Accepted Manuscript Settling/rising of a foreign particle in solid-liquid fluidized beds: Application of dynamic mesh technique Swapnil V. Ghatage, Md. Shakhaoath Khan, Zhengbiao Peng, Elham Doroodchi, Behdad Moghtaderi, Nitin Padhiyar, Jyeshtharaj B. Joshi, G.M. Evans PII: DOI: Reference:
S0009-2509(17)30088-X http://dx.doi.org/10.1016/j.ces.2017.01.064 CES 13411
To appear in:
Chemical Engineering Science
Received Date: Revised Date: Accepted Date:
31 August 2016 26 January 2017 30 January 2017
Please cite this article as: S.V. Ghatage, Md. Shakhaoath Khan, Z. Peng, E. Doroodchi, B. Moghtaderi, N. Padhiyar, J.B. Joshi, G.M. Evans, Settling/rising of a foreign particle in solid-liquid fluidized beds: Application of dynamic mesh technique, Chemical Engineering Science (2017), doi: http://dx.doi.org/10.1016/j.ces.2017.01.064
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Settling/rising of a foreign particle in solid-liquid fluidized beds: Application of dynamic mesh technique
By Swapnil V. Ghatage a, b, Md. Shakhaoath Khan a, Zhengbiao Peng a, Elham Doroodchi a, Behdad Moghtaderi a, Nitin Padhiyar b, Jyeshtharaj B. Joshi b, c and G. M. Evans a,*
a. School of Engineering, University of Newcastle, Callaghan, NSW 2308, Australia. b. Department of Chemical Engineering, Indian Institute of Technology, Gandhinagar, Gujarat 382424, India. c. Homi Bhabha National Institute, Anushaktinagar, Mumbai 400 094, India.
* Author to whom correspondence may be addressed. Phone: +61-240339068, Fax: +61-240339095, E-mail:
[email protected]
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Abstract The modeling of moving objects has been the focus of many studies and has succeeded to attract sufficient attention by researchers. However, commonly used modeling approaches such as discrete element modeling (DEM), direct numerical simulations (DNS) lack simplicity and have been computationally intensive. In the present work, simple method of dynamic mesh in the framework of computational fluid dynamics has been employed. Eulerian-Eulerian simulations of a monodisperse solid-liquid fluidized bed (SLFB) have been carried out. A foreign particle (settling particle or rising bubble) was inserted in the system to study the effect of turbulence in SLFB on the motion of settling particle. The operating and geometrical parameters have been chosen based on the experiments performed by Ghatage et al. (2013). The results showed that the model can satisfactorily predict the settling velocity for low voidage fluidization in 2D as well as 3D simulations. Computational fluid dynamics (CFD) simulations at higher values of superficial liquid velocity showed liquid bubbles confirming the transition to heterogeneous regime. These liquid bubbles directed the settling particle to move zig-zag resulting in lower settling velocity. The size and number of the bubbles increase with an increase in the liquids velocity indicating increased heterogeneity. However, CFD predicted larger and higher number of bubbles than experimentally noted. This resulted in an increase in the deviation of predicted settling velocities from experimentally observed with an increase in superficial liquid velocity. In case of bubbles, it was observed that the dynamic mesh method is greatly dependent on the regime of operation in the column and works only in the range of low voidage when the fluidized bed is homogeneous and does not contain liquid bubbles.
Keywords: Fluidization; moving object; settling; rising bubble; classification velocity; dynamic mesh.
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1. Introduction Fluidized beds are widely used in chemical, petrochemical and allied industries. They provide efficient contact between fluid and solid phases and, hence, are preferred for carrying out various gas-solid, liquid-solid and gas-liquid-solid processes. One of the key parameters which affect the equipment performance is relative velocity or classification velocity of one phase with respect to another when the fluidized particles are characterized by wide range of terminal velocities. In the design of such multiphase fluidized beds, it is important to understand the phase distributions as well as motion of the various phases relative to one other. In the published literature, many researchers have characterized the turbulence in multiparticle systems. Joshi (1983), Grbavcic and Vukovic (1991), Grbavcic et al. (1992), Van der Wielen et al. (1996), Grbavcic et al. (2009) have all studied the effect of turbulence on the settling velocity of a foreign particle in presence of monosized fluidized particles. Most of these studies are experimental and/or theoretical. Vos et al. (1990) measured classification velocity of foreign particle in fluidized bed of transparent particles using visualization technique. Authors used fluidized particles composed of gelatin which had a somewhat brownish but transparent appearance. Di Felice et al. (1991) have proposed a pseudo-fluid model for predicting the settling velocity of a large dense particle in a fluidized bed. The pseudo-fluid model considered a foreign particle settling in a pseudo-fluid consisting of fluid and small fluidized particles. Grbavcic et al. (1992) measured the effective buoyancy and drag for foreign large particles of varying density, settling/rising in a bed of small fluidized particles. Authors considered gravity, drag and buoyancy as the forces applied on the foreign particle. Van der Wielen et al. (1996) proposed a correlation for predicting hindered settling velocity based on mixture density, fluid density, foreign particle density, terminal settling velocity and Richardson-Zaki index of the foreign particle as:
VSD PD M VSD PD L
n
4.8
1 0.79n L
(1)
4 Authors observed that the predictions of the correlation were in good agreement with the pseudo-fluid model proposed by Di Felice et al. (1991). Investigations have also been carried out for developing the relationship between the turbulence in multi-particle and the drag on a single introduced foreign particle (heavy particle/light bubble). However, these relationships have been largely empirical. Ghatage et al. (2013) have analyzed and reviewed the correlations. Authors discussed that the settling velocity of foreign particle decreases with increase in the superficial liquid velocity in SLFB. They observed classification velocities up to 20 percent of that of terminal settling velocity in quiescent liquid.
The hydrodynamics of the fluidized bed is generally modeled using two distinct approaches. The first is the most commonly applied Eulerian-Eulerian approach which is based on the continuum hypothesis, where motion for each phase is represented by the equations of continuity and motion for each phase. Another approach is the Eulerian-Langrangian approach, wherein the discrete element model (DEM) is capable of tracking every individual particle in the fluidized bed and computational fluid dynamics (CFD) model is used to simulate the flow field of the continuous fluid phase. Computational studies on the settling/rising of foreign particles in SLFBs are scarce. Hu et al. (2001) used an arbitrary Langrangian-Eulerian (ALE) moving, unstructured mesh to study the movement of particles using the finite element method (FEM). The fluid flow and particle positions were updated explicitly; whereas particle motion was defined implicitly at each time step. The predicted sedimentation velocities of a particle in a pipe were found to be in excellent agreement with the experimental measurements. However, the study was computationally very intensive even for the case of pipe flow with no neighboring particles. Munster et al. (2012) investigated the terminal settling velocity of a single particle in a fluid using FEM with fictitious boundary method (FBM). The adaptive aligning of the grid deformation allowed the tracking of particle motion through the fluid. They observed 10% deviation with experimental values of terminal settling velocity. Munster et al. (2012) predicted the terminal settling velocity of dense and larger particle (dP = 15 mm) in a fluid using FEM with fictitious boundary method (FBM) and the predictions were within 1% deviation as compared with the experimental results. It may
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be pointed out, however, that all the aforesaid computational studies focused on mainly settling of a single particle in fluid. The rising phenomenon of an air bubble in a liquid fluidized bed is of utmost importance in industrial applications. The interaction of the air bubble with the fluidizing particles could affect local turbulence as well as collision and attachment processes in a flotation system. However, attempts to model the phenomenon of rising bubbles are scarce. The continuum models readily allow the modeling of particle-particle stresses and particle-viscous stresses using spatial gradients of phase volume fractions and velocities. The particle-particle collisions are considered by kinetic theory of granular flow assuming the conservation of solid fluctuation energy. The Eulerian-Eulerian modelling of SLFB has been attempted by many researchers and detailed information is available in the literature (Cheng and Zhu, 2005; Lettieri et al., 2006; Cornelissen et al., 2007; Reddy and Joshi, 2009). Discrete element modeling provides a better and comparatively simpler framework for the simulations of such systems; however, it is limited by the maximum number of particles that can be simulated. Di Renzo et al. (2011) observed that the combined computational fluid dynamics-discrete element method (CFD-DEM) approach using drag force model described by Cello et al. (2010) can satisfactorily predict fluidization characteristics in a binary SLFB. They proposed that chaotic small scale vortices are mainly responsible for mixing of phases. Highly non-uniform concentration profiles along the height of the column were observed at highest velocities studied. Peng et al. (2014) have successfully predicted the hindered settling velocity of foreign particle in SLFB using DEM approach. The authors have presented literature review on the previous attempts of simulating SLFB using CFD-DEM. The particle-particle interactions such as collision and its dependency on solid volume fraction have been the main focus. However, the method is complex and computationally intensive. In addition, Ghatage et al. (2014) and Peng et al. (2014) have discussed instabilities and heterogeneities developed in the SLFB at higher liquid fluidization velocities. Blais et al. (2016) have used CFD-DEM method for simulating SLFB with viscous liquid. The accuracy of both implicit and explicit momentum exchange schemes in reproducing the minimum fluidization velocity (Umf) and pressure drop (ΔP) were checked. It was also found that
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more accurate results were provided by the explicit scheme in which hydrodynamic forces are estimated by local characteristics of flow. Direct numerical simulation (DNS) is a promising method to simulate the motion of foreign particles. However, it is also limited by the maximum Reynolds number and total number of particles surrounding the foreign particle. Squires and Eaton (1990) performed DNS simulations and discussed trajectory biasing in accordance with the tendency of particles to accumulate in regions of low vorticity and high strain rate. The authors studied particles over a wide range of Stokes number, St, which can be given as [Ghatage et al. (2013)]:
P L CV u r St CD V 3 / 4 d P S
(2)
The authors have observed that very light particles (St > 1) are not influenced by the turbulent eddies and are uniformly dispersed. However, no comment on the increase/decrease of settling velocity due to turbulence was made. The dynamic mesh approach is a promising and yet simple method to simulate the motion of moving objects. Mitra et al. (2015) have utilized the dynamic mesh method along with volume of fluid (VOF) method to perform CFD simulations of droplet-particle collision. They observed that the CFD predictions of particle sinking time were in good agreement with the experimentally measured values. However, no attempt in the published literature exists wherein dynamic mesh approach is coupled with any other modelling approach to apply in fluidized beds. It was thought desirable to quantify the effect of turbulence on the motion of a single particle both experimentally and through modeling. For this reason, a foreign particle was inserted in a SLFB and its motion has been studied. There is practically no approach suggested in the published literature which is simple and still robust for the simulation of the motion of
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moving objects in the presence of large number of fluidized particles. In addition, it is noteworthy to mention no attempt to model the rise of a single air bubble in a liquid fluidized bed using CFD is present. Therefore, an attempt has been made to perform CFD simulations using a simple dynamic mesh approach to investigate the settling of foreign particle in SLFB. Firstly, the experimental methodology is presented, followed by the CFD methodology, before presentation and discussion of the simulation results. 2. Experimental methodology The schematic of the experimental setup of the SLFB is shown in Fig. 1. The details pertaining to the setup and procedure have been described in Ghatage et al. (2013). The glass column was of 0.05 m in diameter and 1 m in height. Tap water (L = 1000 kg/m3) was used as the fluidizing liquid in all of the experiments. Precision-diameter stainless steel (P = 7800 kg/m3) particles with mean diameters of 6 mm (±2 µm) were used as the foreign particle for the classification velocity measurements. The fluidized particles were borosilicate glass beads (P = 2230 kg/m3) with a diameter of 5 mm. The particles were chosen such that the terminal Reynolds number, ReP∞ of both fluidized and foreign particles lie well within the turbulent regime (ReP∞ ≈ 3250 and ReD∞, ≈ 7000). In a separate set of experiments a single air bubble was introduced at the bottom of column near the liquid inlet. In these experiments the bubble diameter was varied between 1-4 mm (Ghatage et al., 2013), however, for the present study only 1 mm (ReB∞ = 110) bubbles were considered. Proper arrangements were made to insert a foreign particle (solid particle or air bubble) without disturbing the smooth operation of the fluidized bed. Experiments were performed to analyse the variation of classification velocity with respect to superficial liquid velocity. Firstly, the bed was allowed to fluidize and reach a steady value of bed expansion. The superficial liquid velocity was varied in the range of 0.061-0.22 m/s, corresponding to liquid voidage values of 0.47, 0.52, 0.60, 0.66, 0.70, 0.76 and 0.80. The Reynolds number of liquid, based on superficial liquid velocity and column diameter, was in the range of 300-1100. Then single foreign particle (either particle or bubble) was inserted in the
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system without disturbing the fluidization. A solid particle was inserted ussing two closely separated valves at the top so that the particle could be inserted with no disturbance into the fluidized bed. In the case of the bubble, a tube was provided at bottom which released a bubble at 0.02 m from bottom of the column. A calibrated syringe pump was used to generate of a bubble of precise size. All the experiments were performed at 25±3 °C. A pump was used for the liquid circulation. In order to maintain ambient temperature of the liquid a heat exchanger was used to remove heat generated due to turbulent energy dissipation and fluid friction in the system. The settling velocities of the foreign particle were measured across a vertical distance between 100 mm and 200 mm distance from the distributor using a high speed video camera (model: Photron Fastcam Super-10K) and adequate LED lighting behind the bed. The LED array consisted of 144 high-power diodes. A diffuser plate was used in front of LED array. Large number of LEDs and the diffuser plate ensured the proper imaging of the foreign particle. Though the refractive indices of air, water and fluidized borosilicate glass beads were different i.e. 1.00, 1.33 and 1.474, respectively, it was possible to visualize the foreign particle clearly. The classification velocity was estimated by tracking the centre-motion of the foreign particle from images (512 X 420 pixels) captured at 500 frames per second giving a time resolution of 0.002 sec. Due care was taken to ensure that the foreign particles had reached terminal velocity prior to entering the test section and not influenced by the mean flow. Each reported settling/rising velocity was the average of five measurements, where the reproducibility was observed to be within 2 percent. 3. Computational methodology CFD simulations were performed in two-dimensional (2D) and three-dimensional (3D) geometry using the Eulerian-Eulerian approach and dynamic mesh technique. The standard k-ε model was used as the turbulence model as the flow was essentially turbulent. 3.1. Model formulation
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In the present study, the phases are modeled in Eulerian-Eulerian framework considering interpenetrating continua. The equations of continuity and motion for the solid and liquid phases are given by:
S S S SuS 0 t
(3)
L L L L u L 0 t
(4)
S SuS S SuSuS S PS S S FZ S Sg t
(5)
L L u L L L u L u L L PL L L FZ L Lg t
(6)
Two fluid model (TFM) such as Eulerian-Eulerian model has been successfully employed in the past few decades for simulating fluidized beds in FLUENT (for instance Cheng and Zhu, 2005; Reddy and Joshi, 2009). The solution of equations (5) and (6) need closure relations for the liquid and solid phase stress tensors, solid phase rheology (solid viscosity and solid phase pressure) and fluid-particle interaction force. Table 1 summarizes the simulation details used in the present study. The kinetic theory of granular flow (KTGF) was generally used to provide the closure relation for the solid phase stress tensor, whereas, various empirical (Gidaspow, 1994; Lun et al., 1984) models were used for the phase interaction parameters. KTGF accounts for the binary collisions between the particles; however, omits friction among them. 3.2. Computational geometry and methodology Simulations for the settling particle were carried out in both two dimensional as well as three dimensional geometries. Fig. 2A depicts the two dimensional geometry along with the boundary conditions; whereas Fig. 2B shows the enlarged view of the region near the foreign particle. The dimensions of the geometry were the same as that of the experimental setup. It was difficult to get the structured mesh throughout the geometry. Application of the dynamic mesh with the structured mesh created additional difficulty. Therefore, an unstructured mesh was used in combination with the dynamic mesh method. The triangular mesh was employed giving total number of nodes of 14600 (50 X 1000 mm (L X H)). As the focus of the present study the was
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foreign particle motion, a fine mesh which moved along with the particle was employed for region near the particle surface in order refine the interface region between the foreign particle and the fluidized bed. A 3D geometry was also employed and is shown in Fig. 3A. The column was of 1 m length and 0.05 m diameter. The boundary conditions were same as those for the 2D geometry. The mesh type was strictly restricted to tetrahedral (unstructured). Enlarged views near the dense particle in the vertical and horizontal directions are shown in Fig. 3B and 3C, respectively. The total number of unstructured nodes was 36400 (50 X 50 X 1000 mm (D X D X H)). Fig. 4A shows the 3D geometry employed for simulations of the rising bubble. The dimensions, mesh type and boundary conditions were similar to the previously described 2D and 3D geometries. Fig. 4B depicts an enlarged axial cross-sectional view near the dynamic mesh region. A single bubble of 1 mm at 0.02 m height from bottom was defined as part of the dynamic mesh. The location of bubble in the computational geometry was exactly same as in experiments. The geometry comprised 12000 (50 X 50 X 1000 mm (D X D X H)) unstructured nodes. The simulations were performed at experimentally noted values of superficial liquid velocity. The simulations were carried out as two step procedure. Firstly, unsteady simulations using Eulerian-Eulerian approach were carried out to get steady state bed expansion characteristics of SLFB. Unsteady simulations were defined to attend steady state when the difference of average solid volume fraction was detected to be less than 2 percent. During this step, no slip condition was applied at the wall of foreign particle. TFM calculated the phase distribution and turbulent fluctuations around the particle. Finally, the foreign particle was introduced using dynamic mesh scheme to study the settling/rising over column height. The dynamic mesh method enabled calculation of the forces applied on the foreign particle at each time step in order to determine its new position. It took into account the phase distribution and turbulence near the foreign particle estimated by TFM. When the particle reached a new position, mesh around the particle was modified and TFM considered new mesh for estimating volume
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fraction and turbulence parameters. The calculations continue until the simulation was terminated due to particle reaching bottom of the column. 3.3. Dynamic mesh approach The dynamic mesh method is provided in FLUENT 15. The dynamic mesh method considers mesh to be moving and restructures the mesh near the moving object as it moves. Layering option in dynamic mesh works with structured mesh, however, in present study, smoothing and remeshing techniques were used as they are compatible with unstructured mesh. In smoothing, the stretching of cells adjacent to the moving body is considered using spring constant in accordance with Hooke’s law (Ansys Inc., 2015). The value of zero spring constant represents highly deformable system, whereas, value of 1 corresponds to very stiff system. The value of spring constant was kept constant at 0.1 as mesh can deform significantly due to high settling velocity of dense particle. The boundary node relaxation parameter which represents the inter relation between interior nodes and the boundary nodes, was considered to an optimum value of 0.1. When the velocity of moving body is high, cells around the moving body deform significantly resulting in high skewness. It can lead to convergence problem or in severe cases simulation failure due to negative cell volumes. To avoid such issues by achieving desired cell qualities, cells which exceed a specified skewness are remeshed. It was observed that in order to maintain quality of mesh 0.4 was suitable value for the maximum skewness and was used in simulations. The total number of nodes was continuously changed when dynamic mesh approach was used. It was detected that almost one thousand nodes were vanished or generated when the simulation was complete. It may be attributed to the fact that dynamic mesh works with creation and death of original mesh along the motion of moving body. The foreign particle was considered to be a rigid body and the motion was acquired by incorporating a user defined function (UDF). It uses six degrees of freedom for the closure and considers external force acting on the foreign particle. In the present study, gravity acting on the particle was considered the only external force. In the case of 2D simulations, unit thickness of any geometry was considered by default. So, the volume of cylinder was considered while
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defining the mass of foreign particle in UDF. The location of the centroid of foreign particle was tracked continuously as it moves through the bed. The axial and radial movements of the centroid were monitored along the bed height and over the range of superficial liquid velocities covering voidage range of 0.52 < ϵL < 0.8. The classification velocity of the foreign particle was estimated from the motion of centroid. The simulated results provide temporal and spatial variation of the classification velocity of the foreign particle in SLFB. In the case of 3D simulations, we have checked the role of grid sensitivity. The effect of grid size and grid type was studied on the settling as well as rising phenomena. The number of grids were varied in the range of 12000 to 36000. The simulation was found to be grid independent when the number exceeded 30000. Authors have observed insignificant (less than 6 percent) difference in the results (e.g. bed expansion, classification velocity, etc.) by refining the grid size. However, it significantly increased the computational time required for completing the simulation. Therefore, an optimized mesh quality was used for the present study. 4. Results and discussion In experiments, it was observed that the normalized slip velocity was monotonically decreased with increase in Stokes number i.e. increase in turbulence (Ghatage et al., 2013). Fig. 5 has been reproduced from Ghatage et al. (2013) in order to provide insight into the turbulence involved. The turbulence levels in the published results by various researchers in numerous turbulence devices can be seen. The significance of the study is the operating conditions are remarkably at higher Stokes number (St > 10) whereas those reported previously by researchers are at very low Stokes number (St < 1). The turbulence in SLFB increases with increase in VL. Reynolds number of liquid was observed to be in the range of 300 (VL = 0.061 m/s) to 1100 (VL = 0.22 m/s). In drawing Fig. 5, the particle hindered settling velocity, VSD is calculated by correlation given by Kunii and Levenspiel (1969): 3.1g PD M d PD VSD K M
0.5
,
where, the wall effects are taken care by wall correction factor, K and can be given as:
(7)
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K
VSW VSDW . VS VSD
(8)
A gradual decrease in the slope was seen and it was proposed that normalized slip velocity could have minima for Stokes number greater than 10. For detailed experimental results readers are requested to refer Ghatage et al. (2013). The detailed computational results are discussed in sections below. 4.1. Behavior of fluidized bed The fluidized bed was simulated using Eulerian-Eulerian approach. It was thought desirable to compare the predicted bed expansion characteristics with the Richardson-Zaki equation. It was observed that the predicted values of liquid voidage agree within 15 percent with those estimated using Richardson-Zaki equation (in both 2D and 3D simulations). Peng et al. (2014) performed CFD-DEM simulations of essentially the same fluidized bed having identical geometrical and operating conditions. The authors have compared CFD-DEM predictions with the calculated pressure drop (ΔP) based on weight of particles. The total pressure drop calculated based on the apparent weight of the particles is 1450 Pa. It was observed that their model predicted the value of ΔP to be 1520 Pa. The predicted Umf by revised Ergun equation (Doroodchi et al., 2012) is 0.0423 m/s. The value of Umf equal to 0.0424 m/s was predicted by CFD-DEM model. It can be seen that the CFD-DEM predictions were deviating by less than 5 % compared to calculated values of ΔP and Umf. The present CFD simulations showed consistency with observations of Peng et al. (2014). It was also observed that the bed attains homogeneity after some time (around 10 s) at lower values of liquid voidage. However, at higher liquid voidage, liquid bubbles (having no solid content) appear surrounded by a region of high solid phase fraction. These bubbles were found to persist even after simulation for prolonged time of about 60 s. Similar bubbles were also observed in the experiments; however, the size of bubbles predicted by Eulerian-Eulerian simulations was larger than experimentally observed. The existence of liquid bubbles confirms the existence of heterogeneity.
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4.2. Motion of dense foreign particle through the column The temporal contour plots of bed expansion obtained from 2D simulations at superficial liquid velocity, VL of 0.061 m/s are shown in Fig. 6. Figure depicts the snapshots of SLFB over a vertical plane to locate the foreign particle. It can be viewed in Fig. 6A that the particle was held at the top, the centroid of the particle being at the origin (50 mm below the column top). As can be seen from Fig. 6A, at t = 0 s, the solid volume fraction was defined to be 60% in the packed bed. Then the liquid flow was started, letting the bed to expand. The expanded bed at t = 10 s is depicted in Fig. 6B. The simulation was monitored from 35 s to 65 s, when it was observed that the variation in average volume fraction was less than 2 percent it was construed that a steady state had reached. The steady state bed expansion at t = 65.3 s can be seen in Fig. 6C. At this moment, the foreign particle was released from the origin. As depicted in Fig. 6D, at t = 65.55 s, the foreign particle moved down in the column against the superficial liquid velocity. Fig. 6E shows that foreign particle has dropped further down the column. At t = 66.6 s the particle hit the expanded bed height and entered the fluidized bed. In the bed, the particle was followed by a ‘liquid wake’ till it reached the bottom. The liquid wake can be seen in Figures 6F-6H. The liquid wake was approximately 0.1 m size and had less solid content than surrounding fluidized bed. However, no significant variations were observed in the expanded bed height and the average phase fractions. While moving through the fluidized bed, the classification velocity of settling particle was drastically declined, as is visible in Fig. 6F-6H. As depicted in Fig. 6H, moving slowly through the fluidized bed the particle reached the bottom at t = 68.5 s. The variation of classification velocity along the length of the column is discussed in detail in subsequent sections. 4.3. Variation of classification velocity along the bed height Fig. 7A-7C illustrate the settling profiles for the dense foreign particle at VL = 0.061 m/s. It can be seen from Fig. 7A that, at t = 65.3 s, the foreign particle started moving and hit the fluidized bed, at an axial location of -0.73 m and at time equal to 66.6 s. After hitting the bed, the velocity i.e. slope of the curve decreased significantly. Further, the particle progressed through
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the SLFB. Around t = 68.5 s, the particle reached the bottom of the column i.e. Y = -0.95 m, where the simulation is terminated. The radial movement of the centroid is presented in Fig. 7B. The particle was dropped from the centre of the column. It can be seen that at VL = 0.061 m/s, the particle also moves radially within the range of ±5 mm. The dense steel particle should fall straight down, however, it should be noted that the particle is falling against the upward liquid motion and is affected by the turbulence imparted within the system. Authors believe that the turbulence characterized by higher liquid velocity at the centre is pushing the particle away from the centre. However, due to significant settling velocity of dense particle, it is deflected only by small distance. It would be interesting to see radial deflection of particle centroid at higher values of VL. Once, the dashed line (bed height) is crossed, particle drops through the fluidized bed and is free to reach the bottom (Y = -0.95 m) at any value of X. Figure 7C indicates the variation of classification velocity along the bed height. Initially, velocity accelerated as particle started its motion through column and attained terminal value against the upward liquid. The terminal settling velocity (VSD∞) of the foreign particle in an infinite water medium is around 1.1 m/s, however, considering wall effects (Eq. (8)) it is 0.83 m/s. In the column the settling velocity was observed to be 0.65 m/s. This is because the particle is progressing against the upward liquid velocity of 0.061 m/s. Once the particle is collided with the bed at t = 66.6 s, the classification velocity was suddenly dampened to 0.118 m/s, which is around 18.7 percent of the settling velocity in the liquid above the bed. The classification velocity fluctuates in the range of ±5 percent of average value. After steadily moving through the fluidized bed, the particle is decelerated as it reaches near the bottom of the column. The CFD simulation is terminated as the particle touches the bottom and the classification velocity becomes zero. The simulation at each value of superficial liquid velocity was repeated five times. The reproducibility of classification velocity (as well as particle trajectory) was found to be within ± 8 percent at the lowest superficial liquid velocity i.e. VL = 0.061 m/s. 4.4. Classification velocity of dense solid particle: variation with superficial liquid velocity
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Figures 8-10 give details pertaining to the variation in the settling behaviour with respect to rise in the superficial liquid velocity. To facilitate comparison the time when particle starts moving is defined as t = 0. The axial location of particle centroid is plotted against time on Fig. 8 for three different values of VL i.e. 0.061 m/s, 0.161 m/s and 0.22 m/s. The trends of settling velocity are similar as explained above with respect to Fig. 7A. The slope of the curve gives the settling/classification velocity. The sharp change in the slope can be seen at the instant when foreign particle hits the fluidized bed. It was observed that more time is required for the foreign particle to reach the bottom of the column as VL increased. This is mainly because the foreign particle has to travel more through the fluidized bed due to increase in bed expansion with increase in VL. The classification velocity of foreign particle was least for VL = 0.061 m/s, whereas, it was almost same for other two values of VL. Fig. 9, depicts increase in zig-zag motion of the particle with increase in superficial liquid velocity. It is mainly due to the presence of “liquid bubbles” in the fluidized bed at higher values of VL. The size and number of these bubbles increase with an increase in the liquid velocity indicating enhanced heterogeneity. It should be noted that as superficial liquid velocity is increased, Reynolds number of liquid, Re, rises indicating enhanced turbulence. This in turn increases the zig-zag motion of the particle. Figure 10 shows the variation of classification velocity of foreign particle with time. It can be seen that the settling velocity against superficial liquid velocity above the fluidized bed height was highest for VL = 0,061 m/s and least for VL = 0.22 m/s. Within the fluidized bed, the classification velocity fluctuates between ±5 percent at lower voidage of 0.47 to ±50 percent at maximum voidage of 0.8 covered in this work. Increased turbulence results in more fluctuations at high values of VL. In heterogeneous regime at high liquid velocities, more bubbles were seen in the central region. Therefore, the settling of foreign particle occurs in regions near the wall. Further, it was noted that the root mean square (rms) fluctuating velocity amplifies with an increase in voidage resulting in enhanced zig-zag motion. However, in reality the rms velocity versus voidage has a maximum.
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The predicted average classification velocities at superficial liquid velocities studied, are shown in Fig. 11. It can be concluded that the 2D simulations predict favorably well at lower values of liquid voidage. However, predictions increase steadily, attain maxima at VL = 0.161 m/s and decrease further. The reduction in average classification velocity at higher values of VL is due to heterogeneity developed. The reproducibility of classification velocity at highest superficial liquid velocity was observed to decrease to around ± 14 percent. Inferior reproducibility at higher superficial liquid velocities could be attributed to the fact that the location of liquid bubbles vary in different simulations. To quantify the existence of liquid bubbles in greater depth, it was thought desirable to carry out simulations in 3D geometry. 4.5. 2D versus 3D simulations Figure 12 represent the predicted settling behaviors in 2D and 3D simulations at highest liquid voidage of 0.80 i.e. VL = 0.22 m/s. Equal slope of the curve is predicted by 2D and 3D simulations before hitting the fluidized height (Fig. 12A). However, after the particle hit the bed, 3D simulations predicted comparatively higher value of classification velocity. Also, it is evident that profile is smooth with constant slope in case of 3D simulations. Fig. 12B illustrates that the radial movement of the particle was declined when the simulations were performed in 3D. In order to facilitate the comparison radial co-ordinate for 3D predictions is considered as R =
X Y 2
2
. It is noticeable from Fig. 12C that 2D simulations show highly fluctuating
classification velocities than those predicted by 3D simulations. 3D settling behavior was comparatively less distorted i.e. ± 40 percent around the average value. The principle reason is the occurrence of less number of bubbles in the 3D simulations. The observation is in consistent with one noted in Ghatage et al. (2014) where it was observed that 2D Eulerian-Eulerian simulations showed more bubbles than 3D Eulerian-Eulerian as well as 3D DEM simulations. The heterogeneity and instability in SLFB at higher fluidization is discussed later in greater details. Figure 11 presents a comparison between the predictions of 2D and 3D simulations. Initially both show an increase in VR with an increase in VL, Noticeably 2D and 3D predictions of
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VR show maxima (with respect to
at different liquid velocities i.e. 0.161 and 0.138 m/s
respectively. Surprisingly, a decrease was observed in predicted settling velocity at higher values of
. Also, it was apparent that 2D and 3D predictions increasingly differ from each other with
the increasing liquid velocity. It should be noted that 2D simulations consider unit distance in third dimension which is equal to radius in 3D simulations. Three dimensional zig-zag motion of settling particle can be seen in Fig. 13. It can be seen that the particle starts moving in radial direction even before entering the fluidized bed. It is because the radial profile of the axial liquid velocity is not flat due to the heterogeneity in the bed. 2D simulation results showed in Figs. 7-10 cannot capture the radial motion of the foreign particle precisely, showing an important limitation of applying 2D approach to present study. However, it is apparent from Fig. 11 that the predicted classification velocities by 2D approach are in ±20 percent deviation with predictions of 3D approach. Therefore, 2D approach is simplified approach to predict approximate values of settling velocities of foreign particle. More research is needed to provide detailed insight into the issue. The comparison with experimental results is discussed in detail further. 4.6. Classification velocity of dense particle: comparison of experimental with simulation results Fig. 11 shows the comparison between CFD (both 2D and 3D) predicted and experimentally measured average classification velocity. The results show that the EulerianEulerian approach satisfactorily predicts the classification velocity at lower fluidization. Comparatively, 3D simulations showed better agreement with the experimental measurements when VL < 0.138 m/s. At highest superficial liquid velocity studied, decrease in the prediction of average classification velocity was noted in both 2D and 3D simulations. 2D simulations predicted considerable lower values, which may be attributed to the size and frequency of liquid bubbles as discussed earlier. In CFD simulations performed at high voidage fluidization, it was observed that the pressure gradient force and stress force facilitate the foreign particle to deviate radially thereby avoiding the liquid bubbles associated with heterogeneous regime. This effect may be attributed
19
to the fact that in the liquid bubbles, upward liquid velocity is higher than the superficial liquid velocity, enhancing resistance to foreign particle within the developed bubbles. So, the foreign particle moves through the region of higher local solid hold-up settling at velocities equivalent to more dense fluidized beds and resulting in lower values of classification velocities. It may be pointed out that at high bed voidages the contact forces between particles of fluidized bed and the transiting particle are relatively small but their influence increases at low bed voidages (Peng et al., 2014). It should be noted that experimental images were taken over height 0.1 to 0.2 m from the distributor. The average classification velocity was noted in the experiments due to troubles in continuously tracking the foreign particle using visualization. Therefore, the comparison of experimental trajectories of foreign particle with CFD predictions is avoided. 4.7. Effect of wake behind dense foreign particle on the classification velocity As the particle enters the fluidized bed, a wake was noticed behind the particle. The wake followed the particle till it reaches the bottom of fluidized bed. An attempt was made to study the effect of the wake on the particle classification velocity. New 3D geometry was used wherein a foreign particle was placed at height less than expanded bed height. 3D simulations were carried out in a case wherein foreign particle was completely free from the wake as it was already within the fluidized bed at t = 0 s. It was observed that the particle achieved its terminal classification velocity within the bed after passing through 30 mm bed height. The predicted classification velocity was compared with that predicted in the presence of wake and found to be within 6 percent deviation at lowest value of VL. At VL = 0.22 m/s, the deviation was increased to 12 percent. It concluded the absence of major effect due to observed wake in the range of superficial liquid velocities studied. 4.8. Bubble propagation and contraction/expansion In the simulations at high values of superficial liquid velocities, liquid bubbles were detected. The bubbles generated at bottom of the column and propagated from bottom of the column to the top. The bubbles generated were of size of the order of 1-2 particle diameters at the superficial liquid velocity of 0.11 m/s. The liquid bubbles expanded to 5-8 particle diameters size
20
at the superficial liquid velocity of 0.22 m/s. Initially, the concentration of solid particles was zero at center of liquid bubble. However, on the way particles dispersion effects cause the bubbles to faint from no solid concentration to small values of solid concentration. Overall, the size of the bubbles expand on the route as they rise, however, the expansion effects are accompanied by the solid dispersion in liquid bubbles decreasing the concentration barrier and helping relative uniformity at top. 4.9. Bubble rise velocity Simulations were performed for a single rising air bubble in SLFB. It was observed that at higher values of superficial liquid velocities, where bed operates in heterogeneous regime, fluctuations in bubble motion were excessive causing simulation to stop immediately. If the column is operating in heterogeneous regime and when a gas bubble gets immersed in a liquid bubble, the forces applied on the bubble interface are uneven and can significantly deflect the bubble leading to simulation failure. The simulation of air bubble was performed only at lowest superficial liquid velocity of 0.061 m/s. The predicted bubble rise velocity was 0.018 m/s, which is very close to the reported hindered rise velocity in experiments (Ghatage et al., 2013). 4.10. Flow regime transition from homogenous regime to heterogeneity Present study, showed that transition from homogeneous to heterogeneous regime occurred as the liquid volume fraction was increased. The experimental observed and computational (Eulerian-Eulerian and Eulerian-Langrangian) predicted transition have been discussed in detail in Ghatage et al. (2014). Authors observed transition to heterogeneous behavior when ϵL ≥ 0.54 in SLFB and explained the behavior in relations to concentration profiles, vector plots, vorticity graphs. Authors also proposed that the regime transition can be predicted when classification velocity was plotted against superficial liquid velocity indicated by change in slope of curve. Eulerian-Eulerian simulations with dynamic mesh supported the existence of flow regime transition. At lower values of superficial liquid velocity, foreign particle showed smooth descent within the fluidized bed as can be seen from Figs. 6 and 7. Fig. 7C illustrates that the fluctuation
21
in the classification velocity within the fluidized bed was within ±5 percent. It indicated the homogeneous operation of SLFB. However, at higher fluidization, the particle demonstrated a tendency to move radially towards the wall due to presence of liquid bubbles confirming the presence of heterogeneous flow (Fig. 9). Also, greater fluctuations were detected in classification velocity along the column height. It can be seen in Fig. 10 that the classification velocity collapsed down, even to 0 m/s, at one instant and sometimes amplified to twice the average classification velocity within the bed. Both 2D and 3D simulations (Fig. 9, 10 and 12) proved the existence of heterogeneity at higher fluidization, though the fluctuations in classification velocity were lesser in 3D simulations. 5. Conclusions Unsteady simulations were performed to investigate settling/rising behavior of foreign particle in SLFB. The dynamic mesh method along with Eulerian-Eulerian approach provides promising approach for modeling the settling of foreign particle in SLFB at lower fluidization. 2D simulations were observed to be predicting the classification velocities at lower values of superficial liquid velocities, however, at higher fluidization they show decrease in settling velocity. 3D simulations showed better predictions than 2D simulations, however, still with deviation up to 50 percent. The simulation of rising bubble was performed at lowest velocity corresponding to homogeneous regime of SLFB. It was observed that the predicted value was in ±10 percent deviation of the experimental observation. CFD simulations with dynamic mesh supported the observation of heterogeneous regime at ϵL > 0.54 reported by Ghatage et al. (2014). The occurrence of liquid bubbles confirmed the transition to heterogeneity. The liquid bubbles propagate from bottom to top and bubble expansion as well as solid dispersion effects were observed as they raised.
22
Nomenclature CD
drag coefficient, -
CD∞
drag coefficient in infinite medium, -
CV
virtual mass coefficient, -
dB
bubble diameter, m
dP
diameter of particle comprising fluidized bed, m
dPD
diameter of foreign particle, m
D
column diameter, m
eSS
solid-solid interaction restitution coefficient, -
eWS
solid-wall interaction restitution coefficient, -
Fz
interphase force, N/m3
g
gravitational acceleration, m/s2
H
column height, m
k
turbulent kinetic energy, m2/s2
K
wall correction factor, -
l
characteristic turbulence lengthscale, m
L
length, m
n
Richardson-Zaki index, -
P
pressure, N/m2
R
radial co-ordinate in 3D simulations,
X Y 2
2
,m
23
DVLL
Re
liquid Reynolds number,
L , -
ReB∞
Reynolds number based up on the terminal settling velocity of the particle,
ReP
particle Reynolds number,
ReP∞
Reynolds number based up on the terminal settling velocity of the particle,
St
P L CV u r Stokes number, St CD , V 3 / 4 d P S
u
superficial velocity, m/s
Umf
minimum fluidization velocity, m/s
ur’
rms turbulent velocity in radial direction, m
vP
volume of particle, m3
VL
superficial liquid velocity, m/s
VR
classification velocity, m/s
VSD
interstitial fluidization velocity for dense particle, m/s
VSDW
bounded settling velocity for dense particle, m/s
VSW
bounded settling velocity of fluidizing particle, m/s
VS∞
terminal velocity of particle, m/s
VSD∞
terminal settling velocity of heavy particle, m/s
X, Y
radial and axial co-ordinates respectively in 2D simulations, m
d P VR L
d B VBL
L , -
L , -
d P VSL
L , -
24
X, Y, Z two radial and an axial co-ordinates respectively in 3D simulations, m Greek letters ε
turbulent dissipation rate, m2/s3
fractional phase hold-up, -
ϵL,max packing limit, ΔP
pressure drop, Pa
µ
viscosity of fluid, kg/ms
ρ
density, kg/m3
τ
viscous stress tensor, N/m2
Subscripts B
bubble
D
dense particle
L
liquid
M
mixture
P
particle
S
solid
∞
infinite medium
25
References Aliseda, A., Cartellier, A., Hainaux, F., Lasheras, J.C., 2002. Effect of preferential concentration on the settling velocity of heavy particles in homogeneous isotropic turbulence. Journal of Fluid Mechanics 468, 77-105. Ansys Inc., Fluent theory guide, Release 15, 2015. Blais, B., Lassaigne, M., Goniva, C., Fradette, L., Bertrand, F., 2016. Development of an unresolved CFD-DEM model for the flow of viscous suspensions and its application to solid liquid mixing. Journal of Computational Physics. Accepted manuscript. Brucato, A., Grisafi, F., Montante, G., 1998. Particle drag coefficients in turbulent fluids. Chemical Engineering Science 53, 3295-3314. Cello, F., Di Renzo, A., Di Maio, F.P., 2010. A semi-empirical model for the drag force and fluid-particle interaction in polydisperse suspensions. Chemical Engineering Science 65, 3128-3139. Cheng, Y., Zhu, J., 2005. CFD modeling and simulation of hydrodynamics in liquid-solid circulating fluidized beds. Canadian Journal of Chemical Engineering 83, 177-185. Cornelissen, J.T., Taghipour, F., Escudie, R., Ellis, N., Grace, J.R., 2007. CFD modeling of liquid-solid fluidized bed. Chemical Engineering Science 62, 6334-6348. Di Felice, R., Foscolo, P.U., Gibilaro, L.G., Rapagna, S., 1991. The interaction of particles with a fluid-particle pseudofluid. Chemical Engineering Science 46, 1873-1877. Di Renzo, A., Cello, F., Di Maio, F.P., 2011. Simulation of the layer inversion phenomenon in binary liquid-fluidized beds by DEM-CFD with a drag law for polydisperse systems. Chemical Engineering Science 66, 2945-2958. Doroodchi, E., Peng, Z.B., Sathe, M.J., Abbasi-Shavazi, E., Evans, G.M., 2012. Fluidisation and packed bed behavior in capillary tubes. Powder Technology 223, 131-136. Friedman, P.D., Katz, J., 2002. Mean rise rate of droplets in isotropic turbulence. Physics of Fluids 14, 3059-3073. Ghatage, S.V., Sathe, M.J., Doroodchi, E., Joshi, J.B., Evans, G.M., 2013. Effect of turbulence on particle and bubble slip velocity. Chemical Engineering Science 100, 120-136. Ghatage, S.V., Peng, Z., Sathe, M., Doroodchi, E., Padhiyar, N., Moghtaderi, B., Joshi, J.B., Evans, G.M., 2014. Stability analysis in solid-liquid fluidized bed: Experimental and computational. Chemical Engineering Journal 256, 169-186. Gidaspow, D., 1994. Multiphase flow and fluidization: continuum and kinetic theory descriptions. Academic Press, San Diego. Grbavcic, Z.B., Arsenijevic, Z.L., Garic-Grulovic, R.V., 2009. Prediction of single particle settling velocities through liquid fluidized beds. Powder Technology 190, 283-291. Grbavcic, Z.B., Jovanovic, S.D., Littman, H., 1992. The effective buoyancy and drag on spheres in a water fluidized beds. Chemical Engineering Science 47, 2120-2124. Grbavcic, Z.B., Vukovic, D.V., 1991. Single-particle settling velocity through liquid fluidized beds. Powder Technology 66, 293-295. Hu, H.H., Patankar, N.A., Zhu, M.Y., 2001. Direct numerical simulations of fluid-solid systems using the arbitrary Langrangian-Eulerian technique. Journal of Computational Physics 169, 427-462. Joshi, J.B., 1983. Solid-liquid fluidized beds: some design aspects. Chemical Engineering Research and Design 61, 143-161. Kunii, D., Levenspiel, O., 1969. Fluidization Engineering. Wiley, New York.
26
Lettieri, P., Di Felice, R., Pacciani, R., Owoyemi, O., 2006. CFD modeling of liquid fluidized beds in slugging mode. Powder Technology 167, 94-103. 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. Mitra, S., Doroodchi, E., Pareek, V., Joshi, J.B., Evans, G.M., 2015. Collision behaviour of a smaller particle into a larger stationary droplet. Advanced Powder Technology 26, 280-295. Munster, R., Mierka, O., Turek, S., 2012. Finite element-fictitious boundary methods (FEMFBM) for 3D particulate flow. International Journal for numerical methods in fluids 69, 294313. Munster, R., Mierka, O., Turek, S., 2012. Finite element-fictitious boundary methods (FEMFBM) for time-dependent multiphase flow problems- Application to sedimentation benchmark. 13th Workshop on Two-Phase Flow Predictions, Halle, Germany. Peng, Z., Ghatage, S.V., Doroodchi, E., Joshi, J.B., Evans, G.M., Moghtaderi, B., 2014. Forces acting on a single introduced particle in solid-liquid fluidized bed. Chemical Engineering Science 116, 49-70. Poorte, R.E.G., Biesheuvel, A., 2002. Experiments on the motion of gas bubbles in turbulence generated by an active grid. Journal of Fluid Mechanics 461, 127-154. Reddy, R.K., Joshi, J.B., 2009. CFD modeling of solid–liquid fluidized beds of mono and binary particle mixtures. Chemical Engineering Science 64, 3641-3658. Squires, K.D., Eaton, J.K., 1990. Particle response and turbulence modification in isotropic turbulence. Physics of Fluids 2, 1191-1203. Van der Wielen, L.A.M., Van der Dam, M.H.H., Van Luyben, K.C.A.M., 1996. On the relative motion of a particle in a swarm of different particles. Chemical Engineering Science 51, 9951008. Vos, H.J., Van Houwelingen, C., Zomerdijk, M., Luyben, K.Ch.A.M., 1990. Countercurrent multistage fluidized bed reactor for immobilized biocatalysts. III. Hydrodynamic aspects. Biotechnology and Bioengineering 36, 387-396. Yang, T.S., Shy, S.S., 2003. The settling velocity of heavy particles in an aqueous near-isotropic turbulence. Physics of Fluids 15, 868-879.
List of Figures Fig. 1.
Experimental setup: (1) cylindrical glass column, (2) rectangular encasing column, (3) distributor plate, (4) calming section, (5) rotameter, (6) pump, (7) storage tank, (8) heat exchanger, (9) arrangements for the insertion of the foreign particle (10) bubble insertion tube (11) camera
Fig. 2.
2D Computational geometry: (A) Computational domain (B) Enlarged view near dynamic mesh (dense particle)
27
Fig. 3.
3D Computational geometry: (A) Computational domain (B) Enlarged axial crosssectional view near dynamic mesh (dense particle) (C) Enlarged horizontal crosssectional view near dynamic mesh (dense particle)
Fig. 4.
3D Computational geometry for rising bubble: (A) Axial planar view of 3D geometry with bubble (B) Enlarged axial cross-sectional view near dynamic mesh (air bubble)
Fig. 5.
Comparison of various studies from literature with present study showing effect of turbulence on settling velocity of foreign particle: 250 µm];
Brucato et al. (1998) [215-
Brucato et al. (1998) [425-450 µm];
Friedman and Katz (2002);
Aliseda et al. (2002);
Poorte and Bieshuvel (2002);
Yang and Shy
(2003) [Solid particles in air]; + Yang and Shy (2003) [Tungsten particles]; Yang and Shy (2003) [glass particles]; Present study:
6 mm dense particle in
fluidized bed of 5 mm glass beads Fig. 6.
CFD predicted contour plots of liquid volume fraction at superficial liquid velocity of 0.061 m/s at (A) t = 0 s (B) t = 10 s (C) t = 65.3 s (D) t = 65.55 s (E) t = 66.13 s (F) t = 66.74 s (G) t = 67.52 s (H) t = 68.5 s
Fig. 7.
Predicted settling profile for foreign particle at VL = 0.061 m/s in 2D simulation (A) Axial direction (B) Radial direction (C) Classification velocity
Fig. 8.
Predicted axial settling profile of foreign particle in 2D simulation against time: VL = 0.061 m/s;
Fig. 9.
VL = 0.061 m/s;
VL = 0.161 m/s;
VL = 0.22 m/s
Predicted classification velocity of foreign particle in 2D simulation against time: VL = 0.061 m/s;
Fig. 11.
VL = 0.22 m/s
Predicted axial settling profile of foreign particle in 2D simulation against radial location:
Fig. 10.
VL = 0.161 m/s;
VL = 0.161 m/s;
VL = 0.22 m/s
Variation of average classification velocity against superficial liquid velocity: Experimental measurement; predictions.
2D CFD predictions;
3D CFD
28
Fig. 12.
Predicted settling profile for foreign particle at VL = 0.22 m/s in 2D ( 3D (
) and
) simulations (A) Axial direction (B) Radial direction (C)
Classification velocity Fig. 13.
3D view of predicted settling profile for foreign particle at VL = 0.22 m/s in 3D simulation
29
(9) foreign particle insertion arrangement OUTLET (1) cylindrical glass column
(2) outer rectangular column
50mm
(8) heat exchanger VENT (5) rotameter
(11) camera
(7) storage tank
(10) bubble insertion tube
(6) pump (3) distributor
INLET
(4) calming section
Fig. 1.
30
pressure outlet
pressure outlet
1 m wall
wall
dynamic mesh
Y X
0.05 m
velocity inlet (A)
(B)
Fig. 2.
31
0.05 m
dynamic mesh (dense particle)
1 m
(A)
(B)
(C)
Fig. 3.
32
0.05 m
1 m
dynamic mesh (air bubble)
(A)
(B)
Fig. 4.
NORMALIZED VELOCITY, VSD/VSD (-)
33
STOKES NUMBER, St (-)
Fig. 5.
34
t=0s
A
10 s
65.3 s
B
C
65.55 s
66.13 s
D
E
Fig. 6.
66.74 s
F
67.52 s
G
68.5 s
H
35
RADIAL LOCATION, X (m)
AXIAL LOCATION, Y (m)
AXIAL LOCATION, Y (m)
TIME, t (s)
settling against liquid velocity
A
settling against liquid velocity
settling in fluidized bed
settling in fluidized bed B
Fig. 7.
36
CLASSIFICATION VELOCITY, VR (m/s)
C settling against liquid velocity
foreign particle hits expanded bed height settling in fluidized bed
TIME, t (s)
Fig. 7.
AXIAL LOCATION, Y (m)
37
TIME, t (s)
Fig. 8.
38
AXIAL LOCATION, Y (m)
RADIAL LOCATION, X (m)
Fig. 9.
CLASSIFICATION VELOCITY, VR (m/s)
39
TIME, t (s)
Fig. 10.
CLASSIFICATION VELOCITY, VR (m/s)
40
SUPERFICIAL LIQUID VELOCITY, VL (m/s)
Fig. 11.
41
TIME, t (s)
RADIAL LO 0 -0.015 -0.00
0.0 1
2
3
4
5
6
-0.025
-0.1
-0
-0.2
-0
-0.3
-0
AXIAL LOCATION, Z (m)
AXIAL LOCATION, Z (m)
0
-0.4 -0.5 -0.6 -0.7
-0
-0
-0
-0
-0
-0.8
-0
-0.9
A
B
-1
-1.0
Fig. 12. CLASSIFICATION VELOCITY, VR (m/s)
C
0.6
0.5
0.4
0.3
TIME, t (s)
42
AXIAL LOCATION, Z (m)
Fig. 12.
RADIAL LOCATION, Y (m)
R
43
Fig. 13.
Table 1. Simulation details
Highlights
Parameters
Numerical Value
Column diameter
0.05 m
Column height
1m
Turbulence model
Standard k-ε
Convergence criteria
10−4
Time step
0.0001 s
Iterations per time step
40
Discretization method
Second order upwind
Pressure-velocity coupling
SIMPLE
Packing limit, ϵL, max
0.6
eSS,
0.9
eSW
Operating pressure
1.013 × 105 Pa
Gravitational acceleration
9.81 m/s2
Granular viscosity
Gidaspow (1994)
Granular bulk viscosity
Lun et al. (1984)
Solid pressure
Lun et al. (1984)
Radial distribution
Lun et al. (1984)
44
Performed CFD simulations of solid liquid fluidised bed using Euler-Euler approach. Used dynamic mesh for simulating the foreign particle motion. 3D simulations predicted the settling/rising velocity better than 2D simulations. Discussed the turbulence interactions of particles/bubble with liquid bubbles.
