Stability analysis of unbounded uniform shear flows of dense, slightly inelastic spheres based on a frictional-kinetic theory

Asymptotic and transient stability analyses of unbounded uniform shear flows of dense, slightly inelastic, spherical particles were carried out using a frictional-kinetic theory. This model proposed for describing dense flows is based on a critical state plasticity theory and a simplified kinetic theory. In this model, the bulk and shear viscosities, the “thermal” conductivity, and the energy dissipation rate are proportional to a “mean pressure” which is composed of a quasistatic-frictional-contribution pressure considered for slow, plasticity deformations and a granular-kinetic-theorycollisional-contribution pressure. We studied two-dimensional stability analyses of layering disturbances (i.e., the perturbations whose wave number vectors are aligned only in the gradient) as well as nonlayering disturbances (the wave number vectors have nonzero streamwise components). Although this model has a simpler framework, it predicted similar results to those obtained using a more elaborate frictional-kinetic model. For instance, nonlayering disturbances are asymptotically stable at large time; the maximum transient growth of disturbances increases as the solids fraction or the friction coefficient is increased; and transient growths of disturbances can be significant due to the non-normality of the system. However, the prediction of the asymptotic stability of layering disturbances may be questionable because the collisional-contribution terms of the present model were over-simplified.     

Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds

A computational fluid dynamics (CFD) modeling of the gas–solids two-phase flow in a circulating fluidized bed (CFB) riser is carried out. The Eularian–Eularian method with the kinetic theory of granular flow is used to solve the gas–solids two-phase flow in the CFB riser. The wall boundary condition of the riser is defined based on the Johnson and Jackson wall boundary theory (Johnson & Jackson, 1987) with specularity coefficient and particle–wall restitution coefficient. The numerical results show that these two coefficients in the wall boundary condition play a major role in the predicted solids lateral velocity, which affects the solid particle distribution in the CFB riser. And the effect of each of the two coefficients on the solids distribution also depends on the other one. The generality of the CFD model is further validated under different operating conditions of the CFB riser.     

Experiments and simulations of gas-solid flow in an airlift loop reactor

The hydrodynamics in a gas-solid airlift loop reactor was investigated systematically using experimental measurements and CFD simulation.In the experiments,the time averaged parameters,such as solid fraction and particle velocity,were measured by optical fiber probe.In the simulation,the modified Gidaspow drag model accounting for the interparticles clustering was incorporated into the Eulerian-Eulerian CFD model with particulate-phase kinetic theory.Predicted values of solid fraction and particle velocity ...     

Effects of initial static bed height on fractional conversion and bed pressure drop in tapered-in and tapered-out fluidized bed reactors

In this article, a standard 2D Two-Fluid Model (TFM) closed by the kinetic theory of granular flow (KTGF) has been applied to simulate the behavior of tapered-in and tapered-out fluidized bed reactors. In this regard, two types of chemical reactions with gas volume reduction and increase were considered to investigate the effects of initial static bed height on the fractional conversion and bed pressure drop. To validate the CFD model predictions, the results of hydrodynamic simulations concerning bed pressure drop and bed expansion ratio were compared against experimental data reported in the literature and excellent agreement was observed. The obtained simulation results clearly indicate that there is an appropriate static bed height in a tapered-in reactor in which the fractional conversion becomes maximum at this height; whereas variations of static bed height in a tapered-out reactor have insignificant influences on the fractional conversion. Moreover, it was found that the residence time, temperature, and intensity of turbulence of the gas phase are three important factors affecting the fractional conversion in tapered fluidized bed reactors. In addition, it was observed that increasing the static bed height increases the bed pressure drop for both the tapered-in and tapered-out fluidized bed reactors.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Experimental characterization and CFD simulation of gas maldistribution in turbulent fluidization of Group A particles

The study presented hereby investigates experimentally and with CFD simulations the gas distribution effect on the hydrodynamic of a Geldart Group A turbulent fluidized bed. Experiments were carried out on a cold flow fluidized bed column with an even and uneven gas distribution. Local solid volume fraction profiles were measured using optical probes at different bed heights and along two radial directions. Optical probe measurements allow catching a clear hydrodynamic difference between both even and uneven gas distributions. These results were then used to assess CFD simulations with the code Barracuda™ (MP-PIC approach). It is noteworthy that the choice of drag correlation and boundary conditions strongly influences the agreement between the experimental and CFD results. Once the correct parameters are chosen, CFD simulations captured the effect of gas distribution changes.     

Counter-current three-phase fluidization in a turbulent contact absorber: A CFD simulation

A computational fluid dynamics study of three-phase counter-current fluidization occurring in a turbulent contact absorber was performed. A two-dimensional, transient Eulerian multi-fluid model was used, in which the dispersed solid phase was modeled employing a kinetic theory of granular flow. The grid independence of the model, the effect of wall boundary conditions, the choice of granular temperature model, the effects of order of discretization scheme and drag models were studied for a base case setting. The results of simulations were validated against experimental results obtained from the literature. Once the model settings were finalized, simulations were performed for different gas and liquid velocities to predict the hydrodynamics of the absorber. Computed bed expansion and pressure drop were compared with experimental data. Good agreement between the two was found for low velocities of gas and liquid.     

Horizontal laminar flow of coarse nearly-neutrally buoyant particles in non-Newtonian conveying fluids: CFD and PEPT experiments compared

The horizontal flow of coarse particle suspensions in non-Newtonian carrier fluids was numerically simulated using an Eulerian–Eulerian CFD model. This study was concerned with nearly-neutrally buoyant particles of 5 and 10 mm diameter conveyed by fluids of Ellis rheology in laminar flow, in a 45 mm diameter pipe at concentrations up to 41% v/v. CFD predictions of solid phase velocity profiles and passage times were compared to experimental data obtained by a Positron Emission Particle Tracking (PEPT) technique and Hall effect sensors, and a very good agreement was obtained considering the complexity of the flows studied. CFD predictions of solid–liquid pressure drop were compared to a number of relevant correlations gleaned from the literature. Only one of them showed a good agreement over the whole range of conditions studied. Other correlations generally showed large deviations from CFD, and their limitations in predicting the influence of solids concentration and particle size have been demonstrated. Overall, it emerged that for the flows studied, CFD was capable of giving predictions of pressure drop which were probably better and more reliable than the correlations available in the literature.     

Assessment of the kinetic–frictional model for dense granular flow

This paper aims to quantitatively assess the application of kinetic–frictional model to simulate the motion of dry granular materials in dense condition, in particular, the annular shearing in Couette configuration. The weight of frictional stress was varied to study the contribution of the frictional stress in dense granular flows. The results show that the pure kinetic-theory-based computational fluid dynamics (CFD) model (without frictional stress) over-predicts the dominant solids motion of dense granular flow while adding frictional stress [Schaeffer, D. G. (1987). Instability in the evolution equations describing incompressible granular flow. Journal of Differential Equations, 66(1), 19–50] with the solids pressure of [Lun, C. K. K., Savage, S. B., Jeffrey, D. J., & Chepurniy, N. (1984). Kinetic theories for granular flow: Inelastic particles in Couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics, 140, 223–256] in the CFD model improves the simulation to better conform available experimental results. The results also suggest that frictional stress transmission plays an important role in dense granular flow and should not be neglected in granular flow simulations. Compatible simulation results to the experimental data are seen by increasing the weight of frictional stress to a factor of 1.25–1.5. These improved simulation results suggest the current constitutive relations (kinetic–frictional model) need to be improved in order to better reflect the real dense granular flow.     

Numerical simulations of high pressure carbon dioxide fluid fluidized beds

Hydrodynamics of carbon dioxide fluid-particle mixtures are predicted using a low density ratio-based kinetic theory of granular flow in high pressure carbon dioxide fluid fluidized beds. A coexistence of particle waves and particle aggregates exists along bed height. The threshold to identify the occurrence of particle aggregates is suggested based on standard deviation of solid volume fractions in aggregative fluidization. The existence time fractions and frequencies of particle aggregates are predicted along axial direction. The effect of carbon dioxide fluid temperature and pressure on volume fraction and velocity distributions are analyzed at different inlet carbon dioxide velocities and particle densities in high pressure carbon dioxide fluidized beds. Simulated results indicate that the carbon dioxide-particles fluidization transits from particulate to aggregative states with the increase of inlet carbon dioxide velocities. The computed fluid volume fractions and heterogeneity indexes are close to the measurements in a high pressure carbon dioxide fluidized bed.     

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 circulation 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 performance 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 performance in the full-loop simulation of GSCFB.     

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.     

Non-uniform distribution of gas–solid flow through six parallel cyclones in a CFB system: An experimental study

In large-scale circulating fluidized bed (CFB) boilers, it is common to use multiple cyclones in parallel for the capture of solids, assuming that gas–solid flow to be the same in the cyclones. This article presents a study investigating gas–solid flow through six parallel cyclones in a CFB cold test rig. The six cyclones were located asymmetrically on the left and right walls of the riser. Solid volume fraction and particle velocity profiles at the riser outlets and in the horizontal ducts were measured using a fiber optical probe. Cyclone pressure drop and solid circulating rate were measured for each individual cyclone. Measurements showed good agreement as to the non-uniform distribution of the gas–solid flow, which occurred mainly across the three cyclones on one side: the middle cyclones on both sides had higher particle velocities. Conversely, the solid volume fractions, solid fluxes and solid circulating rates of the middle cyclones were lower than those of the other four cyclones. The apparent reason for the flow non-uniformity among the cyclones is the significant flow non-uniformity at the riser outlets. Under typical operating conditions, the solid volume fractions at the riser outlets had a deviation of up to 26% whereas the solid circulating rates at the stand pipes, 7%. These results are consistent with most other studies in the literature.     

Evaluation of the effect of wall boundary conditions on numerical simulations of circulating fluidized beds

A computational fluid dynamics （CFD） modeling of the gas-solids two-phase flow in a circulating fluidized bed （CFB） riser is carried out. The Eularian-Eularian method with the kinetic theory of granular flow is used to solve the gas-solids two-phase flow in the CFB riser. The wall boundary condition of the riser is defined based on the Johnson and Jackson wall boundary theory （Johnson ＆ Jackson, 1987） with specularity coefficient and particle-wall restitution coefficient.The numerical results show that these two coefficients in the wall boundary condition play a major role in the predicted solids lateral velocity, which affects the solid particle distribution in the CFB riser. And the effect of each of the two coefficients on the solids distribution also depends on the other one. The generality of the CFD model is further validated under different operatin~ conditions of the CFB riser.     

Characterization of countercurrent liquid-upward and solid-downward fluidized system

Acting as an operating mode of fluidization, the flow characteristics of a countercurrent liquid–solid fluidized bed (CCLSFB) were experimentally investigated using a Plexiglas column of 1.5 m in height. Countercurrent liquid-upward and solid-downward fluidization was achieved under a limited solid flowrate before flooding occurred.The “flooding” phenomena and the flooding velocity were identified by measuring the variations in pressure drop in the axial direction of the column. Two different methods were used to quantify the flooding point that led to the instability of the system. Axial solids holdup profiles were also obtained from the pressure drop data along the column and the influences of device structure and operating conditions on the solids holdup were also studied. Seven types of particles with different diameters and densities were used. An agreement was found between the experimental results and the mathematic prediction derived from the Richardson–Zaki equation on the data of the solids holdup.     

Combination of CFD and DOE to analyse solid particle erosion in elbows

Solid particle erosion is a major concern in the engineering industry, particularly where transport of slurry flow is involved. Such flow regimes are characteristic of those in alumina refinement plants. The entrainment of particulate matter, for example sand, in the Bayer liquor can cause severe erosion in pipe fittings, especially in those which redirect the flow. The considerable costs involved in the maintenance and replacement of these eroded components led to an interest in research into erosion prediction by numerical methods at Rusal Aughinish alumina refinery, Limerick, Ireland, and the University of Limerick. The first stage of this study focused on the use of computational fluid dynamics (CFD) to simulate solid particle erosion in elbows. Subsequently an analysis of the factors that affect erosion of elbows was performed using design of experiments (DOE) techniques. Combining CFD with DOE harnesses the computational power of CFD in the most efficient manner for prediction of elbow erosion. An analysis of the factors that affect the erosion of elbows was undertaken with the intention of producing an erosion prediction model.     

Investigation of the characteristics of particulate flows through fibrous filters using the lattice Boltzmann method

A fibrous filter is one of the most common systems used to separate suspended particles from air.Two important factors(i.e.,the pressure drop and capture efficiency) are usually used to evaluate the performance of this type of filter.This study considers three two-dimensional arrangements of fibers(parallel,staggered,and random) to geometrically model fibrous media.The lattice Boltzmann method is employed to numerically simulate fluid flow through the filter.The Lagrangian form of the equation of motion of a particle is numerically solved to track the path of each particle in the flow field,where a one-way interaction between the fluid and particles is considered.The effects of pertinent parameters such as the fiber arrangement,solid volume fraction,particle-to-fiber diameter ratio,particle-to-fluid density ratio,Reynolds number,Stokes number,and size of the fibrous medium on the pressure drop and capture efficiency are studied.The obtained results are compared with existing empirical and theoretical findings and discussed.     

Effect of void fraction and friction factor models on the prediction of pressure drop of R134a during downward condensation in a vertical tube

The theoretical flow models of homogeneous and separated flow are applied to in-tube condensation to predict the pressure drop characteristics of R134a. The homogeneous flow model is modified by ten different dynamic viscosity correlations and various alternative correlations of total, frictional and momentum pressure drops to take account of the partial condensation inside the tube. Numerical analyses were performed to determine the average and local homogeneous wall shear stresses and friction factors by means of a CFD program. The equivalent Reynolds number model is modified by six different two-phase friction factors to determine the total condensation pressure drop in the separated flow model. The refrigerant side total pressure drops, frictional pressure drops, friction factors and wall shear stresses are determined within a ±30% error band. The importance of using the alternative total, momentum and frictional pressure drop correlations for the homogeneous flow model is also shown.     

Eulerian–Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer

Numerical simulation of fully developed hydrodynamics of a riser and a downer was carried out using an Eulerian–Lagrangian model, where the particles are modeled by the discrete element method (DEM) and the gas by the Navier–Stokes equations. Periodic flow domain with two side walls was adopted to simulate the fully developed dynamics in a 2D channel of 10 cm in width. All the simulations were carried out under the same superficial gas velocity and solids holdup in the domain, starting with a homogenous state for both gas and solids, and followed by the evolution of the dynamics to the heterogeneous state with distinct clustering in the riser and the downer. In the riser, particle clusters move slowly, tending to suspend along the wall or to flow downwards, which causes wide residence time distribution of the particles. In the downer, clusters still exist, but they have faster velocities than the discrete particles. Loosely collected particles in the clusters move in the same direction as the bulk flow, resulting in plug flow in the downer. The residence time distribution (RTD) of solids was computed by tracking the displacements of all particles in the flow direction. The results show a rather wide RTD for the solids in the riser but a sharp peak RTD in the downer, much in agreement with the experimental findings in the literature. The ensemble average of transient dynamics also shows reasonable profiles of solids volume fraction and solids velocity, and their dependence on particle density.