Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”

PTEC-10169; No of Pages 11 Powder Technology xxx (2014) xxx–xxx

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Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”☆ Tingwen Li a,b,⁎, Aytekin Gel a,c, Sreekanth Pannala d, Mehrdad Shahnam a, Madhava Syamlal a a

National Energy Technology Laboratory, Morgantown, WV, USA URS Corporation, Morgantown, WV, USA c ALPEMI Consulting LLC, Phoenix, AZ, USA d Oak Ridge National Laboratory, Oak Ridge, TN, USA b

a r t i c l e

i n f o

Available online 11 January 2014 Keywords: Computational fluid dynamics Numerical simulation Circulating fluidized bed Gas–solid flow Riser flow Pressure drop

a b s t r a c t In this work, a detailed grid refinement study was carried out for two well-documented circulating fluidized bed (CFB) systems with the focus on grid convergence of 2D numerical simulations. It is demonstrated that the grid convergence of numerical simulations depends on the flow field variable chosen for verification. For axial pressure gradient, this study shows that no general rule for grid size is available to guarantee the grid-independent results. In addition, the inlet and outlet configuration used in the 2D simulations shows a significant impact on the grid convergence. A 3D grid study is also presented with the intent to probe the differences between 2D and 3D numerical simulations with respect to the grid convergence. For the case considered in this study, the 3D simulation demonstrates better grid convergent behavior than the 2D simulation with comparable grid sizes. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Circulating fluidized beds (CFBs) have been widely utilized in chemical, petrochemical, metallurgical, environmental, and energy industries for applications such as fossil fuel combustion, coal and biomass gasification, and fluid catalytic cracking (FCC). Having several significant advantages—such as fuel flexibility, increased through-put, in-bed sulfur capture, and relatively low NOx emissions with high efficiencies in combustion and gasification—CFB technology is more attractive than any other system in the energy industry [1]. Despite its widespread applications, the complex hydrodynamics of CFBs are still not completely understood and difficult to predict. In most applications, the heat and mass transfer between the phases and the chemical reactions make it even more difficult to predict the behavior of CFB reactors. To optimize the design and operation of industrial processes involving such gas–solid flow, a thorough understanding of hydrodynamics inside the CFB is needed. Our knowledge of CFB systems relies, for the most part, on experimental studies. With the rapid development of high performance computers, computational algorithms, and multiphase flow models, computational fluid dynamics (CFD) modeling has become an effective tool to improve our understanding of complex multiphase ☆ The publisher would like to inform the readership that this article is a reprint of a previously published article. An error occurred on the publisher’s side which resulted in the publication of this article in an incorrect issue. As a consequence, the publisher would like to make this reprint available for the reader's convenience and for the continuity of the special issue. For citation purposes, please use the original publication details; T. Li et al. / Powder Technology 254 (2014) 170–180. DOI of original article: http://dx.doi.org/10.1016/j.powtec.2014.01.021. ⁎ Corresponding author at: National Energy Technology Laboratory, Morgantown, WV, USA. Tel.: +1 304 285 4538. E-mail address: [email protected] (T. Li).

flows and it currently plays an important role in the design and optimization of industrial systems [2]. There are several CFD modeling approaches for gas–solid flow simulations [3]. Among them, the Eulerian–Eulerian (EE) method (also called the two-fluid model or TFM), and the Lagrangian–Eulerian (LE) method are the most widely used approaches to simulate gas–solid flows. The former treats both gas and solid phases as interpenetrating continuum with appropriate constitutive correlations. The latter treats the gas phase as continuum, but tracks the solid phase on the particle scale by solving the motion of each individual particle or swarm of particles. Abundant studies based on EE and/or LE approaches can be found in the literature [4]. Each approach has its own advantages and disadvantages. A common challenge for both approaches is the expensive computational cost in terms of wall clock hours required to reach a converged solution, because of the unsteady and highly coupled multi-scale characteristics of gas– solid flows. For example, the riser, one part of the CFB system of most interest, is a tall and slender column (mostly cylindrical) with complex gas–solid flow inside. The flow in the riser is unsteady and involves structures associated with different spatial and temporal scales [5,6]. To fully resolve the flow behavior, a very fine mesh (typically 10–100 particle diameters), and very small time steps (typically 0.1–1.0 ms) are needed for CFD simulations with either EE or LE approaches. Considering the typical scale of CFB risers for industrial scale, pilot scale or even a laboratory scale 3D CFD simulation becomes highly time-consuming. Various methods have been introduced to reduce the computational cost and accelerate the simulations for gas–solid systems. A class of methods is to introduce new models to reduce the computational cost. For example, instead of tracking a single particle in the LE approach, multiple particles are tracked together as a single computational particle in the coarse-grained discrete element method (DEM) simulations [7], or particles are treated as a single point particle in Multi-Phase Particle-in-

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Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

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T. Li et al. / Powder Technology xxx (2014) xxx–xxx

Cell (MP-PIC) simulations [8]. In the EE approach, the unresolved small structures, mainly in the form of clusters, can be accounted for through sub-grid models that are developed based on fine-grid simulations [9] or based on an energy minimization multi-scale (EMMS) model [10]. Another method to reduce computational cost is to isolate the region of interest from the whole system, such as simulating only the riser and downcomer in CFBs, or decoupling the multiple physics associated with the problem (for example, cold flow simulation of reactors). Considering the fact that mean flows in CFB risers of circular cross section are usually axi-symmetric [11], the computational domain can be further simplified by introducing an axi-symmetric flow assumption or a 2D flow assumption. For investigation of local flow behavior under fully developed conditions, a periodic computational domain is often employed that allows a fine enough spatial and temporal resolution for a detailed fundamental study [5,12]. An axi-symmetric flow assumption most often applies to mathematical modeling developed from empirical correlations [13,14] and is occasionally used in CFD simulations with a steady-flow treatment [15,16]. Although axi-symmetry in the riser flow has been widely justified by the experimental measurements of the mean flow field variables, this assumption leads to unphysical

Table 1 Summary of MFIX equations [26]. A. Governing equations (a) Continuity equations

 Vg ¼ 0 Gas phase ∂t∂ εg ρg þ ∇  εg ρg !

 Vp ¼ 0 Solid phase ∂t∂ εp ρp þ ∇  εp ρp ! (b) Momentum equations

 ! ! V g þ ∇  ε g ρg V g V g ¼ ∇  τ g −ε g ∇P þ ε g ρg g−I gp Gas phase ∂t∂ εg ρg !

 ! ! V p þ ∇  ε p ρp V p V p ¼ ∇  τ p −ε p ∇P þ ε p ρp g þ I gp Solid phase ∂t∂ εp ρp ! B. Constitutive equations (a) Gas stress tensor τ g ¼ 2μ ge Sg
 ! T  1   Sg ¼ 12 ∇! V g þ ∇V g Vg I −3 ∇  ! (b) Solid stress tensor   τ p ¼ −P s þ ημ b ∇  ! V p I þ 2μ p Sp
 ! T  1   ! 1 Sp ¼ 2 ∇ V p þ ∇ V p Vp I −3 ∇ !

accumulation of particles along the axis when applied to transient CFD simulations of a gas–solid flow, as the central axis acts like a reflecting wall to the solid phase and prevents particles from crossing it [17–24]. The majority of numerical simulations of CFB riser flows are carried out with a two-dimensional flow assumption in which a cut-plane along the axis of the cylindrical column is used. Combinations of the aforementioned simplifications can be found in many simulations, for example 2D cold flow simulations of riser flow in FCC process. Although advances in computational hardware will make 3D simulations of full CFB loops more common [25], 2D simulations will continue to play a critical role in the research of gas–solid flow behavior in CFB risers, especially for rapid exploratory study. At the same time, with continuous developments of experimental techniques, more quantitative information of the gas–solid flow field with high accuracy will be available for model validation and thus demanding accurate simulations. Apparently, the assumptions discussed above inevitably introduce limitations or inaccuracy into the CFB simulations, for example, the riser-only simulation fails to predict low-frequency pressure fluctuations associated with the overall pressure balance in CFB loop. Hence it is of great interest to quantify the errors associated with each assumption, especially the widely used 2D flow assumption. The objective of this study is to document some of the differences between 2D and 3D gas–solid flow simulations so that one can adopt the best practices. This is important because CFD is increasingly playing a larger role in the reactor design and optimization, and thereby requiring higher confidence in the computational predictions. The current study consists of two parts. In this part of work, we mainly focus on the grid convergence of CFD simulations of CFB risers. The gas–solid flow in two well-documented CFB risers of square cross-section and circular cross-section has been simulated. Specifically, we carefully examine the grid convergence of the 2D numerical simulations. To justify the grid independence of 2D simulations, both axial and radial profiles of flow field variables are compared for different grid resolutions. For comparison, a grid study for 3D simulations is presented as well. In addition, the effect of solid inlet and outlet configurations is investigated in an attempt to understand the role of different configurations that have been reported in the open literature. In the second part of this paper, detailed discussion on differences between 2D and 3D simulations will be presented.

Ps = εpρpΘp[1 + 4g0εpη] i  h μ p    3 8 8 μ p ¼ 2þα g ηð2−ηÞ 1 þ 5 ηg 0 ε p 1 þ 5 ηð3η−2Þg 0 ε p þ 5 ημ b 3 0

μ p ¼ μ¼

εp ρp Θp g 0 μ 2βμ p

εp ρp Θp g 0 þεp ρ

5 96 ρp dp

pffiffiffiffiffiffiffiffiffi πΘp

2 μ b ¼ 256 5π με p g 0

η ¼ 1þe 2 (c) Granular temperature h

i   ! 3 ∂ V p þ ∇  κ p;Θ ∇Θp þ Π gp −ε p ρp J p ¼ τp : ! 2 ∂t ε p ρp Θp þ ∇  ε p ρp V p Θp h i    64 κ  12 2 2 2 2 κ p;Θ ¼ g p 1 þ 12 5 ηε p g 0 1 þ 5 η ð4η−3Þε p g 0 þ 25π ð41−33ηÞη ε p g 0 0

κ p ¼ κ¼

ρp ε p g 0 Θp κ ρp ε p g 0 Θp þ5ρ6βκεp

pffiffiffiffiffiffi p

75ρp dp πΘp 48ηð41−33ηÞ

J p ¼ p48ffiffiπ ηð1−ηÞ

3=2

ε p g 0 Θp dp

Π gp ¼ −3β Θp þ





! ! 2 81εp μ 2g  V g − V p  3

g 0 d p ρp

pffiffiffiffiffiffi πΘp

(d) Inter-phase momentum exchange  ! V g−V pÞ Igp ¼ β ! ! !  8 ε ρ V −V g ε2p μ g > < 150 2 þ 1:75 p g dp if εg dp ! !p  β¼   > :3 −2:65 εp εg ρg V p − V g if 4 C d εg dp (
 0:687  24 1 þ 0:15 Re  ε g C d ¼ Reεg 0:44 ! !  ρ  V p − V g dp Re ¼ g μ g

ε p N 0:2 εp ≤ 0:2 if Re  εg b1000 if Re  εg ≥1000 Fig. 1. Schematic of the CFB system reported by Zhou et al. [29,30].

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

T. Li et al. / Powder Technology xxx (2014) xxx–xxx

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Table 2 Summary of numerical parameters used in the simulations of square riser. Parameter

Value

Parameter

Value

Width (m) Superficial gas velocity (m/s) Temperature (K) Gas viscosity (Pa·s) Particle diameter (μm) Inter-particle restitution coefficient Angle of wall friction (deg) Specularity coefficient Initial solid volume fraction Averaging time (s)

0.146 5.5 297 1.8e−5 213 0.9 28 0.005 0.15 60

Height (m) Solids flux (kg/m2s) Pressure (atm) Gas molecular weight (kg/kmol) Particle density (kg/m3) Particle-wall restitution coefficient Specularity coefficient Particle-wall frictional angle (deg) Simulation time (s)

9.12 40 1 28.8 2640 0.8 0.005 28 100

2. Numerical model The open source CFD software, Multiphase Flow with Interphase eXchanges (MFIX), was used to conduct the numerical simulations. In MFIX, a multi-fluid, Eulerian–Eulerian approach, with each phase treated as an interpenetrating continuum, was selected. Mass and

momentum conservation equations were solved for the gas and solid (particulate) phases, with appropriate closure relations [26,27]. Constitutive relations derived based on the granular kinetic theory were used for the solid phase. The equations solved in MFIX for simulating the CFB riser flows are summarized in Table 1. The widely used drag correlation proposed by Gidaspow [28] which is a combination of Wen & Yu and

Fig. 2. Schematic of the NETL pilot-scale CFB system.

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

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Table 3 Summary of numerical parameters used in the simulations of NETL B22 CFB riser. Parameter

Value

Parameter

Value

Diameter (m) Superficial gas velocity at bottom (m/s) Temperature (K) Gas viscosity (Pa·s) Particle diameter (μm) Inter-particle restitution coefficient Initial solid volume fraction Averaging time (s)

0.305 7.58

Height (m) Solids flux (kg/m2s)

16.8 193

297 1.8e−5 802 0.8

Pressure (atm) Gas molecular weight (kg/kmol) Particle density (kg/m3) Particle-wall restitution coefficient

1 28.8 863 0.7

0.1 60

Simulation time (s)

80

Fig. 3. Axial profiles of mean pressure gradient predicted by different grid resolutions.

Ergun correlations is used to describe the interphase interaction between gas and solids. For the dense gas–solid flow considered in the current study, turbulence of the gas phase is not of primary concern as particle–particle collisions dominate the flow and, hence, no turbulence model is used. More information on MFIX as well as detailed documentation on the hydrodynamic model equations can be found in the online documentation [26]. The MFIX source code (2012-1 release) was compiled with the Intel Fortran compiler version 11.1.038 and all simulations reported here were executed on a high performance computing cluster with an openSUSE Linux distribution based operating system installed. 3. Simulation setup Two well documented experimental configurations are investigated in the current study. As schematically shown in Fig. 1, the first system is

a

a cold-model CFB riser of 146 × 146 mm square cross-section and a total height of 9.14 m reported by Zhou et al. [29,30]. Sand of mean diameter of 213 μm, particle density of 2640 kg/m [3] and loosely packed bed void fraction of 0.43 was used as the bed material. Solids in the standpipe enter the vessel from the L-valve through a 146 mm ID pipe centered 114 mm above the distributor. The entrained solids are carried by the gas from the riser through a 102 mm ID horizontal pipe at the top of the column into the primary cyclone. Detailed information on the experimental setup and measurements on void fraction and solid velocity profiles are provided in the literature [29,30]. In this study, the flow conditions with a superficial gas velocity of 5.5 m/s and a solid circulating flux of 40 kg/m2s were simulated. The 2D simulation of the central symmetric plane aligned with the inlet and outlet of the riser section was conducted in MFIX. This simple computational domain was discretized by a structured grid employing uniform grid size in each direction. Uniform inflow boundary conditions were imposed at the bottom gas distributor and the solid side inlet and a constant pressure at the outlet was imposed. A partial slip wall boundary condition was applied for the solid phase and a no-slip wall boundary condition was used for the gas phase. Detailed numerical parameters used in the simulations are summarized in Table 2. The second system is a pilot-scale CFB system available at NETL Building 22 (B22) [31]. The experimental system mainly consists of a 0.305 m diameter, 16.8 m tall riser and the associated cyclones, standpipe, L-valve, and gas feeding and solid collecting systems. The high-density polyethylene (HDPE) beads with an average diameter of 802 μm and a density of 863 kg/m3 are used. The solids enter the riser from a side port 0.23 m in diameter and 0.43 m above the gas distributor (from the center line of L-valve). Solids exit the riser through a 0.20 m side port about 0.91 m below the top of the riser. Solids exiting the riser are captured by the primary cyclone and transported through the 0.254 m standpipe and finally returned to the riser through the L-valve. For this system, extensive experimental data were collected from this system via various techniques. The schematic of NETL B22 CFB system is shown in Fig. 2 and a detailed description of the experimental facility and the process instrumentation can be found at https://mfix.netl.doe.gov/challenge/index.php. Again, the 2D simulation was conducted for the central symmetric plane aligned with inlet and outlet of the riser section. A small section of the inlet and outlet was considered in the simulation. The computational domain was discretized with a uniform grid size in each direction. For this system, a series of tests with different inlet and outlet configurations were completed to study their effect on 2D riser flow simulations. Uniform inflow boundary conditions were imposed at the bottom gas distributor and the solid side inlet and a constant pressure at the outlet was imposed. A no-slip wall boundary condition was applied for both solid

b

Fig. 4. Lateral profiles of mean solid concentration (a) and solid vertical velocity (b) at the middle of the riser (height = 4.57 m) predicted by different grid resolutions.

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

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and gas phases and detailed numerical parameters are summarized in Table 3. For both cases, a second order Superbee limiter based scheme was used for spatial discretization and a first-order implicit Euler based scheme was used for the temporal discretization. 4. Results and discussion To use CFD models for the design and optimization of industrial CFB systems, it is important to establish the confidence in the predictions of CFD model. There are different sources of uncertainty that needs to be considered [32]. In this section, we mainly focus on grid convergence, which affects the spatial discretization errors and is considered to be one of the major contributors of uncertainty due to numerical approximation errors. Fig. 6. Axial profiles of pressure gradient predicted by different grid resolutions.

4.1. Grid study of 2D simulations In this paper, we examine the grid convergence of 2D simulations for both cases. Grid independent study is a very important step in numerical simulation, to establish that the discretization errors are relatively small. It has been reported that the grid size has a significant impact on the predicted flow hydrodynamics because of the inherent multiscale (both spatial and temporal) characteristics of gas–solid flow [5]. A rule-of-thumb for grid independence of gas–solid flow is that the grid size should be around 10-particle-diameter [18,33]. The representation of solid side inlet and outlet in the 2D computational domain does not have a physical equivalent in the real configuration. Hence, our analysis will focus on the main riser section excluding the bottom and top regions. However, we have to acknowledge that the inlet and outlet effects might propagate upstream and/or downstream of the riser flow and hence affect the flow behavior predicted in the main riser region. For this reason, a 3D simulation with physically realistic inlet and outlet configurations is preferable. Detailed discussion on differences between 2D and 3D simulations with this respect is presented in Part II of this paper [34]. 4.1.1. Zhou et al.'s square riser For the square riser simulation, with a grid refinement factor of 2 in each direction, three grid resolutions of 15 × 456, 30 × 912, and

a

60 × 1824 denoted by coarse, medium and fine grid, respectively were tested. For these grids, a cell aspect ratio around 2 was maintained during the grid refinement. The simulation has been typically performed for 100 s of real-time with the solid inventory monitored to ensure that the flow reaches statistically steady state, which usually occurred within 40 s. The remaining 60 s simulation results were averaged to obtain the mean flow field information. Fig. 3 presents the axial profile of pressure gradient along the riser, which is a good indicator of the solids distribution along the height. Except for the coarse grid which predicts higher pressure gradient in most regions, the profiles predicted by the medium and fine grids are similar. Differences do exist between results from medium and fine grids in the bottom and top regions. It is reasonable to use the flow behavior in the main section of the riser far from the inlet and outlet, which is usually the region of interest, to justify the grid convergence. With this in mind, it can be concluded that the medium grid is fine enough to reach grid independence even when the grid sizes of dx ≈ 23 dp and dy ≈ 47 dp are larger than the 10-particle-diameter demanded by the standard rule-of-thumb as far as the pressure gradient in the main section is concerned [18,33]. To further verify the grid convergence, the lateral profiles of solid concentration and solid vertical velocity at the middle of the riser

b

Fig. 5. Contour plots of (a) mean solid concentration and (b) mean solid vertical velocity predicted by different grids.

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

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a

b

Fig. 7. Radial profiles of mean solid concentration (a) and solid vertical velocity (b) at the middle of the riser (height = 8.88 m) predicted by different grid resolutions.

(height = 4.57 m) are compared in Fig. 4 for different grids. As it can be seen from the comparison, the profiles predicted by the medium and fine grids demonstrate good agreement. Consistent with the axial pressure gradient profiles shown in Fig. 3, the coarse grid predicts much higher solid concentration along the riser than that predicted by the medium and fine grids (Fig. 4(a)). Considerable discrepancy between the coarse-grid results and the medium and fine grids also exists in the lateral profiles of solid velocity shown in Fig. 4(b). Based on the above analysis, it is tempting to conclude that the medium grid is all that is needed to obtain grid independent results. But Fig. 5 leads to the opposite conclusion because of the considerable differences between the fine and the medium grid results in the lower entrance region. Clearly the grid refinement from medium to fine has a strong impact on the flow behavior in the inlet region, leading to the observed discrepancy, which is consistent with the axial pressure profiles shown in Fig. 3. This observation raises the question about defining grid-independence in the simulation of complex, unsteady, multi-scale

a

flows such as that in a CFB riser, where depending upon the region, different length scales may need to be resolved for grid convergence (e.g., the grid size required to resolve the fully developed region might be different from that required to resolve the inlet region). In addition, the different time scales associated with different regions or flow structures may require different durations of simulation to reach a stationary state. Some low frequency oscillations in the inlet region might not be adequately captured by the current averaging time used for obtaining a stationary state in the mean flow field. When numerical models are being validated, the verification variable for grid study should be the same as the validation variable. In this study, the flow hydrodynamics in the fully developed flow region of the riser are used to evaluate the grid convergence. 4.1.2. NETL B22 riser A similar grid study has been carried out for the second case in which three grid resolutions of 19 × 1050 (coarse), 27 × 1485 (medium) and

b

Fig. 8. Contour plots of mean (a) solid concentration and (b) solid vertical velocity predicted by different grids for 2D simulation (configuration A).

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

T. Li et al. / Powder Technology xxx (2014) xxx–xxx

A

B

C

Fig. 9. Configurations used to model the inlet and outlet in 2D simulations. (color: bluefluidizing gas; red: circulating solids; green: gas–solid mixture).

38 × 2100 (fine) corresponding to grid size of 20-, 14- and 10-particlediamater, respectively, were used to discretize the riser. Mean flow field information was obtained by averaging over the last 60 s of an 80 s simulation. Fig. 6 compares the axial profiles of pressure gradient predicted by different grids. It can be observed that the pressure gradient in most regions tends to decrease as the grid is refined in this study. This trend is consistent with the results shown in Fig. 1. In Fig. 6, it is hard to conclude that the simulation reaches grid independence even though all grids are very fine compared to the particle size. The radial profiles of mean solid concentration and vertical velocity at the height of 8.88 m are presented in Fig. 7. For coarse and medium grids, no apparent core-annular flow pattern can be observed. Particles tend to move upward along the right wall and a strong back flow exists close to the left wall where the solid concentration is very high. For the fine grid, the high solid upward velocity and dilute core migrate towards the central region resembling a core-annular flow pattern. Nevertheless, there still exists strong asymmetric flow behavior in the numerical prediction.

a

7

The mean solid concentration and solid velocity distributions throughout the whole riser are shown in Fig. 8. To show the whole picture of flow field distribution, the actual height-to-diameter ratio is not preserved and the riser height is scaled down by a factor of 5. The converging behavior towards a core-annular flow pattern can be observed as the grid is refined. Considering the fact that the experimental measurements have reported a symmetric core-annular flow regime in most regions of the NETL B22 riser, the failure in predicting the symmetric radial solid concentration and velocity profiles can only be attributed to the strong inlet and outlet effects in 2D simulations. The side-inlet and outlet configuration in the 2D simulation leads to poor mixing throughout the riser and results in asymmetric distribution of solids, even though this configuration seems to be in many features closer to the experimental system which consists of only one inlet and outlet [35]. As the grid is refined, more and more small-scale structures are resolved which greatly improves the mixing inside the riser [36]. The improved mixing by grid refinement tends to overcome the effect of side-inlet and outlet hence leads to the convergent flow behavior towards the typical core-annular pattern. However, an extremely fine grid seems to be needed for predicting symmetric radial profiles in the fully developed flow region according to the current grid study. Alternatively, a two-inlet and two-outlet configuration is usually used in the literature for a symmetric flow prediction from 2D simulations as will be discussed in the next section. 4.2. Effect of inlet and outlet configuration Shah et al. [37]. investigated the effect of type of inlet conditions on the prediction of Eulerian–Eulerian simulations of a CFB riser in a 2D domain. Different inlet arrangements were tested to best represent a CFB riser with an inclined solid side-inlet. They found that both time-averaged axial velocity and solid volume fraction radial profiles were functions of the inlet kinetic energy as well as gas solids mixing patterns at the inlet. An appropriate inlet condition is needed for the 2D numerical simulations in order to match the experimental measurement. For this purpose, in addition to one side-inlet and outlet configuration shown above, two more configurations for inlet and outlet were tested for the 2D simulations of the NETL B22 CFB riser. All inlet and outlet configurations are summarized in Fig. 9. In configuration A, a sliced plane along the riser is used and a

b

Fig. 10. Predictions of mean (a) solid concentration and (b) solid vertical velocity predicted by different grids for configuration B.

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

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T. Li et al. / Powder Technology xxx (2014) xxx–xxx

a

b

Fig. 11. Predictions of mean (a) solid concentration and (b) solid vertical velocity predicted by different grids for configuration C.

small section of inlet and outlet are included. In configuration B, gas and solids are uniformly fed from the bottom distributor and the mixture exit through the top side-outlet. A perfect symmetric configuration is assumed in configuration C with two side-inlets and side-outlets to represent the single side-inlet and outlet in a real system. Among three configurations tested, configuration C is the most widely used one in the literature which assure the symmetric riser flow prediction. The mean solid concentration and vertical velocity predicted by different grid resolutions for configurations B and C are shown in Figs. 8 and 9, respectively. For configuration B, a plug flow of gas and solids are introduced through the bottom which imposes a symmetric flow behavior at the inlet. However, the single side-outlet at the top exit causes strong solid backflow along the opposite side wall. The outlet effect propagates downward to interact with the symmetric flow imposed by the inlet and finally breaks the symmetric flow. Similar grid convergent behavior to configuration A shown in Fig. 8 with respect to solid distribution and velocity can be observed for configuration B. However, no grid independence can be concluded. Given the same grid resolutions used for all configurations, the numerical results of configuration C, which demonstrate good consistency among different grids as can be seen in Fig. 11. Clearly, this two-inlet and two-outlet configuration overcomes the asymmetric flow behavior predicted by the other configurations.

Fig. 12. Axial profiles of pressure gradient predicted by different grid resolutions for configuration C.

To further evaluate the grid convergence for configuration C, the axial profiles of pressure gradient and radial profiles of solid concentration and solid vertical velocity at the height of 8.88 m are compared in Figs. 12 and 13. Even though a perfect symmetric configuration is used, the radial solid concentration profile does show some slight asymmetric behavior, which is mainly due to the strong unsteady multi-scale characteristics of the gas–solid flow in the riser or some large time-scale oscillations not resolved over the time-averaging window. Given the relatively small differences between results of the medium and fine grids, it is possible to claim that grid independent results are achieved on the medium grid. The axial profiles of pressure gradient predicted by the fine grid for different inlet and outlet configurations are compared in Fig. 14. Clearly, the arrangement of inlet and outlet has a profound impact on the 2D riser flow simulation. This is also evident by comparing the flow hydrodynamics shown in Figs. 8, 10 and 11 for different inlet and outlet configurations. An appropriate arrangement is needed by the 2D numerical simulations to match the experimental data. 4.3. Grid study of 3D simulation Due the expensive computational cost of 3D numerical simulations, 2D simulations are usually used to carry out for grid study to shed some light on the grid convergence of 3D simulations. To probe the feasibility of this approach, a grid study of 3D numerical simulation of the NETL B22 riser was performed to compare with the grid study of 2D simulations. The Cartesian cut-cell grid technique in MFIX was used to generate the mesh for 3D simulations. In this approach, a Cartesian grid is used to discretize the computational domain while the boundary cells are truncated to conform to the boundary surface. Consequently, the computational domain for 3D simulation is more realistic than that for 2D simulations. Detailed information on 3D numerical simulations of the NETL B22 CFB riser has been reported [38]. Here only the relevant grid study is presented. Three grid resolutions of 25 × 1050 × 19 (coarse), 35 × 1485 × 27 (medium), and 50 × 2100 × 38 (fine) with a grid refinement ratio of 1.4 were used in the simulations to evaluate the grid convergence of 3D simulations, which are comparable to the grid study of 2D simulations reported above. Due to the expensive computational cost of 3D simulations, only 25 s duration of simulation is completed for the medium and fine grid simulations. In particular, the

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

T. Li et al. / Powder Technology xxx (2014) xxx–xxx

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b

a

Fig. 13. Comparison of radial profiles of (a) solid concentration and (b) solid velocity at the height of 8.88 m predicted by different grids for configuration C.

fine grid simulation for 10 s duration was completed in 22 days on 20 node Intel Xeon E5440 2.83 GHz based CPUs (80 core in total) using Mellanox Infiniband interconnect. Limited by the total simulation time, numerical results for the first 15 s results are excluded to avoid startup effect and only the last 10 s are used for the analysis. Fig. 15 shows the time-averaged solid concentration and vertical velocity along a vertical central slice predicted by the coarse, medium, and fine grids. Due to the short simulation time for time averaging, the mean solid concentration does not show very smooth distributions in the middle of the riser because of the low frequency cluster phenomenon. High solid concentration near the base and top exit because of the side-inlet and outlet is predicted by all grids. Overall, the figure confirms reasonable agreement in the results given by different grids. Slight discrepancy exists near the bottom and top where a fine grid is needed to resolve the complex flow behavior driven by the side inlet and outlet. The axial profiles of pressure gradient and radial profiles of solid concentration and solid vertical velocity at the height of 8.88 m are compared as shown in Figs. 16 and 17. Good consistency can be observed for the axial pressure gradient profiles. The radial profiles of solid concentration and solid velocity demonstrate the typical coreannular flow pattern. As far as the axial pressure gradient is concerned, which is one of the most important measurements reported in experiments, the grid convergence has been achieved for all grids. However, it is hard to tell when the results of solid velocity reach the asymptotic grid convergence range, especially for the solid velocity close to the wall where significant differences exist between predictions of coarse and medium grids. With this regard, the grid independent results tend

Fig. 14. Axial profiles of pressure gradient predicted by the fine grid for different inlet and outlet configurations.

to be obtained at the medium grid. One possible reason for the discrepancy between results of different grids is the short simulation time for the 3D grid study. However, this conclusion cannot hold when the solid concentration and velocity near the inlet region are examined. Clearly, appropriate criterion is needed for determination of the grid convergence based on the objective of the study. Compared to the grid study of 2D numerical simulations shown in Section 4.2 for the NETL B22 CFB riser, the following remarks could be made. On one hand, the configuration C of 2D simulation had a similar conclusion of grid convergence to the grid study of the 3D simulations. However, as far as the axial pressure gradient is concerned, the 3D simulations demonstrate better grid convergence than the 2D simulations with comparable grid resolutions. This might suggest that a 2D grid study can be used to obtain the appropriate grid size for the 3D numerical simulations. On the other hand, a 3D grid study is needed for the 3D simulations considering the fact that some 2D grid studies do not yield grid-independent results.

5. Conclusion In this study, a detailed grid study was reported for the numerical simulations of CFB risers. Depending on the verification variable being examined, different grid convergence behaviors can be observed. Hence, the following conclusions can be made based on the axial profile of pressure gradient inside the riser. For the 2D simulations of a riser with square cross-section, and with group B particles, good grid convergence can be achieved with a relatively coarse grid of 20-particle-diameter compared to the widely accepted rule of 10-particle-diameter (typically required for group A particles). For the 2D simulation of the pilot-scale NETL B22 CFB riser, the grid convergence behavior of the numerical simulation was found to be affected by the inlet and outlet configuration. The inlet and outlet arrangement has a significant impact on the grid convergence and the predicted flow behavior of the 2D CFB riser simulations. Symmetric arrangement tends to predict reasonable flow patterns and yields faster grid convergence than the other arrangements investigated. It is very difficult to reach the grid independence for the asymmetric configurations even when the grid size is close to 10-particlediameter. In summary, this study suggests that the 10-particle rule cannot guarantee grid independent results when complex asymmetric flow occurs in the 2D numerical simulations. Despite the high computational cost of 3D simulations, a 3D grid study was conducted. With the comparable grid size, the 3D grid study shows a better grid convergence for the case tested than the 2D grid study.

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

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Fig. 15. Mean (a) solid concentration and (b) solid vertical velocity predicted by different grids for 3D numerical simulations.

Nomenclature d diameter m e restitution coefficient I momentum transfer kg/m2-s2 g gravitational acceleration m/s2 g0 radial distribution function P pressure Pa U superficial velocity m/s V velocity m/s W volume of removed surface m3

Greek symbols ε volume fraction μ viscosity Pa·s Θ granular temperature m2/s2 ρ density kg/m3

Subscripts g gas p particle Abbreviation 2D two dimensional 3D three dimensional CFB circulating fluidized bed CFD computational fluid dynamics DEM discrete element method EE Eulerian–Eulerian EMMS energy minimization multi-scale FCC fluid catalytic cracking HDPE high-density polyethylene LE Lagrangian–Eulerian MFIX Multiphase Flow with Interphase eXchanges MP-PIC Multi-Phase Particle-in-Cell NETL National Energy Technology Laboratory TFM two-fluid model Acknowledgment

Fig. 16. Axial profile of solid holdup predicted by different grids for the 3D numerical simulations.

This technical effort was performed in support of the National Energy Technology Laboratory's ongoing research in advanced multiphase flow simulation under the RES contract DE-FE0004000. Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008

T. Li et al. / Powder Technology xxx (2014) xxx–xxx

a

11

b

Fig. 17. Radial profiles of (a) mean solid concentration and (b) vertical velocity predicted by different grids for the 3D numerical simulations.

or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

References [1] In: J.R. Grace, A.A. Avidan, T.M. Knowlton (Eds.), Circulating Fluidized Beds, Blakie Academic & Professional, New York, 1997. [2] D. Eskin, J. Derksen, Introduction to a series of featured articles: “multiphase computational fluid dynamics for industrial processes”, Can. J. Chem. Eng. 89 (2011) 203–205. [3] M.A. van der Hoef, M. Ye, M. van sint Annaland, A.T. Andrews IV, S. Sundaresan, J.A.M. Kuipers, Multiscale modeling of gas-fluidized beds, Adv. Chem. Eng. 21 (2006) 65–149. [4] M. Syamlal, S. Pannala, Multiphase continuum formulation for gas–solids reacting flows, in: S. Pannala MS, T. O'Brien (Eds.), Computational Gas–Solids Flows and Reacting Systems: Theory, Methods and Practice, IGI Global, Hershey, PA, 2010. [5] K. Agrawal, P.N. Loezos, M. Syamlal, S. Sundaresan, The role of meso-scale structures in rapid gas–solid flows, J. Fluid Mech. 445 (2001) 151–185. [6] J. Li, M. Kwauk, Exploring complex systems in chemical engineering — the multi-scale methodology, Chem. Eng. Sci. 58 (3–6) (2003) 521–535. [7] M. Sakai, S. Koshizuka, Large-scale discrete element modeling in pneumatic conveying, Chem. Eng. Sci. 64 (3) (2009) 533–539. [8] D. Snider, S. Banerjee, Heterogeneous gas chemistry in the CPFD Eulerian–Lagrangian numerical scheme (ozone decomposition), Powder Technol. 199 (1) (2010) 100–106. [9] Y. Igci, S. Sundaresan, Constitutive models for filtered two-fluid models of fluidized gas-particle flows, Ind. Eng. Chem. Res. 50 (2011) 13190–13201. [10] W. Wang, J.H. Li, Simulation of gas–solid two-phase flow by a multi-scale CFD approach — extension of the EMMS model to the sub-grid level, Chem. Eng. Sci. 62 (1–2) (2007) 208–231. [11] J.R. Grace, X. Bi, M. Golriz, Circulating fluidized beds, in: Y. W-C (Ed.), Handbook of Fluidization and Fluid-Particle Systems, Marcel Dekker, Inc., New York, 2003. [12] S. Cloete, S. Amini, S.T. Johansen, On the effect of cluster resolution in riser flows on momentum and reaction kinetic interaction, Powder Technol. 210 (1) (2011) 6–17. [13] W. Namkung, S.D. Kim, Radial gas mixing in a circulating fluidized bed, Powder Technol. 113 (1–2) (2000) 23–29. [14] J. Sterneus, F. Johnsson, B. Leckner, Gas mixing in circulating fluidised-bed risers, Chem. Eng. Sci. 55 (1) (2000) 129–148. [15] Y.H. Zhang, J.M. Reese, Gas turbulence modulation in a two-fluid model for gas–solid flows, AIChE J 49 (12) (2003) 3048–3065. [16] Y. Zheng, F. Liu, F. Wei, Y. Jin, Numerical simulation of the gas-particle flow in risers — I: the macro flow behavior, Chem. Eng. Commun. 191 (4) (2004) 435–449. [17] L. Cabezas-Gomez, F.E. Milioli, Numerical study on the influence of various physical parameters over the gas–solid two-phase flow in the 2D riser of a circulating fluidized bed, Powder Technol. 132 (2–3) (2003) 216–225. [18] C. Guenther, M. Syamlal, L. Shadle, C. Ludlow, A numerical investigation of an industrial scale gas–solids CFB, Paper Presented at: 7th International Conference on Circulating Fluidized Beds2002Niagra Falls, Ontario, Canada, 2002.

[19] T. Li, K. Pougatch, M. Salcudean, D. Grecov, Numerical modeling of an evaporative spray in a riser, Powder Technol. 201 (3) (2010) 213–229. [20] C.C. Pain, S. Mansoorzadeh, C.R.E. de Oliveira, A study of bubbling and slugging fluidised beds using the two-fluid granular temperature model, Int. J. Multiphase Flow 27 (3) (2001) 527–551. [21] N. Reuge, L. Cadoret, C. Coufort-Saudejaud, S. Pannala, M. Syamlal, B. Caussat, Multifluid Eulerian modeling of dense gas–solids fluidized bed hydrodynamics: Influence of the dissipation parameters, Chem. Eng. Sci. 63 (22) (2008) 5540–5551. [22] S. Vaishali, S. Roy, S. Bhusarapu, M.H. Al-Dahhan, M.P. Dudukovic, Numerical simulation of gas–solid dynamics in a circulating fluidized-bed riser with Geldart group B particles, Ind. Eng. Chem. Res. 46 (25) (2007) 8620–8628. [23] N. Xie, F. Battaglia, S. Pannala, Effects of using two- versus three-dimensional computational modeling of fluidized beds — part I, hydrodynamics, Powder Technol. 182 (1) (2008) 1–13. [24] N. Xie, F. Battaglia, S. Pannala, Effects of using two- versus three-dimensional computational modeling of fluidized beds: part II, budget analysis, Powder Technol. 182 (1) (2008) 14–24. [25] S. Sundaresan, Reflections on mathematical models and simulation of gas-particle flows, Paper Presented at: 10th International Conference on Circulating Fluidized Beds and Fluidization, Technology, 2011, pp. 21–40. [26] S. Benyahia, M. Syamlal, T.J. O'Brien, Summary of MFIX Equations, https://mfix.netl. doe.gov/documentation/MFIXEquations2012-1.pdf2012. [27] M. Syamlal, W. Rogers, T.J. O'Brien, MFIX Documentation: Theory Guide, U.S. Department of Energy (DOE), Morgantown Energy Technology Center, Morgantown, 1993. [28] D. Gidaspow, Multiphase flow and fluidization: continuum and kinetic theory descriptions, Academic Press, Boston, 1994. [29] J. Zhou, J.R. Grace, S. Qin, C.M.H. Brereton, C.J. Lim, J. Zhu, Voidage profiles in a circulating fluidized-bed of square cross-section, Chem. Eng. Sci. 49 (19) (1994) 3217–3226. [30] J. Zhou, J.R. Grace, C.J. Lim, C.M.H. Brereton, Particle-velocity profiles in a circulating fluidized-bed riser of square cross-section, Chem. Eng. Sci. 50 (2) (1995) 237–244. [31] L. Shadle, C. Guenther, R. Cocco, R. Panday, NETL/PSRI Challenge Problem 3, https:// mfix.netl.doe.gov/challenge/index.php2010. [32] A. Gel, T. Li, B. Gopolan, M. Shahnam, M. Syamlal, Validation and uncertainty quantification of a multiphase flow CFD model, Ind. Eng. Chem. Res. 52 (2013) 11424–11435. [33] A.T. Andrews, P.N. Loezos, S. Sundaresan, Coarse-grid simulation of gas-particle flows in vertical risers, Ind. Eng. Chem. Res. 44 (16) (2005) 6022–6037. [34] T. Li, S. Pannala, M. Shahnam, CFD Simulations of Circulating Fluidized Bed Risers, Part II, Evaluation of Differences between 2D and 3D Simulations, Powder Technol. 254 (2014) 115–124. [35] S. Benyahia, H. Arastoopour, T.M. Knowlton, H. Massah, 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) (2000) 24–33. [36] T. Li, A. Gel, M. Syamlal, C. Guenther, S. Pannala, High-resolution simulations of coal injection in a gasifier, Ind. Eng. Chem. Res. 49 (21) (2010) 10767–10779. [37] M.T. Shah, R.P. Utikar, G.M. Evans, M.O. Tade, V.K. Pareek, Effect of inlet boundary conditions on computational fluid dynamics (CFD) simulations of gas–solid flows in risers, Ind. Eng. Chem. Res. 51 (4) (2012) 1721–1728. [38] T. Li, J. Dietiker, M. Shahnam, MFIX simulation of NETL/PSRI challenge problem of circulating fluidized bed, Chem. Eng. Sci. 84 (2012) 746–760.

Please cite this article as: T. Li, et al., Reprint of “CFD simulations of circulating fluidized bed risers, part I: Grid study”, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.008