Fluid-particle Interaction Forces Research Articles

Investigation of the characteristics and mechanisms of the layer inversion in binary liquid–solid fluidized beds with coarse particles

This paper adopts an optimized Euler–Lagrange method proposed in our previous work to study the characteristics and formation mechanisms of layer inversion in binary liquid–solid fluidized beds (LSFBs) with coarse particles. The LSFBs are formed in a cylindrical pipe with a diameter of 50 mm and a length of 0.6 m and consist of two species of coarse particles with different sizes: 6 mm glass spheres (species 1) and 10 mm glass spheres (species 2) with the particle density of 2600 kg/m3. First, the characteristics of the layer inversion of LSFBs with coarse particles are qualitatively analyzed. The positions of species 1 and species 2 are converted during layer inversion. Second, the changes in the trajectory and volume fraction of two species of particles are quantitatively investigated. Finally, the formation mechanisms of layer inversion with coarse particles are analyzed. The results show that the relative magnitude of the fluid–solid interaction force and the gravity is the main reason for determining the layer inversion of binary coarse particles of different sizes. The collision force is to balance the net force of the particle–fluid interaction force and the net gravity, so that the fluidized bed is in relative equilibrium. In addition, through the analysis of the evolution of the network of contact forces, the constraint of the wall on coarse particles is discussed during the layer inversion.

On the Applicability of the Coarse Grained Coupled CFD-DEM Model to Predict the Heat Transfer During the Fluidized Bed Drying of Pharmaceutical Granules.

Fluidized bed dryer often used in the pharmaceutical industry for drying of wet granules. Coupled computational fluid dynamics (CFD) - discrete element method (DEM) is frequently used to model the drying process because of its ability to obtain the relevant information at the particle level. However, it becomes almost impossible to model the industrial scale fluidized bed dryer using the coupled CFD-DEM method because of the presence of large number of particles [Formula: see text]. To reduce the number of particles to be tracked in the simulation, coarse grained coupled CFD-DEM method was developed by researchers where a certain number of particles of the original system was represented by a relatively bigger particle in the coarse-grained system. The appropriate scaling of the particle-particle and particle-fluid interaction forces is necessary to make sure that the dynamics of the coarse-grained particles/parcels accurately represent the dynamics of the original particles. The coarse-graining of the drying process of pharmaceutical granules during fluidization needs systematic coarse-graining of the momentum, heat, and solvent vapor transfer process. A coarse grained coupled CFD-DEM method was used to model the momentum and heat transfer during the fluidization of pharmaceutical granules. It was shown that the heat transfer during the fluidization of large number of particles could be predicted by simulating a smaller number of bigger particles with appropriate scaling of particle-particle heat and momentum transfer, and particle-fluid heat and momentum transfer at significantly smaller computational time. This model can be further extended by including a coarse-grained moisture transport model in future.

Dynamics of suspended sediment transport: A Direct Numerical Simulation study

The dynamics of suspended sediment transport in horizontal open channel flow is analysed using point-particle one-way coupling Direct Numerical Simulations (DNS), with a virtual wall as a simple particle resuspension model. In sediment transport, the bed-load is dominated by the inter-particle interactions, but the suspended sediments are transported essentially in a one-way coupling situation. The validity of one-way coupling DNS with point-particle approach for the transport of suspended sediment is analysed, by comparing the simulations with existing well-designed experiments performed under very similar conditions. The range of the relevant non-dimensional parameters of the simulations is roughly the same as in actual sediment transport, except for the flow Reynolds number. Good agreement is observed between the simulations and the experiments; furthermore, the simulation results of the motion of the suspended sediment are insensitive to the position of the virtual wall, provided this wall is placed in a region where the fluid velocity fluctuation in the wall-normal direction is comparable to the particle settling velocity. Using the simulation results, the interplay between the different fluid–particle interaction forces is analysed, with and without gravity. In the absence of gravity, the dynamics is dominated by the balance between the stress-gradient force and the turbophoretic effects; as the particle-to-fluid density ratio for the sediment particles is on the order of one, the situation is quite different when compared to the dynamics with a density ratio on the order of 1000. When gravity is included, the dynamics is dominated by the interplay between the drag and gravitational forces, and they balance each other. Both with and without gravity, the lift and added-mass forces have only secondary effects and do not play an important role.

A hybrid smoothed particle hydrodynamics coupled to a fictitious domain method for particulate flows and its application in a three-dimensional printing process

A hybrid smoothed particle hydrodynamics (SPH) coupled to a direct-forcing fictitious domain (FD) scheme is proposed for the simulation of particulate flows. The new method is effective in calculating the particle-fluid interaction forces and uses a kernel interpolation function to realize the momentum exchange between fluids and particles. A higher-order interpolation scheme is applied to preserve the consistency and accuracy of the kernel function. We first test our method by simulating the benchmark of flow past a cylinder at Reynolds number ranging from 20 to 200 and obtain the convergent results, including accurate lift and drag coefficients, Strouhal number, length of the recirculation bubble, and separation angle. Subsequently, we verify our new method for the typical particulate flows, including the motion of a neutrally-buoyant cylinder in Couette flow, the motion of a neutrally-buoyant cylinder in a planar Poiseuille flow, the sedimentation of a circular cylinder in a channel, and the motion of a neutrally-buoyant slender particle in Couette flow. A good agreement with the existing experimental data, with other numerical results, and with available theoretical solutions is obtained indicating the accuracy and the robustness of the new method. Subsequently, our SPH-FD is applied to simulate a slender fiber in a three-dimensional (3D) printing process, showing a good potential and advantages in simulating particulate flows of some industrial processes.

Fluid-particle interaction regimes during the evolution of turbidity currents from a coupled LES/DEM model

In this paper, fluid-particle interactions in lock-exchange turbidity currents (TCs) over a flat bed are investigated using a model combining LES and DEM (Large-Eddy Simulation and Discrete Element Method). The reliability of this model is demonstrated via comparing the numerical solutions with measurements of the front positions, fluid velocity profile, and particle concentration profile of lock-exchange TCs. The following physical understandings are obtained. The vorticity field plays an important role for the current evolution by affecting the fluid lift force (i.e., in the direction normal to the fluid-particle slip velocity) acting on the particles. At the very beginning, a longitudinal positive lift force due to strong positive vorticity promotes longitudinal particle transport. Afterwards, the longitudinal lift force decreases and eventually becomes negative, with a magnitude that even exceeds that of the positive longitudinal drag force, because more and more of the settling particles are affected by the negative vorticity near the bottom wall caused by surface friction. Interestingly, in spite of the complex behavior of the fluid-particle interaction forces and their role in TC evolution, only a very small fraction of the initial particle gravitational potential energy is actually transformed into TC kinetic energy (both particle and fluid).

Use of CFD-DEM to evaluate the effect of intermediate stress ratio on the undrained behaviour of granular materials

This study investigates the effect of intermediate stress ratio (b) on the mechanical behaviour of granular soil in true triaxial tests. A CFD-DEM solver with the ability to model compressible fluid and moving mesh has been developed and calibrated based on existing experimental test results on Nevada sand. The effect of b on the undrained true triaxial test, which has been neglected in the literature, was investigated using a reasonable number of models. The effects of the initial confining stress and initial void ratio also have been studied. The developed model was used to calculate the hydrodynamic forces on the particles and evaluate the ratio of the particle–fluid interaction force to the resultant force on the particles. It has been demonstrated that, in numerical studies, the effect of these forces cannot be neglected.

Fluid particle interaction in packings of monodisperse angular particles

Understanding fluid flow in granular materials is essential for many engineering applications, including petroleum recovery, groundwater movement and embankment stability. This study investigates the influence of particle angularity on permeability and fluid-particle interaction forces. A random shape generator based on spherical harmonics is used to create irregular-shaped particles with different levels of angularity. Granular packings of uniformly sized (monodisperse) particles are then constructed with the discrete element method (DEM), and pore-scale computational fluid dynamics (CFD) simulations are used to determine the flow fields and the resulted fluid-particle interaction. The more angular particle assemblies thus generated are less permeable, and their fluid-particle interaction forces are higher. However, angularity has limited influence on flow rate distribution and flow tortuosity. The influence of angularity is localized. An increase in angularity generates a larger variance of the pressure distribution on the particle surfaces, thus increasing the pressure component of the fluid-particle interaction force.

A novel CFD-DEM coarse-graining method based on the Voronoi tessellation

In unresolved flow CFD-DEM simulations, the porosity values for each CFD cell are determined using a coarse-graining algorithm. While this approach enables coupled simulations of representative numbers of particles, the influence of the porosity local to the particles on the fluid-particle interaction force is not captured. This contribution considers a two-grid coarse-graining method that determines a local porosity for each particle using a radical Voronoi tessellation of the system. A relatively fine, regular point cloud is used to map these local porosity data to the CFD cells. The method is evaluated using two different cases considering both disperse and tightly packed particles. The data show that the method conserves porosity data, is reasonably grid-independent and can generate a relatively smooth porosity field. The new method can more accurately predict the fluid-particle interactive force for polydisperse particle system than alternative methods that have been implemented in unresolved CFD-DEM codes.

Roles of solid effective stress and fluid-particle interaction force in modeling shear-induced particle migration in non-Brownian suspensions

The applicability of some constitutive equations for the solid stress tensor used in the mixture model to describe the shear-induced migration of neutrally buoyant particles in Newtonian fluids is investigated. It is shown that in moderately dense suspensions, where direct particle contacts and interparticle forces are negligible, migration must be due to the lubrication forces between the particles. Results highlight that the tensor accounting for these forces is part of the stress tensor of the fluid phase, not of the solid phase and, in particular, that it coincides with the part of the particle-presence stress tensor related to the lubrication forces.

Different methods of numerical simulation of non-premixed combustion in the packed bed

ABSTRACT It is difficult to choose the appropriate numerical simulation methods to model the character of non-premixed diffusion combustion in particle packed bed among so many various methods. Four different numerical methods were used to simplify the gas flow through the packed beds, the non-premixed diffusion combustion of methane in a plane-parallel packed bed was simulated considering the chemical equilibrium and thermal radiation. The gas flow field, temperature and flame characteristics were analyzed using computational fluid dynamics coupled with discrete element method (CFD-DEM) which calculates the fluid-particle interaction force considering the drag force and the pressure gradient force, the gas flow velocity magnitudes in the particle packed bed simulated by CFD-DEM are smaller than those by porous media and Ergun equation. The maximum velocity of gas varies from 0.22 m/s to 0.80 m/s using four different methods. Compared the flame shape and height with experimental test values, the flame heights simulated by M2 and M3 are both 10% smaller than that of the experimental result, which is reasonable because of carbon black. The maximum combustion temperature simulated by M4 is more 400 K higher than those by M2 and M3. This study shows that only using CFD-DEM, the flame height of non-premixed diffusion combustion in a packed bed can be reasonably simulated. For industrial engineering packed bed, CFD-DEM is the priority choice to calculate the fluid-particle interact force.

Lattice Boltzmann investigation on fluid flows through packed beds: Interaction between fluid rheology and bed properties

Non-Newtonian fluid flows through packed beds are common in many industries. Our understanding of this flow system is very limited, and the correlations for describing the fluid-particle interaction are not fully established. To overcome these problems, this paper presents a comprehensive study of this system on a sub-particle scale, with a special reference to the interaction between fluid rheology and bed properties. This is done by conducting about five hundred Lattice Boltzmann simulations under different conditions. The fluid rheology is represented by the power-law model to consider the shear-thinning, shear thickening and Newtonian behaviors of fluids. The simulation condition covers a wide range of bed porosity, particle size distribution and Reynolds number (Re). The results show that the effect of fluid rheology on the fluid behavior is strong. This effect varies significantly with bed porosity which is a function of particle size distribution. The interplay between fluid rheology and bed properties is however not strong in determining the distributions of particle-fluid interaction force. Based on the simulation data, a new drag correlation is established and validated against the experimental data in the literature. This correlation is more accurate and consistent than those reported in the past. It can estimate the mean drag forces on individual particles of different sizes, and is recommended to be used generally in the modeling of particle-fluid flows either for Newtonian fluids or for non-Newtonian fluids obeying the power-law model.

A coupled DEM-SPH model for moisture migration in unsaturated granular material under oscillation

Granular materials, such as mineral products, soil and chemical fertilizer, normally contain unsaturated free moisture. This unsaturated moisture could migrate in the granular material and its processing, resulting in handling and safety concerns due to a change in the material properties. In this work, a method of coupling the Discrete Element Method (DEM) and the Smoothed Particle Hydrodynamics (SPH) was proposed to investigate moisture migration in unsaturated granular materials under oscillation. The particles and water were simulated through DEM and SPH, respectively and a python coupling framework was programmed to perform the exchange of particle-fluid interaction forces. Subsequently, experiments with plastic pellets and a coal sample were used to calibrate the models, with DEM calibrated by an angle of repose experiment and draining experiments calibrating the coupled model. Finally, the coupled model was validated by comparing the results to those of experiments involving moisture migration under oscillation. It was found that, compared to measurements, the coupled SPH-DEM model predicted the same moisture migration trend and also provided good agreement for the prediction of the mass of drained water.

Computing drag and interactions between fluid and polydisperse particles in saturated granular materials

Fundamental numerical studies of seepage induced geotechnical instabilities and filtration processes depends on accurate prediction of the forces imparted on the soil grains by the permeating fluid. Hitherto coupled Discrete Element Method (DEM) simulations documented in geomechanics have most often simulated the fluid flow using computational fluid dynamics (CFD) models employing fluid cells that contain a number of particles. Empirical drag models are used to predict the fluid-particle interaction forces using the flow Reynolds number and fluid cell porosity. Experimental verification of the forces predicted by these models at the particle-scale is non-trivial. This contribution uses a high resolution immersed boundary method to model the fluid flow within individual voids in polydisperse samples of spheres to accurately determine the fluid-particle interaction forces. The existing drag models are shown to poorly capture the forces on individual particles in the samples for flow with low Reynolds number values. An alternative approach is proposed in which a radical Voronoi tesselation is applied to estimate a local solids volume fraction for each particle; this local solids fraction can be adopted in combination with existing expressions to estimate the drag force. This tessellation-based approach gives a more accurate prediction of the fluid particle interaction forces.

Micromechanical analysis of bubbles formed in fluidized beds operated with a continuous single jet

Advancement in the knowledge of bubble dynamics and properties can significantly aid to improve the design and operation of gas-solid fluidized beds. In this work, bubble properties in a single jet fluidized bed were studied by the combined approach of CFD and DEM. The results illustrated that the process of the continuous injection of a central air jet to the bed was successfully reproduced, with the formation of a series of bubbles which rise through the bed and burst at the bed top. During this process, the series of bubbles align vertically which show coalescence in three different levels of the bed. However, the coalescence patterns depend upon jet velocity and are fairly regular. The bubbles are categorized into two types: primary/leading bubbles and trailing bubbles. The size of primary bubbles keeps increasing with bed height while the size of trailing bubbles decreases since trailing bubbles coalesce with primary bubbles. Primary bubbles, although formed at different times, are of similar shape at different heights of the bed while trailing bubbles are generally elongated in shape. Trailing bubbles have a higher velocity than primary bubbles. The spatial analysis of pressure gradient, drag, and particle-fluid interaction force shows that the presence of bubbles leads to different particle flow zones where forces vary significantly. Moreover, the bubble passage can be delineated by the temporal variation of the particle-fluid interaction force.

Flow and force analysis on the formation of expanded beds in gas fluidization of fine ellipsoids

A flow regime called expanded beds in gas fluidisation exists for fine powders. Some attempts have been made in the past to analyse the formation mechanism of expanded beds, indicating that the essential condition for an expanded bed to exist is that the van der Waals force balances the contact force and the particle-fluid interaction force balances the weight of the bed at bulk scale. However, how particle shape affects the expanded bed formation is still not clear. In this work, CFD-DEM approach is applied to elucidate the particle-particle and particle-fluid interaction forces on the dynamic formation of expanded beds with fine ellipsoids. The results illustrate that at the start-up stage, the bulk disconnects into two major bulks with a lowest contact force on the axial direction, especially for fine ellipsoids. Spheres have a smoother expansion process than ellipsoids, and ellipsoids need longer start-up time. A slower gas introduction process has a more moderate change in bed height. The fractures gradually disappear when the cohesive forces become smaller. At the transition stage, when the aspect ratio deviates from 1.0, the pressure drop fluctuation significantly increases. At the stable stage, when the aspect ratio decreases or increases from 1.0, the contact forces and van der Waals forces increase, and the distributions of particle-fluid interaction forces become less uniform in the beds. Ellipsoidal particles undergo an orientation rearrangement during the expansion process.

Investigation of causes of layer inversion and prediction of inversion velocity in liquid fluidizations of binary particle mixtures

Liquid fluidization plays an important role in mineral processing such as solid classifiers and biological reactors. When particle properties differ in size, density or shape, segregation can occur. Typically, a segregation phenomenon so-called layer inversion in two-phase solid-liquid fluidization of binary mixtures has been reported in the literature. At low liquid velocities, the two species form distinct layers with the denser smaller particles at the bottom and the lighter larger particles at the top. At high liquid velocities, however, the two layers are inverted with smaller particles being at the top while larger ones at the bottom. In this work, glass beads (193 μm) and activated carbon (778 μm) are used in the simulation as those in Jean and Fan (1986), and the layer inversion is successfully reproduced by CFD-DEM. The underlying segregation mechanism is analyzed in terms of particle-fluid interaction forces. The results reveal that the layer inversion is caused by the relative change of particle-fluid interaction forces on particles. For large particles, the reduction of the pressure gradient force cannot be compensated by the increased drag force, resulting in the downward flow. Meanwhile, small particles tend to move upward because the increased drag force exceeds the decreased pressure gradient force. In addition, the effects of particle and liquid properties on layer inversion are examined, and different drag force models in predicting the layer inversion are also assessed. It indicates that Rong et al.'s drag model represents the layer inversion with the best accuracy. Finally, a model based on the force balance criterion is proposed to predict the inversion velocity showing a better accuracy.

Revised partial coupling in fluid–particulate systems

Fluid equations in Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) simulations solve the volume-averaged Navier–Stokes equations. Full coupling between the dispersed phase and continuous phase is made by the exchange of source terms as well as the void fraction. The void fraction is calculated from the presence of the particles in the computational fluid cells while the source terms are calculated from the point mass force models of the fluid–particle interaction forces. Dense particulate system with large spatiotemporal variations in the void fraction shows hard convergence behavior. This can impact the robustness of the solver during the time integration process. One option is to use partial coupling by neglecting the explicit effect of void fraction in the fluid momentum equations while retaining its effect on force models. Although the partial coupling is more stable and shows better convergence behavior, the mobility of the particles is found to be reduced as compared to the full-coupling approach. In the current work, we propose a revised partial coupling in which a modified fluid velocity is used in point mass force models to compensate for the omission of the void fraction in the fluid governing equations. The effectiveness of this method is demonstrated in a fluidized bed and in sediment transport simulations. In both cases it is shown that the use of the proposed method gives very good comparisons with the fully coupled simulations while reducing the fluid calculation time by factors ranging from 1.35 to 4.35 depending on the flow conditions. The revised partial coupling is not recommended as a substitute for full coupling in dense systems but as an alternate approach when full coupling leads to numerical difficulties.

Particle scale modelling of solid flow characteristics in liquid fluidizations of ellipsoidal particles

Particle shape is one of the most important parameters that can cause significant changes of flow characteristics in liquid fluidized beds, which however has not been well studied in the past. In this work, CFD-DEM approach is used to investigate the hydrodynamics of ellipsoidal particles in liquid fluidizations. The non-uniformity distributions of pressure gradient and porosity with bed height are successfully captured for ellipsoids at high liquid superficial velocities, consistent with those reported in literature. The results also show that ellipsoids intend to enter the freeboard region and entrainment may occur. Disc-shape particles expand more significantly than spherical and elongated particles. The force analysis indicates that with particle aspect ratio deviating from 1.0, the drag force acting on ellipsoids increases while pressure gradient force reduces. Particle shape effects shown above are closely related to particle orientations which can significantly affect particle-fluid interaction force and particle terminal velocities.

Comparative DEM-CFD study of binary interaction and acoustic agglomeration of aerosol microparticles at low frequencies

The paper concerns the problem of acoustic agglomeration due to the acoustic wake in diluted aerosols and addresses the development of the time-accurate discrete element method (DEM) simulation technique. The case of weak entrainment of heavier mono-sized microparticles at low-frequency sound waves is considered. The agglomerative motion of two identical micron-sized spherical particles is simulated numerically, and contribution of the particles boundary layer in transition from the diluted to the dense phase is investigated. A comparative study of the DEM approach against more accurate computational fluid dynamics (CFD) computations is performed. The 3D incompressible viscous flow of aerosol medium described by Navier–Stokes equations is considered regarding the fine scale of particles. The numerical results regarding the agglomeration rate, drag coefficient, and perturbation velocities are discussed. Moreover, the correction to the fluid–particle interaction force is proposed to increase the accuracy of the DEM model.

Dynamic characteristics of binary sphere mixtures under air impact

This paper presents a numerical study on the packing densification process of binary sphere mixtures under air impact using a combined computational fluid dynamics and discrete element method (CFD-DEM) scheme. The effects of particle size ratio (PSR) on the force and stress characteristics including the depth-averaged normal force, probability density function (PDF) of normal forces, distributions of strong forces, mean stress distribution in the axial cross-section, and depth-averaged mean stress for various contact types, are comprehensively analyzed. In addition, the distribution of fluid-particle interaction forces is also discussed to explain the densification mechanism during air impact. The results reveal that the force and stress characteristics are significantly affected by both PSR and air impact. For each PSR, the packing density increases with the gas inlet velocity to a maximum and then decreases. Meanwhile, both the depth-averaged normal force and the mean stress in initial packing increase linearly with the depth, while the relationship between the depth-averaged normal force or mean stress and the depth is in power law growth in the final packing after air impact. The contact type of L-S (L-large sphere, S-small sphere) plays a leading role in the PDF of normal forces, while the effects of S-S contact type on the packing system is weak. Furthermore, apart from the L-L contact, the strong force percentage of other contacts increases after air impact densification. The air impact can effectively improve the uniformity of the normalized mean stress distribution for the packing of binary mixtures. Finally, the distribution of fluid-particle interaction forces demonstrates that the packing can be densified by obvious rearrangement of small particles for adjacent pore filling, and this trend will become more apparent with the increase of PSR.