter values. The particle size was the same as the real material and the particle shape was modelled using two spherical particles rigidly clumped together to form a single grain. Laboratory shear tests and compressions tests were used to determine the material internal friction angle and stiffness, respectively. These tests were replicated numerically using DEM models with different sets of particle friction coefficients and particle stiffness values. The shear test results are found to be dependent on both the particle friction coefficient and the particle stiffness. The compression test results show that it is only dependent on the particle stiffness. The combination of shear test and compression test results can be used to determine a unique set of particle friction and particle stiffness values. The calibration process was validated experimentally and numerically by modelling a blade moving through granular material. Results show that the forces acting on the blade can be accurately modelled with DEM and the maximum error is found to be 26%. The relative particle-blade displacements were used to predict the position and shape of the shear lines in front of the blade. A good qualitative correlation was achieved between the experiments and the DEM simulations.     

DEM simulation of polydisperse systems of particles in a fluidized bed

Numerical simulations based on three-dimensional discrete element model (DEM) are conducted for mono-disperse, binary and ternary systems of particles in a fluidized bed. Fluid drag force acting on each particle depending on its size and relative velocity is assigned. The drag coefficient corresponding to Ergun’s correlation is applied to the system of fluidized bed with particle size ratios of 1:1 for the mono-disperse system, 1:1.2, 1:1.4 and 1:2 for the binary system and 1:1.33:2 for the ternary system b...