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Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations
PTEC-10168; No of Pages 10 Powder Technology xxx (2014) xxx–xxx
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Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations☆ Tingwen Li a,b,⁎, Sreekanth Pannala c, Mehrdad Shahnam a a b c
National Energy Technology Laboratory, Morgantown, WV, 26507, USA URS Corporation, Morgantown, WV 26507, USA Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
a r t i c l e
i n f o
Available online 13 January 2014 Keywords: Computational fluid dynamics Numerical simulation Circulating fluidized bed Gas–solids flow Riser flow Pressure drop
a b s t r a c t Two-dimensional (2D) numerical simulations have been widely reported in the literature for qualitative, even quantitative, study of the complex gas–solids flow behavior in circulating fluidized bed (CFB) risers. It is generally acknowledged that there exist quantitative differences between 2D and three-dimensional (3D) numerical simulations. However, no detailed study evaluating such differences can be found for simulations of CFB risers. This paper presents 2D and 3D numerical simulations of three different CFB risers. Axial pressure gradients from both 2D and 3D simulations are compared with the experimental data. It has been clearly demonstrated that the 2D simulation cannot satisfactorily reproduce the 3D simulation results. A further comparison of radial profiles of void fraction and solids velocity for an axi-symmetric riser configuration is reported and the quantitative differences between 2D and 3D simulations are analyzed. In conclusion, 2D simulation is only recommended for qualitative evaluation and 3D modeling is recommended for predictive simulations. © 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). However, the complex gas– solids flow behavior inside CFBs coupled with the heat and mass transfer across the phases, along with chemical reactions challenges the design and operation of these industrial systems. A thorough understanding of hydrodynamics inside a CFB is needed. With the fast development of high-speed computers and computational algorithms, computational fluid dynamics (CFD) modeling has become an effective tool to improve our understanding of complex multiphase flows and it Abbreviations: 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; MP-PIC, Multi-Phase Particle-inCell; MFIX, Multiphase Flow with Interphase eXchanges; NETL, National Energy Technology Laboratory; PSRI, Particulate Solid Research Inc.; TFM, two-fluid model; UDF, User Defined Function. ☆ 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) 115–124 DOI of original article: http://dx.doi.org/10.1016/j.powtec.2014.01.022. ⁎ Corresponding author at: National Energy Technology Laboratory, Morgantown, WV, 26507, USA. Tel.: +1 304 285 4538. E-mail addresses: [email protected], [email protected] (T. Li).
currently plays an important role in the design and optimization of industrial systems. With advanced predictive models for reacting multiphase flows, CFD can greatly accelerate the entire reactor development process with enhanced confidence levels and better performance. One limitation of CFD modeling of CFB systems is the expensive computational cost required by the unsteady and highly coupled multi-scale characteristics of gas–solids flows. Various methods have been introduced to reduce the computational load and accelerate the simulations for gas–solids systems from both the model and computational domain perspectives as summarized in Part I [1]. One widely used assumption of CFB riser simulations is the two-dimensional flow assumption in which a cut-plane along the axis of the cylindrical column is used. A two-dimensional numerical simulation works reasonably well for a fundamental study and has wide applications for gas–solid flow study in the literature. Nowadays, three-dimensional simulations of CFB riser have become more and more affordable with the continuous advances in computational hardware. It is then of great interest to quantify the errors associated with assumptions in CFD simulations, especially the widely used 2D flow assumption. The differences between 2D and 3D simulations of gas–solids fluidized beds have been discussed in several papers. Peirano et al. [2] compared 2D and 3D simulations of bubbling fluidized beds and concluded that 2D simulations should be used with caution and only for sensitivity analysis, whereas 3D simulations are able to reproduce both the stationary statistics and the dynamics of the system. Cammarata et al. [3] carried out both 2D and 3D CFD simulations of bubbling fluidized beds and suggested that 3D simulations should be preferable for validating the CFD models with available correlations and experimental data. Xie
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Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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et al. [4] investigated the range of validity for employing simulations based on a 2D Cartesian coordinate system to approximate both cylindrical and rectangular fluidized beds. The results of three different fluidization regimes–bubbling, slugging, and turbulent–demonstrated that a 2D Cartesian system can be used to successfully simulate and predict a bubbling regime where the superficial velocity is close to the minimum fluidization velocity. However, caution must be exercised when using the 2D Cartesian simulation for other fluidized regimes. A budget analysis that explains all the differences in detail was presented by Xie et al. [5] showing the role of third direction that is not resolved in 2D simulations. Reuge et al. [6] also studied the differences between 3D simulations and 2D axi-symmetric and Cartesian simulations. Their results again indicated that 3D simulations are necessary for correctly reproducing the experimental bed expansions and heights of fluctuation of a bubbling fluidized bed, while the 2D simulations widely overestimated both quantities. The 2D Cartesian calculations showed better agreement with the experiments and the 3D simulation than the 2D axi-symmetric calculations, but they still significantly overestimated the bed expansions and heights of fluctuation. Significant quantitative differences between 2D and 3D simulations on bed expansion, solids concentration, and gas and solids velocities were also reported by Li et al. [7] in a CFD study of gas mixing in fluidized beds. Similar differences in flow hydrodynamics were observed by Liu et al. [8] even though the mixing extent predicted by the 2D simulation is quantitatively similar to the 3D results. Li et al. [9] further reported that significant differences existed between 2D and 3D simulations with respect to bed expansion, bubble distribution, and void fraction and solids velocity profiles for a bubbling fluidized bed with submerged horizontal tube bundle. According to the work by Li et al. [10,11]., 2D simulation can neither be used to accurately simulate a 3D system nor a pseudo-2D system. Unfortunately, all of the above work focuses on relatively low-gas velocity fluidization regimes. Not many comparisons between 2D and 3D simulations of CFB riser can be found in the literature, despite the wide application of 2D assumptions in riser-flow simulations and the generally acknowledged limitation of 2D modeling. Li et al. [12] reported both 2D and 3D numerical simulations of a well-documented CFB riser with a square cross-section. It was found that 2D simulations under-predicted the solids inventory even with the finest grid (10-particle-diameter grid size). On the other hand, a 3D simulation with a relatively coarse grid was found to be in much better agreement with the experimental data. The objective of this study is to document some of the differences between 2D and 3D gas–solids flow simulations so that one can adopt the best practices. In this part of the work, we focus on the differences between 2D and 3D numerical simulations of CFB riser. For this purpose, we carry out a detailed analysis of the differences between 2D and 3D simulations of CFB risers to further the investigation of Li et al. [12]. Three cases of CFB riser simulations with different system configurations and operating conditions are considered in the current study, representing a wide variety of applications. Comparison between 2D and 3D simulations, as well as available experimental data for the axial profile of the pressure gradient, is reported for each case. Further comparison of radial profiles of void fraction and solids velocity is made for a particular case. Finally, a deliberate analysis is presented to address the inherent differences between 2D and 3D simulations.
on the model equations and the numerical implementation, can be found at the MFIX website, https://mfix.netl.doe.gov. There is an option to use the Lagrangian–Eulerian (LE) approach in MFIX [16,17], but that was not exercised in this study because with typical CFBs the LE approach is still computationally prohibitive. In addition, the commercial CFD software-ANSYS FLUENT is employed to simulate one case of gas– solids flow in an axi-symmetric riser. Similar Eulerian–Eulerian approach based on the granular kinetic theory is utilized. Detailed information on model equations solved in FLUENT can be found in the ANSYS FLUENT theory guide [18]. For all cases, both 2D and 3D simulations with identical numerical parameters and equivalent flow conditions were conducted. For brevity, additional details on numerical models as well as some grid studies are not provided here but can be found in Part I of this paper [1]. 2.1. Case 1: CFB riser with a square cross-section The first test case is based on a well-documented experiment of a circulating fluidized bed with a square cross-section as shown in Fig. 1 [19,20]. The CFB riser has a cross sectional dimension of 146 × 146 mm and total height of 9.14 m. Sand with mean diameter and density of 213 μm and 2640 kg/m3 respectively and loosely packed bed void fraction of 0.43 is used as the bed material. In this study, a superficial gas velocity of 5.5 m/s and a solids circulating flux of 40 kg/m2s are considered. As schematically shown in Fig. 2, a 2D simulation of the central symmetric plane aligned with the inlet and outlet and a full 3D simulation of the riser section are conducted with MFIX. Based on the 2D grid study reported in Part I, 2D and 3D simulations with grid resolutions of 30 × 456 and 30 × 30 × 456, respectively, are compared here. Detailed information on the numerical settings and simulation setup has been reported by Li et al. [12].
2. Numerical tests and simulation results The numerical simulations were mainly conducted with the opensource software, Multiphase Flow with Interphase eXchanges (MFIX), developed at the National Energy Technology Laboratory (NETL). In MFIX, a multi-fluid, Eulerian–Eulerian approach is used, with each phase treated as an interpenetrating continuum. Mass and momentum conservation equations are solved for the gas and solids (particulate) phases, with appropriate closure relations [13–15]. Constitutive relations derived from granular kinetic theory are used for the solids phase. More information on MFIX, as well as detailed documentation
Fig. 1. Schematic of the CFB system reported by Zhou et al. [19,20].
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Detailed comparisons between numerical results and experimental data on vertical and lateral voidage distributions and solids velocity profiles have been reported elsewhere [12]. In addition to the significant difference between 2D and 3D predictions of pressure gradients and solids inventory, it has been found that the lateral void fraction distributions for 2D and 3D simulations (not shown here) differ substantially even though both qualitatively capture the core-annulus flow. It can be concluded from this case that the 3D geometry is a basic requirement to accurately simulate a CFB riser with a rectangular cross-section with asymmetrical inlet and outlet. Although the 3D simulation yields much better agreement with the experimental measurements than the 2D simulation, there are still differences between experimental data and the 3D numerical predictions. One possible reason for this discrepancy is the grid resolution might not be sufficient to reach the grid independent results for 3D simulation even though the same grid size for 2D simulation yields a reasonably grid-independent pressure gradient in the main riser section as discussed in Part I. Unfortunately, no grid study is performed for the 3D simulation. The unresolved structures by the coarse grid usually lead to over-prediction of interphase drag hence under-prediction of solids holdup and pressure gradient [21,22]. Further grid refinement or an appropriate sub-grid model for coarse-grid simulation is needed to address this issue. Another possible reason for the discrepancy is the simplification of the solids inlet and outlet configurations. 2.2. Case 2: NETL B22 CFB riser
Fig. 2. Schematics of 2D and 3D simulations of CFB riser with a square cross-section.
The axial pressure gradient is one of the most common measurements from experiment and based on which the axial distribution of solids is typically obtained. Furthermore, the solids inventory can be estimated through the overall pressure drop across the riser. Fig. 3 shows the axial profiles of pressure gradient predicted by 2D and 3D simulations. As shown in Fig. 3, there are significant differences between 2D and 3D results. The 2D simulation predicts a much lower pressure gradient throughout the riser, indicating a lower solids inventory inside the system compared to that of the 3D simulation. The solids inventories were calculated as the integral of the solids volume fraction over the whole riser, and the prediction of the 3D simulation is 7 times greater than the 2D simulation. The main reason for this difference is believed to be related to the 3D effects of system geometry and flow behavior.
Fig. 3. Axial profiles of pressure gradient predicted by 2D and 3D simulations as well as estimated from the experimental data of apparent voidage (Experimental data from Zhou et al., 1995).
In the second test case, NETL's pilot-scale B22 CFB riser, which is 0.305 m in diameter and 16.8 m tall, is simulated. A schematic of the whole CFB system is given in Fig. 4 [23]. Two types of particles, belonging to Geldart groups A and B, respectively, are simulated: glass beads (59 μm diameter and density of 2425 kg/m3) and high-density polyethylene (HDPE) beads (800 μm diameter and density of 863 kg/m3). For this system, detailed experimental data on pressure fluctuations, pressure gradient, solids mass flux, and solids velocity are available for both types of particles under different operational conditions. The original experimental data were collected for the third challenge problem for CFD simulation organized by NETL and PSRI [23,24]. The experimental data were released at the 2010 AIChE annual conference [25]. A complete description of the experimental facility, along with process instrumentation and detailed experimental data, can be accessed from the MFIX website at https://mfix.netl.doe.gov/challenge/index.php. Only the riser along with small sections of the inlet and outlet was simulated for this system. Fig. 5 depicts the 2D and 3D simulation configurations of NETL B22 CFB riser. The Cartesian grid method implemented in MFIX by Dietiker [26] has been used to simulate the cylindrical riser and a small section of the side inlet and outlet as shown in Fig. 5. The sliced symmetric plane aligned with the side inlet and outlet is used for the 2D simulation. A uniform grid with a grid size of 1.6 cm, which corresponds to the coarse grid reported in Part I, is used for both 2D and 3D simulations. Two cases are studied in this work: one case with group A particles with a solids circulation rate of 9.26 kg/s and a superficial gas velocity of 5.14 m/s and the second case with group B particles with a solids circulation rate of 14 kg/s and a superficial gas velocity of 7.58 m/s. The superficial gas velocities are based on the flow conditions measured at the bottom distributor. The simulations were conducted for more than 50 seconds of real time. To ensure the initial transient effects are not included in the analysis, only the last 30 seconds of the simulations are used for extracting the mean flow field information. Full details on the numerical simulation setup were reported by Li et al. [27]. Fig. 6 shows the axial profiles of pressure gradients predicted by both 2D and 3D simulations along with the data measured in several repeated experiments for the two cases under consideration. The 3D simulations predict high-pressure gradients in the bottom and top regions of the riser, where the side inlet and the T-shaped abrupt exit effects
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 4. Schematic of the NETL pilot-scale CFB system (Shadle et al., 2010b).
dominate [28]. However, the 2D simulations cannot capture this behavior for both cases. In addition, the 2D simulations significantly overpredict the pressure gradient in the major section of the riser compared to the 3D simulations. Although the agreement between the measured and 3D-predicted pressure gradient is very good for the case of group B particles (Fig. 6b), the same is not true for the group A particles (Fig. 6a). This can be attributed to the coarse grid resolution used in the present study and its inability to capture the small-scale clustering associated with group A particles. According to the grid study of 3D
simulations reported in Part I, the grid size of 1.6 cm is fine enough for the larger group B particles, but is too coarse for the smaller group—A particles. For group B particles, good agreement has also been observed between 3D numerical predictions and experimental data for pressure gradients for the other operating conditions [27]. In addition, a quantitative comparison between numerical results and experimental data with respect to radial profiles of solids velocity and solids mass flux at various elevations has been made, and a reasonably good agreement has been obtained for this case [27]. To overcome the high-computational cost of
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 5. Schematics of 2D and 3D simulations of NETL CFB riser.
fine grid simulations, appropriate sub-grid closure models are suggested for a coarse grid simulation to account for the unresolved small-scale structures [29,30]. The constitutive sub-grid models proposed by Igci and Sundaresan [31] has been implemented in MFIX and applied to the present geometry. The simulation results will be reported in a separate manuscript. Comparisons of the mean void fraction distribution from both 2D and 3D simulations are shown in Fig. 7. For the ease of presentation, the height of the riser is scaled down by a factor of 5. As shown in Fig. 7, in 2D simulations, particles migrate to the side wall adjacent to the side inlet and then gradually accumulate towards the opposite side for group A particles; and for group B particles, the behavior is just the opposite. On the other hand, a good symmetrical flow behavior is predicted by the 3D simulation in most regions of the riser except for the bottom and top regions where the effects of the side inlet and exit dominate. Furthermore, the cross-sectional plots of void fraction and solids velocity distributions in the fully developed region (not shown here) confirm the good axi-symmetric flow behavior predicted by the 3D simulations. The experimental data also shows similar axisymmetric flow behavior in most riser sections and thus the 3D simulations are more reasonable than 2D simulations even qualitatively. The asymmetric flow behavior in the fully developed region of the riser in the 2D simulation is attributed to the predicted poor mixing behavior in the solids inlet region. For 2D simulations, a two-inlet configuration is required in order to achieve a symmetric flow prediction, as suggested by Benyahia et al. [32], which can be found in many numerical simulations. This approach remedies the asymmetric issue of 2D simulations in the fully developed region. However, it cannot be used to study the effect of the inlet and outlet in most systems, which usually have a single inlet and outlet on one side. To demonstrate this, the axial pressure gradient profile predicted by the 2D simulation with a symmetric twoinlet and two-outlet configuration, referred to as configuration C in Part I, is compared against the 3D result and experimental data in Fig. 8. As can be seen from the comparison, the symmetric inlet and outlet configuration predicts better agreement to the 3D results and experimental
Fig. 6. Axial profiles of pressure gradient predicted by 2D and 3D simulations as well as experimental data for (a) group A particle (Gs = 9.26 kg/s and Ug = 5.14 m/s); (b) group B particles (Gs = 14 kg/s and Ug = 7.58 m/s).
data in the middle region of riser but quite different results in the lower and upper regions. 2.3. Case 3: Malcus et al.'s CFB riser The CFB riser used by Malcus et al. [33] has been selected as the third test case, since the system configuration and flow behavior are symmetric. The cold-flow CFB apparatus consists of a 7 m tall riser with an inner diameter of 0.14 m and a smooth exit at the top. To ensure symmetrical solids flow behavior in the experimental system, particles are introduced into the system through eight annular orifices at the bottom of the riser. FCC particles with a particle density of 1740 kg/m3 and a mean diameter of 89 μm were used. Measurements of apparent void fraction and radial distribution of solids concentration for different operational conditions were reported by Malcus et al. [33]. The commercial CFD software ANSYS FLUENT is used to simulate Case 3. The schematic for both 2D and 3D simulations is shown in Fig. 9. To achieve uniform solids feeding along the circumferential direction, a ring type of solids inlet is used in the 3D simulation instead of eight equally spaced orifices used in the experimental system. The smooth top exit is further simplified as a straight top exit to ensure the axi-symmetry in geometry. Those simplifications are employed deliberately to guarantee a perfect axi-symmetric system configuration in the 3D simulation, which will be compared to the 2D simulation. The computational domain for 2D and 3D simulations are discretized by 10 K and 185 K cells, respectively, with comparable grid sizes. No grid study is conducted for this case. Only one set of flow conditions with a solids circulation rate of 4.65 kg/s (solids mass flux of 302 kg/m2s) and a superficial gas velocity of 4.7 m/s is simulated. As no clear indication can be found on how the superficial gas velocity was determined in the experiment, the superficial gas velocity here is based on the ambient conditions at the top exit. The uncertainty in the superficial velocity
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 7. Mean voidage distributions predicted by 2D and 3D simulations (a) group A particles (Gs = 9.26 kg/s and Ug = 5.14 m/s); (b) group B particles (Gs = 14 kg/s and Ug = 7.58 m/s).
might affect the comparison between the experimental data and simulation results [34], but it should have no impact on the direct comparison between 2D and 3D simulations. Again, all simulations have been monitored to run long enough for stationary state analysis. Fig. 10 shows the axial profiles of pressure gradient predicted by the 2D and 3D numerical simulations as well as the experimental pressure gradient (calculated from the apparent axial solids concentration as reported by Malcus et al. [33]). The 2D simulation predicts a drastically different profile compared to that of the 3D simulation, although the perfect axi-symmetry in the system geometry and operational condition is maintained. As a simplification of the 3D system, the 2D simulation does not yield satisfactory agreement with the 3D simulation even though it exhibits better agreement with the experimental measurement towards the top region of the riser. The poor agreement between the 3D simulation and the experimental data is mainly attributed to the insufficient grid resolution used for the fine FCC particles. In addition, the differences in the bottom zone can be attributed to the simplified ring-type annular solids feeder used in the 3D simulation, which cannot capture the strong solids mixing caused by solids jets through dispersed orifices. Simplification to the smooth top exit could also have some effect on the flow behavior.
Fig. 8. Axial profiles of pressure gradient predicted by the 2D simulation with symmetric inlet and outlet configuration and 3D simulation as well as experimental data for group B particles (Gs = 14 kg/s and Ug = 7.58 m/s).
Fig. 11 presents the radial profiles of mean solids concentration and vertical solids velocity at a height of 2.1 m above the distributor. Both numerical results show very good symmetry with respect to the central axis, which is consistent with the experimental measurements. At that height, the cross-sectional averaged solids concentrations of 0.108 and 0.109 for 2D and 3D simulations, respectively, under-predict the cross-sectional averaged solids concentration of 0.17 as estimated from the pressure gradient or 0.2 as from the ECT measurements.
Fig. 9. Schematics of 2D and 3D simulations of Malcus et al.'s CFB riser.
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 10. Axial profiles of pressure gradient predicted by 2D and 3D simulations along with the experimental data.
Fig. 12. Axial profiles of pressure gradient predicted by 2D and 3D simulations with filtered model and experimental data.
Even though the cross-sectional averaged solids concentrations of 2D and 3D simulations at the height of 2.1 m are close to each other, the discrepancy between the radial profiles of solids concentration as presented in Fig. 11(a) is not negligible. The 2D simulation predicts a more uniform radial solids concentration profile than the 3D simulation. Compared to the experimental data obtained using ECT, along two orthogonal directions, the radial variation of solids concentration as captured by the 3D simulation shows better agreement despite the fact that the 2D results have better quantitative agreement in the central core region. The difference in the solids velocity is more pronounced, as can be seen in Fig. 11(b). The 2D simulation predicts significant downward velocity close to the wall, which is absent in the 3D simulation. Those differences are believed to be inherent in the 2D simplification of the cylindrical domain and will be discussed in next section.
As mentioned above, most simulations of CFB systems with Group A particles suffer from insufficient grid resolution, which fail to resolve the particle clustering and subsequent drag reduction. Several sub-grid closure models have been proposed for a coarse grid simulation in order to account for the unresolved small-scale structures [31,35,36]. It should be noted that the objective of this study is to document the differences between 2D and 3D simulations of CFB risers with comparable grid sizes. The experimental data are only shown for reference and differences between numerical predictions and experimental measurements are not of primary concern. However, to support the above analysis regarding the discrepancy between numerical simulation and experimental data, a sub-grid model was tested in the current study. The filtered two-fluid model proposed by Igci and Sundaresan [31] was implemented into both 2D and 3D simulations through User Defined Function (UDF) with appropriate wall corrections, as reported by Igci and Sundaresan [37] and Igci et al. [38]. For brevity, details of the filtered two-fluid model are not reported here. Numerical results on the axial pressure gradient and the radial solids concentration distribution are compared against the experimental data in Figs. 12 and 13, respectively. As can be seen from these figures, better agreement between the numerical simulation and experimental data exists for the 3D simulation after accounting for the effect of unresolved clusters through the filtered model. 3. Further discussion So far, differences between 2D and 3D simulations of CFB risers with rectangular and circular cross-sections are presented mainly with respect to the axial profile of pressure gradient, which is one of the most common measurements reported in most CFB experiments and is
Fig. 11. Radial profiles of mean (a) solids concentration and (b) vertical solids velocity at the height of 2.1 m.
Fig. 13. Radial profiles of mean solids concentration predicted by 2D and 3D simulations with filtered model at the height of 2.1 m.
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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extensively used to validate CFD simulations. We have not considered 2D simulations with the axi-symmetric assumption, as it has been generally accepted that the unphysical accumulation of particles along the axis prevails in such unsteady flow simulations. As far as the axial profile of the pressure gradient (which is equivalent to the apparent voidage or solids holdup) is concerned, differences between 2D and 3D numerical simulations are obvious even for the perfectly axi-symmetric system. The 2D simulation can hardly reproduce the same quantitative results as the 3D simulation in any of the representative cases we have looked at, even though for some cases the 2D simulations compare more favorably with the experimental data than the 3D simulations. This suggests that the axial profile of the pressure gradient alone may not be enough for validating a numerical simulation. In this section, the reasons for the differences between 2D and 3D simulations are discussed briefly. First of all, the 2D flow assumption confines the inherent 3D gas– solids flow within a plane that alters the flow characteristics, as no riser system has a real 2D flow, especially in the transient sense. Even a perfectly designed axi-symmetric cylindrical system has significant angular movements, which apparently cannot be captured in a 2D simulation. To demonstrate this, contributions from each velocity component to the kinetic energy of the solids phase are evaluated as r x ¼ Kx=ðKx þ Ky þ KzÞ
ð1Þ
r y ¼ Ky=ðKx þ Ky þ KzÞ
ð2Þ
r z ¼ Kz=ðKx þ Ky þ KzÞ
ð3Þ
where, Kx, Ky, and Kz are contributions due to the velocity component in the X, Y, and Z direction, respectively. Fig. 14 presents the ensemble average of rx, ry, and rz over 100 samples within 6 s along X–Z slice plane for Case 3. The contribution from the vertical particle velocity dominates
the solid phase kinetic energy due to the strong gas flow in that direction. The contribution from the velocity component in the Y direction, which is the third direction of the X–Z plane, is significant, especially close to the wall. This is physically consistent: as the radial velocity goes to zero, to conserve continuity, the fluid or solids have to flow along the other two directions to compensate. Thus, the angular (circumferential) velocity is not negligible compared to the radial velocity. A 2D numerical simulation is not capable of accurately accounting for the 3D effects resulting from the boundary conditions imposed by the geometry of the column wall, and the flow can only vary in the axial direction, thus having a far greater amplification of the boundary effect on the axial flow. In addition, the 2D simulation is not capable of predicting the differences between risers with square and circular cross-sections. Secondly, it is tricky to impose correct inlet and outlet boundary conditions for 2D simulations, as they are not accurately accounted. In riseronly simulations, correct boundary conditions–including the gas flow rate and the solids circulation rate–need to be specified for the simulation. Usually, the inflow boundary conditions are set based on the solids mass flux inside the riser. Without careful consideration of the inlet and outlet configuration and geometry (and hence the boundary conditions), the flow behavior in the inflow and outflow regions are not captured properly, and that could affect the flow behavior in the entire unit. For example, imposed symmetric inflow and outflow boundaries are widely used in 2D simulations. However, this configuration cannot predict the significant asymmetry of void fraction, particle velocity, and solids flux near the top of the riser because of the lateral motion of gas particles as they approach the exit. Nor can this configuration predict the significant asymmetry due to the reentry of circulated solids from one side at the bottom in most systems [39]. Finally, it is not straightforward to compare numerical results, such as the axial pressure gradient and the radial solids concentration, from
Fig. 14. Distribution of b Kx/(Kx + Ky + Kz)N, bKy/(Kx + Ky + Kz)N, and b Kz/(Kx + Ky + Kz) N along the X–Z plane of Case 3 (The slice plane has been stretched in the diameter direction for presentation).
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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a 2D simulation to the experimental data measured in a 3D cylindrical column. Given the same lateral/radial profile of solids concentration in a 2D Cartesian simulation and a 3D cylindrical simulation, the crosssectional average quantities are quite different. To demonstrate this, a widely used correlation for radial voidage distribution in CFB risers by Zhang et al. [40] is used here: ε ¼ ε½
0:191þðr=RÞ2:5 þ3ðr=RÞ11
ð4Þ
In this correlation, the local voidage, ε, in the fully developed region of a riser is a function of the normalized radial position, r/R, based solely upon the cross-sectional average voidage, ε. The average cross sectional solids holdup obtained by integrating the above equation is different for planar and cylindrical columns, as shown in Fig. 15. This influence has to be considered when quantitative validation of the 2D simulation against experimental data is carried out [41]. On the other hand, with the same cross-sectional average solids holdup, the radial profiles are quite different for 2D and 3D simulations, as already shown in Fig. 11(a). By comparing the ratio of wall area to the volume of cylindrical columns to that of a 2D configuration, the 2D simulations inherently underestimate the wall effects that are usually important in lab-scale riser flows. Considering the wall effect on clustering behavior, it is expected that the 2D simulation predicts more uniform radial profiles of solids concentration than the 3D simulation of a cylindrical gas–solids system, as already shown above. Given the aforementioned paradox, it is not possible for the 2D simulations to match both the axial profile of the pressure gradient and the radial profile of voidage at the same time. A similar issue persists when one compares the radial solids mass flux profile predicted by a 2D simulation to the experimental measurement from a cylindrical column. To demonstrate this, it is assumed that the solids circulation rates are the same for simulation and measurement. This is true for simulations with solids inflow boundary condition determined from the solids circulation rate. For certain simulations [22,36], a fixed solids inventory estimated based on the experimental pressure drop is used, hence the solids circulation rate is the critical parameter for the CFD to match the experiment. Given this assumption, it is unlikely to get a comparable mass flux distribution from 2D simulations to a 3D system, noting the fact that solids circulation rates differ to a certain extent when integrating a typical solids flux profile (with high up-flux in the central region and strong back-flux close to side walls) over the cross-sections of 2D and 3D cylindrical columns. Bearing in mind the close relationship among solids concentration, solids velocity, and solids mass flux, it is doubtful that the 2D simulations can have a good prediction of solids velocity in cylindrical risers.
9
4. Conclusion In this paper, differences between 2D and 3D numerical simulations of CFB risers are evaluated for CFB risers with rectangular cross-sections and circular cross-sections. In general, different arrangements of inlet and outlet and various flow conditions are investigated for the cylindrical columns. Significant differences between 2D and 3D numerical simulations with comparable grid sizes have been observed for all the cases with respect to axial profiles of pressure gradient. Radial distributions of certain flow field variables, including solids concentration and velocity, are further compared. Again, the quantitative differences between 2D and 3D simulations are significant. The 2D flow assumption does not work well for all systems considered in the current study. Reasons for the differences between 2D and 3D simulations are discussed accordingly. As an overall conclusion, the 3D numerical simulation is needed to accurately capture the quantitative flow behavior in CFB risers. The 2D numerical simulation can only be used as an effective tool for qualitative studies. Nomenclature ε r R K Ug Gs
Voidage Radial distance Column radius Kinetic energy Superficial gas velocity Solids circulation rate
– m m J m/s kg/s
Acknowledgment 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 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
Fig. 15. Cross-sectional averaged solids holdup calculated from Zhang et al.'s correlation for radial voidage distribution by integrating over 2D planar column and 3D cylindrical column.
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Powder Technology journal homepage: www.elsevier.com/locate/powtec
Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations☆ Tingwen Li a,b,⁎, Sreekanth Pannala c, Mehrdad Shahnam a a b c
National Energy Technology Laboratory, Morgantown, WV, 26507, USA URS Corporation, Morgantown, WV 26507, USA Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
a r t i c l e
i n f o
Available online 13 January 2014 Keywords: Computational fluid dynamics Numerical simulation Circulating fluidized bed Gas–solids flow Riser flow Pressure drop
a b s t r a c t Two-dimensional (2D) numerical simulations have been widely reported in the literature for qualitative, even quantitative, study of the complex gas–solids flow behavior in circulating fluidized bed (CFB) risers. It is generally acknowledged that there exist quantitative differences between 2D and three-dimensional (3D) numerical simulations. However, no detailed study evaluating such differences can be found for simulations of CFB risers. This paper presents 2D and 3D numerical simulations of three different CFB risers. Axial pressure gradients from both 2D and 3D simulations are compared with the experimental data. It has been clearly demonstrated that the 2D simulation cannot satisfactorily reproduce the 3D simulation results. A further comparison of radial profiles of void fraction and solids velocity for an axi-symmetric riser configuration is reported and the quantitative differences between 2D and 3D simulations are analyzed. In conclusion, 2D simulation is only recommended for qualitative evaluation and 3D modeling is recommended for predictive simulations. © 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). However, the complex gas– solids flow behavior inside CFBs coupled with the heat and mass transfer across the phases, along with chemical reactions challenges the design and operation of these industrial systems. A thorough understanding of hydrodynamics inside a CFB is needed. With the fast development of high-speed computers and computational algorithms, computational fluid dynamics (CFD) modeling has become an effective tool to improve our understanding of complex multiphase flows and it Abbreviations: 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; MP-PIC, Multi-Phase Particle-inCell; MFIX, Multiphase Flow with Interphase eXchanges; NETL, National Energy Technology Laboratory; PSRI, Particulate Solid Research Inc.; TFM, two-fluid model; UDF, User Defined Function. ☆ 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) 115–124 DOI of original article: http://dx.doi.org/10.1016/j.powtec.2014.01.022. ⁎ Corresponding author at: National Energy Technology Laboratory, Morgantown, WV, 26507, USA. Tel.: +1 304 285 4538. E-mail addresses: [email protected], [email protected] (T. Li).
currently plays an important role in the design and optimization of industrial systems. With advanced predictive models for reacting multiphase flows, CFD can greatly accelerate the entire reactor development process with enhanced confidence levels and better performance. One limitation of CFD modeling of CFB systems is the expensive computational cost required by the unsteady and highly coupled multi-scale characteristics of gas–solids flows. Various methods have been introduced to reduce the computational load and accelerate the simulations for gas–solids systems from both the model and computational domain perspectives as summarized in Part I [1]. One widely used assumption of CFB riser simulations is the two-dimensional flow assumption in which a cut-plane along the axis of the cylindrical column is used. A two-dimensional numerical simulation works reasonably well for a fundamental study and has wide applications for gas–solid flow study in the literature. Nowadays, three-dimensional simulations of CFB riser have become more and more affordable with the continuous advances in computational hardware. It is then of great interest to quantify the errors associated with assumptions in CFD simulations, especially the widely used 2D flow assumption. The differences between 2D and 3D simulations of gas–solids fluidized beds have been discussed in several papers. Peirano et al. [2] compared 2D and 3D simulations of bubbling fluidized beds and concluded that 2D simulations should be used with caution and only for sensitivity analysis, whereas 3D simulations are able to reproduce both the stationary statistics and the dynamics of the system. Cammarata et al. [3] carried out both 2D and 3D CFD simulations of bubbling fluidized beds and suggested that 3D simulations should be preferable for validating the CFD models with available correlations and experimental data. Xie
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Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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et al. [4] investigated the range of validity for employing simulations based on a 2D Cartesian coordinate system to approximate both cylindrical and rectangular fluidized beds. The results of three different fluidization regimes–bubbling, slugging, and turbulent–demonstrated that a 2D Cartesian system can be used to successfully simulate and predict a bubbling regime where the superficial velocity is close to the minimum fluidization velocity. However, caution must be exercised when using the 2D Cartesian simulation for other fluidized regimes. A budget analysis that explains all the differences in detail was presented by Xie et al. [5] showing the role of third direction that is not resolved in 2D simulations. Reuge et al. [6] also studied the differences between 3D simulations and 2D axi-symmetric and Cartesian simulations. Their results again indicated that 3D simulations are necessary for correctly reproducing the experimental bed expansions and heights of fluctuation of a bubbling fluidized bed, while the 2D simulations widely overestimated both quantities. The 2D Cartesian calculations showed better agreement with the experiments and the 3D simulation than the 2D axi-symmetric calculations, but they still significantly overestimated the bed expansions and heights of fluctuation. Significant quantitative differences between 2D and 3D simulations on bed expansion, solids concentration, and gas and solids velocities were also reported by Li et al. [7] in a CFD study of gas mixing in fluidized beds. Similar differences in flow hydrodynamics were observed by Liu et al. [8] even though the mixing extent predicted by the 2D simulation is quantitatively similar to the 3D results. Li et al. [9] further reported that significant differences existed between 2D and 3D simulations with respect to bed expansion, bubble distribution, and void fraction and solids velocity profiles for a bubbling fluidized bed with submerged horizontal tube bundle. According to the work by Li et al. [10,11]., 2D simulation can neither be used to accurately simulate a 3D system nor a pseudo-2D system. Unfortunately, all of the above work focuses on relatively low-gas velocity fluidization regimes. Not many comparisons between 2D and 3D simulations of CFB riser can be found in the literature, despite the wide application of 2D assumptions in riser-flow simulations and the generally acknowledged limitation of 2D modeling. Li et al. [12] reported both 2D and 3D numerical simulations of a well-documented CFB riser with a square cross-section. It was found that 2D simulations under-predicted the solids inventory even with the finest grid (10-particle-diameter grid size). On the other hand, a 3D simulation with a relatively coarse grid was found to be in much better agreement with the experimental data. The objective of this study is to document some of the differences between 2D and 3D gas–solids flow simulations so that one can adopt the best practices. In this part of the work, we focus on the differences between 2D and 3D numerical simulations of CFB riser. For this purpose, we carry out a detailed analysis of the differences between 2D and 3D simulations of CFB risers to further the investigation of Li et al. [12]. Three cases of CFB riser simulations with different system configurations and operating conditions are considered in the current study, representing a wide variety of applications. Comparison between 2D and 3D simulations, as well as available experimental data for the axial profile of the pressure gradient, is reported for each case. Further comparison of radial profiles of void fraction and solids velocity is made for a particular case. Finally, a deliberate analysis is presented to address the inherent differences between 2D and 3D simulations.
on the model equations and the numerical implementation, can be found at the MFIX website, https://mfix.netl.doe.gov. There is an option to use the Lagrangian–Eulerian (LE) approach in MFIX [16,17], but that was not exercised in this study because with typical CFBs the LE approach is still computationally prohibitive. In addition, the commercial CFD software-ANSYS FLUENT is employed to simulate one case of gas– solids flow in an axi-symmetric riser. Similar Eulerian–Eulerian approach based on the granular kinetic theory is utilized. Detailed information on model equations solved in FLUENT can be found in the ANSYS FLUENT theory guide [18]. For all cases, both 2D and 3D simulations with identical numerical parameters and equivalent flow conditions were conducted. For brevity, additional details on numerical models as well as some grid studies are not provided here but can be found in Part I of this paper [1]. 2.1. Case 1: CFB riser with a square cross-section The first test case is based on a well-documented experiment of a circulating fluidized bed with a square cross-section as shown in Fig. 1 [19,20]. The CFB riser has a cross sectional dimension of 146 × 146 mm and total height of 9.14 m. Sand with mean diameter and density of 213 μm and 2640 kg/m3 respectively and loosely packed bed void fraction of 0.43 is used as the bed material. In this study, a superficial gas velocity of 5.5 m/s and a solids circulating flux of 40 kg/m2s are considered. As schematically shown in Fig. 2, a 2D simulation of the central symmetric plane aligned with the inlet and outlet and a full 3D simulation of the riser section are conducted with MFIX. Based on the 2D grid study reported in Part I, 2D and 3D simulations with grid resolutions of 30 × 456 and 30 × 30 × 456, respectively, are compared here. Detailed information on the numerical settings and simulation setup has been reported by Li et al. [12].
2. Numerical tests and simulation results The numerical simulations were mainly conducted with the opensource software, Multiphase Flow with Interphase eXchanges (MFIX), developed at the National Energy Technology Laboratory (NETL). In MFIX, a multi-fluid, Eulerian–Eulerian approach is used, with each phase treated as an interpenetrating continuum. Mass and momentum conservation equations are solved for the gas and solids (particulate) phases, with appropriate closure relations [13–15]. Constitutive relations derived from granular kinetic theory are used for the solids phase. More information on MFIX, as well as detailed documentation
Fig. 1. Schematic of the CFB system reported by Zhou et al. [19,20].
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Detailed comparisons between numerical results and experimental data on vertical and lateral voidage distributions and solids velocity profiles have been reported elsewhere [12]. In addition to the significant difference between 2D and 3D predictions of pressure gradients and solids inventory, it has been found that the lateral void fraction distributions for 2D and 3D simulations (not shown here) differ substantially even though both qualitatively capture the core-annulus flow. It can be concluded from this case that the 3D geometry is a basic requirement to accurately simulate a CFB riser with a rectangular cross-section with asymmetrical inlet and outlet. Although the 3D simulation yields much better agreement with the experimental measurements than the 2D simulation, there are still differences between experimental data and the 3D numerical predictions. One possible reason for this discrepancy is the grid resolution might not be sufficient to reach the grid independent results for 3D simulation even though the same grid size for 2D simulation yields a reasonably grid-independent pressure gradient in the main riser section as discussed in Part I. Unfortunately, no grid study is performed for the 3D simulation. The unresolved structures by the coarse grid usually lead to over-prediction of interphase drag hence under-prediction of solids holdup and pressure gradient [21,22]. Further grid refinement or an appropriate sub-grid model for coarse-grid simulation is needed to address this issue. Another possible reason for the discrepancy is the simplification of the solids inlet and outlet configurations. 2.2. Case 2: NETL B22 CFB riser
Fig. 2. Schematics of 2D and 3D simulations of CFB riser with a square cross-section.
The axial pressure gradient is one of the most common measurements from experiment and based on which the axial distribution of solids is typically obtained. Furthermore, the solids inventory can be estimated through the overall pressure drop across the riser. Fig. 3 shows the axial profiles of pressure gradient predicted by 2D and 3D simulations. As shown in Fig. 3, there are significant differences between 2D and 3D results. The 2D simulation predicts a much lower pressure gradient throughout the riser, indicating a lower solids inventory inside the system compared to that of the 3D simulation. The solids inventories were calculated as the integral of the solids volume fraction over the whole riser, and the prediction of the 3D simulation is 7 times greater than the 2D simulation. The main reason for this difference is believed to be related to the 3D effects of system geometry and flow behavior.
Fig. 3. Axial profiles of pressure gradient predicted by 2D and 3D simulations as well as estimated from the experimental data of apparent voidage (Experimental data from Zhou et al., 1995).
In the second test case, NETL's pilot-scale B22 CFB riser, which is 0.305 m in diameter and 16.8 m tall, is simulated. A schematic of the whole CFB system is given in Fig. 4 [23]. Two types of particles, belonging to Geldart groups A and B, respectively, are simulated: glass beads (59 μm diameter and density of 2425 kg/m3) and high-density polyethylene (HDPE) beads (800 μm diameter and density of 863 kg/m3). For this system, detailed experimental data on pressure fluctuations, pressure gradient, solids mass flux, and solids velocity are available for both types of particles under different operational conditions. The original experimental data were collected for the third challenge problem for CFD simulation organized by NETL and PSRI [23,24]. The experimental data were released at the 2010 AIChE annual conference [25]. A complete description of the experimental facility, along with process instrumentation and detailed experimental data, can be accessed from the MFIX website at https://mfix.netl.doe.gov/challenge/index.php. Only the riser along with small sections of the inlet and outlet was simulated for this system. Fig. 5 depicts the 2D and 3D simulation configurations of NETL B22 CFB riser. The Cartesian grid method implemented in MFIX by Dietiker [26] has been used to simulate the cylindrical riser and a small section of the side inlet and outlet as shown in Fig. 5. The sliced symmetric plane aligned with the side inlet and outlet is used for the 2D simulation. A uniform grid with a grid size of 1.6 cm, which corresponds to the coarse grid reported in Part I, is used for both 2D and 3D simulations. Two cases are studied in this work: one case with group A particles with a solids circulation rate of 9.26 kg/s and a superficial gas velocity of 5.14 m/s and the second case with group B particles with a solids circulation rate of 14 kg/s and a superficial gas velocity of 7.58 m/s. The superficial gas velocities are based on the flow conditions measured at the bottom distributor. The simulations were conducted for more than 50 seconds of real time. To ensure the initial transient effects are not included in the analysis, only the last 30 seconds of the simulations are used for extracting the mean flow field information. Full details on the numerical simulation setup were reported by Li et al. [27]. Fig. 6 shows the axial profiles of pressure gradients predicted by both 2D and 3D simulations along with the data measured in several repeated experiments for the two cases under consideration. The 3D simulations predict high-pressure gradients in the bottom and top regions of the riser, where the side inlet and the T-shaped abrupt exit effects
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 4. Schematic of the NETL pilot-scale CFB system (Shadle et al., 2010b).
dominate [28]. However, the 2D simulations cannot capture this behavior for both cases. In addition, the 2D simulations significantly overpredict the pressure gradient in the major section of the riser compared to the 3D simulations. Although the agreement between the measured and 3D-predicted pressure gradient is very good for the case of group B particles (Fig. 6b), the same is not true for the group A particles (Fig. 6a). This can be attributed to the coarse grid resolution used in the present study and its inability to capture the small-scale clustering associated with group A particles. According to the grid study of 3D
simulations reported in Part I, the grid size of 1.6 cm is fine enough for the larger group B particles, but is too coarse for the smaller group—A particles. For group B particles, good agreement has also been observed between 3D numerical predictions and experimental data for pressure gradients for the other operating conditions [27]. In addition, a quantitative comparison between numerical results and experimental data with respect to radial profiles of solids velocity and solids mass flux at various elevations has been made, and a reasonably good agreement has been obtained for this case [27]. To overcome the high-computational cost of
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 5. Schematics of 2D and 3D simulations of NETL CFB riser.
fine grid simulations, appropriate sub-grid closure models are suggested for a coarse grid simulation to account for the unresolved small-scale structures [29,30]. The constitutive sub-grid models proposed by Igci and Sundaresan [31] has been implemented in MFIX and applied to the present geometry. The simulation results will be reported in a separate manuscript. Comparisons of the mean void fraction distribution from both 2D and 3D simulations are shown in Fig. 7. For the ease of presentation, the height of the riser is scaled down by a factor of 5. As shown in Fig. 7, in 2D simulations, particles migrate to the side wall adjacent to the side inlet and then gradually accumulate towards the opposite side for group A particles; and for group B particles, the behavior is just the opposite. On the other hand, a good symmetrical flow behavior is predicted by the 3D simulation in most regions of the riser except for the bottom and top regions where the effects of the side inlet and exit dominate. Furthermore, the cross-sectional plots of void fraction and solids velocity distributions in the fully developed region (not shown here) confirm the good axi-symmetric flow behavior predicted by the 3D simulations. The experimental data also shows similar axisymmetric flow behavior in most riser sections and thus the 3D simulations are more reasonable than 2D simulations even qualitatively. The asymmetric flow behavior in the fully developed region of the riser in the 2D simulation is attributed to the predicted poor mixing behavior in the solids inlet region. For 2D simulations, a two-inlet configuration is required in order to achieve a symmetric flow prediction, as suggested by Benyahia et al. [32], which can be found in many numerical simulations. This approach remedies the asymmetric issue of 2D simulations in the fully developed region. However, it cannot be used to study the effect of the inlet and outlet in most systems, which usually have a single inlet and outlet on one side. To demonstrate this, the axial pressure gradient profile predicted by the 2D simulation with a symmetric twoinlet and two-outlet configuration, referred to as configuration C in Part I, is compared against the 3D result and experimental data in Fig. 8. As can be seen from the comparison, the symmetric inlet and outlet configuration predicts better agreement to the 3D results and experimental
Fig. 6. Axial profiles of pressure gradient predicted by 2D and 3D simulations as well as experimental data for (a) group A particle (Gs = 9.26 kg/s and Ug = 5.14 m/s); (b) group B particles (Gs = 14 kg/s and Ug = 7.58 m/s).
data in the middle region of riser but quite different results in the lower and upper regions. 2.3. Case 3: Malcus et al.'s CFB riser The CFB riser used by Malcus et al. [33] has been selected as the third test case, since the system configuration and flow behavior are symmetric. The cold-flow CFB apparatus consists of a 7 m tall riser with an inner diameter of 0.14 m and a smooth exit at the top. To ensure symmetrical solids flow behavior in the experimental system, particles are introduced into the system through eight annular orifices at the bottom of the riser. FCC particles with a particle density of 1740 kg/m3 and a mean diameter of 89 μm were used. Measurements of apparent void fraction and radial distribution of solids concentration for different operational conditions were reported by Malcus et al. [33]. The commercial CFD software ANSYS FLUENT is used to simulate Case 3. The schematic for both 2D and 3D simulations is shown in Fig. 9. To achieve uniform solids feeding along the circumferential direction, a ring type of solids inlet is used in the 3D simulation instead of eight equally spaced orifices used in the experimental system. The smooth top exit is further simplified as a straight top exit to ensure the axi-symmetry in geometry. Those simplifications are employed deliberately to guarantee a perfect axi-symmetric system configuration in the 3D simulation, which will be compared to the 2D simulation. The computational domain for 2D and 3D simulations are discretized by 10 K and 185 K cells, respectively, with comparable grid sizes. No grid study is conducted for this case. Only one set of flow conditions with a solids circulation rate of 4.65 kg/s (solids mass flux of 302 kg/m2s) and a superficial gas velocity of 4.7 m/s is simulated. As no clear indication can be found on how the superficial gas velocity was determined in the experiment, the superficial gas velocity here is based on the ambient conditions at the top exit. The uncertainty in the superficial velocity
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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Fig. 7. Mean voidage distributions predicted by 2D and 3D simulations (a) group A particles (Gs = 9.26 kg/s and Ug = 5.14 m/s); (b) group B particles (Gs = 14 kg/s and Ug = 7.58 m/s).
might affect the comparison between the experimental data and simulation results [34], but it should have no impact on the direct comparison between 2D and 3D simulations. Again, all simulations have been monitored to run long enough for stationary state analysis. Fig. 10 shows the axial profiles of pressure gradient predicted by the 2D and 3D numerical simulations as well as the experimental pressure gradient (calculated from the apparent axial solids concentration as reported by Malcus et al. [33]). The 2D simulation predicts a drastically different profile compared to that of the 3D simulation, although the perfect axi-symmetry in the system geometry and operational condition is maintained. As a simplification of the 3D system, the 2D simulation does not yield satisfactory agreement with the 3D simulation even though it exhibits better agreement with the experimental measurement towards the top region of the riser. The poor agreement between the 3D simulation and the experimental data is mainly attributed to the insufficient grid resolution used for the fine FCC particles. In addition, the differences in the bottom zone can be attributed to the simplified ring-type annular solids feeder used in the 3D simulation, which cannot capture the strong solids mixing caused by solids jets through dispersed orifices. Simplification to the smooth top exit could also have some effect on the flow behavior.
Fig. 8. Axial profiles of pressure gradient predicted by the 2D simulation with symmetric inlet and outlet configuration and 3D simulation as well as experimental data for group B particles (Gs = 14 kg/s and Ug = 7.58 m/s).
Fig. 11 presents the radial profiles of mean solids concentration and vertical solids velocity at a height of 2.1 m above the distributor. Both numerical results show very good symmetry with respect to the central axis, which is consistent with the experimental measurements. At that height, the cross-sectional averaged solids concentrations of 0.108 and 0.109 for 2D and 3D simulations, respectively, under-predict the cross-sectional averaged solids concentration of 0.17 as estimated from the pressure gradient or 0.2 as from the ECT measurements.
Fig. 9. Schematics of 2D and 3D simulations of Malcus et al.'s CFB riser.
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
T. Li et al. / Powder Technology xxx (2014) xxx–xxx
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Fig. 10. Axial profiles of pressure gradient predicted by 2D and 3D simulations along with the experimental data.
Fig. 12. Axial profiles of pressure gradient predicted by 2D and 3D simulations with filtered model and experimental data.
Even though the cross-sectional averaged solids concentrations of 2D and 3D simulations at the height of 2.1 m are close to each other, the discrepancy between the radial profiles of solids concentration as presented in Fig. 11(a) is not negligible. The 2D simulation predicts a more uniform radial solids concentration profile than the 3D simulation. Compared to the experimental data obtained using ECT, along two orthogonal directions, the radial variation of solids concentration as captured by the 3D simulation shows better agreement despite the fact that the 2D results have better quantitative agreement in the central core region. The difference in the solids velocity is more pronounced, as can be seen in Fig. 11(b). The 2D simulation predicts significant downward velocity close to the wall, which is absent in the 3D simulation. Those differences are believed to be inherent in the 2D simplification of the cylindrical domain and will be discussed in next section.
As mentioned above, most simulations of CFB systems with Group A particles suffer from insufficient grid resolution, which fail to resolve the particle clustering and subsequent drag reduction. Several sub-grid closure models have been proposed for a coarse grid simulation in order to account for the unresolved small-scale structures [31,35,36]. It should be noted that the objective of this study is to document the differences between 2D and 3D simulations of CFB risers with comparable grid sizes. The experimental data are only shown for reference and differences between numerical predictions and experimental measurements are not of primary concern. However, to support the above analysis regarding the discrepancy between numerical simulation and experimental data, a sub-grid model was tested in the current study. The filtered two-fluid model proposed by Igci and Sundaresan [31] was implemented into both 2D and 3D simulations through User Defined Function (UDF) with appropriate wall corrections, as reported by Igci and Sundaresan [37] and Igci et al. [38]. For brevity, details of the filtered two-fluid model are not reported here. Numerical results on the axial pressure gradient and the radial solids concentration distribution are compared against the experimental data in Figs. 12 and 13, respectively. As can be seen from these figures, better agreement between the numerical simulation and experimental data exists for the 3D simulation after accounting for the effect of unresolved clusters through the filtered model. 3. Further discussion So far, differences between 2D and 3D simulations of CFB risers with rectangular and circular cross-sections are presented mainly with respect to the axial profile of pressure gradient, which is one of the most common measurements reported in most CFB experiments and is
Fig. 11. Radial profiles of mean (a) solids concentration and (b) vertical solids velocity at the height of 2.1 m.
Fig. 13. Radial profiles of mean solids concentration predicted by 2D and 3D simulations with filtered model at the height of 2.1 m.
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
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extensively used to validate CFD simulations. We have not considered 2D simulations with the axi-symmetric assumption, as it has been generally accepted that the unphysical accumulation of particles along the axis prevails in such unsteady flow simulations. As far as the axial profile of the pressure gradient (which is equivalent to the apparent voidage or solids holdup) is concerned, differences between 2D and 3D numerical simulations are obvious even for the perfectly axi-symmetric system. The 2D simulation can hardly reproduce the same quantitative results as the 3D simulation in any of the representative cases we have looked at, even though for some cases the 2D simulations compare more favorably with the experimental data than the 3D simulations. This suggests that the axial profile of the pressure gradient alone may not be enough for validating a numerical simulation. In this section, the reasons for the differences between 2D and 3D simulations are discussed briefly. First of all, the 2D flow assumption confines the inherent 3D gas– solids flow within a plane that alters the flow characteristics, as no riser system has a real 2D flow, especially in the transient sense. Even a perfectly designed axi-symmetric cylindrical system has significant angular movements, which apparently cannot be captured in a 2D simulation. To demonstrate this, contributions from each velocity component to the kinetic energy of the solids phase are evaluated as r x ¼ Kx=ðKx þ Ky þ KzÞ
ð1Þ
r y ¼ Ky=ðKx þ Ky þ KzÞ
ð2Þ
r z ¼ Kz=ðKx þ Ky þ KzÞ
ð3Þ
where, Kx, Ky, and Kz are contributions due to the velocity component in the X, Y, and Z direction, respectively. Fig. 14 presents the ensemble average of rx, ry, and rz over 100 samples within 6 s along X–Z slice plane for Case 3. The contribution from the vertical particle velocity dominates
the solid phase kinetic energy due to the strong gas flow in that direction. The contribution from the velocity component in the Y direction, which is the third direction of the X–Z plane, is significant, especially close to the wall. This is physically consistent: as the radial velocity goes to zero, to conserve continuity, the fluid or solids have to flow along the other two directions to compensate. Thus, the angular (circumferential) velocity is not negligible compared to the radial velocity. A 2D numerical simulation is not capable of accurately accounting for the 3D effects resulting from the boundary conditions imposed by the geometry of the column wall, and the flow can only vary in the axial direction, thus having a far greater amplification of the boundary effect on the axial flow. In addition, the 2D simulation is not capable of predicting the differences between risers with square and circular cross-sections. Secondly, it is tricky to impose correct inlet and outlet boundary conditions for 2D simulations, as they are not accurately accounted. In riseronly simulations, correct boundary conditions–including the gas flow rate and the solids circulation rate–need to be specified for the simulation. Usually, the inflow boundary conditions are set based on the solids mass flux inside the riser. Without careful consideration of the inlet and outlet configuration and geometry (and hence the boundary conditions), the flow behavior in the inflow and outflow regions are not captured properly, and that could affect the flow behavior in the entire unit. For example, imposed symmetric inflow and outflow boundaries are widely used in 2D simulations. However, this configuration cannot predict the significant asymmetry of void fraction, particle velocity, and solids flux near the top of the riser because of the lateral motion of gas particles as they approach the exit. Nor can this configuration predict the significant asymmetry due to the reentry of circulated solids from one side at the bottom in most systems [39]. Finally, it is not straightforward to compare numerical results, such as the axial pressure gradient and the radial solids concentration, from
Fig. 14. Distribution of b Kx/(Kx + Ky + Kz)N, bKy/(Kx + Ky + Kz)N, and b Kz/(Kx + Ky + Kz) N along the X–Z plane of Case 3 (The slice plane has been stretched in the diameter direction for presentation).
Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007
T. Li et al. / Powder Technology xxx (2014) xxx–xxx
a 2D simulation to the experimental data measured in a 3D cylindrical column. Given the same lateral/radial profile of solids concentration in a 2D Cartesian simulation and a 3D cylindrical simulation, the crosssectional average quantities are quite different. To demonstrate this, a widely used correlation for radial voidage distribution in CFB risers by Zhang et al. [40] is used here: ε ¼ ε½
0:191þðr=RÞ2:5 þ3ðr=RÞ11
ð4Þ
In this correlation, the local voidage, ε, in the fully developed region of a riser is a function of the normalized radial position, r/R, based solely upon the cross-sectional average voidage, ε. The average cross sectional solids holdup obtained by integrating the above equation is different for planar and cylindrical columns, as shown in Fig. 15. This influence has to be considered when quantitative validation of the 2D simulation against experimental data is carried out [41]. On the other hand, with the same cross-sectional average solids holdup, the radial profiles are quite different for 2D and 3D simulations, as already shown in Fig. 11(a). By comparing the ratio of wall area to the volume of cylindrical columns to that of a 2D configuration, the 2D simulations inherently underestimate the wall effects that are usually important in lab-scale riser flows. Considering the wall effect on clustering behavior, it is expected that the 2D simulation predicts more uniform radial profiles of solids concentration than the 3D simulation of a cylindrical gas–solids system, as already shown above. Given the aforementioned paradox, it is not possible for the 2D simulations to match both the axial profile of the pressure gradient and the radial profile of voidage at the same time. A similar issue persists when one compares the radial solids mass flux profile predicted by a 2D simulation to the experimental measurement from a cylindrical column. To demonstrate this, it is assumed that the solids circulation rates are the same for simulation and measurement. This is true for simulations with solids inflow boundary condition determined from the solids circulation rate. For certain simulations [22,36], a fixed solids inventory estimated based on the experimental pressure drop is used, hence the solids circulation rate is the critical parameter for the CFD to match the experiment. Given this assumption, it is unlikely to get a comparable mass flux distribution from 2D simulations to a 3D system, noting the fact that solids circulation rates differ to a certain extent when integrating a typical solids flux profile (with high up-flux in the central region and strong back-flux close to side walls) over the cross-sections of 2D and 3D cylindrical columns. Bearing in mind the close relationship among solids concentration, solids velocity, and solids mass flux, it is doubtful that the 2D simulations can have a good prediction of solids velocity in cylindrical risers.
9
4. Conclusion In this paper, differences between 2D and 3D numerical simulations of CFB risers are evaluated for CFB risers with rectangular cross-sections and circular cross-sections. In general, different arrangements of inlet and outlet and various flow conditions are investigated for the cylindrical columns. Significant differences between 2D and 3D numerical simulations with comparable grid sizes have been observed for all the cases with respect to axial profiles of pressure gradient. Radial distributions of certain flow field variables, including solids concentration and velocity, are further compared. Again, the quantitative differences between 2D and 3D simulations are significant. The 2D flow assumption does not work well for all systems considered in the current study. Reasons for the differences between 2D and 3D simulations are discussed accordingly. As an overall conclusion, the 3D numerical simulation is needed to accurately capture the quantitative flow behavior in CFB risers. The 2D numerical simulation can only be used as an effective tool for qualitative studies. Nomenclature ε r R K Ug Gs
Voidage Radial distance Column radius Kinetic energy Superficial gas velocity Solids circulation rate
– m m J m/s kg/s
Acknowledgment 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 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
Fig. 15. Cross-sectional averaged solids holdup calculated from Zhang et al.'s correlation for radial voidage distribution by integrating over 2D planar column and 3D cylindrical column.
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Please cite this article as: T. Li, et al., Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations, Powder Technol. (2014), http://dx.doi.org/10.1016/j.powtec.2014.04.007