On the Computational Modeling of Unfluidized and Fluidized Bed

On the Computational Modeling of Unfluidized and Fluidized Bed Dynamics Lindsey C. Teaters Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061

Francine Battaglia1 Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061 e-mail: [email protected]

Two factors of great importance when considering gas–solid fluidized bed dynamics are pressure drop and void fraction, which is the volume fraction of the gas phase. It is, of course, possible to obtain pressure drop and void fraction data through experiments, but this tends to be costly and time consuming. It is much preferable to be able to efficiently computationally model fluidized bed dynamics. In the present work, ANSYS FLUENTV is used to simulate fluidized bed dynamics using an Eulerian–Eulerian multiphase flow model. By comparing the simulations using FLUENT to experimental data as well as to data from other fluidized bed codes such as Multiphase Flow with Interphase eXchanges (MFIX), it is possible to show the strengths and limitations with respect to multiphase flow modeling. The simulations described herein will present modeling beds in the unfluidized regime, where the inlet gas velocity is less than the minimum fluidization velocity, and will deem to shed some light on the discrepancies between experimental data and simulations. In addition, this paper will also include comparisons between experiments and simulations in the fluidized regime using void fraction. [DOI: 10.1115/1.4027437] R

Keywords: Eulerian–Eulerian modeling, gas–solid, fluidization, pressure drop

1

Introduction

Fluidized bed technology has various industrial uses ranging from fluid catalytic cracking, combustion, gasification, and pyrolysis, to coating processes used in the pharmaceutical industry [1,2]. Most notably, the recent demand for cleaner, sustainable energy has boosted biomass applications to the forefront of possible solutions [3,4]. Biomass feedstock is available in many forms including wood chips, straw, corn stalks, animal waste, or any other waste organic material. It is clear from the types of feedstock mentioned that these do not constitute conventional combustible material. The shape, water content, and often low heating value, makes these materials poor candidates for conventional combustion: this is where fluidized bed technology can be utilized [3]. The process of fluidization can be described simply as supplying a flow of gas through a bed of granular material at a sufficient velocity such that the granular bed behaves as a fluid [5,6]. The actual physics behind fluidization that constitute the crux of the present work, however, are not so simple. Fluidization of biomass material is still a fairly new topic of interest; as such, the characteristics of biomass fluidization are relatively unexplored [3,6]. It is critical for efficient biomass gasification to be able to 1 Corresponding author. Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 3, 2013; final manuscript received April 10, 2014; published online July 24, 2014. Assoc. Editor: D. Keith Walters.

Journal of Fluids Engineering

understand and predict important fluidization aspects such as pressure drop and minimum fluidization velocity. Experimental studies are conducted on small-scale fluidized beds and computational fluid dynamics (CFD) codes are used to model existing experimental setups and validate the numerical modeling. If CFD models can be shown to predict experimental data accurately, then these models can be used to design large-scale fluidized bed facilities without prior physical testing. Benyahia et al. [7] successfully used FLUENT to model gas–solids flow behavior in a circulating fluidized bed using a twodimensional transient model incorporating kinetic theory for the solids particles. Fluid catalytic cracking (FCC) particles and air were modeled in a reactor at an inlet gas velocity near minimum fluidization conditions. In this case, the simulations predicted the multiphase flow behavior seen in experiments reasonably well. Only the bed dynamics corresponding to an inlet gas velocity at minimum fluidization or above were explored. Another study by Taghipour et al. [8] used FLUENT to model a two-dimensional gas– solids fluidized bed comprised of glass beads and air using a multifluid Eulerian–Eulerian model and kinetic theory for solids particles. In this study, different drag models were simulated as well as different values representative of collisional elasticity. The predictions given by simulations compared well with bed expansion properties observed in experiments and compared well qualitatively with flow patterns and instantaneous gas–solids distributions. Pressure drop values corresponding to inlet gas velocities at and above minimum fluidization velocity also compared reasonably well. Pressure drop values corresponding to inlet gas velocities below minimum fluidization velocity were very far off from those values measured during the experiments. This phenomenon is one of the facets to be explored herein, and is again mentioned in a study performed by Sahoo et al. [9]. The study [9] examined the effects of varying bed material and static bed height. The particles that were studied had very large diameters (Geldart D). It was again observed that the time-averaged pressure drop data for the simulations matched the experiments well for velocities exceeding minimum fluidization, but was not the case for velocities lower than minimum fluidization. Herzog et al. [10] conducted a study which compared modeling fluidized bed hydrodynamics with the open source software packages OpenFOAM and MFIX against the results obtained using FLUENT. The basis of experimental comparison for this study was taken from the numerical validation study previously mentioned by Taghipour et al. [8]. Herzog et al. [10] concluded that MFIX and FLUENT gave good comparisons with experimental data in the bubbling regime and also showed good agreement with each other for pressure drop. The curves of pressure drop versus inflow velocity reported by Herzog et al. correctly showed an increasing pressure drop trend until the point of minimum fluidization and compared reasonably well with the experimental data in the unfluidized regime. It is important to note that the model parameters which need to be specified in FLUENT were not revealed in the publication. The main objective of the present work is to use the commercial CFD code ANSYS FLUENTV (v12.0) to model fluidized bed behavior and compare modeling results from FLUENT to experimental data as well as data from an alternative CFD code, MFIX. FLUENT is a comprehensive commercial code that does not focus solely on multiphase flows, while MFIX is specific for fluidized bed reactor modeling and design. It is further desired to use these comparisons to establish the strengths and limitations of using FLUENT to model multiphase flow. More specifically, present work will examine the validity of using FLUENT to model granular beds in the unfluidized bed regime versus the fluidized bed regime through pressure drop and phasic volume fraction studies. R

2

Fluidization Theory

While many different configurations for fluidized bed reactors exist, some having complex geometries, reactors can most

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Fig. 2 Relationship between pressure drop and inlet gas velocity

Fig. 1 Schematic of the fluidized bed domain

generally be thought of as having a cylindrical geometry. Figure 1 depicts the primary section of a fluidized bed reactor having an internal diameter D and a total height H, the product of these two dimensions is the area of the centerplane of the reactor. The reactor has an air inlet hose and distributor (not shown) located below the gas plenum. The gas plenum region creates a constant pressure distribution. A distributor plate located directly above the gas plenum produces a near uniform flow of gas to be passed through the granular bed. The flow of gas through the granular bed is the mechanism by which fluidization is achieved. The bed of granular material has an initial height h0 . The area directly above the granular bed is the freeboard which is characterized by having only a gas phase. The outlet condition of a fluidized bed reactor is dependent on reactor design. Experimental fluidized beds, however, may have outlets open to the atmosphere for fundamental studies. Directly above the distributor plate, the gas flow is assumed to be uniform, and the volume fraction of granular solids is assumed to be zero since reactors generally include a screen located above the distributor plate to prevent backflow of bed material. Since a uniform gas flow profile is assumed, the distributor plate is not generally modeled. Therefore, the superficial inlet gas velocity can be calculated using Q Ug ¼ A

(1)

where A is the circular cross-sectional area of the cylindrical reactor and Q is the volumetric flow rate in the gas plenum region. Accordingly, the superficial inlet gas velocity is also the value used to specify the inlet gas velocity boundary condition. The most fundamental characteristic studied in fluidized beds is the relationship between pressure drop across the bed and inlet gas velocity (superficial gas velocity at the inlet) [5,11–13]. Flowing gas upward through the bed of granular material creates a drag force and a buoyancy force on the particles. As the gas velocity is increased, the drag force increases, which in turn increases pressure drop DP. At a certain inlet gas velocity the drag and buoyancy forces on the granular material balance the gravitational force, which is equal to the bed weight. When the bed becomes fluidized, the pressure drop across the bed remains a constant value DPbed , regardless of further increasing the inlet gas velocity, as shown in Fig. 2. This is typically true for a bubbling granular 104501-2 / Vol. 136, OCTOBER 2014

bed of Geldart B particles [6]. The inlet gas velocity corresponding to the moment of fluidization is known commonly as the minimum fluidization velocity Umf . Minimum fluidization velocity and pressure drop are key for characterizing and understanding operation and design of fluidized beds. Pressure drop can be ascertained through experiments or a simple force balance. Total pressure drop across the bed can be expressed as mg A

DPbed ¼

(2)

where m is the mass of the granular bed material, g is gravity, and A is the cross-sectional area of the bed. Alternatively, for a fixed bed, the mass can be expressed in terms of a bulk density qb and an initial volume  V0 . The bulk density is defined assuming that the density of the gas phase is negligible compared to the density of the solids phase granular material. Bulk density is given by qb ¼ es qs

(3)

where es is the solids volume fraction and qs is the solids density. The mass of the bed can therefore be represented as V0 m ¼ qb 

(4)

Substituting Eq. (4) into Eq. (2) and noting that  V0 ¼ Ah0 , the pressure drop is DPbed ¼ qb gh0

(5)

where h0 is the initial height of the granular bed. The Ergun correlation [11] is used to predict minimum fluidization velocity Umf for a fluidized bed having a single solids phase. The Ergun correlation is expressed as 1:75 150ð1  emf Þ Re2 þ Remf ¼ Ar ws e3mf mf w2s e3mf

(6)

where emf is the volume fraction of the gas (void fraction) at fluidization, ws is the solids sphericity, and Remf is the Reynolds number at fluidization given by Remf ¼

qg ds Umf lg

(7)

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for Remf < 20 and Ar is the Archimedes number given by Ar ¼

qg ds3 ðqs  qg Þg l2g

(8)

where qg is the gas density, ds is the solids diameter, and lg is the gas viscosity. Assuming that the drag force balances the buoyancy and gravity forces on a particle at minimum fluidization, the following relationship for Umf can be attained [11]   ðds ws Þ2 qs  qg e3mf Umf ¼ (9) 1  emf 150lg

3

Numerical Modeling

3.1 Governing Equations. An Eulerian–Eulerian multiphase flow model is selected in ANSYS FLUENTV [14] to simulate granular flow in a fluidized bed. The Eulerian–Eulerian model represents each phase as interpenetrating continua, where each phase is separate, yet interacting, and the volume of a phase cannot be occupied by another phase. The equations and models employed will be briefly discussed as extensive details by the second author can be found in Refs. [15,16]. The laws of conservation of mass and momentum are satisfied for each phase. In both phase equations for momentum are terms that account for the interaction force between the gas and solids. The interaction force is the product of the moment exchange coefficient and the slip velocity between the phases, which includes a drag coefficient. The Gidaspow drag model [5] is chosen to calculate the momentum exchange coefficient. Another important relation is the solids pressure that appears in the solids phase momentum equation, when the solids volume fraction e*s,max is below a maximum value. The solids pressure is calculated using the formulation of Lun et al. [17] based on kinetic theory for granular flow. FLUENT [14] solves governing integral equations for conservation of mass and momentum. The methodology employs a finite volume approach for flow solutions, which is beneficial for local satisfaction of the conservation equations and for relatively coarse grid modeling. The phase-coupled semi-implicit method for pressure linked equations (PC-SIMPLE) algorithm [18] is employed to solve the momentum equations, shared pressure, and volume fraction equations in a segregated manner. A block algebraic multigrid scheme is used to solve a vector equation of the velocity components of all phases simultaneously. A pressure correction equation is then employed for total volume continuity rather than conservation of mass. Pressure and velocity corrections are applied to satisfy the total volume continuity constraint. For spatial discretization, a second-order upwind scheme is chosen for the momentum equations and quadratic upwind interpolation for convective kinematics (QUICK) scheme [19] is chosen for volume fractions equations. The gas inlet of a fluidized bed is generally characterized by a distributor plate having evenly distributed holes such as to enforce a nearly uniform flow (see Fig. 1). Therefore, the inlet boundary condition is modeled with a uniform velocity profile and constant pressure. The volume fraction of solids at the inlet is zero. The outlet boundary condition is specified as ambient pressure, and a backflow solids volume fraction equal to zero. The wall boundary condition for the gas phase is specified as no-slip and the solids phase boundary condition for the reactor walls is a free slip condition. R

3.2 Modeling Approaches. Computational modeling of fluidized beds encompasses a great deal of simplifications from experimental setups and bed material characteristics, especially when the experiments use irregular-shaped particles such as biomass particles. The following discussion will compare and Journal of Fluids Engineering

contrast methods for better predicting fluidized bed hydrodynamics of biomass particles. Fluidization of nearly spherical and uniform density particles, like glass beads, is well-characterized. Fluidization of biomass particles, however, is not as easy to characterize due to the irregular shape and nonuniform density of the particles. The first computational study related to biomass fluidization was performed by Deza et al. [15] for ground walnut shell in a 10.2 cm diameter reactor using MFIX. Subsequently, Gavi et al. [20] performed a study using FLUENT to computationally validate experimental data of walnut shell in a 15.2 cm fluidized bed reactor. Further details of the experiments can be found in Refs. [15,21]. Gavi et al. [20] explored two modeling approaches that they labeled as the “standard approach” and a “new approach,” hereafter referred to as STD and NEW. The STD approach employed the nominal material density of the walnut shell, assuming nonporous, spherical particles and no further adjustments in the parameters. The solids packing limit was specified as the theoretical packing limit of perfectly spherical particles, equal to 0.63. Gavi et al. [20] mentioned that because the drag models were developed for regularly shaped and uniformly dense particles, additional considerations were needed to improve the accuracy of the drag models. Since high drag and low packing had been experimentally observed, purportedly due to porosity of the biomass material, Gavi et al. [20] used an effective density derived from the experimental bed mass and volume, and a solids packing limit equal to that experimentally observed with glass beads of 0.58 (their initial validation case), referred to as the NEW approach. For initial conditions, the bulk density was calculated from the new effective density and the initial solids packing of 0.55 was specified as slightly lower than the solids packing limit to ease the onset of fluidization. Because the initial solids packing was reduced from the solids packing limit used to calculate the effective density, the initial bed height was increased to introduce the correct amount of mass. The third approach to be considered as part of this study is referred to as the MOD approach. Battaglia et al. [22] and Kanholy et al. [16] proposed a new approach to model the ground walnut shell experiments [20]. In both studies [19,22] MFIX was employed to predict the fluidization dynamics, and analyzed how best to capture pressure drop, minimum fluidization velocity, and mean void fraction, simultaneously. These studies [16,22] considered two adjustments in system parameters in order to match the experimentally measured pressure drop: modifying void fraction and modifying bed height. Adjusting only the bed mass and subsequently the bed height provided the best predictions, which matched with the experiments for all desired criteria. The multifluid Eulerian–Eulerian model in MFIX is very similar to that used in FLUENT (refer to Ref. [16]). The continuity and momentum equations are solved for both the gas phase and the solids phase, and the Gidaspow model is used for the interphase drag force. Kinetic theory for granular flow is used to calculate the solids stress tensor and the solids–solids interaction force in the rapid (viscous) granular flow regime. A blending function provides a smooth transition between the viscous and plastic shearing regimes. The governing equations are discretized using a finite volume approach on a staggered grid to reduce numerical instabilities. Discretization of time derivatives are first-order and discretization of spatial derivatives are second-order. The SIMPLE algorithm is modified and uses an equation for the solids volume fractions that includes the effect of the solids pressure to help facilitate convergence for both loosely and densely packed regions. The purpose of this paper is to find the best possible approach to model the ground walnut shell bed in the unfluidized and fluidized regimes using FLUENT based on the recommendations of Gavi et al. [20] and Battaglia et al. [16,22]. Gavi et al. [20] did not show results in both the unfluidized bed regime for the STD and NEW approaches. Battaglia et al. [22], however, did show pressure drop data in the unfluidized bed regime for the MOD OCTOBER 2014, Vol. 136 / 104501-3

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Table 1 Walnut shell bed properties and model parameters for the simulations Property

STD

NEW

MOD

dp (cm) qp (g/cm3) e w e*g

0.055 1.30 0.9 0.6 0.56

0.055 0.986 0.9 0.6 0.55

0.055 1.30 0.9 0.6 0.564

e*s,max h0 (cm)

0.63 15.2

0.58 16.5

0.63 11.7

approach. Of course the unfluidized regime is of less interest, but it is important that the models predict both regimes, especially when beds defluidize due to changes in the material such as agglomeration. 3.3 Problem Description. A simplified schematic of the fluidized bed geometry used in the work of Gavi et al. [20] is shown in Fig. 1. The apparatus is modeled as a two-dimensional geometry, which represents the centerplane of the cylindrical domain. The dimensions are for an inner diameter of 15.2 cm and a total height of 60 cm. Using FLUENT, we have simulated the STD and NEW cases based on the parameters specified by Gavi et al. [20], who also used FLUENT. Also, we used FLUENT to simulate the reactor in [20] based on the recommended parameters provided by Battaglia et al. [22]. The MOD case also follows the theoretical approach as presented in Ref. [16]. The static bed height varies for each modeling approach, as shown in Table 1. For the STD case, the static bed height is the same the experimental conditions described in Ref. [20]. The static bed height is increased in the NEW approach to correct for the initial mass of the bed because the solids density is reduced [20]. However, as shown in Ref. [16], it is common that all of the material in the bed does not fluidize and therefore, the mass of the bed is reduced to account only for the fluidizing mass; thus, the initial height of the static bed is reduced. The cases shown in Table 1 were simulated for 35 s of flow time with time averaging taken between 5 and 35 s over 30,000 time realizations (every 0.001 s) for each of the cases. The inlet gas velocity was specified as 2 Umf and represents 36.2 cm/s. Following the grid resolution study of Teaters [23], square grid cells with dimensions of 2.5 mm  2.5 mm were sufficient to produce a grid-insensitive solution with a relative error of less than 1% using a convergence criterion of 106.

4

Results and Discussion

4.1 Fluidized Regime. Figure 3 presents time-averaged void fraction versus normalized bed height using h0. The data is also plane averaged across the diameter to provide a mean value of the void fraction at each vertical section. The experimental data from Gavi et al. [20] is shown in Fig. 3 as solid circles and is normalized using the initial bed height. Our simulations using the parameters of the STD and NEW cases specified in Ref. [20] and the MOD case using the parameters in Ref. [22] are also shown. As reported by Gavi et al. [20], due to the poor agreement of void fraction within the bed (h/h0 < 1) for the STD case, they modified the parameters using their NEW approach. It is evident that the STD and MOD approaches match the experimentally measured void fraction fairly well, and that the NEW approach overpredicts the bed expansion due to the lower effective density and increased initial static bed height incorporated in the approach (refer to Table 1 for the properties). However, as demonstrated by Battaglia et al. [22], using the experimental conditions (shown as the STD approach) overpredicts the pressure drop and does not accurately predict all of the hydrodynamics (refer to Sec. 4.2 for further discussions). Figure 4 shows localized time-averaged void fraction profiles for each of the approaches and the experiments [20] at four 104501-4 / Vol. 136, OCTOBER 2014

Fig. 3 Time- and plane-averaged void fraction versus height normalized with bed height comparing experiments [20] with simulations

vertical heights of h/h0 ¼ 0.25, 0.5, 0.75, and 1. The four images show profiles at varying bed heights normalized with initial static bed height. It is clear from Fig. 4 that each of the approaches yield results that match the experimental data fairly well, especially higher in the bed. However, the NEW approach shows two distinct peaks for h/h0 ¼ 0.25 and 0.5, which are not consistent with the other data. The data for the STD and NEW cases were reproduced in this work and it is important to note that the trends were not completely consistent with that reported by Gavi et al. [20]. We speculate that not all of the parameters used by Gavi et al. were reported; thus there may be some inconsistencies with models, which will be discussed in the next section. Despite these small discrepancies, we conclude that while the STD approach models the same experimental conditions, the pressure drop is not predicted well. As discussed in the work of Kanholy et al. [16], unfluidized material that accumulates at the bottom of the bed will change the fluidization characteristics, especially the pressure drop. Thus, the MOD approach is found to best represent all of the fluidization features and predictions match well with the experiments. 4.2 Unfluidized Regime. Many times in reported studies, only the fluidized regime of the bed is simulated. Another important consideration when modeling fluidized beds is the prediction of pressure drop in the unfluidized regime. The contrast between the increasing trend in pressure drop in the unfluidized regime and the near constant value the pressure drop in the fluidized regime allows for the minimum fluidization velocity to be identified (see Fig. 2). Figure 5 shows a plot of pressure drop versus inlet gas velocity for the three approaches (STD, NEW, and MOD), the experimental data [20], and the MFIX simulation data [22]. A horizontal line, labeled “Theoretical,” is shown to compare the theoretical value of the pressure drop calculated using Eq. (2) for the amount of mass specified in the experiment. The FLUENT simulations shown in Fig. 5 for the STD, NEW, and MOD methods used the drag parameters corresponding to case 1 in Table 2. Figure 5 shows data for several inlet gas velocities in the unfluidized and fluidized regimes. In the fluidized regime, it is clear that the MOD approach correctly predicts the pressure drop in the fluidized regime, consistent with the MFIX results [22] as to be expected. In fact, the theoretical pressure drop is higher than that measured in the experiments [20], which further supports the fact that all of the material in the bed is not fluidizing. The STD and NEW approaches greatly overpredict the pressure drop; the reason being that the two modeling approaches assume all of the bed Transactions of the ASME

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Fig. 4 Time-averaged void fraction profiles comparing walnut shell bed simulations with experimental data [20] at (a) h/h0 5 0.25, (b) h/h0 5 0.5, (c) h/h0 5 0.75, and (d) h/h0 5 1

Fig. 5 Pressure drop versus inlet gas velocity comparing experiments [20] with modeling approaches

material fluidizes; thus a greater pressure is required to fluidize the bed. For pressure drop values corresponding to inlet gas velocities of 10 and 15 cm/s in the unfluidized regime, none of the three approaches correctly predict the linearly increasing trend, except for the simulations performed using MFIX [22]. Journal of Fluids Engineering

In an effort to determine the inconsistencies with the results in the unfluidized regime, a parametric study, as outlined in Table 2, was performed for inlet gas velocities of 10 and 15 cm/s using the MOD approach. The MOD approach was chosen for its reliability in void fraction and fluidized bed pressure drop predictions. Key parameters thought to play a potential role in pressure drop in the unfluidized regime are the solids packing limit, frictional viscosity model and frictional packing limit, drag model, and finally, the packed bed model. Frictional viscosity plays a major role in the plastic regime where momentum exchange occurs mainly from particles rubbing against each other, as might be expected in a low inlet gas velocity flow, characteristic of the unfluidized regime. The packed bed model inhibits the granular bed from expanding vertically. Figure 6 shows pressure drop versus inlet gas velocity for each of the cases shown in Table 2. The most obvious conclusion is that none of the cases in the parametric study capture the correct pressure drop in the unfluidized regime; however, there is valuable information to be drawn from the plot. Many of results overlap in the unfluidized regime so the values of the pressure drop at 10 and 15 cm/s are reported in Table 2. It is clear that the addition of the packed bed model in case 2, compared with case 1, reduces the pressure drop to almost negligible values. Physically, this makes sense since the packed bed model is designed to inhibit motion of the granular bed as previously stated. Cases 3, 4, and 6 alter the solids packing limit, making it equivalent to the initial solids volume fraction of 0.436. The frictional packing limit must be value lower than the solids packing limit in order for the model OCTOBER 2014, Vol. 136 / 104501-5

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Table 2 Pressure drop parametric study cases for drag models Parameters es;max Frictional viscosity model Frictional packing limit Drag model Packed bed model DP (Pa) @ 10 cm/s DP (Pa) @ 15 cm/s

Case 1

Case 2

Case 3

Case 4

Case 5

Case 6

0.63 Schaeffer 0.5 Gidaspow No

0.63 Schaeffer 0.5 Gidaspow Yes

0.436 Schaeffer 0.36 Gidaspow No

0.436 Johnson– Jackson 0.36 Gidaspow No

0.63 Schaeffer 0.5 Syamlal– O’Brien No

0.436 Schaeffer 0.36 Syamlal–O’Brien No

636 637

94 131

636 636

605 636

634 658

638 635

value of solids packing limit in case 3. Both Fig. 6 and Table 2 reveal that none of these adjustments to the simulation case setup have any substantial effect on pressure drop in the unfluidized regime. In a final attempt to predict the unfluidized regime, the porous media model (PMM) was employed in FLUENT to predict the pressure drop (refer to Ref. [27] for details of the PMM model). As shown in Fig. 7, the PMM predicts accurately the pressure drop prior to fluidization; however, the PMM cannot be used after the bed fluidizes. Ideally, if the minimum fluidization is not known for a system, a single model is preferable to predict the transition from an unfluidized to a fluidized regime. The use of the PMM model precludes such an approach.

5

Fig. 6 Pressure drop versus inlet gas velocity using the MOD approach for the parametric study and compare with experiments [20]

Conclusions

Computational fluid dynamics was used to model the gas–solid hydrodynamics of fluidized beds. An Eulerian–Eulerian multifluid model and granular kinetic theory were used to model fluidization and to capture the complex physics. The commercial code FLUENT was used to study fluidization of ground walnut shell beds. Current codes only allow for modeling of spherical, uniform-density particles. Owing to the fact that biomass material, such as walnut shell, is abnormally shaped and has nonuniform density, a study was conducted to find the best modeling approach to accurately predict pressure drop, minimum fluidization velocity, and void fraction in the bed. It was shown that the best modeling approach to capture the physics of the biomass bed was by correcting the amount of mass present in the bed in order to match the experimentally observed pressure drop, whereby only the initial bed height of the system is altered. Referred to as the MOD approach, it was shown to accurately predict void fraction and pressure drop in the fluidized regime. Even the MOD approach, however, could not be shown to correctly predict pressure drop in the unfluidized regime. Accordingly, the models that represent the plastic regime will require further development in order to capture the complex physics in the unfluidized regime, where the bed remains densely packed.

Acknowledgment Fig. 7 Pressure drop versus inlet gas velocity using the porous media model as compared with experiments [20] and MFIX [22]

to have an effect on the bed dynamics, and was set to 0.36. Therefore, in the cases where the solids packing limit is altered, the frictional packing limit is also altered. Case 3 can be directly compared to case 1; the conclusion being that changing the solids packing limit had no effect. Case 4 uses the Johnson and Jackson frictional viscosity model [24] as opposed to the Schaeffer model [25] (case 3). Case 5 uses the Syamlal–O’Brien drag model [26] as opposed to the Gidaspow model (case 1), but keeps the theoretical value of solids packing limit for spherical particles. Case 6 also uses the Syamlal–O’Brien drag model, but uses the altered 104501-6 / Vol. 136, OCTOBER 2014

The authors would like to thank Mr. Alex Strasser for providing the results using the porous media model.

References [1] Kunii, D., and Levenspiel, O., 1991, Fluidization Engineering, ButterworthHeinemann, Boston, MA. [2] Demirbas, A., and Arin, G., 2002, “An Overview of Biomass Pyrolysis,” Energy Sources, 24(5), pp. 471–482. [3] Cui, H., and Grace, J. R., 2007, “Fluidization of Biomass Particles: A Review of Experimental Multiphase Flow Aspects,” Chem. Eng. Sci., 62(1–2), pp. 45–55. [4] Papadikis, K., Bridgewater, A., and Gub, S., 2008, “CFD Modeling of the Fast Pyrolysis of Biomass in Fluidized Bed Reactors, Part A: Eulerian Computation of Momentum Transport in Bubbling Fluidized Beds,” Chem. Eng. Sci., 63(16), pp. 4218–4227. [5] Gidaspow, D., 1994, Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions, Academic, Boston, MA. [6] Deza, M., 2012, “Modeling the Hydrodynamics of a Biomass Fluidized Bed,” Ph.D. thesis, Virginia Tech, Blacksburg, VA.

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[7] Benyahia, S., Arastoopour, H., Knowlton, T. M., and Massah, H., 2000, “Simulation of Particles and Gas Flow Behavior in the Riser Section of a Circulating Fluidized Bed Using the Kinetic Theory Approach for the Particulate Phase,” Powder Technol., 112(1–2), pp. 24–33. [8] Taghipour, F., Ellis, N., and Wong, C., 2005, “Experimental and Computational Study of Gas–Solid Fluidized Bed Hydrodynamics,” Chem. Eng. Sci., 60(24), pp. 6857–6867. [9] Sahoo, A., Ramesh, C., and Biswal, K. C., 2009, “Experimental and Computational Study of the Bed Dynamics of Semi-Cylindrical Gas–Solid Fluidized Bed,” Can. J. Chem. Eng., 87(1), pp. 11–18. [10] Herzog, N., Schreiber, M., Egbers, C., and Krautz, H. J., 2012, “A Comparative Study of Different CFD-Codes for Numerical Simulation of Gas–Solid Fluidized Bed Hydrodynamics,” Comput. Chem. Eng., 39, pp. 41–46. [11] Ergun, S., 1952, “Fluid Flow Through Packed Columns,” Chem. Eng. Progress, 48(2), pp. 89–94. [12] Gera, D., and Gautum, M., 1995, “Analysis of Throughflow Velocity in TwoDimensional Fluidized Bed Bubbles,” ASME J. Fluids Eng., 117(2), pp. 319–322. [13] Delebarre, A., 2002, “Does the Minimum Fluidization Velocity Exist?” ASME J. Fluids Eng., 124(9), pp. 595–600. [14] ANSYS, Inc., 2009, Release 12.0 FLUENT Theory Guide. [15] Deza, M., Franka, N. P., Heindel, T. J., and Battaglia, F., 2009, “CFD Modeling and X-ray Imaging of Biomass in a Fluidized Bed,” ASME J. Fluids Eng., 131(11), p. 111303. [16] Kanholy, S. K., Chodak, J., Lattimer, B. Y., and Battaglia, F., 2012, “Modeling and Predicting Gas–Solid Fluidized Bed Dynamics to Capture Nonuniform Inlet Conditions,” ASME J. Fluids Eng., 134(11), p. 111303. [17] Lun, C. K. K., Savage, S. B., and Jeffrey, D. J., 1984, “Kinetic Theories for Granular Flow—Inelastic Particles in Coutte-Flow and Slightly Inelastic Particles in a General Flowfield,” J. Fluid Mech., 140, pp. 223–256.

Journal of Fluids Engineering

[18] Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC. [19] Leonard, B. P., 1979, “A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation,” Comput. Methods Appl. Mech. Eng., 19, pp. 59–98. [20] Gavi, E., Heindel, T. J., and Fox, R. O., 2010, “Modeling Fluidization in Biomass Gasification Processes,” 7th International Conference on Multiphase Flow, ICMF 2010, Tampa, FL, May 30–June 4, Paper No. 1956. [21] Franka, N. P., and Heindel, T. J., 2009, “Local Time-Averaged Gas Holdup in a Fluidized Bed With Side Air Injection Using X-Ray Computed Tomography,” Powder Technol., 193(1), pp. 69–78. [22] Battaglia, F., England, J. A., Kanholy, S., and Deza, M., 2010, “On the Modeling of Gas–Solid Fluidization: Which Physics Are Most Important to Capture?,” Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition, IMECE2010-40213, Vol. 7: Fluid Flow, Heat Transfer and Thermal Systems, Parts A and B, pp. 1111–1120. [23] Teaters, L., 2012, “A Computational Study of the Hydrodynamics of Gas–Solid Fluidized Beds,” M.S. thesis, Virginia Tech, Blacksburg, VA. [24] Johnson, P. C., and Jackson, R., 1987, “Frictional-Collisional Constitutive Relations for Granular Materials, With Application to Plane Shearing,” J. Fluid Mech., 176, pp. 67–93. [25] Schaeffer, D. G., 1987, “Instability in the Evolution Equations Describing Incompressible Granular Flow,” J. Differ. Eq., 66(1), pp. 19–50. [26] Syamlal, M., and O’Brien, T. J., 1989, “Computer Simulation of Bubbles in a Fluidized Bed,” Am. Inst. Chem. Eng. Symp. Ser., 85, pp. 22–31. [27] Strasser, W., 2010, “CFD Study of an Evaporative Trickle Bed Reactor: MalDistribution and Thermal Runaway Induced by Feed Disturbances,” Chem. Eng. J., 161(1–2), pp. 257–268.

OCTOBER 2014, Vol. 136 / 104501-7

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