Generalized Fluidization - ACS Publications - American Chemical

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“Generalized Fluidization” Revisited Atta Ullah,†,‡ Wei Wang,†,* and Jinghai Li† †

The EMMS Group, State Key Laboratory of Multiphase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ‡ Graduate University of Chinese Academy of Sciences, Beijing, 100049, China ABSTRACT: The generalized fluidization diagram was drawn by Kwauk [Scientia Sinica, 1963, 12 (4), 587−612] and Kwauk [Science Press, Beijing: 1992] for fluidization under steady-state motion. In this article, we try to extend the work of Kwauk and redraw the diagram by taking into account the effects of mesoscale structures on drag force closure. The generalized choking is then defined on the new diagram, which is characterized by the bistable, coexisting states in both concurrent and countercurrent flows. The theoretical predictions are tested against experimental data, showing fair agreement especially for countercurrent gasup flows and concurrent-down flows. recirculation flux and pressure profile along the whole loop of a CFB carbonator, including the cyclone, down-comer and the loop seal, can be predicted with great accuracy by using EMMS drag correction along with consideration of proper friction forces.19 Further work is, however, needed to generalize this approach. Another traditional yet fundamental approach would be to use the basic, steady-state force balance analysis to grasp how the flow regime transitions are affected by operating conditions, as discussed in the literature.1,20,21 By substituting the relative velocity between particles and fluid for the velocity of classical fluidization, Kwauk1,3 extended the steady-state fluidization diagram to describe the overall field of all possible combinations of particle-fluid motion, including concurrent-up, concurrent-down, countercurrent systems and so on. Such diagram contained classical fluidization curve for which solids velocity is zero. The condition for which both gas and particle velocities were zero, was marked by “fluid at stand still”. The flooding curve was defined by equating the derivative of velocity of either phase with respect to voidage equal to zero, whereas keeping the velocity of the other phase constant. The generalized fluidization diagram by Kwauk was drawn based on correlations for homogeneous fluidization. In recent years, the mesoscale, heterogeneous structure has been widely recognized as the key factor affecting the flow behavior of twophase flow systems. In this article, we try to extend the work of Kwauk by taking into account the effect of heterogeneous structures in force balance analysis, and then redraw the whole realm of generalized fluidization. Physical explanations of the relevant regime transitions are provided. The model predictions are also validated against experimental data.

1. INTRODUCTION The classical fluidized system refers to beds possessing fixed solids inventories, in which the fluid flows upward through and suspends solid particles with negligible entrainment.1 By allowing distinct transport of solid particles, now the realm of fluidization has extended to circulating fluidized bed (CFB), downer, and so on,2 which were termed by Kwauk1,3 as the generalized fluidization. Within a generalized fluidized system, several flow regimes may coexist in different units. For example, around the whole loop of a CFB, the gas and solids experience concurrent-up flow in riser, turbulent vortical flow in cyclone, countercurrent flow with downward solids in downcomer (concurrent-down flow may occur in a downcomer, depending on the separation performance of cyclone), and bubbling or moving bed in loopseal.4,5 The interactions between these units and the transitions between respective flow regimes may cause complex hydrodynamic phenomena and flow instabilities, in which “choking”6 is of great importance to operation and has been extensively discussed in the literature.5,7−12 In a jetting fluidized bed gasifier,13 one can also find coexistent sections under different flow regimes: coal particles are bubbling fluidized in the chamber (i.e., Ug > 0, Gs ≈ 0), whereas the ashagglomerated slag are discharged downward through the central tube against upward flowing gas (i.e., countercurrent flow in discharger, Ug > 0, Gs < 0). In a downer reactor,14,15 likewise, two neighboring zones are interlinked but under different flow regimes: one is the classical bubbling fluidization above the distributor and the other is the concurrent downward flow below the distributor. One can easily find more examples of generalized fluidized systems with multiple flow regimes. In all, the different units of these systems are operated under different flow regimes and their flow behaviors are strongly coupled. To understand their complex flow phenomena and especially their possible flow instabilities, one may carry out three-dimensional, full-loop, computational fluid dynamics (CFD) simulation, which is an emerging approach, though computationally demanding, to investigate comprehensively the whole system instead of any individual unit.16−18 Recently, it has been shown that the © XXXX American Chemical Society

Special Issue: Multiscale Structures and Systems in Process Engineering Received: December 15, 2012 Revised: February 12, 2013 Accepted: February 12, 2013

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dx.doi.org/10.1021/ie3034653 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Figure 1. A generalized fluidization diagram with eq 2 and R-Z exponent n = 4.4 for an air−FCC particle system (dp = 75 μm, ρp = 1500 kg/m3, ρg = 1.3 kg/m3, μg = 1.8 × 10−5Pa·s, ut = 0.2184m/s, Ar = 24.8), which is similar to the results of Kwauk:3 (A) minimum fluidization; (B) free settling; (C) start point of flooding. Ug* = Ug/ut, Us* = Gs/(ρput)).

flows, in which the regime to the left of the dash blue line (Ug = ut) is the restrained concurrent-up flow that exists only with support of the air distributor while to the right is the complete concurrent-up flow. To the left of the classical fluidization line, the solids are transported following the gravity, while the zerogas-velocity line demarcates between the concurrent-down and countercurrent solids-down flows. The flooding line is also drawn in Figure 1 following the definition of Kwauk3 by

2. GENERALIZED FLUIDIZATION DIAGRAM WITH RICHARDSON−ZAKI DRAG For classical fluidization, especially for homogeneously fluidized systems, one may relate the superficial fluid velocity with terminal velocity of single particle by using Richardson−Zaki (R-Z) correlation,22 that is, Ug = εn ut (1)

⎛ ∂Ug ⎞ ⎜ ⎟ =0 ⎝ ∂ε ⎠G

Following the method presented by Kwauk,1,3 we assume that the R-Z correlation still holds true for solids transport systems by replacing superficial fluid velocity with superficial relative velocity. Then, the R-Z correlation can be extended to Ur = εur = utε n

s

A significant character of the flooding line lies in that, in its range of gas velocity (between C and B), and for solidsdownward flows (Gs < 0), there may coexist two states at one specific gas velocity. That is, two ε coexist for a given set of Ug and Gs. In contrast, in the area of concurrent-up flow (to the right of the classical fluidization), there is only one state for any given set of gas and solids velocities. However, as found in experiments of concurrent-up riser flows,9,23,24 there does exist an area with two stable states corresponding to the coexistence of the dilute top and the dense bottom. Such contradiction should be attributed to the use of Richardson-Zaki correlation, which is valid for homogeneous fluidization. To take into account the effect of a heterogeneous structure which is intrinsic in gas−solid flows, in what follows we will rewrite the R−Z relation by incorporating a structure-dependent drag force for redrawing the generalized fluidization diagram.

(2)

where the real relative velocity is given as ur = ug − us =

Ug ε

−

Gs (1 − ε)ρp

(4)

(3)

For a given particle material, the exponent n is an empirical function of Ret.22 Thus, the generalized fluidization diagram can be drawn with eq 2 by first specifying a set of gas and solids velocities, and then calculating voidage as a function of them. Figure 1 gives such a contour with exponent n = 4.4 (air−fluid catalytic cracking (FCC) particle system, dp = 75 μm, ρp = 1500 kg/m3, ρg = 1.3 kg/m3, μg = 1.8 × 10−5Pa·s, ut = 0.2184m/s, Ar = 24.8), which is similar to the diagram of Kwauk3 (for Kwauk’s case, n = 2.36). As presented in Kwauk,3 on the above diagram, one may locate, first, the points of minimum fluidization (point A: Ug = Umf, Gs = 0, ε = εmf) and free settling of single particles (point B: Ug = ut, ε = 1) in blue dots, respectively, then, the line of classical fluidization (solid blue line between A and B: Ug > Umf, Gs = 0), and finally, different flow regimes. The regimes to the right of the classical fluidization line are for concurrent-up

3. GENERALIZED FLUIDIZATION DIAGRAM WITH STRUCTURE-DEPENDENT DRAG The generalized R-Z correlation in eq 2 can be rearranged as a force balance equation between drag force and effective gravity as follows, B


Industrial & Engineering Chemistry Research βRZur ε where

βRZ =

= (1 − ε)(ρp − ρg )g

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dimensional flows and should be more reasonable for idealistic analysis on infinitely big, fluidized beds. To compare with realistic fluidized beds, one should incorporate the EMMS drag with CFD and perform a simulation on a finite-sized domain or reactor. Indeed, the domain size will affect the effect of the drag force in the force balance, as discussed in Appendix A.1. So, it is better to view the analysis and comparison against experiments here as qualitative. Moreover, the EMMS drag does not take into account the effects of such corrections on other kinetic theory closures such as particle stresses, granular temperatures, etc. To make up for these deficiencies, we coupled the EMMS drag correction with kinetic theory descriptions available through periodic domains. Here, the EMMS drag model, which is a function of both voidage and slip velocity, is fed to FLUENT as a UDF. Details on how to obtain the heterogeneity index curve are presented in Appendix A.1. We do not mean that this drag model is quantitatively applicable to all flow regimes of generalized fluidization. In particular, the effect of such a structure-dependent drag model would be influenced by the domain size, as discussed in Appendix A.1, which somewhat reflects the scale-up effect that is a notoriously hard topic to the chemical engineering community. However, we wish to emphasize that studying such a structure-dependent drag model may shed light on the importance of mesoscale structure, and help to find a more general-purpose drag model in future. Redrawing the diagram with eq 7 yields Figure 3, which looks somewhat twisted compared to Figure 1. Again, we can distinguish the points of minimum fluidization and free settling, the line of classical fluidization and different flow regimes. To be more descriptive, we also include several typical reactors as insets. It is to be noted that the maximum superficial gas velocity for the restrained concurrent-up flow is not equal to the terminal velocity. As indicated by the blue dotted line to the right side, it is about 4.7 times the terminal velocity for this case, which is comparable to the reported values of the incipient “transport velocity” (roughly 3.5 to 4 times the terminal velocity30 or around 6.4 times the terminal velocity according to the correlation Utr = 1.53(g(ρp − ρg)dp/ρg)0.5 in the work of Bi et al.31). The most striking difference lies in that Figure 3 predicts two or even three coexistent states in the concurrentup, the countercurrent gas-upward, and the concurrent-down flows. In experiments, there are also reports about two coexistent states and even three coexistent states in gas−solid concurrent-up risers and in countercurrent gas-up flows.8,32−35 These findings induce this revisit to the choking phenomenon, aiming to provide more explanation of the coexistent states on the overall regime of generalized fluidization.

(5)

(1 − ε)(ρp − ρg )g u tε n − 2

(6)

Such a force balance equation assumes the dominant roles of the drag force and gravity, ignoring the other factors such as gas turbulence, gas, and solid phase stresses and wall friction. If we retain the dominant forces unchanged and modify the drag force to account for the heterogeneous flow structure, we can obtain a new balance equation as follows, βu r = (1 − ε)(ρp − ρg )g (7) ε where the structure-dependent drag coefficient can be formulated by β = βWY HD =

3ε(1 − ε)ρg C D0|ur| 4d p

ε−2.7HD

(8)

where the drag coefficient of Wen and Yu, βWY, is used as the standard to scale the other drag coefficients, whereas HD (=β/ βWY) is the heterogeneity index defined in Wang and Li’s work.26 For example, Figure 2 shows a fitting function of HD 25

Figure 2. The heterogeneity index HD obtained through fine-grid periodic simulation results.

obtained through fine-grid periodic simulation using the EMMS/matrix drag model27 for the whole range of operating voidage. There are several ways to obtain a structure-dependent drag. One of them is to perform a finely resolved simulation with a homogeneous drag law over periodic domains28,29 and thus obtain the effects of the resolved structure on the drag force. Another way is to use the energy-minimization multiscale (EMMS) drag model, which considers the presence of mesoscale structure in its conservation equations and closes it with a stability condition.8,26 Indeed we may directly use the EMMS drag in the force balance without conducting simulations in periodic domains. However, the EMMS model is based on zero dimensional force balance without any geometric limitation of domain size or reactor size. Thus, direct use of it lacks the detailed effects caused by two and three-

4. GENERALIZED CHOKING As reviewed by Yang,12 the term “choking” was first coined by Zenz6 to describe a flow instability in vertical pneumatic transport. It was later employed in the context of the so-called “fast fluidization” in risers of circulating fluidized beds. The pneumatic transport relates only with the concurrent-up flow in a riser, while CFB flow is more complicated, involving a combination of interconnected concurrent and countercurrent flows within a loop. So it is not surprising that more disputes about the choking mechanism ensue when CFB is involved, as extensively discussed by Bi et al.31 and Yang.12 The choking instability is related to the phenomenon that, under a constant mass flow rate of solids, with the decrease of superficial gas velocity, the pressure drop per unit length of pipe first C



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Figure 3. Generalized fluidization diagram with eq 7 and the EMMS drag coefficient (air−FCC particle system, dp = 75 μm, ρp = 1500 kg/m3, ρg = 1.3 kg/m3, μg = 1.8 × 10−5Pa·s, ut = 0.2184m/s): (A) minimum fluidization; (B) free settling; (C) start point of generalized choking/flooding. Ug* = Ug/ut, Us* = Gs/(ρput)). Countercurrent system from Goyal and Rehmat,66 concurrent-up and concurrent-down systems from Reh15 and classical fluidization system from Lindeburg67 are included for insets.

decreases and reverses its trend at certain velocity and then undergoes a rapid or even jump increase. In mathematics, we may describe this jump change of choking with infinite gradient, that is, ⎛ ∂(∇p) ⎞ z⎟ ⎜⎜ ⎟ =∞ ∂ U ⎝ g ⎠ G s

(9)

In a gas−solid riser, the pressure drop per unit length can be approximated by (∇p)z ≈ (1 − ε)ρpg, then, ⎛ ∂ε ⎞ ⎜⎜ ⎟⎟ = ∞ ⎝ ∂Ug ⎠G s

(10)

which is equivalent to eq 4. So it seems that the flooding phenomenon bears the same physical mechanism with the choking in the generalized fluidization diagram. Drawing eq 10 or eq 4 in Figure 3 gives the generalized choking or flooding line, which covers the regimes from the concurrent-up to concurrent-down two-phase flows. Figure 4 shows a close-up of the coexistent states in concurrent-up flows, which looks like the phase diagram predicted by the famous van der Waals equation. We can see that, for dimensionless solids velocity Us* = 0.02, though three states may coexist at around Ug* = 5.0, the section between points b and c is actually unstable because the solids volume fraction (1 − ε) increases with gas velocity thereon. Therefore, only two states are stable within the concurrent-up flow area. A similar flow regime diagram has even been predicted by using two-fluid model CFD simulation with EMMS drag coefficient.10 For a pneumatic transport riser, if one keeps the solids flux constant (for this case, Us* = 0.02) and gradually decreases the superficial gas velocity, the voidage will undergo a gradual decrease through point “d”, to point “c”, and then a jump

Figure 4. Close-up of the generalized fluidization diagram with eq 7 with explanation of the choking bistable state (air−FCC particle system, dp = 75 μm, ρp = 1500 kg/m3, ρg = 1.3 kg/m3, μg = 1.8 × 10−5 Pa·s, ut = 0.2184m/s).

decrease to point “a”. Such a jump change explains the flow instability at the choking in the pneumatic transport system, which can be attributed to the two coexisting, stable states as described by the generalized choking/flooding line. For a CFB riser, however, we may not encounter such an obvious instability, because the riser can operate smoothly at a certain state between point “c” and point “a” with a coexisting dilute top (with respect to point “c”) and dense bottom (with respect to point “a”), which is determined elaborately by the pressure drop balance (or, the distribution of solids inventory) around the whole loop. In appearance, the strong flow instability in the D



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Figure 5. Comparison of experimental results (symbols) with simulated hydrodynamic curves. Experimental data from Kwauk et al.32 Experiments were conducted with air−FCC particle system (dp = 58 μm, ρp = 1780 kg/m3, ρg = 1.3 kg/m3, μg = 1.8 × 10−5Pa·s, ut = 0.18m/s). (Ug* = Ug/ut, Us* = Gs/(ρput).

fluidization was presented by Kwauk et al.32 They presented the regime diagrams for three different types of solids along with the bed collapse experimental results. The properties of the solids can be found in the work of Bingyu and Kwauk.36 Their results were presented by plotting the experimental data on generalized regime diagram for nonideal gas−solid system. Bingyu and Kwauk36 have derived an analytical expression to predict the experimental results. Their work resulted in correction of a homogeneous system by an analytical function depending upon the prevailing voidage and solids velocity. Figure 5 presents the comparison of the experimental data of Kwauk el al.32 and Bingyu and Kwauk36 for their FCC catalyst. The hydrodynamic curves have been obtained by assuming heterogeneity for each grid in a double periodic domain characterized by a heterogeneity index shown in Figure 2. Though the physical properties of particles for generating Figure 2 are not the same as what were used in Kwauk et al.,32 both of them are FCC catalysts, belonging to Geldart Group A (experimental FCC particles: dp = 58 μm, ρp = 1780 kg/m3, ut = 0.18m/s and simulated FCC particles: dp = 75 μm, ρp = 1500 kg/m3, ut = 0.2184m/s). Recent simulation practices also reveal that the drag correction based on one set of physical properties of FCC particles may apply well to the other similar particles.37,38 Thus the comparison presented here can be viewed qualitatively realistic. The data for positive solid and positive gas velocities is the case for concurrent-up flows. The curves characterized by negative solids velocities and positive gas velocities are for countercurrent systems. The case of zero solids velocity is that of classical fluidization where there is no net solids flux. The comparison of experimental data with simulated curves in Figure 5 is encouraging. The experimental trends for both countercurrent and concurrent-up flow systems have been reproduced by simulations, which show coexisting states for a wide range of concurrent-up and countercurrent flows. There is, however, quantitative disparity, especially for the dense bottom side voidage. It can be explained by considering the fact that the hydrodynamic curves were obtained from simulations over periodic domains. Hence, the

pneumatic transport tube will thus be replaced with an operable transition with varying inflection point of the S-shaped axial profile of voidage.7,9 It should be noted that, as shown by the gap between the blue-dot lines “a−c” and “b−d” in Figure 4, the jump change in pneumatic transport may occur at different superficial gas velocity, depending on whether gas velocity increases or decreases. Such a retardation phenomenon or hysteresis needs yet more validation. We may expect such hysteresis in concurrent-down flows since they also show similar bi-stable states as in concurrent-up systems. From the above discussion, we can also distinguish the flooding and choking phenomena. Flooding is a flow instability phenomenon mainly in countercurrent flow, where the underlying mechanism lies in the maximum solids flux for a given superficial gas velocity. It is not necessarily accompanied with the bistable state. For example, in the countercurrent discharger of a jetting fluidized bed gasifier, the discharge rate of solids waste is controlled by the maximum rate at flooding. Choking represents another flow instability phenomenon in concurrent flows. However, its mechanism lies in that bistable state existing for a given gas velocity and solids flux, though the generalized choking and flooding line merges these two instabilities.

5. COMPARISON WITH EXPERIMENTS To validate the simulated diagram, we will first present the comparison with Kwauk et al.32 separately as they were the first to present experimental results for generalized fluidization. In the remaining subsections to follow, we will also compare the simulation results with experiments classified on the basis of flow direction. Though these experiments selected for comparison were performed with various FCC particles that may differ slightly from that is used in our simulation settings, their Archimedes numbers are similar with relative errors of around 40%. Thus, we expect that, at least qualitative knowledge can be obtained from the following comparisons. 5.1. Experiments at ICM. To our knowledge, first experimental evidence for coexisting states for generalized E



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Figure 6. Fluidization diagram for concurrent-down systems with experimental data plotted as symbols.

Figure 7. Fluidization diagram for countercurrent systems with experimental data plotted as symbols (hollow symbols represent the dilute top voidage, whereas filled symbols represent the dense bottom values).

5.2. Gas-down Solids-down (Concurrent-down) Flow. The flow systems where both phases flow along the gravity are generally called as downers. It has been observed experimentally that this type of flow arrangement provides relatively uniform distribution of the solid particles in the column, although small particle clusters of the size of 2−6 times the particle diameter have also been observed in downers operating at relatively low gas velocity and particle fluxes.43,44 Figure 6 displays the generalized fluidization diagram with focus on concurrent-down systems that is, negative gas and solid velocities. The experimental data plotted in this figure is summarized in Appendix A.2. It is seen from the figure that for higher gas velocities, the comparison of experiments and

simulated system did not account for appropriate boundary conditions, which may have significant effects on the reproduction and concentration of flow structures.29 In addition, solids acceleration also plays an important role by contributing to the total pressure drop.39,40 Periodic domain simulations do not take this extra contribution into account, which may become significant in concurrent up flows.41,42 It should also be noted that the Archimedes number for a simulated system is 24.86 while that for experimental FCC particles is 13.6. More realistic quantitative comparison will be discussed in the following sections by selecting experiments with closer Archimedes numbers to what were used in Figure 2. F



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theoretical curves is in good agreement. That can be attributed to the fact that downer flows are relatively homogeneous, both radially and axially, with no significant changes close to the wall.45 There is evidence of existence of an acceleration region in such a down flow arrangement;46 however, the acceleration region is much smaller compared to the fully developed region.47,48 This is also the reason why the data in Figure 6 are presented in single, discrete symbols for a specific gas velocity, as the reported data are mainly for a fully developed region in terms of cross-sectionally averaged values. Although for the current data, geometric conditions may not have caused significant disparity between the simulations and experiments, some deviations between current simulation settings and experiments may be expected for higher superficial gas velocities and/or solids circulation rates due to increased wall friction effects.49 5.3. Gas-up Solids-down (Countercurrent) Flow. Gasupward and solids-downward countercurrent operations can be used to obtain a higher solids-to-gas loading in the column with a relatively uniform dispersion of particles.50 These types of systems have an acceleration region near the solids entrance and a fully developed zone afterward.50 These authors observed that there exists a central dilute core which is surrounded by the dense annular region at the wall. In the fully developed zone, increasing gas velocity yields increased solids holdup due to the countercurrent nature of the two phases. Experiments for Kwauk et al.32 presented in subsection 5.1 contained countercurrent flow as well. In Figure 7, other experimental results of countercurrent systems are plotted against a simulated diagram. For the range of gas and solid velocities presented, the comparison yields good results for the cases with low solid fluxes. Here we presented only one voidage value for every operating condition of the experiments of Luo et al.,50 because the authors presented their experimentally determined solids holdup data in the fully developed region on a volume averaged basis. The other set of data from Youchu et al.51 represents the downcomer flow where a dense bottom region and a top dilute region characterize the bistable regions. The dense bottom voidage is however overpredicted for two sets of gas velocity. If solids flux keeps on increasing, there will come a point where the curve will predict a single dense phase voidage as predicted by the flooding curve. This is in very good agreement with the observations in the work of Youchu et al.51 5.4. Turbulent Fluidized Beds. The turbulent fluidization regime is a transition between bubbling or slugging fluidization, where there is a dense “continuous” phase composed of a gas− solid emulsion, and the fast fluidization regime, where the continuous phase is a more dilute phase.52 Conventional FCC regenerators are usually operated in a turbulent fluidization regime.53 Such a bed is characterized by carryover of some particles from the dense bed to the freeboard region. Thus there exists a dilute region above the dense bottom where particles are present with either zero or negligible circulation. Hence, such a system can be approximated by a zero solids velocity line in the generalized fluidization diagram, which is labeled as a “classical fluidization” curve as shown in Figure 8. It is obvious from the diagram that such a regime may allow two phases before reaching its rightmost inflection point. The minimum dense region voidage predicted by the simulated curve is about 70% and a maximum voidage of 1, which can be found by observing the “free sedimentation” curve in Figure 3. The comparison of predictions of simulated system and experiments is presented in Figure 8.

Figure 8. Fluidization diagram for turbulent fluidized bed system with experimental data plotted as symbols (hollow symbols represent the dilute top voidage, whereas filled symbols represent the dense bottom values).

Figure 8 gives comparison between experimental data and simulation results. It should be noted that while we selected the experimental data with a similar Archimedes number, we chose to plot the averaged values of the dense and dilute regions. With some exceptions, most of the experimental data are scattered around the curve. There still is, however, a significant difference between the voidage predicted and experiments, especially for the dense bottom region. The main reason for such a discrepancy may be the fact that in turbulent beds there may be nonzero solids flux. However, in the diagram we have compared the results with the curve for zero solids flux. It is also recognized that the turbulent regime is the transition between bubbling fluidization and fast fluidization, where large bubbles break down into small bubbles or voids.54 Therefore, to predict the hydrodynamics of such systems, the effects of both the mesoscale structures, that is, bubbles and clusters, should be taken into account. However, the current version of EMMS model only accounts for the effects of clusters, which correspond well to the situation in the dilute top region. That is, perhaps, why the prediction is in better agreement with experimental data in the dilute top region of the bed. It should also be noted that, solids entrainment or circulation may exist in a turbulent fluidized bed, though not as significant as in a CFB. That nonzero solids flux may contribute in part to the discrepancy in Figure 8. 5.5. Gas-up Solids-up (Concurrent-up) Flow. Systems where both gas and solids flow in a direction opposite to gravity are generally known as risers. Risers have been the focus of a lot of experimental investigation (say, for example, Miller and Gidaspow,55 Yerushalmi et al.,56 Grace et al.,57 Horio et al.,58 Pärssinen and Zhu,35 and Wei et al.59). Figure 9 shows the generalized fluidization diagram with hydrodynamic curves for concurrent-up gas and solid flows. The hollow and solid symbols represent the cross-sectionally averaged voidage for the dense bottom and dilute top, respectively. As is shown in Figure 9, an increase of solids flux brings about the increase of the range of voidage existing in the column. Relevant experimental data is listed in detail in the Appendix. G



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Figure 9. Fluidization diagram for concurrent-up systems with experimental data plotted as symbols. Corresponding solids velocity for respective operating line is shown in the legend.

flux will slow down the flow development, which would result in the increase of the acceleration region.41,42 Similarly, various geometric factors such as overall riser height, column diameter, inlet geometry, constriction of column exit, etc. have also been shown to affect flow structure inside the column significantly.40,60−62 In all, although the hydrodynamic head of solids remains the most critical factor, some other factors, such as acceleration region, appropriate boundary conditions, and geometrical effects need to be considered in the comprehensive modeling of riser-type equipment and accurate flow field predictions.42,63,64

Discrepancy between prediction and experimental data is clearer than the other investigated systems. The bistable region predicted by this work is much smaller than experimental and the curves mainly show single voidage, whereas most of the experimental data display the dense and dilute characterization for the same operating conditions. The predictions for the dilute top voidage are, however, in fair agreement with the experiments. Several factors may contribute to the disagreement. One of the reasons may be the fact that current simulations were performed in a doubly periodic domain. Such an arrangement is devoid of boundary walls (which are spots refluxing of particles toward the bottom in forms of clusters within annulus). Furthermore, the present simulation setting does not account for the overall acceleration, or, the axial distribution, especially of the solid particles, which may become significant in riser flow featuring significant axial heterogeneity.39 The increase of solids

6. CONCLUSION AND PROSPECTS The generalized fluidization diagram was redrawn with consideration of the heterogeneous structures in fluidized beds. The generalized choking was distinguished with the bistable coexistent states in concurrent-up or -down flows. The H



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diagram with EMMS drag force allows capture of the generalized choking while the homogeneous drag fails. The predictions are in fair agreement with the experimental data, especially for the concurrent-down and countercurrent flows. Indeed, there are clear discrepancies between the predictions and experimental data, especially for the concurrent-up riser flows. In our opinion, besides the effect of heterogeneous mesoscale structure, domain size or filter size, wall boundary conditions, system configuration such as inlet and outlet geometry, and solids acceleration in the column all contribute toward the disparity between simulations and experiments. In addition, we can expect that the interaction between these factors may further complicate the situation. As hard as these issues are, we are glad to see that our preliminary, qualitative step by considering the effect of mesoscale heterogeneity may greatly improve our understanding of what a comprehensive generalized fluidization diagram would look like. With such a diagram, we can at least predict the bistable states of gas−solid flows and find physical interpretation for the choking and flooding instabilities widely encountered in fluidized beds. If more factors can be properly considered, as discussed in our earlier work,61 where geometric factors are introduced to draw an operating diagram, we can expect more understanding of what happens in such complex fluidized systems. Additionally, for a general purpose diagram, material properties should be allowed to vary, as discussed preliminarily in Appendix A.3. All these deserve more effort.

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Table A1. Parameter Settings for Fine-Grid Simulations particle diameter dp particle density ρp fluid density ρg fluid viscosity μg maximum packing limit for particles εs,max particle restitution coefficient e domain size grid specification (Δx/dp) = (Δy/dp) physical time step

75 × 10−6 m 1500 kg m−3 1.3 kg m−3 1.8 × 10−5 Pa s 0.61 0.9 1.5 cm × 6 cm 12.5 2 × 10−4 s

In periodic domains, no global acceleration exists so the effective weight of the solid particles can be directly correlated to the drag force by βur = ε(1 − ε)(ρp − ρg)g. Furthermore, in the absence of any acceleration, the results of concurrent up flow conditions can be applied to the concurrent down flows, or even to countercurrent flows, due to Galilean relativity. Once the slip velocity is know as a function of voidage, it can then be used to calculate the heterogeneous drag coefficient by β = (ε(1 − ε)(ρp − ρg)g)/ur. On the other hand, by specifying the particle and gas properties, the Wen−Yu drag coefficient, βWY can be readily calculated for all the voidage range. Once both drag coefficients are known, the heterogeneity index for this two-dimensional periodic domain can then be calculated from eq 8 as (β/βWY). Figure 2 shows the plot and curve fitting equation of the heterogeneity index, HD, obtained in this manner. The heterogeneity index obtained in the current work is valid over the whole range of voidage. Furthermore, the HD curve approaches unity toward both the dilute and dense ends representing homogeneity. It should be noted that the quantitative difference of the predicted slip velocity, and then, the heterogeneity, may exist for different sized periodic domains, as discussed in Agrawal et al.28 and Wang.65 That is to say, the system has scale-up effects. A periodic domain analysis only provides some qualitative ideas for the regime diagram and the quantitative validation relies further on its domain size and geometric factors. For a different sized reactor, the most direct way is to perform simulation for all possible regimes, but it is of course not affordable even in the near future. An alternative approach is to simplify the geometric factors and include them as the third axis to draw an operating diagram instead of traditional flow regime diagram.61 The effect of domain size on the averaged axial slip velocity was, however, explored for current grid resolution with EMMS/ matrix drag model and is presented in Figure A1. Quantitatively more rational diagram may be obtained by performing more sets of such simulations over various sized periodic domains until reaching the plateau on which the slip velocity will not change with domain size. However, considering the facts that we are still short of drag models that are fit for all flow regimes and many factors cannot be taken into account appropriately in a periodic domain simulation, the current work is better to be viewed as qualitative, to shed light on the possible characteristics of generalized fluidization diagram and general-purpose drag laws. So, we did not devote more efforts to improve quantitatively the predicted slip velocity.

APPENDIX A

A.1. Heterogeneity Index, HD

To generate the fluidization diagrams, we require the slip velocity and then the heterogeneity index which were obtained from doubly periodic domain simulations. Fine-grid simulations of gas-particle systems in a doubly periodic domain were performed for voidage ranging from minimum fluidization (0.4, for this case) to dilute transport (about 1.0). Following Lu et al.,27 the pressure gradient was specified across longitudinal direction, that is, the y direction. For the granular temperature, the algebraic option in Fluent was adopted. Both particle and gas were initially at rest with zero velocity in all directions. At the start of simulation, perturbations were introduced in certain grids. These perturbations gradually grew throughout the domain, resulting in inhomogeneous distribution. Once statistically steady state was established, the net flow of the suspension was then in the vertical direction. Favre-averaged slip velocity was obtained, as in Agrawal et al.,28 to represent the average relative velocity between the two phases in the periodic domain. Once the whole range of slip velocity is known as a function of voidage, then, by specifying a set of gas and solids velocities independently, voidage can be calculated as a function of them. With the set of known gas and solids velocity and voidage, a generalized fluidization diagram such as in Fig. 3 can be plotted. It is to be noted that the grid dependence of the EMMS/matrix model was tested for the fine-grid simulation for three different grid resolutions where (Δx/Δp) = (Δy/Δp) varied from 25 to 6.25. The EMMS/ matrix model was found to be very weakly dependent upon grid resolution. For the sake of brevity, in the text to follow, finegrid will refer to the intermediate grid resolution, where (Δx/ Δp) = (Δy/Δp) = 12.5. Characteristics and material properties of the two dimensional system used are presented in Table A1.

A.2. Experimental Data

Here we present the experimental data used in current manuscript for comparison with simulations. The tabulated data in Table A2 is classified according to respective flow conditions. In addition to particle characteristics and operating conditions, it also contains the dimensions (diameter and I



Article

height) of the column used by respective authors to get the data. Experimental operating conditions presented in the table are superficial gas velocity and solids circulating flux, whereas the fluidization diagrams present these results in dimensionless gas and solids velocities. A.3. Effect of Particle Properties on Behavior of Gas−Solid Fluidization

We present a brief introduction to the effect of heterogeneity for the system of particles with different but uniform diameter. Considering the same fluid properties, the effect of particle properties can be best described by Archimedes number, Ar. For every Ar, one can set out to solve the force balance equation given as eq 7. In such a way, we can obtain the interphase relative or slip velocity. Once the slip velocity is known, we may then define various dimensionless numbers to represent the system status. The dimensionless numbers we chose, for the current presentation, are from the work of Reh.4 These dimensionless numbers include Ω, Fr*, and Re. All these numbers are defined in Figures A2 and A3. These dimensionless numbers depend upon slip velocity, which in turn depends upon voidage (ε) or particle volume fraction (φ). It is to be noted that these diagrams are only for the case where there is no overall acceleration as addressed by Reh.4 For the

Figure A1. Variation of the domain averaged slip velocity with the width of domain for average solids concentration of 5%. Grid resolution: Δx/dp = Δy/dp = 12.5. The figure includes snapshots of the instantaneous solid fraction in the domain at t = 10 s for respective domain sizes.

Table A2. Operating Conditions and Particle Characteristics from Experimental Literature for Comparison with the Fine-Grid Simulation Results ρp

Ar

ut

70

1300

17.52

0.175

54

1761

20

0.155

82

985

21

0.2

67 65

1500 1550

17.72 17.52

0.2 0.18

75 82 67

1400 985 1500

23.2 21.33 17.72

0.24 0.2 0.19

72 65

1300 1623

19 17.5

0.2 0.19

67 67

1500 1500

17.72 17.72

0.2 0.2

65

1720

18.56

0.19

70 67 67

1770 1500 1884

22 17.72 22.3

0.22 0.2 0.26

61.3 65

1780 1375

16.12 13.8

0.2 0.16

70

2130

28.7

0.31

78 65

1560 1780

29 19.22

0.286 0.23

dp

dc, h

(Ug, Gs)

Gas up−Solids down Countercurrent Flow (0.11, −4) (0.23, −4) (0.34, −4) (0.11, −40) (0.23, −40) (0.34, −40) 0.05, 4 (0.071, −79.31) (0, −79.31) (0.1415, −163.25) Concurrent-down Flow they have presented some of the experimental data of −0.5 to −4 (Gs = −92) Aubert et al.68 −0.5 to −4 (Gs = −121.7) 0.1, 9.3 (−3.7, −49) (−3.7, −101) (−3.7, −194) 0.025, 5 −0.16 to −3.8 (Gs = −46) −0.16 to −3.8 (Gs = −90) −0.16 to −3.8 (Gs = −139.5) −0.16 to −3.8 (Gs = −209.25) −0.16 to −3.8 (Gs = −300) 0.05, 4.6 −0.4 to −5 (Gs = −120) 0.05, 5 −0.5 to −4 (Gs = −79) 0.1, 9.3 (−3.7, −50) (−3.7, −101) (−3.7, −202) Concurrent-up Flow 0.2, 7 (2, 40) 0.15, 3 (1.6, 15.4) 0.097, 3 (1.6, 14.6) 0.1, 15.1 (3.5, 100) (5.5, 53) (5.5, 108) (5.5, 201) 0.1, 16 (3, 18) (3, 27.8) (3, 43.7) (3, 58.9) (3, 75.1) (3,79.4) (3, 61.8) (4.5, 186) (5, 186) 0.1, 5.3 (3.06, 31) (3.3, 31) (3.47, 31) (3.63, 31) (3.88, 31) (4.13, 31) 0.12, 5.75 (3, 35) (3, 55) 0.1, 15.1 (1.9, 26) (2.4, 38) (3, 44) (3.5, 59) (3.5, 69) 0.019 × 0.114 (rectangular column), 7.6 (3.5, 150) (3.5, 200) (5, 100) (5, 150) (5, 200) Turbulent Fluidized Beds 0.2, 1.6 0.158 (Gs ≈ 0) 0.05, 0.75 (with expanded bed section of 0.1 m diameter 0.45 and 0.85 (Gs = 0) and 0.3 m height) 0.26 − 0.9, 6.4 (diameter varied with height for upper 0.55 to 1.13 (Gs = 0) and lower regenerators) 0.29, 4.5 0.25 to 0.94 (Gs = 0) 0.1, 3.6 1.0 (Gs = 0) 0.025, 5

J

ref 50 51 69 43 70

71 68 72 73 74 48 42 75 76 77 78 79 80 53 81 82



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Figure A2. 3D surface plot (left) and contour plot (right) for system where gas-particle drag force can be modeled with Wen−Yu drag coefficient.

Figure A3. 3D surface plot (left) and contour plot (right) for system where gas-particle drag force can be modeled with EMMS corrected drag coefficient.

homogeneous distribution of particles, we chose the Wen−Yu correlation to represent drag force. The result of this method for the Wen−Yu drag coefficient is displayed in Figure A2. This figure presents a 3D surface for Ar−Ω−φ with projections onto the Ar−φ plane. The figure on the right is the contour plot of the same diagram as on left, except that now we also have lines for Fr* and Re. The direction of arrows show the direction of increasing magnitude and colours of arrows show the respective dimensionless number. It should be noted that, if the homogeneous drag is used in force balance analysis, one can only predict the streaked area in Figure A2, which is surrounded by the minimum fluidization line (ε = 0.4) and single-particle sedimentation line (ε = 1). However, a large amount of experimental data shows that the circulating fluidized bed operates near the line defined by Fr* = 1 . Thus, there is a vacant area between the lines of Fr* = 1 and ε = 1, whose state cannot be predicted by using the homogeneous drag.

If, however, we assume that the drag force needs correction and can be modified with a heterogeneity index, then we have the force balance of eq 8. For simplicity and qualitative analysis, we assume that the heterogeneity of Figure 2 is valid for all particles. Then the slip velocity and hence the generalized status graph of Reh,4 is modified. This behavior can be observed in Figure A3. As is seen in the 3D surface plot for Ar−Ω−φ, we observe turning point behaviour on the contour plot in the right plane, which corresponds to the folded surface in the surface plot on the left. That implies bi-stable states may exist after the particles are fluidized beyond the minimum fluidization state. It should also be noted that, by using the EMMS drag, one can predict the flow states between the lines of Fr* = 1 and ε = 1, which do exist in circulating fluidized beds but cannot be predicted by using the homogeneous drag. That shows again the advantage of using the structure-dependent drag model, though quantitative disparity reflected by the smaller vacant area still exists. Indeed, a general-purpose diagram should be more complex since the domain-size or K



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(4) Reh, L. Fluid Dynamics of CFB Combustors, Circulating Fluidized Bed Technology V. Proceedings of the 5th International Conference on Circulating Fluidized Beds, Beijing; Kwauk, M., Li, J., Eds.; 1995; pp 1−15. (5) Bi, H. T.; Grace, J. R. Flow regime diagrams for gas−solid fluidization and upward transport. Int. J. Multiphase Flow 1995, 21 (6), 1229−1236. (6) Zenz, F. A. Two-phase fluid−solid flow. Ind. Eng. Chem. 1949, 41 (12), 2801−2806. (7) Bi, H. T.; Grace, J. R.; Zhu, J. X. Types of choking in vertical pneumatic systems. Int. J. Multiphase Flow 1993, 19 (6), 1077−1092. (8) Li, J.; Kwauk, M. Particle-Fluid Two-Phase Flow: The EnergyMinimization Multi-Scale Method; Metallurgy Industry Press: Beijing, 1994; p 204. (9) Li, J.; Wen, L.; Ge, W.; Cui, H.; Ren, J. Dissipative structure in concurrent-up gas−solid flow. Chem. Eng. Sci. 1998, 53 (19), 3367− 3379. (10) Wang, W.; Lu, B.; Li, J. Choking and flow regime transitions: Simulation by a multi-scale CFD approach. Chem. Eng. Sci. 2007, 62 (3), 814−819. (11) Wang, W.; Lu, B.; Zhang, N.; Shi, Z.; Li, J. A Review of multiscale CFD for gas−solid CFB modeling. Int. J. Multiphase Flow 2010, 36 (2), 109−118. (12) Yang, W.-C. “Choking” Revisited. Ind. Eng. Chem. Res. 2004, 43 (18), 5496−5506. (13) Cao, J.; Cheng, Z.; Fang, Y.; Jing, H.; Huang, J.; Wang, Y. Simulation and experimental studies on fluidization properties in a pressurized jetting fluidized bed. Powder Technol. 2008, 183 (1), 127− 132. (14) Wang, Z.; Bai, D.; Jin, Y. Hydrodynamics of cocurrent downflow circulating fluidized bed (CDCFB). Powder Technol. 1992, 70 (3), 271−275. (15) Reh, L. Challenges of circulating fluid-bed reactors in energy and raw materials industries. Chem. Eng. Sci. 1999, 54 (22), 5359− 5368. (16) Zhang, N.; Lu, B.; Wang, W.; Li, J. Virtual experimentation through 3D full-loop simulation of a circulating fluidized bed. Particuology 2008, 6 (6), 529−539. (17) Zhang, N.; Lu, B.; Wang, W.; Li, J. 3D CFD simulation of hydrodynamics of a 150 MWe circulating fluidized bed boiler. Chem. Eng. J. 2010, 162 (2), 821−828. (18) Lu, B.; Wang, W.; Li, J. Eulerian simulation of gas−solid flows with particles of Geldart groups A, B, and D using EMMS-based mesoscale model. Chem. Eng. Sci. 2011, 66 (20), 4624−4635. (19) Nikolopoulos, A.; Nikolopoulos, N.; Charitos, A.; Grammelis, P.; Kakaras, E.; Bidwe, A. R.; Varela, G. High-resolution 3-D full-loop simulation of a CFB carbonator cold model. Chem. Eng. Sci. 2013, 90 (0), 137−150. (20) Wallis, G. B. One-Dimensional Two-Phase Flow; McGraw-Hill: New York, 1969; p 408. (21) Matsen, J. M. Drift flux representation of gas−particle flow. Powder Technol. 2000, 111 (1−2), 25−33. (22) Richardson, J. F.; Zaki, W. N. Sedimentation and Fluidization: Part I. Trans. Inst. Chem. Eng. 1954, 23, 35−53. (23) Wirth, K.-E. Axial pressure profile in circulating fluidized beds. Chem. Eng. Technol. 1988, 11 (1), 11−17. (24) Yerushalmi, J.; Avidan, A. High velocity fluidization. In Fluidization; Davidson, J. F., Clift, R., Harrison, D., Eds.; Academic Press: London, 1985; pp 226−291. (25) Wen, C.; Yu, Y. Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 1966, 62, 100−111. (26) Wang, W.; Li, J. Simulation of gas−solid two-phase flow by a multiscale CFD approachExtension of the EMMS model to the subgrid level. Chem. Eng. Sci. 2007, 62, 208−231. (27) Lu, B.; Wang, W.; Li, J. Searching for a mesh-independent subgrid model for CFD simulation of gas-solid riser flows. Chem. Eng. Sci. 2009, 64 (15), 3437−3447.

scale-up effect may exist on the structure-dependent drag force and also the force balance, and hence, the folding of 3D surface could be quite intricate, which needs more efforts to clarify it.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +86 10 8254 4837. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This article is in memory of Prof. Mooson Kwauk for his pioneering work on generalized fluidization half a century ago. The authors are grateful to Prof. Reh for having helpful discussion regarding fluidized beds during his visit to IPE in 2012. The authors also wish to thank Dr. Bona Lu for her helpful discussions and acknowledge the financial supports from MOST by National Basic Research Program of China under Grant No. 2012CB215003, from the National Natural Science Foundation of China under Grant No. 21176240, from the Chinese Academy of Sciences by the “Strategic Priority Research Program” under Grant No. XDA07080100, and from Pakistan Institute of Engineering & Applied Sciences (PIEAS).

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NOMENCLATURE Ar = Archimedes number, ρg(ρp − ρg)gdp3/μg2 CD0 = standard drag coefficient for a particle d = diameter, m Fr = Froude number, Ur/(gdp)1/2 Fr* = modified Froude number, 3/4Fr2(ρg/(ρp − ρg)) Gs = solids flux, kg/(m2·s) h = column or bed height (m) HD = heterogeneity index Re = Reynolds number, dpρgUr/μg U = superficial velocity, m/s U* = dimensionless superficial velocity (U* = U/ut) u = real velocity, m/s

Greek Letters

β = drag coefficient in a control volume, kg/(m3·s) ε = volume fraction of gas or voidage φ = volume fraction of solid particles ρ = density, kg/m3 μ = dynamic viscosity, Pa·s Ω = omega number, Ur3ρg2/(g(ρp − ρg)μg)

Subscripts

g = gas p = particle r = relative velocity s = solid t = terminal velocity mf = minimum fluidization tr = transport c = column

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REFERENCES

(1) Kwauk, M. Generalized fluidization: I, steady-state motion. Sci. Sin. 1963, 12 (4), 587−612. (2) Golriz, M.; Grace, J.; Bi, H., Circulating Fluidized Beds. In Handbook of Fluidization and Fluid-Particle Systems; CRC Press: Boca Raton, FL, 2003. (3) Kwauk, M. Fluidization-Idealized and Bubbleless, with Applications; Science Press: Beijing, 1992. L



Article

of a circulating fluidized bed reactor with a V-valve. Powder Technol. 1997, 91 (1), 11−16. (52) Grace, J. R. High-velocity fluidized bed reactors. Chem. Eng. Sci. 1990, 45 (8), 1953−1966. (53) Kim, S. W.; Namkung, W.; Kim, S. D. Solids Behavior in Freeboard of FCC Regenerator. J. Chem. Eng. Jpn 2000, 33 (1), 78− 85. (54) Lee, G. S.; Kim, S. D. Bed expansion characteristics and transition velocity in turbulent fluidized beds. Powder Technol. 1990, 62 (3), 207−215. (55) Miller, A.; Gidaspow, D. Dense, vertical gas−solid flow in a pipe. AIChE J. 1992, 38 (11), 1801−1815. (56) Yerushalmi, J.; Turner, D. H.; Squires, A. M. The Fast Fluidized Bed. Ind. Eng. Chem. Process Design Dev. 1976, 15 (1), 47−53. (57) Grace, J. R.; Issangya, A. S.; Bai, D.; Bi, H.; Zhu, J. Situating the high-density circulating fluidized bed. AIChE J. 1999, 45 (10), 2108− 2116. (58) Horio, M.; Ishii, H.; Nishimuro, M. On the nature of turbulent and fast fluidized beds. Powder Technol. 1992, 70 (3), 229−236. (59) Wei, F.; Lin, H.; Cheng, Y.; Wang, Z.; Jin, Y. Profiles of particle velocity and solids fraction in a high-density riser. Powder Technol. 1998, 100 (2−3), 183−189. (60) Gupta, S. K.; Berruti, F. Evaluation of the gas−solid suspension density in CFB risers with exit effects. Powder Technol. 2000, 108 (1), 21−31. (61) Wang, W.; Lu, B.; Dong, W.; Li, J. Multi-scale CFD simulation of operating diagram for gas−solid risers. Can. J. Chem. Eng. 2008, 86 (3), 448−457. (62) Xu, G.; Gao, S. Necessary parameters for specifying the hydrodynamics of circulating fluidized bed risersa review and reiteration. Powder Technol. 2003, 137 (1−2), 63−76. (63) Andrews; Loezos, P. N.; Sundaresan, S. Coarse-grid simulation of gas-particle flows in vertical risers. Ind. Eng. Chem. Res. 2005, 44 (16), 6022−6037. (64) Huilin, L.; Gidaspow, D.; Bouillard, J.; Wentie, L. Hydrodynamic simulation of gas−solid flow in a riser using kinetic theory of granular flow. Chem. Eng. J. 2003, 95 (1−3), 1−13. (65) Wang, J. Length scale dependence of effective interphase slip velocity and heterogeneity in gas−solid suspensions. Chem. Eng. Sci. 2008, 63 (8), 2294−2298. (66) Goyal, A.; Rehmat, A. Fuel Evaluation for a Fluidized-Bed Gasification Process (U-GAS). In Clean Energy from Waste and Coal; American Chemical Society: Washington, DC, 1992; Vol. 515, pp 58− 71. (67) Lindeburg, M. R. Civil Engineering Reference Manual for the PE Exam, 11th ed.; Professional Publications, Inc.: Belmont, CA, 2008; p 1456. (68) Aubert, E.; Barreteau, D.; Gauthier, T.; Pontier, R. Pressure Profiles and Slip Velocities in a Cocurrent Downflow Fluidized Reactor. In Circulating Fluidized Bed Technology IV. Proceedings of the Fourth International Conference on Circulating Fluidized Beds, Hidden Valley Conference Center and Mountain Resort, Somerset, Pennsylvania, U.S.A., August 1−5, 1993. (69) Bolkan, Y.; Pugsley, T. S.; Berruti, F. Computer Simulation of the Performance of Fluid Catalytic Cracking Risers and Downers. Ind. Eng. Chem. Res. 1994, 33 (12), 3043−3052. (70) Liu, W. High Density Solids Downflow Gas−Solids Reactors; University of Western Ontario: London, Ontario, Canada, 1999. (71) Herbert, P. M.; Gauthier, T. A.; Briens, C. L.; Bergougnou, M. A. Flow study of a 0.05 m diameter downflow circulating fluidized bed. Powder Technol. 1998, 96 (3), 255−261. (72) Qi, X.-B.; Zhang, H.; Zhu, J. Solids concentration in the fully developed region of circulating fluidized bed downers. Powder Technol. 2008, 183 (3), 417−425. (73) Louge, M.; Chang, H. Pressure and voidage gradients in vertical gas−solid risers. Powder Technol. 1990, 60 (2), 197−201. (74) Xu, G.; Nomura, K.; Nakagawa, N.; Kato, K. Hydrodynamic dependence on riser diameter for different particles in circulating fluidized beds. Powder Technol. 2000, 113 (1−2), 80−87.

(28) Agrawal, K.; Loezos, P. N.; Syamlal, M.; Sundaresan, S. The role of meso-scale structures in rapid gas−solid flows. J. Fluid Mech. 2001, 445, 151−185. (29) Igci, Y.; Pannala, S.; Benyahia, S.; Sundaresan, S. Validation studies on filtered model equations for gas−particle flows in risers. Ind. Eng. Chem. Res. 2011, 51 (4), 2094−2103. (30) Li, Y. Hydrodynamics. In Advances in Chemical Engineering; Mooson, K., Ed.; Academic Press: New York, 1994; Vol. 20, pp 85− 146. (31) Bi, H. T.; Grace, J. R.; Zhu, J. X. Regime transitions affecting gas−solids suspensions and fluidized beds. Chem. Eng. Res. Des. 1995, 73, 154−161. (32) Kwauk, M.; Ningde, W.; Youchu, Y.; Bingyu, C.; Zhiyuan, S. In Fast Fluidization at ICM, Circulating Fluidized Bed Technology. Proceedings of the First International Conference on Circulating Fluidized Beds, Halifax, Nova Scotia, Canada; Basu, P., Ed.; Pergamon Press: Halifax, Nova Scotia, Canada, 1985. (33) Lehner, P.; Wirth, K. E. Characterization of the flow pattern in a downer reactor. Chem. Eng. Sci. 1999, 54 (22), 5471−5483. (34) Liu, W.; Luo, K. B.; Zhu, J. X.; Beeckmans, J. M. Characterization of high-density gas−solids downward fluidized flow. Powder Technol. 2001, 115 (1), 27−35. (35) Pärssinen, J. H.; Zhu, J. X. Axial and radial solids distribution in a long and high-flux CFB riser. AIChE J. 2001, 47 (10), 2197−2205. (36) Bingyu, C.; Kwauk, M. In Generalized Fluidization of Non Ideal Systems, Circulating Fluidized Bed Technology. Proceedings of the First International Conference on Circulating Fluidized Beds, Halifax, Nova Scotia, Canada; Basu, P., Ed.; Pergamon Press: Halifax, Nova Scotia, Canada, 1985; pp 127−132. (37) Yang, N.; Wang, W.; Ge, W.; Li, J. Choosing structuredependent drag coefficient in modeling gas-solid two-phase flow. Particuology 2003, 1, 38−41. (38) Jiradilok, V.; Gidaspow, D.; Damronglerd, S.; Koves, W. J.; Mostofi, R. Kinetic theory based CFD simulation of turbulent fluidization of FCC particles in a riser. Chem. Eng. Sci. 2006, 61 (17), 5544−5559. (39) Pugsley, T. S.; Berruti, F. A predictive hydrodynamic model for circulating fluidized bed risers. Powder Technol. 1996, 89 (1), 57−69. (40) Bai, D. R.; Jin, Y.; Yu, Z. Q.; Zhu, J. X. The axial distribution of the cross-sectionally averaged voidage in fast fluidized beds. Powder Technol. 1992, 71 (1), 51−58. (41) Yan, A.; Zhu, J. Scale-Up Effect of Riser Reactors (1): Axial and Radial Solids Concentration Distribution and Flow Development. Ind. Eng. Chem. Res. 2004, 43 (18), 5810−5819. (42) Huang, W. X.; Zhu, J. X.; Pärssinen, J. H. Comprehensive Study on the Solids Acceleration Length in a Long CFB Riser. Chem. Eng. Technol. 2006, 29 (10), 1197−1204. (43) Bolkan, Y.; Berruti, F.; Zhu, J.; Milne, B. Modeling circulating fluidized bed downers. Powder Technol. 2003, 132 (2−3), 85−100. (44) Krol, S.; Pekediz, A.; de Lasa, H. Particle clustering in down flow reactors. Powder Technol. 2000, 108 (1), 6−20. (45) Lanza, A.; Islam, M. A.; de Lasa, H. Particle clusters and drag coefficients in gas−solid downer units. Chem. Eng. J. 2012, 200−202 (0), 439−451. (46) Cao, C.; Weinstein, H. Characterization of downflowing high velocity fluidized beds. AIChE J. 2000, 46 (3), 515−522. (47) Zhu, J. X.; Yu, Z. Q.; Jin, Y.; Grace, J. R.; Issangya, A. Cocurrent downflow circulating fluidized bed (downer) reactors A state of the art review. Can. J. Chem. Eng. 1995, 73 (5), 662−677. (48) Zhang, H.; Huang, W. X.; Zhu, J. X. Gas−solids flow behavior: CFB riser vs. downer. AIChE J. 2001, 47 (9), 2000−2011. (49) Qi, X.-B.; Zhang, H.; Zhu, J. Friction between gas−solid flow and circulating fluidized bed downer wall. Chem. Eng. J. 2008, 142 (3), 318−326. (50) Luo, K. B.; Liu, W.; Zhu, J. X.; Beeckmans, J. M. Characterization of gas upward−solids downward countercurrent fluidized flow. Powder Technol. 2001, 115 (1), 36−44. (51) Youchu, L.; Yongqi, L.; Fengming, W.; Kai, H.; Wensheng, M.; Xiaohui, C.; Peiyun, W. Behavior of gas−solid flow in the downcomer M



Article

(75) Namkung, W.; Kim, S. W.; Kim, S. D. Flow regimes and axial pressure profiles in a circulating fluidized bed. Chem. Eng. J. 1999, 72 (3), 245−252. (76) Laura Mastellone, M.; Arena, U. The effect of particle size and density on solids distribution along the riser of a circulating fluidized bed. Chem. Eng. Sci. 1999, 54 (22), 5383−5391. (77) Qi, X. B.; Huang, W. X.; Zhu, J. Comparative study of flow structure in circulating fluidized bed risers with FCC and sand particles. Chem. Eng. Technol. 2008, 31 (4), 542−553. (78) Xu, J.; Zhu, J. X. Experimental study on solids concentration distribution in a two-dimensional circulating fluidized bed. Chem. Eng. Sci. 2010, 65 (20), 5447−5454. (79) Horio, M.; Kuroki, H. Three-dimensional flow visualization of dilutely dispersed solids in bubbling and circulating fluidized beds. Chem. Eng. Sci. 1994, 49 (15), 2413−2421. (80) Venderbosch, R. H. The Role of Clusters in Gas−Solids Reactors. An Experimental Study; University of Twente: Enschede, Netherlands, 1998. (81) Ellis, N. Hydrodynamics of Gas-Solid Trubulent Fluidized Beds. University of British Columbia: Vancouver, Canada, 2003. (82) Qi, X.; Zhu, H.; Zhu, J. Demarcation of a new circulating turbulent fluidization regime. AIChE J. 2009, 55 (3), 594−611.

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