Comparative analysis on gas–solid drag models in MFIX-DEM simulations of bubbling fluidized bed

In this study,the open-source software MFIX-DEM simulations of a bubbling fluidized bed(BFB)are applied to assess nine drag models according to experimental and direct numerical simulation(DNS)results.The influence of superficial gas velocity on gas–solid flow is also examined.The results show that according to the distribution of time-averaged particle axial velocity in y direction,except for Wen–Yu and Tenneti–Garg–Subramaniam(TGS),other drag models are consistent with the experimental and DNS results.For the TGS drag model,the layer-by-layer movement of particles is observed,which indicates the particle velocity is not correctly predicted.The time domain and frequency domain analysis results of pressure drop of each drag model are similar.It is recommended to use the drag model derived from DNS or fine grid computational fluid dynamics–discrete element method(CFD-DEM)data first for CFD-DEM simulations.For the investigated BFB,the superficial gas velocity less than 0.9 m·s^(-1) should be adopted to obtain normal hydrodynamics.

Compressed wormlike chain moving out of confined space: A model of DNA ejection from bacteriophage

The molecular biomechanics of DNA ejection from bacteriophage is of interest to not only fundamental biological understandings but also practical applications such as the design of advanced site-specific and controllable drug delivery systems. In this paper, we analyze the viscous motion of a semiflexible polymer chain coming out of a strongly confined space as a model to investigate the effects of various structure confinements and frictional resistances encountered during the DNA ejection process. The theoretically predicted relations between the ejection speed, ejection time, ejection length, and other physical parameters, such as the phage type, total genome length and ionic state of external buffer solutions, show excellent agreement with in vitro experimental observations in the literature.

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.

Experimental Modelling of Transverse Oscillations in Aquaculture Netting Parallel to the Flow – Sounds Baffling

Numerous studies have been undertaken to improve the viability, durability and suitability of materials and methods used for aquaculture enclosures. While many of the previous studies considered macro-deformation of nets, there is a paucity of information on netting micro-deformation. When aquaculture pens are towed, industry operators have observed the motion described as ＂baffling＂ – the transverse oscillation of the net planes parallel and near parallel to the flow. The difficulty to observe and assess baffling motion in a controlled experimental environment is to sufficiently reproduce netting boundary conditions and the flow environment experienced at sea. The focus of the present study was to develop and assess experimental methods for visualisation and quantification of these transverse oscillations. Four netrig configurations with varied boundary conditions and model-netting properties were tested in a flume tank. While the Reynolds number was not equivalent to full-scale, usage of the pliable and fine mesh model netting that enabled baffling to develop at low flow velocities was deemed to be of a larger relevance to this initial study. Baffling was observed in the testing frame that constrained the net sheet on the leading edge, similarly to a flag attachment onto a pole. Baffling motion increased the hydrodynamic drag of the net by 35%–58% when compared to the previously developed formula for taut net sheets aligned parallel to the flow. Furthermore, it was found that the drag due to baffling decreased with the increasing velocity over the studied Reynolds numbers（below 200）; and the drag coefficient was non-linear for Reynolds numbers below 120. It is hypothesised that baffling motion is initially propagated by vortex shedding of the netting twine which causes the netting to oscillate; there after the restoring force causes unstable pressure differences on each side of the netting which excites the amplitude of the netting oscillations.

Multi-scale numerical simulation of fluidized beds: Model applicability assessment

In the past few decades,multi-scale numerical methods have been developed to model dense gas-solidflow in fluidized beds with different resolutions,accuracies,and efficiencies.However,ambiguity needsto be clarified in the multi-scale numerical simulation of fluidized beds:(i)the selection of the submodels,parameters,and numerical resolution;(ii)the multivariate coupling of operating conditions,bed configurations,polydispersity,and additional forces.Accordingly,a state-of-the-art review is performed to assess the applicability of multi-scale numerical methods in predicting dense gas-solid flow influidized beds at specific fluidization regimes(e.g.,bubbling fluidization region,fast fluidization regime),with a focus on the inter-particle collision models,inter-phase interaction models,collision parameters,and polydispersity effect.A mutual restriction exists between resolution and efficiency.Higherresolution methods need more computational resources and thus are suitable for smaller-scale simulations to provide a database for closure development.Lower-resolution methods require fewercomputational resources and thus underpin large-scale simulations to explore macro-scale phenomena.Model validations need to be further conducted under multiple flow conditions and comprehensivemetrics(e.g.,velocity profiles at different heights,bubbles,or cluster characteristics)for furtherimprovement of the applicability of each numerical method.

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.

Fluid-solid drag models selection for simulating wheat straw particle movement in anaerobic digester

Computational fluid dynamics(CFD)has been utilized to simulate the movements of wheat straw particles for agitator speed selection in full-scale wet digestion.Previous research has found that the current drag model generally used for depicting the motion of spherical particles cannot match the movement behavior of wheat straw particles with their non-spherical shape.In this study,the sedimentation experiment and horizontal flow experiment of straw particles were determined using a V20-3D camera and a micro Particle Image Velocimetry(PIV)system.With analyses of the experimental data and CFD simulation results,the prediction accuracies of the non-spherical drag models of Hölzer and Sommerfeld(HS),Kishore and Gu(KG),Haider and Levenspiel(HL),Richter and Nikrityuk(RN),and Fabio Dioguardi(FD)were evaluated by the motion of individual straw particles.The results showed that the KG model has a significant advantage over the other drag models,both simulating the particle settling velocities in a one dimensional settling experiment and simulating the predictable trajectory in a two-dimensional horizontal flow experiment.Therefore,the KG drag model was selected to simulate with CFD the wheat straw particle movement to select agitator speeds.Additionally,the realizable k-turbulence model was proven to be superior to the other turbulence models for simulating the continuous phase flow with CFD.

Dynamic Analysis for the Global Performance of An SPM-Feeder-Cage System Under Waves and Currents

In the present study, the dynamic response of a coupled SPM-feeder-cage system under irregular waves and shear currents is analyzed. A numerical model is developed by using the commercial software Orca Flex. Hydrodynamics coefficients of the vessel are calculated by using a 3D diffraction/radiation panel program. First- and second-order wave forces are included in the calculations. Morison equation is used to compute the drag force on line elements representing the net. Drag coefficients are determined at every time step in the simulation considering the relative normal velocity between the structural elements and the fluid flow. The dynamic response of the coupled system is analyzed for various environments and net materials. The results of the study show the effects of solidity ratio of the net and vertical positions of the cage on the overall dynamic response of the system, confirming the viability of this type of configuration for future development of offshore aquaculture in deep waters.

Drag models for simulating gas–solid flow in the turbulent fluidization of FCC particles

This paper examines the suitability of various drag models for predicting the hydrodynamics of the turbulent fluidization of FCC particles on the Fluent V6.2 platform. The drag models included those of Syamlal-O＇Brien, Gidaspow, modified Syamlal-O＇Brien, and McKeen. Comparison between experimental data and simulated results showed that the Syamlal-O＇Brien, Gidaspow, and modified Syamlal-O＇Brien drag models highly overestimated gas-solid momentum exchange and could not predict the formation of dense phase in the fiuidized bed, while the McKeen drag model could not capture the dilute charac- teristics due to underestimation of drag force. The standard Gidaspow drag model was then modified by adopting the effective particle cluster diameter to account for particle clusters, which was, however, proved inapplicable for FCC particle turbulent fluidization. A four-zone drag model （dense phase, sub- dense phase, sub-dilute phase and dilute phase） was finally proposed to calculate the gas-solid exchange coefficient in the turbulent fluidization of FCC particles, and was validated by satisfactory agreement between prediction and experiment.

Two-fluid modeling of Geldart A particles in gas-solid micro-fluidized beds

The fiuidization behavior of Geldart A particles in a gas-solid micro-fluidized bed was investigated by Eulerian-Eulerian numerical simulation. The commonly used Gidaspow drag model was tested first. The simulation showed that the predicted minimum bubbling velocities were significantly lower than the experimental data even when an extremely fine grid size （of approximately one particle diameter） was used. The modified Gibilaro drag model was therefore tested next. The predicted minimum bubbling velocity and bed voidage were in reasonable agreement with the experimental data available in literature. The experimentally observed regime transition phenomena from bubbling to slugging were also reproduced successfully in the simulations. Parametric studies indicated that the solid-wall boundary conditions had a significant impact on the predicted gas and solid flow behavior.

Multi-fluid Eulerian simulation of mixing of binary particles in a gas-solid fluidized bed with a cohesive particle-particle drag model

A particle-particle(p-p)drag model is extended to cohesive particle flow by introducing solid surface energy to characterize cohesive collision energy loss.The effects of the proportion of cohesive particles on the mixing of binary particles were numerically investigated with the use of a Eulerian multiphase flow model incorporating the p-p drag model.The bed expansion,mixing,and segregation of Geldart-A and C particles were simulated with varying superficial velocities and Geldart-C particle proportions,from which we found that the p-p drag model can reasonably predict bed expansion of binary particles.Two segregation types of jetsam-mixture-flotsam and mixture-flotsam processes were observed during the fluidization processes for the Geldart-A and C binary particle system.The mixing processes of the binary particle system can be divided into three scales:macro-scale mixing,meso-scale mixing,and micro-scale mixing.At a constant superficial velocity the optimal mixing was observed for a certain cohesive particle proportion.

Numerical investigations on gas-solid flow in circulating fluidized bed risers using a new cluster-based drag model

A cluster-based drag model is proposed for the gas-solid circulating fluidized bed(CFB)riser by including the cluster information collected from image processing and wavelet analysis into the calculation of system drag.The performance of the proposed drag model is compared with some commonly used drag models.A good agreement with the experimental data is achieved by the proposed cluster-based drag model.Error analysis of the proposed cluster-based drag model based on the local distributions of solids holdup and particle velocity is conducted.The clustering phenomenon in the low-density and high-density CFB risers and the effect of the cluster size on the simulation accuracy are also numerically studied by the proposed drag model.

A new drag model for TFM simulation of gas-solid bubbling fluidized beds with Geldart-B particles

In this work, a new drag model for TFM simulation in gas-solid bubbling fluidized beds was proposed, and a set of equations was derived to determine the meso-scale structural parameters to calculate the drag characteristics of Geldart-B particles under low gas velocities. In the new model, the meso-scale structure was characterized while accounting for the bubble and meso-scale structure effects on the drag coefficient. The Fluent software, incorporating the new drag model, was used to simulate the fluidization behavior. Experiments were performed in a Plexiglas cylindrical fluidized bed consisting of quartz sand as the solid phase and ambient air as the gas phase. Comparisons based on the solids hold-up inside the fluidized bed at different superficial gas velocities, were made between the 2D Cartesian simulations, and the experimental data, showing that the results of the new drag model reached much better agreement with exoerimental data than those of the Gidasoow dra~ model did.

Validation of EMMS-based drag model using lattice Boltzmann simulations on GPUs

lnterphase momentum transport in heterogeneous gas-solid systems with multi-scale structure is of great importance in process engineering. In this article, lattice Boltzmann simulations are performed on graphics processing units （GPUs）, the computational power of which exceeds that of CPUs by more than one order of magnitude, to investigate incompressible Newtonian flow in idealized multi-scale particle-fluid systems. The structure consists of a periodic array of clusters, each constructed by a bundle of cylinders. Fixed pressure boundary condition is implemented by applying a constant body force to the flow through the medium. The bounce-back scheme is adopted on the fluid-solid interfaces, which ensures the no-slip boundary condition. The structure is studied under a wide range of particle diameters and packing fractions, and the drag coefficient of the structure is found to be a function of voidages and fractions of the clusters, besides the traditional Reynolds number and the solid volume fractions. Parameters reflecting multi-scale characters are, therefore, demonstrated to be necessary in quantifying the drag force of heterogeneous gas-solid system. The numerical results in the range 0.1 〈 Re 〈 10 and 0 〈 Ф 〈 0.25 are compared with Wen and Yu＇s correlation, Gibilaro equation, EMMS-based drag model, the Beetstra correlation and the Benyahia correlation, and good agreement is found between the simulations and the EMMS-based drag model for heterogeneous systems.

CFD modeling of liquid–solid fluidization: Effect of drag correlation and added mass force

Computational fuid dynamics （CFD） has been widely used to study the hydrodynamics of gas-solid fluidization; however, its applications in liquid-solid fluidization are relatively rare. In this study, CFD simulations of a liquid-solid fluidized bed are carried out, focusing on the effect of drag correlation and added mass force on the hydrodynamics of liquid-solid fluidization. It is shown that drag correlation has a significant effect on the simulation results and the correlation proposed by Beetstra et al. （2007） gives the best agreement with experimental data. We further show that the added mass force does play an important role in CFD simulation of liquid-solid fluidization, and therefore should not be ignored in CFD simulations,

A comparative assessment of empirical and lattice Boltzmann method-based drag models for simulation of gas-solid flow hydrodynamics in a bubbling fluidized bed

In simulations of fluidized beds using computational fluid dynamics （CFD）, the description of gas-solid flow hydrodynamics relies on a drag model to account for the momentum transfer between gas and solid phases. Although several studies of drag models have been published, there have been few investigations of the application of lattice Boltzmann method （LBM）-based drag models to bubbling fluidized bed simu- lations. In the present study, a comprehensive comparison of empirical and LBM-based drag models was carried out to assess the performance of these models during simulations of gas-solid flow hydrodynam- ics in a bubbling fluidized bed. A CFD model using the MFIX code based on the Eulerian-Eulerian approach and the kinetic theory of granular flow was used to simulate a 2D bubbling fluidized bed with Geldart B particles. The simulation results were validated by comparison with experimental data. Statistical anal- ysis of the results shows that LBM-based drag models can reliably model gas-solid flow hydrodynamics in a bubbling fluidized bed.

Effect of adjusted mesoscale drag model on flue gas desulfurization in powder-particle spouted beds

An energy minimum multiscale model was adjusted to simulate the mesoscale structure of the flue gas desulfurization process in a powder-particle spouted bed and verified experimentally.The obtained results revealed that the spout morphology simulated by the adjusted mesoscale drag model was unstable and discontinuous bubbling spout unlike the stable continuous spout obtained using the Gidaspow model.In addition,more thorough gas radial mixing was achieved using the adjusted mesoscale drag model.The mass fraction of water in the gas mixture at the outlet determined by the heterogeneous drag model was 1.5 times higher than that obtained by the homogeneous drag model during the simulation of water vaporization.For the desulfurization reaction,the experimental desulfurization efficiency was 75.03%,while the desulfurization efficiencies obtained by the Gidaspow and adjusted mesoscale drag models were 47.63%and 75.08%,respectively,indicating much higher accuracy of the latter technique.

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study,a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed.Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop.One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore,and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations.Predictions are compared with experimental data measured by Lali et al.,where the computed porosities from model B are closer to the measured data than other models.Furthermore,the predicted pressure drop rises as liquid velocity increases,while it decreases with the increase of particle size.Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient,and particle concentration,granular temperature,granular pressure,and granular viscosity go down accordingly.

Numerical study on hydrodynamics of gas-solids circulating fluidized bed with L-valve

L-valve is often used as a non-mechanical valve for the circulation of solids in gas-solids fluidized bed(GSFB)due to its advantages in simple construction and easy control.The information on solids circu-lation rate as well as the hydrodynamics performance of the CFB with L-valve is of great importance for its better control and design.This paper proposes a Eulerian-Eulerian approach based numerical model integrating the computational fluid dynamics(CFD)with turbulent model,the kinetic theory of granular flow(KTGF)and the drag model,thus the solids circulation rate and the local phase velocity as well as solids volume fraction can be predicted simultaneously.With this model,the hydrodynamics perfor-mance of the full loop GSCFB with a L-valve is analyzed in detail.It is found that the drag model affects the simulation significantly and the(energy minimization multiscale)EMMS method shows good per-formance in the full-loop simulation of GSCFB.

Numerical simulation and experimental validation of gas–solid flow in the riser of a dense fluidized bed reactor

Gas-solid flow in the riser of a dense fluidized bed using Geldart B particles （sand）, at high gas velocity （7.6-15.5 m/s）s） and with comparatively high solid flux （140-333.8 kg]m^2 s）, was investigated experimentally and simulated by computational fluid dynamics （CFD）, both two- and three-dimensional and using the Gidaspow, O＇Brien-Syamlal, Koch-Hill-Ladd and EMMS drag models, The results predicted by EMMS drag model showed the best agreement with experimental results. Calculated axial solids hold-up profiles, in particular, are well consistent with experimental data. The flow structure in the riser was well represented by the CFD results, which also indicated the cause of cluster formation. Complex hydrody-namical behaviors of particle cluster were observed. The relative motion between gas and solid phases and axial heterogeneity in the three subzones of the riser were also investigated, and were found to be consistent with predicted flow structure. The model could well depict the difference between the two exit configurations used, viz., semi-bend smooth exit and T-shaped abrupt exit. The numerical results indicate that the proposed EMMS method gives better agreement with the experimental results as compared with the Gidaspow, O＇Brien-Syamlal, Koch-Hill-Ladd models. As a result, the proposed drag force model can be used as an efficient aporoach for the dense zas-solid two-ohase flow.