Liquid Fluidized Beds Research Articles

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.

Hydrodynamic characteristics of particles with different roughness and deformability in a liquid fluidized bed

The effects of particle roughness and deformability on the fluid dynamics of liquid fluidized beds were investigated using a 190.5-mm-diameter column and particles with different surface finish and stiffness. Glass beads and plastic “BBs” coated using different techniques were employed as the rigid particles, while cooked starch pearls (tapioca) and sodium alginate gel beads produced from different gelling solutions served as the deformable particles. The particles were characterized by measuring their densities, diameters, Young’s moduli and coefficients of restitution. Terminal settling velocities were also measured by the free-falling method, and the bed voidages over a wide range of fluid flow rates were estimated from pressure drop measurements along the column height. Correlations for rigid smooth spheres underestimated the single-particle terminal settling velocity for particles with many asperities, especially for the soft spheres. The Richardson-Zaki equation, derived empirically for rigid particles, provided a satisfactory description of the liquid fluidized bed expansion, especially for rigid particles. Although the voidage deviations observed for the soft particles were less than 10%, the fluidization behavior of these particles was affected much more by the particle Stokes number than for rigid spheres. Though there is evidence in the literature that particle surface roughness is responsible for the deviation from predicted bed expansion in the fluidization of bioparticles, results presented in this study indicate that the mechanical properties of these soft particles can also be a major influencing factor.

A new two-phase coupling model using a random fluid fluctuating velocity: Application to liquid fluidized beds

Liquid solid fluidized beds are widely applicable two-phase contactors by which solid and liquid phase constantly exchange energy/mass at the interface. In this paper, a new DEM simulation approach to analyse the hydrodynamic behaviour of fluidized beds has been introduced and validated. In this approach, a random liquid fluctuating velocity following a Gaussian distribution is used to simulate the fluid phase. The mean and standard deviation of the distribution were functions of the liquid velocity and bed concentration. The liquid fluctuating velocity was able to produce a random motion of the particle across the entire bed. This new methodology can predict bed expansion and porosity, particle mixing time and velocity as a function of liquid velocity. The simulation results revealed that using DEM only along with the simulation methodology presented in this study suffices to predict the hydrodynamics of a fluidized bed to a reasonable accuracy.

Motion characteristics of binary solids in a liquid fluidised bed with inclined plates

Rectangular inclined channels prove promising for solid classification based on the principle of particle differential sedimentation. In the present work, we investigated the motion characteristics of binary solids in a modified fluidised bed (mFB) with inclined plates. We developed a theoretical model for the particle motion behaviour that accounts for the average solid volume fraction in the inclined channel and interactions between binary solids. The experimental system was designed to be consistent with the idealised theoretical arrangements to maximise the measurement accuracy. The experimental particles were mixtures of silica sand particles of sizes 425–710μm and 710–880μm, respectively. Specifically, we investigated the flow hydrodynamics of the binary suspension in terms of the settling length of both particle species and the bed expansion behaviour. We also analysed the utilisation factor and the separation efficiency of the mFB. The results showed that the average solid volume fraction in the inclined channel fluctuated slightly for a given total solid inventory. The utilisation factor and separation efficiency of the system decreased when increasing either the fluidisation velocity or the solid inventory. The prediction results were in good agreement with the experimental data with an absolute deviation of less than 15%.

Expansion behaviour of a binary solid-liquid fluidised bed with different solid mass ratio

This study reports the effect of particle mass compositions on the bed expansion behaviour of a binary solid liquid fluidised bed (SLFB) system. Experiments were performed comprising equal density (2230kgm−3) spherical glass beads particles of diameter 3, 5 and 8mm and water as fluidising medium with different particle mass ratios varying from 0.17 to 6.0. In the expanded bed, both segregated and intermixed zones were observed depending on the different particle diameter combinations. In a completely segregated SLFB, the bottom monosized layer exhibited a negative deviation ∼23% whereas a positive deviation ∼25% was found in the top monosized layer when compared with the corresponding pure monosized system. A small mixing zone spanning approximately two particle diameters thick was observed to exist even in a completely segregated SLFB for higher diameter ratio cases. A slight decrease in the mixing zone height was noted with increasing liquid superficial velocity. For lower diameter ratio cases, a relatively lager mixing zone height was observed which increased with increasing liquid superficial velocity. The bed expansion ratio was noted to decrease with increasing solid mass ratio however it increased with increase in the fluidising velocity ratio following a reasonable power law trend. The expanded bed height of the binary mixture was not entirely additive of its corresponding mono-component bed heights and both positive and negative deviations were observed. Finally, a two-dimensional (2D) Eulerian-Eulerian (E-E) model incorporating the kinetic theory of granular flow (KTGF) was used to quantify the binary system hydrodynamics. The model predicted expanded bed height agreed with experimental measurements within ±6% deviation. Presence of a mixing zone was also confirmed by the CFD model and simulated particle phase volume fraction distribution qualitatively agreed with the experimental visualisations.

Investigation of interstitial fluid effect on the hydrodynamics of granular in liquid-solid fluidized beds with CFD-DEM

Interstitial fluid between two approaching particles will give rise to an energy dissipation in the process of their collision due to the viscous effect. Compared with gas-solid fluidized bed, particles in the liquid-solid fluidized bed will generate more energy dissipation due to the viscosity of liquid being much higher than that of the gas. In the present study, the Discrete Element Method (DEM) was employed to simulate the hydrodynamics of the particle flow in a liquid fluidized bed. The interstitial fluid effect was taken into account by incorporating a dynamic coefficient of restitution for colliding particles into the damping coefficient. Probability distribution of particle velocity gradient was analyzed with variation of superficial liquid velocity for particles with different diameters. Effect of fluid properties on particle flow hydrodynamics was also studied. Simulated results show that particle velocity gradient and granular temperature are clearly affected when a dynamic coefficient of restitution is employed and the effects of interstitial fluid on the hydrodynamics of wet particle fluidization should be considered in numerical simulations. Simulated particle pressure agrees well with experimental data in the literature.

The effect of column tilt on flow homogeneity and particle agitation in a liquid fluidized bed

The motion of particles in a solid-liquid fluidized bed was experimentally studied by video tracking of marked particles in a matched refractive index medium. In this study, two fluidized states are compared, one carefully aligned in the vertical direction ensuring a homogeneous fluidisation and another one with a non-homogeneous fluidisation regime that results from a slight tilt of the fluidisation column of 0.3° with respect to the vertical. As a result of the misalignment, large recirculation loops develop within the bed in a well-defined spatial region. It is found that in that range of solid fraction (between 0.3 and 0.4), the inhomogeneous motion of the particles leads to significant differences in velocity fluctuations as well as in self-diffusion coefficient of the particles in the vertical direction, whereas the fluidisation height remains unaffected. At lower (less than 0.2) or higher (higher than 0.5) concentration, particle agitation characteristics are almost unchanged in the vertical direction.

Modeling the hydrodynamic forces between fluid–granular medium by coupling DEM–CFD

The hydrodynamics flow of solid–liquid fluidized beds has been studied through the simulation by means of coupling Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD). The coupling has been done through the drag force. The interaction forces between a fluid (liquid) and a granular medium (particles) is translated through a drag force. The effect of local particles concentration on the drag force is modeled by a porosity function f(ε)m=ε−m.n. The value of exponent of porosity (m.n) shows substantial dependence on the size of the REV (Representative Volume Element). A validation of the method by comparison with experimental data is presented. It is proposed also as an illustration of three different geometries of fluidizing columns (column simple, column with interior plate and column with two lateral inlets). For each of them, simulation results are analyzed, through a fluidization indicator. These examples illustrate the ability of the coupling DEM–CFD method presented in this work to optimize complex granular flow.

CFD-DEM simulation of liquid-solid fluidized bed with dynamic restitution coefficient

In liquid-solid fluidized beds, the existence of interstitial liquid among colliding particles generates more energy dissipation than that in the gas-solid fluidized bed. In this paper, a numerical modelling method to account for the energy dissipation by means of dynamic restitution coefficient for wet particles in liquid-solid fluidized beds is evaluated. The dynamic restitution coefficient model is based on a semi-empirical correlation generated from freely falling particles bouncing on a wet plate. We employed the Discrete Element Method (DEM) to numerically investigate the hydrodynamics of wet particles under the effect of interstitial fluid by incorporating dynamic restitution coefficient into damping coefficient. Simulation of the liquid-solid two-phase flow used a coupled DEM-Navier Stokes solver. Simulated distribution of granular pressure as well as particle velocities in the liquid fluidized beds were in good agreement with experimental data, thus the effects of dynamic restitution coefficient on the hydrodynamics of wet particle fluidization should be considered in numerical simulations. Two granular pressure models were also compared at different solid fraction for different particle sizes, the results indicated that Gidaspow's granular pressure model shows better predicted results when applied for small particles, while Batchelor's model provided more reasonable results for particles with larger diameter.

A simple model for predicting solid concentration distribution in binary‐solid liquid fluidized beds

A simple mathematical model for predicting the solid concentration profile in binary‐solid liquid fluidized beds is presented. The main assumption is that the solid concentration distribution follows the logistic function, which is supported by the literature. Various equations have been derived to solve key system quantities (e.g., bed expansion height, length and position of the transition zone). In contrast to previous models that often involve adjustable parameters and strongly rely on the availability of experimental data, the present model only requires inputs of fluid and particle properties, operating conditions, and correlations for dispersion and slip velocity. The results showed that the model is applicable to different binary‐solid systems that have size and/or density differences. The model's capability of predicting the layer inversion phenomenon has also been demonstrated. The model is simple but proves capable of accurately predicting key information for the design, operation and scale up of liquid fluidized beds. © 2016 American Institute of Chemical Engineers AIChE J, 63: 469–484, 2017

Segregation and dispersion of binary solids in liquid fluidised beds: A CFD-DEM study

Liquid fluidised beds often operate with particles of different sizes and densities, encountering partial or complete segregation of solid particles at certain operating conditions. In this study, the segregation and dispersion of binary particle species of the same size but different densities in liquid fluidised beds have been investigated based on the analysis of computational fluid dynamics – discrete element method (CFD-DEM) simulation results.The vertical fluid drag force acting on the particles was found to be responsible for the particle segregation. The mechanisms governing the particle dispersion strongly depended upon the solid–liquid two-phase flow regime, which transited from pseudo-homogeneous to heterogeneous when the superficial liquid velocity reached a certain value. In the homogeneous or pseudo-homogeneous flow regime (Rep≤40, ∈L, ave≤0.74), particle collisions acted as the main mechanism that drove the dispersion of particles. However, after the system became heterogeneous, the magnitude of the vertical collision force decreased towards zero and correspondingly, the magnitude of the vertical fluid drag force was approaching that of the particle net weight force as the superficial liquid velocity increased. Therefore, in the heterogeneous flow regime (Rep>40, ∈L, ave>0.74), the local turbulence of the fluid flow and particle collisions (if there were any) were found to be the main mechanisms that drove the dispersion of particles in all directions. The dispersion coefficient of individual particles varied significantly throughout the system in the heterogeneous flow regime. The simulation results reasonably agreed with the experimental data and the prediction results by existing correlations.

English

English

Direct modeling of voidage at layer inversion in binary liquid-fluidized bed

In liquid-fluidized bed chemical and biochemical reactors composed of binary mixtures, peculiar segregation effects can determine layers rich in one or the other component to revert their position in the bed (layer inversion phenomenon), with significant influence on the process performance. In contrast to previous modeling formulation that focused on the simultaneous prediction of the layer inversion velocity and voidage, in the present work two approaches for the direct prediction of the critical voidage are presented, validated and discussed. One is a straightforward extension of a similar model developed for binary gas-fluidized beds (named PSM) and the other one includes more appropriate treatment of the expanded bed conditions typical of liquid-fluidized beds (named ePSM). Both are tested in their prediction capability in comparison with three previously available models, all against experimental values of the inversion voidage, and for float/sink experimental observations available in the literature. Using the simplified PSM formulation the average discrepancy from inversion experiments results considerable (0.097 in voidage units), while with the ePSM it is much smaller (0.052), good in comparison with the others (0.051, 0.086 and 0.033). With dense float/sink experiments the agreement is very good for both PSM and ePSM. Analysis of the effects of the relevant variables on the inversion voidage is carried out, showing how it is possible to derive an inversion map, a universal one for the PSM and one at each composition with ePSM. Finally, the addition to ePSM of the separate calculation of the inversion velocity is shown by comparing the predicted and experimentally observed expansion characteristics of the two solids with velocity. Qualitative matching of trends is found with reasonable quantitative agreement.

Numerical prediction of flow hydrodynamics of wet molecular sieve particles in a liquid-fluidized bed

The Eulerian–Eulerian framework was used in the numerical simulation of liquid hydrodynamics and particle motion in liquid-fluidized beds. The kinetic theory of granular flow, which accounts for the viscous drag influence on the interstitial liquid phase, was used in combination with two-fluid models to simulate unsteady liquid–solid two-phase flows. We focus on local unsteady features predicted by the numerical models. The solid fraction power spectrum was analyzed. A typical flow pattern, such as core annular flow and particle back-mixing near the wall region of liquid–solid fluidized beds is obtained from this calculation. Effects of the restitution coefficient of particle–particle collisions on the distribution of granular pressure and temperature are discussed. Good agreement was achieved between the simulated results and experimental findings.

Bed Expansion and Particle Classification in Liquid Fluidized Beds with Structured Internals

AbstractThe inclusion of a structured packing as internal in a liquid‐solid fluidized bed allows expansion of the liquid velocity operation range before elutriation, promoting the liquid solid contact and mixing. The bed expansion of liquid‐solid fluidized beds provided with structured packing as internals is examined, for solids denser than the liquid phase and within a wide range of operating conditions. A correlation to estimate the bed expansion in liquid‐solid fluidized beds using structured packing as internals is developed. In addition, the feasibility of employing structured packing as internals for favoring classification of different density particles is demonstrated by analyzing the mass elutriated from the column at different liquid velocities for single particles or binary mixtures.

Residence time distribution of solid particles in liquid fluidised bed separator

Residence time distribution (RTD) of coal particles in a floatex density separator (FDS) was investigated using stimulus response technique. The mean residence time of the underflow particles was observed to increase with a decrease in the particle size as well as density. The resistance to settling is enhanced at higher bed pressure and the residence time of the particles increases. A linear correlation of the mean residence time with the terminal settling velocity of the particles was observed. The mixing behaviour in the FDS was neither plug flow type nor fully mixed type. The n-tank in series model described the mixing pattern in the FDS well with ‘n’ values in the range of 3–5. The relatively low values of ‘n’ indicated that the flow behaviour in the FDS was closer to the well mixed state.

Stability analysis in solid–liquid fluidized beds: Experimental and computational

Abstract In this study the transition from homogeneous to heterogeneous flow in a solid–liquid fluidized bed (SLFB) is examined both experimentally and numerically. The experimental apparatus comprised a refractive index-matched SLFB, comprising 5 mm diameter borosilicate glass and sodium iodine solution, which allowed for both instantaneous particle image velocimetry of the liquid flow field and solids hold-up measurements to be undertaken for superficial liquid velocities in the range of 0.06–0.22 m/s. The motion of individual, spherical steel balls (with diameters 6, 7, 8, 9 mm) was then tracked as it settled through the fluidized bed for differing superficial liquid velocities. It was observed that, for all the steel balls covered in this work, there was a change in slope in their respective classification velocity curves at a superficial liquid velocity of 0.08 m/s. This value was very close to the critical velocity of 0.085 m/s predicted from 1-D linear stability analysis; and therefore deemed to be the critical condition that marked the transition from homogeneous to non-homogenous flow. It is proposed that the change in slope of the classification velocity curve is due to the encounter of the settling foreign particles with liquid bubbles whose presence marks the onset of heterogeneous flow. Additional computational analysis, involving both Eulerian–Eulerian (E–E) and Eulerian–Lagrangian (E–L) approaches, is used to confirm the presence of liquid bubbles at a critical liquid hold-up of 0.54, which corresponds to that predicted from 1-D linear stability analysis. In summary, the study has highlighted that experimentally the transition condition for a SLFB can be obtained simply by observing the behavior of the classification velocity of a single foreign particle at different superficial liquid velocities. This transition condition was found to agree with the 1D linear stability criterion, Eulerian–Eulerian CFD (3D) and Eulerian–Lagrangian DEM (3D) approaches.

Forces acting on a single introduced particle in a solid–liquid fluidised bed

In a liquid fluidised bed system, the motion of each phase is governed by fluid–particle and particle–particle interactions. The particle–particle collisions can significantly affect the motion of individual particles and hence the solid–liquid two phase flow characteristics. In the current work, computational fluid dynamics–discrete element method (CFD–DEM) simulations of a dense foreign particle introduced in a monodispersed solid–liquid fluidised bed (SLFB) have been carried out. The fluidisation hydrodynamics of SLFB, settling behaviour of the foreign particle, fluid–particle interactions, and particle–particle collision behaviour have been investigated. Experiments including particle classification velocity measurements and fluid turbulence characterisation by particle image velocimetry (PIV) were conducted for the validation of prediction results.Compared to those predicted by empirical correlations, the particle classification velocity predicted by CFD–DEM provided the best agreement with the experimental data (less than 10% deviation). The particle collision frequency increased monotonically with the solid fraction. The dimensionless collision frequency obtained by CFD–DEM excellently fit the data line predicted by the kinetic theory for granular flow (KTGF). The particle collision frequency increased with the particle size ratio (dP2/dP1) and became independent of the foreign particle size for high solid fractions when the fluidised particle size was kept constant. The magnitude of collision force was 10–50 times greater than that of gravitational force and maximally 9 times greater than that of drag force. A correlation describing the collision force as a function of bed voidage was developed for Stp>65 and dP2/dP1≤2. A maximum deviation of less than 20% was obtained when the correlation was used for the prediction of particle collision force.

Particle-liquid mass transfer in solid–liquid fluidized beds

Abstract Solid–liquid mass transfer coefficient (kSL) was measured in both conventional solid–liquid fluidized bed (SLFB) and solid–liquid multistage fluidized bed (SLMFB) by using the system of dissolution of benzoic acid in water. The particle size was varied in the range of 165–890 μm and the voidage in the range of 0.4–0.9. The dependence of solid–liquid mass transfer coefficient on important variables associated with the distributor design has been studied for SLFB. It was observed that the orifice density (number of orifices per unit area), per cent free area and the pressure drop across the distributor play important role on the values of kSL. The effect of the inerts (glass beads) on the mass transfer coefficient was investigated. For the voidages below 0.6, intensification in kSL was observed due to the presence of inerts in the system. As the voidage increases, the presence of inerts was found to have increasing effect on the mass transfer coefficient. For SLMFB, an increment of up to 15% in mass transfer rate was observed in comparison to that in conventional SLFB under a wide range of operating conditions like superficial liquid velocity and particle diameter. All the past correlations have been critically analyzed and suitable recommendations have been made. A new generalized correlation has been proposed for the estimation of mass transfer coefficient for both SLFB and SLMFB based on the experimental data. These correlations have been shown to be valid for all the available data in the published literature.

Solid circulation rate and particle collisions in quasi two-dimensional water fluidized beds of spherical particles

The equations for the overall particle circulation rate and the frequency of particle–particle collisions in the quasi two-dimensional water-fluidized bed were proposed. The equations were based on the experimental results obtained from the water fluidized beds of mono-sized spherical glass particles dp=1.94, 2.98, 4.00 and 6.00mm in diameter and the correlation for the mean particle speed from our previous paper [14]. The optimal porosity of the fluidized bed was defined as the porosity at which the overall circulation rate or the frequency of collisions shows their maximum. The optimal porosities were calculated from the derivatives of the proposed correlations. The calculated optimal porosity was in the range 0.68–0.72 for the overall circulation rate, and 0.59–0.64 for the frequency of particle–particle collisions. The results obtained are in accordance with the experimental findings from the literature [2,3,23] which show that the maximum values of the heat and mass transport coefficients in the liquid fluidized beds are reached in the range of porosities between 0.6 and 0.8. By visual observations of the monolayer fluidized bed of spherical particles 10mm in diameter we concluded that the collisions in the liquid fluidized beds in most cases are not pairwise, but that the particles which collide often move together for some time in agglomerates before separating. The majority of collisions in fluidized beds differ very much from the instantaneous collisions as regarded in the kinetic theory of gases. Therefore, the overall circulation rate is a better measure of the dynamics of the fluidized bed and the intensity of transport properties than the frequency of collisions.