Disturbances in the Hydrodynamic Behavior of a Spouted Bed Caused

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Disturbances in the Hydrodynamic Behavior of a Spouted Bed Caused by an Optical Fiber Probe: Experimental and CFD Study Dyrney A. Santos,† Gustavo C. Alves,† Claudio R. Duarte,*,† and Marcos A. S. Barrozo† †

School of Chemical Engineering, Federal University of Uberlândia, Bloco K - Santa Mônica, 38400-902, Uberlândia, MG, Brazil ABSTRACT: In this work the disturbances in the hydrodynamic behavior caused by the use of an optical fiber probe in a conical-cylindrical spouted bed have been analyzed based on experimental results and CFD simulations using an EulerianEulerian multiphase model. The insertion of the probe inside the spouted bed caused a decrease in the fountain height and in the particle velocity for the spout region. The CFD simulations using the Representative Unit Cell model (RUC) drag model and considering the presence of the probe predicted better the experimental data of the particle velocity distribution than the other simulations performed in this work with other drag models.

1. INTRODUCTION In processes, such as drying of granular materials1,2 and coating of particles3, is essential an effective contact between the involved phases in order to reach higher rate of mass transfer, energy, and momentum. In this context arise the spouted bed which was originally developed as a substitute for a fluidized bed for coarse particles to overcome the poor quality of gas fluidization obtained with such particles. Besides their ability to handle coarse particles, spouted beds have structural and cyclic flow patterns with effective fluid−solid contact.4 The spouted beds can also be used in many other processes, such as gasification5 and pyrolysis,6 mechanical extraction,7 seeds inoculation,8 and coating,9 although most of these are still under research and development. Spouted beds are divided into three different regions each with its own specific flow behavior, which increase the complexity in its study: a spout at the center, where the gas and particles rise at high velocity and the particle concentration is low; a fountain zone, where particles rise to their highest positions and then rain back onto the surface of the annulus; and an annulus zone between the spout and the column wall, where particles move slowly downward as a dense phase. The mechanisms of solids movement in spouted beds are still not completely understood. Knowledge of the solids flow pattern in spouted beds is essential to their design, because the particles’ trajectories must meet process requirements. Thus, among many other variables, the particles velocity distribution and porosity have received considerable attention.10 For the measurement of these properties there are different nonintrusive and intrusive techniques. A brief and interesting description of nonintrusive method that uses ultrasonic computed tomography is given by Warsito et al.11 The authors illustrate their application in a slurry bubble column to get the general structures of the distributions of gas bubbles and solid particles in the column. Duarte et al.12 used a high video camera (maximum speed of 2000 frames per second) in order to obtain particle velocity profiles in the annular region as well the fountain in a two-dimensional spouted bed made of acrylic. The phosphor tracer technique was used by Du and Wei13 to study the effect of particle © 2012 American Chemical Society

properties, including particle size, particle density, and particle sphericity, on the lateral mixing behavior in a riser with FCC (Fluidized Catalytic Cracking) particles as fluidized materials. On the other hand, intrusive techniques, generally measure these dynamics properties through the insertion of probes throughout the phases, which causes perturbations and consequent large measurement errors.14 The optical fiber probe is an intrusive technique relatively simple, robust, and promoting, depending on their geometry, minimum disturbance to the flow field. This probe exhibit chemical stability, thermal tolerance, electrical passivity, and immunity to electromagnetic interference.15 Many researchers have used optical fiber probe in systems containing dense phases, such as in fluidized beds,16 in conical spouted beds,10 in cylindrical spouted beds,17 and jet spouted beds.18 Despite this widespread use of optical fiber probes in the investigation of particle flow dynamics in spouted beds, most researchers do not take the disturbance caused by means of the use of this technique into account. So, a more detailed study about the distortion caused by the insertion of this kind of probe into the flow should be made. Nowadays, with the great development of the computational area, as regards the improvement of data processing and storage, arise a useful tool, called CFD (Computational Fluid Dynamics), in order to obtain detailed information about flow phenomena. Studies of numerical simulation bythe CFD technique have become popular in the field of gas−solid flow. Otherwise, this great technological advantage contrasts with the scarce of experimental data, which are of fundamental importance to validate mathematical models. The two approaches commonly used in the simulation of multiphase flows are the Euler−Lagrange and the Euler−Euler. In the Euler−Lagrange approach, the fluid phase is treated as a continuum by solving the time average Navier−Stokes equations, while the dispersed phase is solved by tracking a Received: Revised: Accepted: Published: 3801

October 17, 2011 January 26, 2012 February 6, 2012 February 6, 2012 dx.doi.org/10.1021/ie2023838 | Ind. Eng. Chem. Res. 2012, 51, 3801−3810

Industrial & Engineering Chemistry Research

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the optical fiber probe (2); an air compressor of 7.5 hp (3); an orifice flow meter (4), and pressure transducers (5, 6). All signals from pressure transducers were logged into a computer (7) via a data acquisition system and processed by LabVIEW 7.1 software. The Plexiglas spouted bed column is shown in Figure 2. Its main dimensions are shown in Table 1.

large number of particles (or bubbles, droplets) through the calculated flow field. This approach is suitable for particle volume fractions less than 0.1.19 In the Euler−Euler approach, the different phases are treated mathematically as interpenetrating continua. Since the volume of a phase cannot be occupied by the other phases, the concept of phasic volume fraction is introduced. These volume fractions are assumed to be continuous functions of space and time and their sum is equal to one.19 Duarte et al.12 and Du et al.20 used the Euler−Euler approach in two-dimensional simulations to obtain solids velocity profile and porosity profile in a spouted bed, which were compared with corresponding experiments from He et al.17 To calculate the stress distribution in the granular phase, solids viscosity, and solids pressure, the kinetic theory of granular flow developed by Lun et al.21 was used. The authors devised good predictions using this model. Many other researchers have adopted this kind of approach in the simulations of spouted beds obtaining relevant information about their fluid dynamics.22−26 All the above studies have contributed significant insights toward understanding of the fluid dynamics of spouted beds. However, while simulating the properties of the flow obtained experimentally by means of an intrusive technique, they have neglected the possible disturbance caused on the simulated profiles by the insertion of the probe. Other aspects that require other investigations include the effect of gas−solids drag coefficient on the hydrodynamics of spouted beds. Some authors20,27 have investigated the influence of different of some drag models on simulations of a spouted bed, and they found significant effects.20,27 In this study, we investigated the possible disturbance caused by the use of an intrusive technique by means of experiments and simulations carried out in a conical-cylindrical spouted bed. We also investigated the influence of different drag models on numerical velocity and compared with experimental data. The Eulerian multiphase model and the kinetic theory of granular flow have been used.

Figure 2. Photo of the spouted bed showing the orifices on its lateral wall (a) and a schematic diagram with its main dimensions (b).

Table 1. Geometric Factors of the Conical-Cylindrical Spouted Bed parameter

value

Hc (m) Dco (m) Di (m) H0 (m) A (m) B (m) C (m)

0.1028 0.119 0.02 0.12 0.0528 0.0778 0.1478

main dimensions of the spouted bed

apparatus heights

The optical fiber probe measurement system used in this study, Particle Velocity Analyzer PV6D version 1.1.7, was developed by the Institute of Process Engineering Chinese Academy of Sciences. It consists of a probe, two photomultipliers, and a high-speed data acquisition card connected to a computer. The probe contains two light-emitting-receiving channels or bundles of fibers. A schematic representation of the optical fiber probe is shown in Figure 3, and Table 2 presents its main dimensions.

2. EXPERIMENTAL SETUP Particles for the current study were glass beads of 2.18 mm in mean diameter, 2458.4 kg/m3 particle density, and a sphericity of 1.0. The spouting fluid was air at room temperature. For these particles the loosely packed voidage was found to be 0.37. The experimental apparatus is shown schematically in Figure 1. It was composed by a conical-cylindrical spouted bed (1);

Figure 3. Typical optical fiber probe for particle velocity measurement.

Table 2. Characteristic Dimensions of the Two Different Optical Fiber Probes Used in This Paper Figure 1. Experimental apparatus used in the study of the conicalspouted bed. 3802

number of channels

DO (mm)

DC (mm)

DG (mm)

De (mm)

2

5.0

1.1

2.5

2.31

dx.doi.org/10.1021/ie2023838 | Ind. Eng. Chem. Res. 2012, 51, 3801−3810


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where F⃗q, F⃗lif t, and F⃗vm are an external body force, a lift force, and a virtual mass force, respectively. In this investigation, only drag and gravity are considered with the lift force and virtual mass force neglected. In order to couple the momentum transfer between gas and particle phases, a model for the drag force is required. This drag force is represented by the momentum exchange coefficient between the phases considered. Numerous correlations for calculating the momentum exchange coefficient of gas−solid systems have been reported in the literature, including those of Syamlal and O’Brien,29 Gidaspow et al.,30 and Wen and Yu.31 The momentum exchange coefficient (Ksf) between solid phase s and fluid phase f can be written in the following general form

By off-line cross-correlation of sampled signals the time delay (τ) can be obtained, and the particle velocity (vs) can be calculated for a known effective distance (De) between the two light receivers, as shown in the following equation De τ

vs =

(1)

The effective distance of the optical velocity probe was determined using a rotating disk with particles glued to it, a variable speed motor, a digital tachometer, and a probe holder. All of the details about the calibration methodology are described by Zhu et al.28 The data are broken into shorter segments, and each segment is used for the calculation of one cross-correlation function. So, with each cross-correlation function it was possible to calculate many values of velocities in a certain fixed condition which were used to the mean and standard deviation calculations. To investigate the possible disturbance caused by the use of this intrusive technique a quantitative and qualitative study has been performed. The height variation and displacement of the fountain as a consequence of the probe position inside the spouted bed has been analyzed. The fountain height was measured with a ruler taped to the column wall of the spouted bed.

Ksf =

∂ (αs) + ∇·(αsvs⃗ ) = 0 ∂t

∫V αf dV

Rer =

ρ f |vf⃗ − vs⃗ |ds μf

(9)

In this paper, the drag models from Gidaspow et al.,30 Gidaspow,32 and Du Plessis33 are investigated. Gidaspow et al.30 proposed a combination of the Wen and Yu31 model for high void fraction and the Ergun equation34 for dense phase, as follows for αf > 0.8

(2)

Ksf = (3)

3 αsα f ρ f |vs⃗ − vf⃗ | −2.65 CD αf 4 ds

(10)

for αf ≤ 0.8 Ksf = 150

(4)

αs(1 − α f )μ f α f ds2

+ 1.75

ρ f αs|vs⃗ − vf⃗ | ds (11)

where the drag coefficient CD was expressed by ⎧ 24 [1 + 0.15 Rer ≤ 1000 ⎪ ⎪ (Rer α f ) CD = ⎨ (Re α )0.687 ], r f ⎪ ⎪ Rer > 1000 ⎩ 0.44,

∂ (α f ρ f vf⃗ ) + ∇·(α f ρ f vf⃗ vf⃗ ) ∂t ⃗ ,f = −α f ∇p + ∇·τf + α f ρ f g ⃗ + α f ρ f (Fq⃗ , f + Flift (5)

(12)

To avoid the discontinuity of the two equations, Gidaspow32 introduced a switch function that gave a rapid transition from dense regime to the dilute regime

∂ (αsρsvs⃗ ) + ∇·(αsρsvs⃗ vs⃗ ) ∂t = −αs∇p − ∇ρs + ∇·τs + αsρsg ⃗ ⃗ , s + Fvm ⃗ , s) + (K fs(vf⃗ − vs⃗ )) + αsρs(Fq⃗ + Flift

(8)

where ds is the diameter of particles in the solid phase (s), and μf is the fluid viscosity. The definition of fd includes a drag coefficient (CD) that is based on the relative Reynolds number (Rer), defined as

The conservation of the gas and solids momentum is given by the following equations

⃗ , f ) + (K fs(vf⃗ − vs⃗ )) + Fvm

(7)

ρ ds2 τs = s 18μ f

where vf⃗ and vs⃗ are the velocities of the gas and solid phases. The gas volume, Vf, is defined by

Vf =

τs

where fd is the drag function, and τs is the “particulate relaxation time” defined as

3. CFD SIMULATIONS 3.1. Description of the Model. A multiphase flow arises when the average motion of one material is essentially different from that of another. Thus, to modeling a multiphase flow, it is necessary to take into account the properties’ conservations as well as the interaction between the involved phases. In the present investigation, the Eulerian multiphase model is used to model the complex gas−solids flow in a spouted bed. 3.1.1. Conservation Equations of Mass and Momentum and Drag Models. The mass conservation equation for fluid and solid phases is represented by the following equations ∂ (α f ) + ∇·(α f vf⃗ ) = 0 ∂t

αsρsfd

ϕfs =

(6) 3803

arctan[1.75(0.2 − αs)150] + 0.5 π

(13)



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Table 3. Constitutive Equations for Granular Formulation stress tensor of gas phase32 stress tensor of particulate phase particulate pressure

⎯v + (∇→ ⎯v )T ] − 2 μ (∇·→ ⎯v )I τf = μ f [∇→ f f f 3 f 32

(23)

⎯v )I + μ [∇→ ⎯v + (∇→ ⎯v )T ] − 2 (∇·→ ⎯v )I τs = (− ps + λs∇·→ s s s s s 3

{

32

ps = αsρsθs + 2ρs(1 + ess)α2s g0, ss θs

radial distribution function36

⎡ ⎛ α ⎞1/3⎥ ⎢ s ⎟ g0, ss = ⎢1 − ⎜⎜ ⎟ ⎥ ⎝ αs ,max ⎠ ⎥⎦ ⎢⎣ μs =

(25)

(26)

10ρsds θπ θ 4 2 α s ρsdsg0, ss(1 + ess) + π 5 96(1 + ess)αsg0, ss ⎡ ⎤2 4 ⎢⎣1 + (1 + e)αsg0, ss ⎥⎦ 5

solids bulk viscosity32 granular energy diffusion coefficient32

k θs = 32

transfer of kinetic energy32

⎡ ⎤2 θ 6 2 ⎢1 + (1 + e)αsg0, ss ⎦⎥ + 2α s ρsdsg0, ss(1 + ess) ⎣ π 384(1 + ess)g0, ss 5

φfs = − 3Ksf θ

(14)

The RUC or Representative Unit Cell model, proposed by Du Plessis,33 is based on pressure drop through porous media, like Ergun’s equation. The difference is that the RUC model uses analytically derived constants rather than the semiempirical coefficients 150 and 1.75 used in the Ergun’s equation.34 Then, the drag model can be written as α f ds2

ρ f αs|vs⃗ − vf⃗ | ds

(15)

where ⎧ α3f ⎪ ⎪ 26.8 , α f ≤ 0.99 ARUC = ⎨ [He(1 − Het )(1 − He)2 ] ⎪ ⎪ 785.0, α f > 0.99 ⎩ (16)

αf ⎧ , α f > 0.01 ⎪ 2 BRUC = ⎨ (1 − He) ⎪ α f ≤ 0.01 ⎩ 2.25,

θ ⎯v ⎞⎟ − ∇·→ s π ⎠

(29)

(30)

(31)

work, the Gidaspow32 and RUC33 models were implemented by means of the user defined functions (UDF) which were written in C-code and compiled in the Fluent software. 3.1.2. Kinetic Theory of Granular Flow Equations. As can be noted in the solid phase momentum equation (eq 6), it requires a description of the solid phase stress. For the granular phase, it is clear that any mathematical model intended for modeling a granular flow must account for the different regimes within the flow. To model the solid phase stress, the kinetic theory of granular flow derived by Lun et al.21 was adopted in this paper. This theory is an extension of the classical kinetic gas theory35 on dense particulate flows taking nonideal particle−particle collisions and gas-particle drag into account. The basic idea that governs the granular kinetic theory is that the grains are in a state of continuous and chaotic restlessness within the fluid. This chaotic random motion exists at very low concentrations (due to friction between gas and particles, gas turbulence, pressure variation in the fluid, etc.) or at higher concentrations (due to grain collisions). The actual particle velocity vS⃗ is decomposed in a local mean ⎯ ⎯u and a random fluctuating velocity → C according to velocity →

So, the momentum exchange coefficient can be expressed as follows Ksf = (1 − ϕfs)Ksf , Ergun + ϕgSKsf , Wen − Yu

(28)

150ρsds θπ

⎛4 γθs = 3(1 − ess 2)α2s ρsg0, ss θ⎜ ⎝ ds

collision dissipation energy

+ BRUC

(27)

θ 4 2 αs ρsdsg0, ss(1 + ess) s 3 π

λs =

αs(1 − α f )μ f

(24)

⎤−1

solids phase shear viscosity32

Ksf = ARUC

}

s

s

equation (17)

⎯ → ⎯v = → ⎯u + → Cs s s

where Het = (1 − α f )1/3

(18)

He = (1 − α f )2/3

(19)

(20)

Taking the analogy of the gas, a “temperature”, θs, called granular temperature can be introduced as a measure of the particle velocity fluctuation, i.e.

30

The Gidaspow et al. is the unique model, among the other mentioned above, that is included in Fluent 12.1. In the present

θs = 3804

⎯ → ⎯ 1 → ⟨ Cs. Cs⟩ 3

(21)



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where the brackets denote ensemble averaging. The transport equation derived from kinetic theory takes the form 3⎡ ∂ → ⎯ ⎤ ⎢⎣ (ρsαsθs) + ∇·(ρsαs vs θs)⎥⎦ 2 ∂t ⎯v + ∇·(k ∇θ ) − γ + φ = ( −ps I + τs):∇→ θs s s fs θs

(22)

Here (−psI ̿ + τ):∇v s⃗ is the generation of energy by the solid ̿ stress tensor, (kθs∇θs) is the diffusion of energy (kθs is the diffusion coefficient), γθs stands for the collisional dissipation of energy, and ϕfs denotes the energy exchange between the gas and solid phase. The constitutive equations required to close the governing equations are listed in Table 3. The particulate pressure is described by the eq 25 in Table 3. This term is composed by a kinetic and colisional contribution. Based on the sensitivity analysis by Wang,19 the frictional terms had no significant effect on the simulation results. So, taking the computational efforts into account, these terms were set to zero in the current work. 3.2. Simulation Conditions. The simulations were conducted with and without the probe inside the spouted bed in order to investigate the possible disturbances caused by the use of this intrusive technique. As regards the position of the probe inside the spouted bed, nine different geometries were created, by means of the preprocessor GAMBIT 2.3.16, with the probe interval spacing of 0.05 m since the center until the spouted bed’s wall. Figure 4

Figure 5. Characteristic curves used in the grid independence test.

• Pressure-velocity coupling was obtained using the SIMPLE-algorithm60; • The First-Order-Upwind-method was used for interpolating the cell-center values to the cell boundaries; • A no-slip wall boundary condition was used; • Restitution coefficients of particles e = 0.9; • A time step of 1 × 10−4 s was chosen; • The relative error between two successive iterations was 1 × 10−3 for each scaled residual component. Each simulation was conducted with a time of 15 s. The first 5 s of all the simulations were discarded, and the means values were obtained from the last 10 s. The time of 15 s for the simulations was selected to make sure that the fountain reaches a statistically steady state height.

4. RESULTS AND DISCUSSION 4.1. Results of the Disturbance Caused to the Flow by the Use of the Optical Fiber Probe. In this section, we present the numerical and experimental analyses of the possible disturbances caused to the flow in a spouted bed by the use of an intrusive technique. The height variation and the displacement of the fountain have been experimentally recorded and compared with simulations carried out under the same conditions. The simulated fountain height, used to compare with experimental datas, was determined as the axial position when the air volume fraction reaches a value of approximately one. To calculate the gas-particle drag force in these simulations, the Gidaspow et al.30 drag model has been used. Figures 6, 7, and 8 show the calculated and experimental distributions of the granular solid phase with gas superficial velocities of 30, 33, and 36 m/s, respectively, with the probe at different positions inside the spouted bed. The experimental pictures show that, in all the operating conditions (Figures 6-8), the introduction of the probe inside the spouted bed caused a disturbance into the flow. This disturbance was detected by means of the displacement of the fountain in relation to the central axis of the spouted bed. In all the cases the fountain was deflected in the opposite direction to the insertion of the probe. It also can be observed that there is a good agreement between simulated and experimental behavior

Figure 4. Typical mesh adopted in this paper: (a) without the presence of the probe, (b) containing the probe at the center of the spouted bed.

(a) shows the 3D dimensions meshed geometry of the spouted bed without the presence of the probe, while Figure 4 (b) shows one of the nine 3D dimensions meshed geometry taking the presence of the probe into account. The effect of grid size on the simulation results was examined by comparing the characteristic curves of a spouted bed (Figure 5) simulated from three sizes grid (i.e., Partition 1, 26928 cells; Partition 2, 57684 cells; Partition 3, 105084 cells). As can be seen in Figure 5, there are no more differences on the simulated results when refining the mesh represented by Partition 2 within the range investigated in the current simulations (i.e., velocities above minimum spouting condition). Thus, the more accurate grid partition with the smallest grid size, partition 2, was selected for the current study. The following conditions were adopted in the simulations: • The finite volume discretization method was used; • Inlet velocity as inlet boundary condition; • Outlet pressure as outlet boundary condition; 3805



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Figure 6. Volume fraction (αs) of the granular solid phase with gas superficial velocity of 30 m/s: (a) Experiment and simulated without the probe; (b) Experiment and simulated with the probe at the center of the spouted bed; (c) Experiment and simulated with the probe at 0.5 cm from the center of the spouted bed.


recorded for each conditions described in Figures 6-8. It was observed that the fountain height decreased with the introduction of the probe. As the probe position changes toward the spouted bed’s wall, the fountain height gradually increases. At a distance of about 1.0 cm from the center of the spouted bed the fountain height variation is not observed anymore, and the fountain height achieved the same magnitude as the absence of the probe. The simulated under the same conditions show similar characteristics as the experimental did. It can be observed a slightly deviation between simulated and experimental when the probe is 0.5 cm from the center of the spouted bed. It was possible, for all conditions established experimentally to predict through simulations the disturbance caused by the introduction of the probe into the flow. This analysis is of fundamental importance when simulating the properties of the flow obtained experimentally by means of an intrusive technique, although many researchers do not take the disturbance phenomenon into account. 4.2. Radial Profile of Solids Velocity. To further evaluate the simulation results, time-averaged velocity distributions of the particulate phase (glass beads of 2.18 mm in mean diameter) at three different heights, 0.0528, 0.0778, and 0.1478 m above the base of the column, are compared with experimental data. Figures 9 and 10 show the experimental and simulated results, respectively, for gas superficial velocity of 33 and 36 m/ s. The simulations have been performed using the drag models proposed by Gidaspow et al.,30 Gidaspow,32 and Du Plessis.33 These simulations do not take into account the presence of the probe. It can be seen that the particle velocities in the spout region decrease with the increase of the heights. For the axial positions below the fountain, the particles descend slowly in the


of the solid phase in the spouted bed. Thus, the simulated results of the distributions of the solid phase also show that the insertion of the probe caused a displacement of the fountain toward the same direction as the experiments did. As regards the quantitative analysis of the disturbance caused by the introduction of the probe, the fountain height was 3806



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Figure 9. Time-average solid phase velocity distributions in apparatus heights of (a) 0.0528 m; (b) 0.0778 m; and (c) 0.1478 m (fountain region) and gas superficial velocity of 33 m/s.

gas superficial velocity of 27 m/s, using the RUC33 and Gidaspow et al.30 drag models. Figure 12 also show the experimental data in the same conditions. The simulated results of Figure 12 showed that the insertion of the probe, for both drag models, caused a decrease in the particle velocity for the spout region. It also can be seen that CFD simulations using the RUC33 drag model and considering the presence of the probe predicted better the experimental data of the particle velocity distribution than the other simulations.

annulus zone, whereas much higher particle velocities are obtained in the spout, with a maximum at the axis. The comparisons between CFD predictions and experimental data, presented in Figures 9 and 10, showed that, in general, for the spout region, the RUC33 drag model overpredicted the particle velocities, and the Gidaspow et al.30 and Gidaspow32 drag models underpredicted the particle velocities. In the height of 0.1478 m (fountain region), the experimental data were between the simulations with the drag models of Gidaspow et al.30 and RUC,33 as can be seen in Figures 9c and 10c. The differences observed in the velocity profiles using different drag models can be confirmed through observation of Figure 11, which shows Ksf as a function of Rer at a fixed solid fraction (αs) equal to 10%. As mentioned in the previous section, the insertion of the probe inside the spouted bed caused a decrease in the fountain height and hence in the particle velocity. Figure 12 shows the time-averaged particle velocity distributions at height of 0.0778 m, simulated by means of 3D dimensions meshed geometries of the spouted bed, containing the probe at different positions (see Figure 4b) and without the probe (see Figure 4a). For each position of the probe a simulation was conducted, and a point near the probe (the distance from the probe’s wall was determined by preliminary simulations) was monitored with a time of 15 s. The last 10 s was used to calculate the mean velocity characteristic of that position. This procedure was done for all the positions related with the experimental data. So, for the condition shown in Figure 12, 20 simulations were done in a total of 300 s. The simulations have been performed with a

5. CONCLUSIONS From experimental data and CFD simulations, it was possible to investigate the disturbances caused by the use of an optical fiber probe in the hydrodynamic behavior of a conicalcylindrical spouted bed. The displacement of the fountain in relation to the central axis of the spouted bed as the probe position has been changed from the center to the spouted bed’s wall was identified. The insertion of the probe inside the spouted bed caused a decrease in the fountain height. The fountain height variation as a function of the probe position was quantified by experimental procedure and CFD simulation. The CFD simulations based on an Eulerian Granular Multiphase Model showed good agreement with experimental results. The influence of different drag models on particle velocity profile considering or not the presence of the probe in the simulations was also analyzed. The insertion of the probe 3807



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Figure 10. Time-average solid phase velocity distributions in apparatus heights of (a) 0.0528 m; (b) 0.0778 m; and (c) 0.1478 m (fountain region) and gas superficial velocity of 36 m/s.

Figure 12. Comparison between solid phase velocity distributions simulated with and without the probe in an apparatus height of 0.0778 m and gas superficial velocity of 27 m/s.

Figure 11. The momentum exchange coefficients (Ksf) for different drag models as a function of relative Reynolds number (Rer) at a fixed solid fraction (αs) equal to 10%.

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caused a decrease in the particle velocity for the spout region. The CFD simulations using the RUC33 drag model and considering the presence of the probe predicted better the experimental data of the particle velocity distribution than the other simulations performed in this work.

AUTHOR INFORMATION

Corresponding Author

*Fax: 55-34-32394188. E-mail: [email protected]. Notes

The authors declare no competing financial interest. 3808



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ACKNOWLEDGMENTS The authors are grateful to the FAPEMIG and CNPq for its financial support. LIST OF SYMBOLS CD: drag coefficient [-] ds: particle diameter [m] Dco: diameter of cylindrical part [m] Di: diameter of gas inlet [m] ess: restitution coefficient [-] Do: diameter of the optical fiber probe [mm] Dc: diameter of the probe’s channels [mm] DG: central distance between two channels [mm] De: effective distance calibrated through experiments [mm] g0,ss: radial distribution function [-] Hf : fountain height [cm] Hewp: experimental fountain height without probe [cm] Hswp: simulated fountain height without probe [cm] H0: static height [m] Hc: height of cone section [m] Kfs: coefficient of momentum exchange between fluid phase f and solid phase s Ksf,Ergun: coefficient of momentum exchange calculated by the Ergun equation Ksf,Wen‑Yu: coefficient of momentum exchange calculated by the Wen-Yu equation ARUC: parameter in the RUC model BRUC: parameter in the RUC model Fq: external body force [N] Flift,s: lift force [N] Fvm,s: virtual mass force [N] ps: solids pressure [Pa] Rer: relative Reynolds number [-] v:⃗ velocity vector [m.s−1] V: volume [m3]

Greek Symbols

α: volume fraction [-] ρ: density [kg.m−3] μ: dynamic viscosity [cP] φfs: switch function in the Gidaspow (1994) drag model τ: time delay [s] τq: stress tensor [Pa] Θs: granular temperature [-]

Subscript

f : fluid phase s: solid phase

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REFERENCES

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Disturbances in the Hydrodynamic Behavior of a Spouted Bed Caused

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