Particle-particle Restitution Coefficient Research Articles

CFD-DDPM coupled with an agglomeration model for simulation of highly loaded large-scale cyclones: Sensitivity analysis of sub-models and model parameters

The Dense Discrete Phase Model coupled with an agglomeration model is developed and validated for the simulation of industrial cyclones with high solid loads. The performance of the model is influenced by sub-models, model parameters, and numerical parameters. To optimize the performance of the present CFD model, an extensive sensitivity analysis was performed, varying one sub-model or parameter at a time, and systematically assessing the effect on the results through comparisons with measured pressure drop and separation efficiency of a highly loaded pilot-scale cyclone. The investigation shows that the turbulence model and particle-particle restitution coefficient have the strongest influence. This study concludes with the recommendation of a set of sub-models, model parameters, and numerical parameters providing the best prediction of the hydrodynamics of large-scale highly loaded cyclones. In addition, the impact of some operating conditions on the performance of a large-scale highly loaded cyclone were examined. • Simulation of highly loaded cyclones: effects of sub-models and model parameters. • Particle-particle restitution coefficient and turbulence model influence the most. • The impact of particle-particle interaction force modeling is minor. • Most suitable sub-models, model parameters, and numerical parameters are suggested. • The impact of operating conditions on the performance of the cyclone was examined.

CFD Simulation of Particles Mixing and Segregation in a Rotary Coating Disk: Influence of Drag Models and Restitution Coefficient

In this paper, the dynamics of a transverse plane of a rotary coating disk of a binary mixture system comprising sand and urea particles were simulated using the two-fluid model along with the kinetic theory of granular flow in Fluent 19.1. Although some parameters relating to the material properties and size of the rotary coating disk have been researched, the effects of both drag force and restitution coefficient on the flow characteristics have yet to be examined. Thus, this paper numerically examines the effect of the inclusion of drag models and particle-particle restitution coefficients on particle dynamics in a rotary disk operating in the rolling regime of the granular bed. Three particle-particle drag models were considered: the Schiller-Naumann, Syamlal-O’Brien, and Gidaspow. The Syamlal-O’Brien and Gidaspow models were both able to successfully simulate particle segregation in a perfect rolling regime, whereas the Schiller-Naumann drag model appeared to be unable to predict the segregation of the particles and the rolling flow regime under the assumed conditions. Four different values of the restitution coefficient were also investigated: 0.7, 0.8, 0.9, and 0.95. The higher restitution values of 0.9 and 0.95 were found to substantially affect flow characteristics, ensuring suitable rolling regime behaviour for the bed during the rotational movement. The lower restitution coefficients of 0.7 and 0.8, on the other hand, indicated that irregular velocity vectors could be obtained in the active region of the granular bed.

Validation and sensitivity analysis of an Eulerian-Eulerian two-fluid model (TFM) for 3D simulations of a tapered fluidized bed

In the present work, the hydrodynamics behavior of a 3D small-scale cold flow modeling of a gas-solid tapered fluidized bed is evaluated with the Eulerian-Eulerian two-fluid modeling (TFM) approach. The sensitivity of different modeling parameters, including lift and virtual mass forces, viscous force, gas-solid drag force, granular temperature, granular viscosity, granular pressure, particle-wall specularity coefficient, particle-particle restitution coefficient, and particle-wall restitution coefficient, are systematically investigated to optimize the performance of the present numerical model. The results from different sensitivity analyses reveal that the gas-particle drag force is a more important force to resolve the correct time-averaged axial and radial solids holdup profiles of the tapered fluidized bed than the other investigated parameters. The highest accuracy possible from simulations is achieved from the Gibilaro drag model followed by the Arastoopour and EMMS/bubbling models. In contrast, all other drag models over-predict the gas-particle interaction force. The assessment of the lift and virtual mass forces, viscous force, granular temperature, granular viscosity, granular pressure, and particle-wall restitution coefficient results reveal that these parameters are less critical for the numerical simulations of the tapered fluidized bed than the gas-solid drag force. However, the assessment of particle-wall specularity coefficient and particle-particle restitution coefficient reveals that adjusting these parameters in the numerical simulations is helpful to achieve a better agreement between the experimental data and model results. For the higher gas flow rate, the current work shows that a better agreement can be achieved by tuning the parameter values in the standard sub-models than the previously published TFM studies. Meanwhile, for the lower gas flow rate, the accuracy of the present work is slightly lower than the previously published work but acceptable with the experimental measurements. The current work has an advantage over the previously published work in terms of lower computational effort by using the simplified geometry and mean particle diameter assumptions.

Comparative CFD modeling of a bubbling bed using a Eulerian–Eulerian two-fluid model (TFM) and a Eulerian-Lagrangian dense discrete phase model (DDPM)

Eulerian–Eulerian and Eulerian-Lagrangian numerical approaches are both widely used to investigate hydrodynamic behavior in dense gas-solid fluidized bed reactors, yet there has been a lack of comparative investigations involving the two. Therefore, the present work compares the numerical performance of a two-fluid model (TFM) and a dense discrete phase model (DDPM) in describing the hydrodynamic behavior of a pilot-scale bubbling bed reactor. The effects of several different parameters – drag force, grid size, fluid time-step, time-averaging interval, particle-wall specularity coefficient, particle-particle restitution coefficient, particle-wall reflection coefficient, and numbers of parcels (the latter two parameters only for the DDPM) – are investigated and compared for the two approaches using two-dimensional (2D) simulations. The numerical results for both models indicate that sub-grid drag correction based on the energy minimization and multiscale (EMMS) theory is the most essential modeling parameter to account for the multiscale structures (i.e., bubbles and void spaces) and to resolve the axial and radial solid distributions. Both the TFM and DDPM, coupled with the EMMS/bubbling drag, predict similar hydrodynamics behavior; however, the better accuracy in terms of axial and radial solids concentration profiles is achieved from the TFM approach. Further, our grid size analysis results indicate that the DDPM generates a better grid-independent solution than the TFM. This important advantage of the DDPM over TFM makes it a suitable candidate for large-scale industrial applications by employing it on much coarser grids. Meanwhile, the results from the time-step, time-averaging interval, specularity coefficient, restitution coefficient, reflection coefficient, and numbers of parcels represent a minor effect on the overall hydrodynamics behavior of the pilot-scale bubbling bed reactor.

Multiscale modeling of bubbling fluidized bed reactors using a hybrid Eulerian-Lagrangian dense discrete phase approach

The fundamental problem encountered in the bubbling fluidized bed reactors is the presence of multiscale structures which cannot be resolved by the conventional drag models. In this study, a novel hybrid Eulerian-Lagrangian dense discrete phase model (DDPM) based on energy minimization and multiscale (EMMS) drag is proposed for the first time to analyze the hydrodynamics of bubbling fluidized bed reactors with Geldart A, A/B, and B particles. By comprehensive and comparative investigations of a number of key modeling parameters (grid size, drag force, particle number per parcel, turbulence, and particle-particle restitution coefficients), our proposed DDPM-EMMS model stands out of the currently-available counterparts in terms of improved grid-independency, multiscale structures resolvability with coarser grids, better parcel-independency, and better performance with laminar treatment against turbulence.

Optimisation of interaction parameters for CFD modelling of multiphase flow using NR method

Accurate modelling of fluid and particle flow is essential for reliable predictions of gas–solid reactions in the multiphase reactor. Due to the promising features such as short contact time, less back mixing of solids and low residence time, downer column has been used in industries than conventional riser configuration. However, the effective simulation and validation of the hydrodynamic characteristics have been scarce. A RANS model with an appropriate Eulerian-Eulerian approach poses a challenging task of choosing the hydrodynamic simulation parameters, such as i) particle-particle restitution coefficient, ii) particle-wall restitution coefficient and iii) specularity coefficient. The objective of the present study was to optimise these model parameters to obtain close validation with experimental data so that accurate downer hydrodynamics can be predicted. The error obtained from validating the experimental data with the CFD simulation output is our function which needs to be minimised. Newton Raphson multi-parameter root finding method was used for this purpose. The Jacobian evaluation required multiple CFD simulations at each iteration. A 61% reduction in error was achieved after 3 iterations. Thus, the optimised model parameters of hydrodynamics used for further modelling study in predicting hydrodynamic characteristics of a 200 mm diameter 8 m column. Highlights Validation of hydrodynamics of multiphase flow in downer employing Eulerian-Eulerian Approach Optimisation of hydrodynamic interactive model parameters viz., Restitution and Specularity coefficient coupled with Newton Raphson multi-parameter root finding and Jacobian Method. Agreement between experimental and simulation with optimised modelling parameters

Calibration of parameters for DEM simulations of solar particle receivers by bulk experiments and surrogate functions

Bauxite particles known as proppants from the fracking industry are an emerging heat transfer medium for solar thermal power plants. The discrete element method (DEM) has just recently been applied to these systems and the information on parameters for contact force models is scarce; calibrated parameters cannot be found. In this work a novel, three-stage calibration approach based on multiple bulk experiments and surrogate functions is presented. The experiments comprise the angle of repose, the residence time on a horizontal conveyor and the impact on an inclined plate. Particle-particle and particle-wall parameters for the Hertz contact force model and the modified linear spring dash-pot rolling friction model are determined for five different proppants and two wall materials. The assumptions of the calibration procedure and the calibration results themselves are checked and discussed on the basis of a sensitivity analysis. It is shown that almost all parameters can be constricted to unique values by the approach and that most parameters only gradually differ between particle types. Additionally, the influence of coarse graining on the parameters is examined. The behavior of the restitution coefficients is explained in detail by kinetic gas theory. It is found that only the particle-wall restitution coefficient is invariant to coarse graining, but not the particle-particle restitution coefficient, which must decrease with coarse-graining factor.

Numerical simulation of gas-solid flows in fluidized bed gasification reactor

A numerical model for simulating a fluidized bed gasifier should include appropriate parameters to capture the dynamics of gas-solid flows, gasification kinetics and the interaction between these two. The focus of the present study is to analyze the effects of coal gasification chemistry models reported in literature on the prediction of product gas composition in a fluidized bed gasification reactor. Numerical results are validated against the experimental data available in literature. The validated model is used to examine the available chemical kinetics schemes for water gas shift reaction, steam methane reforming reaction and char heterogeneous reactions. It is also used to assess the effects of hydrodynamic models parameters such as drag model, particle-particle restitution coefficient and specularity coefficient on exit gas composition. Results show that the predictions of product gas composition are notably affected by the choices of the kinetics schemes for water gas shift and steam methane reforming reactions. Systematic analysis using the available choices to simulate initial processes such as moisture removal, volatile and tar cracking is reported. Drag models and the value of specularity coefficient are shown to have no effect on product gas composition, and the particle-particle restitution coefficient slightly influences the predicted gas composition.

Effects of specularity and particle-particle restitution coefficients on the recirculation characteristics of dispersed gas-particle flows through a sudden expansion

We numerically investigate the effects of restitution and specularity coefficients on the characteristics of dispersed gas-particle flows through a sudden expansion. The studies are carried out using an indigenous finite volume flow solver in a collocated framework with two-fluid model. Parametric studies are performed to gain insights into the differences in recirculation patterns that arise due to variations in restitution and specularity coefficients. The simulations show that particle-particle interactions, quantified by restitution coefficient (e) have a greater impact on recirculation characteristics than particle-wall interactions, which are quantified by specularity coefficient (ϕ). Studies reveal that the recirculation lengths tend to decrease as particle collisions become more elastic (as e tends to unity) while they increase, as the value of ϕ increases. However, the changes in recirculation length are very gradual and less pronounced when only particle-wall interactions are considered as compared to particle-particle interactions. From the range of parametric variations studied in this work, the maximum recirculation length has been found when the value of ϕ is maximum and that of e is minimum.

Effects of specularity and particle-particle restitution coefficients on the hydrodynamic behavior of dispersed gas-particle flows through horizontal channels

Specularity coefficient (ϕ) and particle–particle restitution coefficient (e) are two important parameters governing the flow physics of dispersed gas-particle flows. In this work, a detailed numerical analysis is carried out to get an insight into the effects of these two parameters in the flow hydrodynamics of dispersed gas-particle flows through horizontal channels. Investigations have also been carried out to find the ϕ-e pair for which the phase velocities become an extremum. It has been found that at a particular value of e, both gas and particle velocities at the centerline of the channel increase with increase in the value of ϕ, whereas near the wall, they tend to decrease. At a fixed non-zero value of ϕ, both gas and particle velocities tend to increase with increase in the value of e. For ϕ equal to zero, which corresponds to free-slip boundary condition for particle velocity, there is no significant variations in gas and particle velocities with changes in e. Out of all combinations of values of ϕ and e investigated herein, it is found that both gas and particle velocities attain a maximum value when both the values of ϕ and e are maximum.

Boundary conditions effects on the particle dynamic flow in a rotary drum with a single flight

This study presents an experimental and numerical investigation of the particle dynamic flow in a rotary drum with one flight, under different boundary conditions. The Euler-Euler approach with the kinetic theory of granular flow was used for all CFD simulations. The influence of different specularity coefficient values and no-slip boundary condition was assessed varying the particle-particle restitution coefficient and the rotational speeds. The particle-particle restitution coefficient of glass beads was experimentally measured and the effect of this parameter on the particle dynamics was also investigated. A high-speed video camera was used to measure the flight unloading profile and the bed height of particles in rolling regime at the drum bottom. Quantitative and qualitative analysis were performed in order to compare the simulated results with the experimental data, and then to determine the appropriate parameters to represent the real particle flow. It was observed that the specularity coefficient value of 0.5 and the restitution coefficient of 0.9 represented well the particle flow behavior in the flight at the rolling regime for the different rotational speeds analyzed.

CFD modeling the hydrodynamics of binary particle mixture in pseudo-2D bubbling fluidized bed: Effect of model parameters

The hydrodynamics of binary coal-sand mixture in a pseudo-2D rectangular bubbling fluidized bed (0.385m×0.005m×0.128m) was simulated using the multi-fluid Eulerian model incorporating the kinetic theory of granular flow. Parametric studies of the boundary wall condition, particle-particle restitution coefficient, friction packing limit, as well as transport equation for granular temperature were performed to investigate their influences on the predicted mixing/segregation behavior. The CFD simulation results demonstrated that the predicted mixing behavior was closely related to the expression for granular temperature transport equation and specularity coefficient. When the full transport equation for granular temperature was adopted, the predicted mixing degree decreased with the increase of specularity coefficient. And the best agreement between simulation results and experimental data was achieved when specularity coefficient was equal to 1.0. Nevertheless, when the algebraic transport equation for granular temperature was adopted, the system was always predicted in well-mixing rather than segregation state. Under the full transport equation for granular temperature and the no slip boundary wall condition, the predicted mixing degree decreased with the increase of the particle-particle restitution coefficient and frictional packing limit. The supplementary simulations indicated that for the considered gas-solid system there exist a critical bed thickness larger than which the system was in well-mixing state and the simulation results were independent from the investigated parameters. The hydrodynamic analysis indicated that the reduction of bubble size and the solid axial movement could be the mechanism responsible for the occurrence of axial segregation.

3D numerical simulation of a lab-scale pressurized dense fluidized bed focussing on the effect of the particle-particle restitution coefficient and particle–wall boundary conditions

3D numerical simulations of dense pressurized fluidized bed are presented. The numerical prediction of the mean vertical solid velocity are compared with experimental data obtained from Positron Emission Particle Tracking. The results show that in the core of the reactor the numerical simulations are in accordance with the experimental data. The time-averaged particle velocity field exhibits a large-scale toroidal (donut shape) circulation loop. Two families of boundary conditions for the solid phase are used: rough wall boundary conditions (Johnson and Jackson, 1987 and No-slip) and smooth wall boundary conditions (Sakiz and Simonin, 1999 and Free-slip). Rough wall boundary conditions may lead to larger values of bed height with flat smooth wall boundary conditions and are in better agreement with the experimental data in the near-wall region. No-slip or Johnson and Jackson׳s wall boundary conditions, with sufficiently large value of the specularity coefficient (ϕ≥0.1), lead to two counter rotating macroscopic toroidal loops whereas with smooth wall boundary conditions only one large macroscopic loop is observed. The effect of the particle-particle restitution coefficient on the dynamic behaviour of fluidized bed is analysed. Decreasing the restitution coefficient tends to increase the formation of bubbles and, consequently, to reduce the bed expansion.

Comparison of numerical approaches to model FCC particles in gas–solid bubbling fluidized bed

A comparative study has been carried out to determine the ability of computational fluid dynamics (CFD) and computational particle fluid dynamics (CPFD) codes to predict the hydrodynamics of FCC particles in a bubbling fluidized bed. Simulations were conducted in both 2-dimensional (2-D) and 3-dimensional (3-D) CFD configuration and in a 3-D CPFD model. The new structure based force-balance (FB) model of Ahmadi Motlagh et al. (2014. Chem. Eng. Sci. 120, 22–36.) was incorporated in CFD to simulate the behavior of FCC in the bubbling fluidization regime. This model modifies the conventional drag correlation by considering the effect of interparticle forces on the formation of agglomerates inside the bed, updating the drag calculations by replacing the particle diameter in the Wen and Yu correlation by an agglomerate diameter. The effects of superficial gas velocity, particle diameter, particle-particle restitution coefficient and specularity coefficient on voidage are examined. The sensitivity of different gas–solid drag closures in CFD are tested and compared. Experimental time-average axial and radial voidage profiles were simulated with varying degrees of agreement with experimental data obtained using different advanced experimental techniques in the “Traveling fluidized bed” (Dubrawski et al., 2013. Powder Technol. 235, 203–220; Tebianian et al., 2014. Extending the comparison of voidage measurement and modeling techniques in fluidized beds. In: Proc. 11th International Conference on Fluidized Bed Technology, (Eds.), J. Li, X.J. Bao and W. Wang. Chemical Industry Press, Beijing 137–142.). Both the FB and CPFD models were successful in resolving key issues in 3-D, whereas 2-D models tended to seriously underpredict particle volume fraction, especially near the wall.

Parameter study of a kinetic-frictional continuum model of a disk impeller high-shear granulator

A disk impeller high shear granulator was modeled with a kinetic-frictional continuum model. A parameter study was made and the parameterization of the equations was assessed to investigate if the model is suited for modeling high shear granulation. A dry granule mixing was studied and the parameters investigated were the particle diameter, the angle of internal friction, the particle-particle restitution coefficient, the particle density, the particle velocity boundary condition, the packing limit and the numerical parameter frictional packing limit. All the particle related parameters can be expected to change during a granulation. The flow field prediction of the model is in agreement with the behavior described by Knight et al. (2001), showing a rigid torus. This is in contrast to a discrete element model simulation that predicts inner rotation within the torus (Gantt and Gatzke 2006). The general flow field of this system is fairly insensitive to all parameter changes, except a change to no slip boundary condition for the particle phase, even though several parameters significantly affect the solid phase viscosity. The model was used to predict the change in impeller torque when going from mixing a dry powder to a wet system. It is shown that the models have some potential for qualitative descriptions of the wet state. (

Modeling on High-Flux Circulating Fluidized Bed with Geldart Group B Particles by Kinetic Theory of Granular Flow

Modeling of the hydrodynamic behaviors of high-flux circulating fluidized beds (HFCFBs) with Geldart group B particles has been performed using a Eulerian multiphase model with the kinetic theory of granular flow (KTGF). The essential models involved are the dispersed k-e turbulence model, the Gidaspow shear viscosity model, and the Syamlal—O'Brien drag model, and the boundary condition is the Johnson and Jackson wall boundary condition. The sensitivities of key model parameters (i.e., particle-particle restitution coefficient (e), particle—wall restitution coefficient (e w ), and specularity coefficient (ϕ)) on the predicted gas velocity, solids velocity, and solids volume fraction were tested. It was found that e has remarkable dependence on the particle diameter. Large-sized particles experience a more sensitive effect of e on predictions. The particle—wall restitution coefficient e w has somewhat of an effect on the simulated values of gas velocity, solids velocity, and solids volume fraction; however, no critical changes in the trends of their radial distributions have been found. The specularity coefficient ϕ has a slight effect on the gas velocity and solids velocity distributions but a pronounced effect on the solids volume fraction distribution. An increase in specularity coefficient results in a reduction in the solids volume fraction near the wall. Based on the comparisons of simulated results with experiments, a group of suitable model parameters for modeling the flow of Geldart group B particles in HFCFB risers by a Eulerian multiphase model with KTGF was determined and verified. Besides, some interesting simulated results that are difficult to measure experimentally were presented under the suggested model parameters.

Anisotropic energy distribution in three-dimensional vibrofluidized granular systems.

We examine the energy flows in a three-dimensional model of a granular system consisting of N inelastic hard spheres contained in an open cylinder of radius R under the influence of gravity. Energy is supplied to the system in the vertical direction by a vibrating base and is transferred to the perpendicular directions through particle-particle collisions. We examine how the local and global dissipation of energy by particle-particle and particle-wall collisions depends on the number of particles, the velocity of the vibrating base, and the restitution coefficients.