handbook of combustion (online) || modeling of circulating fluidized bed combustion

12Modeling of Circulating Fluidized Bed CombustionWei Wang and Jinghai Li

12.1Introduction

Circulating fluidized bed (CFB) combustion was introduced to industrial powergeneration at the beginning of the 1980s [1]. The industrial application of hightemperature CFB reactors with internal combustion by fuel injection can be furthertraced back to the invention of aluminum hydroxide calcination technology byLurgi [2]. In general, as shown in Figure 12.1 [3], a CFB combustor loop mainlyconsists of a highly-expandedfluidized bed or furnace,with solids externally recycled,through gas solid separators/cyclones, standpipes/downcomers, aerated U-seals/siphons, and, in some cases, external heat exchangers. As summarized in theliterature [2, 4, 5], a CFB combustor has following features:

. highly expanded bed of polydisperse particles in the regimes between classicalbubbling fluidization and pneumatic transport;

. highmean relative velocity between gas andparticles due to clustering of particles,normally exceeding the terminal velocity of average particles (say, superficial gasvelocity �6m s�1, net solids flux ranges from 0.5 to 20 kgm�2 s�1 [6]);

. uniform temperature across the combustor (around 850 �C) due to recycle andmixing of heat carrying, hot ashes;

. well mixed solids with residence time normally between several minutes andhours, and nearly plug flow of gas with residence time around several seconds;

. staged addition of air at different levels, thus allowing controlled gas emission, forexample, low NOx, over furnace height;

. wide fuel flexibility, covering biomass, peat, low-grade coal containing high sulfurand ash content, coal refuse, petroleum coke,municipal waste and sewage sludgeand so on;

. high combustion efficiency compared to bubbling fluidized bed combustor;

. efficient sulfur removal due to addition of limestone sorbent;

. smaller cross section of furnace due to high release rate of heat;

. good turndown and load-following capacity due to high fluidizing velocity andlarge solids inventory with easy control of heat absorption.

Handbook of Combustion Vol. 4: Solid FuelsEdited by Maximilian Lackner, Franz Winter, and Avinash K. AgarwalCopyright � 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32449-1

j435

Owing to the above advantages, CFB combustors have been developed widely andscaled up progressively. From the first industrial CFB coal combustor of 84 MWth

with external heat exchange at Vereinigte AluminumWerke AG (VAW) in L€unen [7],large-scale atmospheric CFB combustor units are now in the range of 300 MWe ormore. Some600MWe supercritical and even 800MWeultra-supercritical CFBboilersare now in project or in design [8].

Despite themanifold applications of CFB combustors, improved design and scale-up requires better knowledge on issues such as fluid dynamics, mixing, heat/masstransfer between gas and particles, bed-to-wall heat extraction, and cyclone separa-tion. These issues are, however, hard to master only from experiments, as they areinherently relatedwithmultiscale structures inCFBcombustors anddiffer greatly fordifferent experimental conditions, while measurements over large-scale facilitiesunder high temperature are hard to carry out and cost much. By comparison,simulation with reliable models costs less and enables detailed analysis of theabove issues. With the development of computing technology, various modelingapproaches, including both semi-empirical and computational fluid dynamics(CFD) based approaches, have been proposed for CFB combustion simulation.

Figure 12.1 Schematic drawing of a JEA 300 MWe CFB boiler unit [3]: (1) furnace, (2) cyclone,(3) heat exchanger, and (4) backpass.

436j 12 Modeling of Circulating Fluidized Bed Combustion

In particular, the so-called multiscale CFD approach, which is a hybrid approachcombining CFD and multiscale modeling of structures, has received growingattention. To help understand the CFB combustion behavior and to facilitatethe application of simulation, this chapter summarizes certain key aspects withrespect to CFB combustion, namely the fluid dynamics and heat/mass transfer andreaction kinetics, and then summarizes the current modeling approaches, withemphasis on the multiscale CFD, which is detailed with an example for industrialapplication.

12.2Fluid Dynamics

Owing to the wide size distribution of particles and various gas–particle contactmodes around the CFB loop, several flow regimes may exist in different sections ofa CFB combustor. For example, fuel particles normally range from a few micronsup to a few centimeters in diameter, which is in contrast to the inert ash particles,which are normally have a comparatively narrower size distribution, with a meandiameter of, say, around 200 mm for the combustion of coal. Owing to compar-atively lower gas velocity, coarse particles in the furnace bottom below thesecondary air inlet may be operated in bubbling or turbulent fluidization.Meanwhile, the circulating bulk of inert ash particles is normally in so-calledfast fluidization, though �fast fluidization� in its own right is an ambiguous interms of a flow regime [9, 10]. The solids entrained out of the furnace are in swirlflow in the cyclone, by which the collected particles are deposited within thedowncomer, and returned to the furnace through a dense siphon operated inmoving packed bed or bubbling fluidized bed due to aeration. Classification ofparticles in terms of hydrodynamics is referred to in the work of Geldart(Chapter 11) [11]. A general classification should, however, include more factors,such as viscosity, temperature, and pressure [12, 13]. The following sections onlygive a brief introduction to the fluid dynamics with regard to those encountered inCFB boilers. More detailed description about fluidization regimes can be found inthe literature [14].

12.2.1Moving Packed Bed

In amoving packed bed, solidsmovewith respect to the circumferential walls and gasflows through the bed pores. The drag force exerted by gas on particles causes themajor part of the pressure drop through unit length of the bed, DP/DL, which isusually correlated as [15]:

DPDL

¼ 150ð1�eÞ2

e3� mgUg

ð#dpÞ2þ 1:75

1�e

e3� rgU

2g

#dpð12:1Þ

12.2 Fluid Dynamics j437

where

e is the cross-sectionally averaged or bed averaged voidagemg is the gas viscosityUg is the superficial gas velocity# is the sphericity of particlesdp is the mean diameter of particlesrg is the gas density.

12.2.2Bubbling Fluidization

For coarse particles (say, categories B and D in Geldart�s classification), when the gasflow rate is increased to exceed theminimum fluidization velocityUmf, bubbles formand the bed enters bubbling fluidization. The transition velocity between the packedbed and bubbling fluidized bed can be estimated by equating Ergun�s relation withthe pressure drop relation for fluidized beds, that is, DP/DL¼ (1� e)�(rp�rg)g.

From the start of the minimum fluidization the bed behaves as a pseudo-fluid,featuring an inhomogeneous structure of bubbles and emulsions. This �emulsion�is normally characterized by the superficial gas velocity (Umf) and minimumfluidization vodiage (emf), while the �bubble� is characterized by its diameter andrise velocity. For an isolated bubble in a large bed, both theoretical analysisand experimental correlations [16, 17] show that the bubble rise velocity (UB) canbe scaled with the bubble diameter (dB) as UB � (gdB)

0.5. To account for the effectsof neighboring bubbles, Darton et al. [18] proposed a model for determining thebubble diameter; the visible bubble velocity can be calculated by the followingrelation [19]:

UB

Ug�Umf¼ 1:45Ar�0:18 ð12:2Þ

where Ar is Archimedes number. By comparison, Johnsson et al. [20] have arguedthat this relation results in a height-dependent voidage in CFB combustor bottom,while their correction predicts a constant voidage in the bottom.

12.2.3Fast Fluidization

The circulating particles, mainly of inert ashes, are carried by gas with a superficialslip velocity higher than the terminal velocity of single particles. The dynamicevolution of particle clusters results in both this high slip velocity and a high refluxof solids along the combustor wall, which further ensure the uniform temperaturedistribution across the combustor. This meso-scale clustering, together with variousgeometric constraints, results in manifold axial and lateral distributions that arecharacteristic of a CFB. The relevant regime in a phase diagram is sometimes called


�fast fluidization� [2]. However, its physical definition remains somewhat unam-biguous, in particular with respect to its boundaries marking the transition from/tothe pneumatic transport and the turbulent fluidization. Relevant disputes can befound to in the literature [21, 22] with emphasis on the widely cited �choking�phenomenon. Recent multiscale CFD simulation sheds light on its underlyingphysics and points out that the probable reason for the disputes lies in the geometriceffects of riser height as well as the inlets and outlets [9, 10]. In what follows wedisregard the disputes on the position of the �fast fluidization� in a flow regimediagram, and mainly give some models that may be useful in describing the macro-scale profiles in a CFB combustor.

12.2.3.1 Axial Voidage ProfileThe typical axial voidage profile of fast fluidization is characterized by a dense flowregion at the bottom coexisting with a dilute flow region at the top, which is the so-called S-shaped profile of voidage (Figure 12.2). The gradual transition between thedilute top and the dense bottomwas explained by assuming cluster diffusion [23], or,alternatively, by a model developed by Kunii and Levenspiel [24], as follows:

et�e

et�ea¼ exp �c0ðh�hiÞ½ � ð12:3Þ

Figure 12.2 Typical axial profile of cross-sectionally averaged solid volume fraction.Air-FCC (fluid catalytic cracking) particles,experimental data are taken from the database

of Lothar Reh, whose initial height Hini

corresponds to a solid inventory of 200 kg,and simulation results are adopted fromReference [25].


where

the density decay constant c0 can be correlated from experimental dataea is the asymptotic voidage in the dense bottomet is the asymptotic voidage in the dilute toph is the heighthi is the inflection point height, which can be taken as the height of the secondaryair inlet for a CFB boiler for a first approximation [5].

The above empirical correlations should be used with caution, as the inflectionheight or the dense bottom height is actually related to the solids inventory, thepressure balance around the CFB loop, and even geometric factors. As shown inFigure 12.3, a large pressure gradient occurs in the lower parts of both the riser andthe downcomer, corresponding to the interconnected dense regions. For a givenamount of solids inventory, particles are distributed in such away that pressure dropsaround the CFB loop are balanced. More solids inventory results in a denser bottomsection. Solidsflux can be adjusted by changing gasflow rate and solids inventory, thelatter of which effects through affecting the pressure balance. Such complexity owingto the coupling between hydrodynamic and geometric factors makes it difficult tounify experimental findings from different research groups. This is why the usage ofexperimental correlations normally depends greatly on one�s experience. CFDsimulation in later sections allows much easier adjustment of various factors and,consequently, comprehensive understanding of the complex performance.

Sim. CFB loopExp. riserExp. down comer

CycloneRiser

L-valve

Downcomer

0.0 5.0×103

1.0×104

1.5×104

× (m

)

Pressure (Pa) 2.0×104

1.0

0.5

0.0

0

2

4

8

6

z (m)

Figure 12.3 Typical pressure balance around a CFB loop [25]. Simulated pressure data were takenfrom the center line all across the CFB loop; z refers to the vertical height from the primary air inlet, xrefers to the distance from the axis of the riser (Ug¼ 3.5ms�1, Hini¼ 1.7m).


12.2.3.2 Lateral Voidage ProfileA fast fluidized bed normally features a core region with upward flowing gas andsparsely dispersed particles, coexisting with a thick annulus region mainly ofdownward flowing clusters adjacent to the wall. The up-and-down flows of solidsin the core and the annulus regions form the internal circulation that is usually moreintensive than the external circulation. This is the main reason for the uniformtemperature distribution in a CFB furnace. The lateral distribution of time-averagevoidage e(y) can be related to cross-sectionally averaged voidage by a function ofnormalized distance y from the center to the wall [26] as follows:

ln eðyÞ ¼ ln e � ð0:191þy2:5 þ 3y11Þ ð12:4Þ

12.2.3.3 Meso-Scale StructureIn a CFB, gas and particles are heterogeneously dispersed, resulting in various formsof structures over multiscales in terms of time and space. If we call the scale withrespect to the smallest space being observed, for example, a single particle inexperiment, the micro-scale, and call the scale with respect to the cross-sectionaveraging under constraint of boundaries as the macro-scale, then the wide span ofscales between the micro- and macro-scales can be named the meso-scale, whichbears the most diverse nature of all structures, with rich information. In theliterature, dynamic clusters are usually used to represent the meso-scale structures,whose time-averaged properties, namely the equivalent cluster diameter dc and thecluster voidage egc, can be determined, as summarized in Reference [27], as follows:

dc ¼ 1�e

40:8�94:5ð1�eÞ ð12:5Þ

egc ¼ 0:58ð1�eÞ1:480:013þð1�eÞ1:48 ð12:6Þ

12.2.3.4 EMMS Model and ExtensionsTo account for themultiscale structure in a CFB, the energy-minimizationmultiscale(EMMS) model was proposed by Li and Kwauk [28] for time–mean global behaviorunder force balance, in which the multiscale structure was characterized with two-scale resolution, that is, the cluster scale in terms of particle-rich dense phase(marked by the subscript �c�) and the dispersed particle scale in terms of fluid-richdilute phase (marked by the subscript �f�). The total variable set, including particlevelocity (usk), gas velocity (ugk), and voidage (egk) with respect to each phase �k� (krefers to c or f), together with the cluster diameter (dc) and the volume fraction ofclusters (d) was determined by a set of conservation equations and a stabilitycondition of Nst ! min, where Nst denotes the mass-specific energy consumptionfor suspending and transporting particles (Wkg�1). The intrinsic flow regimediagram, which eliminates the geometric influence of the riser height on the flowregime transitions, can be calculated with this model, as shown in Figure 12.4 [9].


The intrinsic flow regime diagram is illustrated with a set of iso-velocitiesdescribing the relation between solid flux, Gs, and average solids fraction of theriser, es0, at superficial gas velocity Ug. It encompasses three regimes, that is, dilutetransport to the left of the diagram, dense upflow to the right, and in between thejump transition featuring a plateau area. A continuous transition can also be definedabove the critical point or the summit of the plateau area. The jump transition ismarked by the coexistence of both the dense upflow and the dilute transport alongwith saturation carrying of particles. Such a jump change between states ofmotion isrelated to the widely cited �choking� phenomenon [21], which normally occurs with arapid increase of pressure dropwhenkeeping constant the solidsfluxwith decreasingconveying gas velocity.

The extent of the choking area varieswith riser height [29]. It expands, as illustratedin Figure 12.5, due to the increased capacity of a higher column for holding solids,and the critical point, in turn, will rise to a higher position as to the critical gas velocity(U�

g ) and critical solids flux (G�s ). Thus, the choking observed in a high riser may be

absent for a short riser, as it may be easily obscured by the comparatively strongeffects of developingflownear the inlet/outlet. This is probablywhy the phenomenonof choking often causes disputes, as different researches may use quite differentdesigns of CFB.We can expect to draw a series of operating diagrams, which demandgeometrical parameters besides commonly believed parameters such as gas velocityand solids flux, and thus help CFB design and operation.

To determine the apparent flow regimes, EMMSwas extended to the sub-grid levelto couple with CFD by calculating the structure-dependent drag coefficient. Thisextended model is named after the EMMS/matrix [30], which features a two-stepscheme. The first step is to determine the cluster parameters in terms of dc and egc.

Figure 12.4 Intrinsic flow regime diagram of a CFB riser for an air-FCC system (dp¼ 54 mm,rp¼ 930 kgm�3) calculated by using the EMMS model without CFD. The intrinsic flow regimediagram is independent of the riser height [9].


The current version of the EMMS/matrix accepts the original definition of EMMS,such that dc and egc are subject to the stability condition,Nst ! min, under the globalconditions of superficial gas velocity and solid flux, that is:

dcdp

¼Gs

rpð1�emaxÞ � Umf þ emfGs

rpð1�emf Þ� �h i

Nstg � rp

rp�rg� Umf þ emf

Gsrpð1�emf Þ

� � ð12:7Þ

where:

Nst ¼rp�rgrp

Ug�egf�eg

1�egdð1�dÞUgf

� �g!min ð12:8Þ

Obviously, alternativemodels or correlations of dc and egc are acceptable under theframework of this two-step scheme. The remaining variables, that is, (ugc, usc, d) forthe dense phase and (ugf, usf, egf) for the dilute phase as well as the inertial termsassociated to each phase (ac, af, ai), are resolved in the second step by deterministicsolution of the set of conservation equations together with the optimization results(egf ! emax, af ! g). The solution of the second step can be simplified according tothe Galilean relativity by organizing the conservation equations as functions of slip

Figure 12.5 Flow regime transition dependson the riser height [29]. The riser heightdetermines the variation from apparent tointrinsic flow regime diagrams. Dark cyancolumns represent different riser heights, with

the relevant flow regime diagram sketchedabove, and the curve denotes the variationof thecritical point with the final end as the intrinsiccritical point.


velocities [9]. It follows that:

34

esce2gc

dpCD;crg uslip;c

�� uslip;c ¼ ðrp�rgÞð1�egÞðac�gÞ ð12:9Þ

34

e2gf

dpCD;frg uslip;f

�� uslip;f ¼ ðrp�rgÞðaf�gÞ ð12:10Þ

34ð1�dÞ2

dcCD;irg uslip;i

�� uslip;i ¼ ðrp�rgÞðeg�egcÞðai�gÞ ð12:11Þ

With the slip velocity (uslip) and voidage (eg) calculated from CFD, the threedependent variables in the above equations, that is, uslip,c, uslip,i and ac can bedetermined, and then the EMMS-corrected drag coefficient bEMMS can be deter-mined as follows:

bEMMS ¼ eg

uslipFgs ¼

ðrp�rgÞeguslip

ð1�egÞðac�gÞ ð12:12Þ

and the heterogeneity index can be defined as:

HD ¼ bEMMS

b0ð12:13Þ

where b0 refers to the drag coefficient from Wen and Yu [31]. More definitions orrelations are as follows:

ai ¼ ð1�dÞð1�egÞðac�gÞdðeg�egcÞ þ g ð12:14Þ

uslip ¼ ug�us ð12:15Þ

uslip;c ¼ ugc�usc ð12:16Þ

uslip;f ¼ ugf�usf ð12:17Þ

uslip;i ¼ egf ðugf�uscÞ ð12:18Þ

egug ¼ degcugc þð1�dÞegfugf ð12:19Þ

esus ¼ descusc þð1�dÞesfusf ð12:20Þ

eg ¼ degc þð1�dÞegf ð12:21Þ


Recent exploration of its underlying physics reveals that this EMMS/matrix dragcoefficient, as depicted by the surface in Figure 12.6, seems to reach a mesh-independent solution of the effect of sub-grid structures on the interphase momen-tum transfer [29]. This extended EMMSmodel serves as the basis of multiscale heat/mass transfer modeling and, further, the basis of multiscale CFD simulation of CFBcombustion in the following sections.

12.2.3.5 Gas and Solids MixingFor empirical models or CFD models with rather coarse mesh, dispersion coeffi-cients of gas and solids in lateral or axial directions are needed to account for theheterogeneous distributionwithin a cell or grid. There aremany reports on the valuesof these kinds of parameters in the literature. However, it is hard to find generalagreement between them, as these parameters are intrinsically dependent on theirspecificmodels and themesh schemes used. Some empirical valuesmay be found inReference [32].

12.3Heat and Mass Transfer

Heat is transferred within a CFB combustor between gas and particles as well asbetween bed material and wall. Mass transfer occurs between gas and particles.

Figure 12.6 Typical surface plot of the heterogeneity index as a function of voidage and Reynoldsnumber (Re¼ egrgdp|ug–us|/mg) for an air-FCC particle system (rg¼ 1.18 kgm�3, rp¼ 930 kgm�3,dp¼ 54 mm, Ug¼ 1.52ms�1, Gs¼ 14.3 kgm�2 s�1, emf¼ 0.4, 3.4� 10�3<Re< 34) [29].

12.3 Heat and Mass Transfer j445

12.3.1Particle–Fluid Heat/Mass Transfer

12.3.1.1 Classical CorrelationsVarious correlations for particle–fluidmass transfer in a fluidized bed originate fromthe work of Ranz and Marshall [33], such as the proposal for the mass transferbetween a single sphere and neighboring fluid:

Sh ¼ kpdpyBDm

¼ 2þ 0:6 Re0:5Sc0:33 ð12:22Þ

where

Sh, Re, and Sc are Sherwood number, Reynolds number, and Schmidt number(mg/rgDm), respectively,kp is the mass transfer coefficient (m s�1),yB is the logarithmic mean fraction of the inert bulk fluid,Dm is the gas phase diffusion coefficient.

As reviewed in Reference [34], for a fixed bed or a packed bed withRe< 80, the factorrepresenting the convective contribution changes from 0.6 to 1.8, which reflects theeffects of neighboring particles. For lower Re, the magnitude of apparent Sh forfluidized beds drops below the value of 2.0 that corresponds to the lower limit of thediffusion. This can be attributed to the existence of meso-scale structure, such asbubbles in bubbling fluidized beds, as described by the model in Reference [34].Notably, the above discussion on the mass transfer coefficient is based on theassumption that particles are well mixed and the gas is in plug flow. Any attemptsto use these correlations should ensure that themodels are consistent with this basicassumption.

There is little information on particle–fluid mass transfer in fast fluidized beds.One reason for this is the expectation that themass transfer rate is high in a CFB andtherefore of minor importance to the overall reaction rate. For example, the reactioncoefficient kr of ozone decomposition over FCC (fluid catalytic cracking) particleswasreported to be of the order of magnitude of 10 s�1, while the corresponding overallmass transfer coefficient over single particles (kpap) is of the order of 105 s�1 [35];then, the Damk€ohler number (Da)¼ kr/(kpap)� 1, which means that the masstransfer effect is negligible if particles are assumed to be uniformly suspended.However, meso-scale structure may result in a significant decrease of mass transferrate, as summarized in Reference [36], makingDa� 1. For char combustion, we canexpect even more complex coupling between transfer and reactions, as the com-bustion reaction coefficient is so high (according to Reference [32]) as to becomparable with the mass transfer coefficient in a boiler.

In most cases, heat transfer is analogous to mass transfer, and then particle–fluidheat transfer coefficients can be expressed in a similar form by replacing Sh and Scwith Nu and Pr, respectively. For a CFB boiler, both gas and circulating bulk of inertashes are well mixed and their temperatures are quite uniform across the furnace,whereas the temperature of the active char particles may differ from that of inert


material due to devolatilization and combustion. The effect of inert material on theparticle–fluid heat/mass transfer can be referred to in the literature [14]. Forsimplicity, some empirical correlations, as suggested by Ross et al. [37] for thetemperature difference between char and inert particles, can be used, for example:

Tp�Tb ¼ 6:6� 104CO2 ð12:23Þwhere

Tp is the temperature of particlesTb is the temperature of the bedCO2 is the molar concentration of oxygen in kmolm�3.

12.3.1.2 Heat/Mass Transfer with Meso-Scale StructuresInhomogeneous distribution of particles can be expected to promote bypassing of gasaround clusters and, thus, to decrease the effective interphase transfer rates. Toresolve this influence, a multiscale mass transfer model named EMMS/mass, whichadopts the structural parameters of EMMS/matrix model, has been presented [35,38]. It consists of mass conservation equations for the gas mixture and transferredcomponent in the dense and dilute phases, respectively. For example, for thevaporization of component A, the equations read:

qqtðwkegkrgÞþr � ðwkegkrgugkÞ�Sk�C ¼ 0 ð12:24Þ

qqtðwkegkrgxA;kÞþr � ðwkegkrgxA;kugk�wkegkrgDmrxA;kÞ�Sk�CA ¼ 0

ð12:25Þwhere

wk is the volume fraction of phase k, which is d for the dense phase (clusters)and 1 – d for the dilute phase (dispersed particles),xA,k denotes the mass fraction of A in phase k,Cdenotes theoverallmass exchange ratebetween thecluster anddispersephases,Sk is the vaporization source term, which read as follows:

Sk ¼ wkkkð1�egkÞaprgðxA;sat�xA;kÞ; ð12:26Þ

where kk denotes the mass transfer coefficient between gas and particles in homo-geneous suspension of phase k; various Ranz–Marshall-like relationsmay be used inthis regard. The meso-scale mass exchange rate of A, CA, depending on clusterrenewal, can be approximated by C�xA,y if it is dominated by convection, where thesubscript y denotes the carrier gas. Note that the sum of the mass conservationequations for the gas in the dense and dilute phases leads to the conventional massconservation equation for the gas:

qqtðegrgÞþr � ðegrgugÞ�S ¼ 0 ð12:27Þ


where S (¼Sc þ Sf) is the total source termdue to gas–solidmass exchange. Once thestructural parameters (wk, egk, ugk) were determined, the EMMS/mass model couldbe solved in terms of concentrations fields. The overall mass transfer coefficient canalso be determinedwith the inlet/outlet concentrations togetherwith the assumptionof gas plug flow mentioned above.

EMMS/mass model was found to be able to explain the scatter of Sh in CFB. Theobvious drop of Sh at Re0 around 50–100 reflects the jump change effect of thevoidage encountered at choking (Figure 12.7). Interestingly, the curves of Sh forclassical fluidized beds and fixed beds also display an abrupt drop around the samerange ofRe0 [34]. Onemay expect that certain jump changes of state of motion with acommon nature can be found to explain these phenomena.

The importance of multiscale effects of mass transfer can be further delineated bycoupling EMMS/mass with the two-fluid model (TFM) [38]. Even for the ozonedecomposition case, which, as discussed above, seems to be a reaction-controlledprocess, the overall reaction rate is still controlled by the competition between masstransfer and surface reaction. This is because the meso-scale clustering suppressesthe exchange between particle in clusters and neighboring gas, and thus the overallShdecays. As a result, as compared inFigure 12.8 (TypesA andB), it is insufficient yetto correctly capture the flow dynamics by using the EMMS/matrix drag coefficient inCFD simulation. EMMS/mass modeling of mass transfer does improve the predic-

Figure 12.7 Comparison of Sh betweenthis work and the literature data [35]. (a)Conventional Sh–Re0 (Re0¼Ugdprg/mg) curveof (1) Subbarao and Gambhir [39], (2)Kettenring and Manderfield [40], (3) Resnickand White [41], (4) Venderbosch et al. [42],(5) Gunn [43], (6) Van der Ham et al. [44],(7) Dry et al. [45], and (8) Dry and White [46];(b) EMMS/mass predicted surface of Sh as afunction of Ug and Gs and its comparison with

the experimental data for the case ofReference [39]. Red solid dots are taken fromone group of the data (rp¼ 2600 kgm�3,dp¼ 196mm). The conventional correlation bySh versus Re0 shows disparity between differentsources of data and poor correlation betweenShand Re0 while the EMMS/mass description ofSh shows fair agreement between model andexperimental data.


tion. By comparison, the conventional approach, as shown in Figure 12.8 (Type C),which totally neglects the effect of meso-scale structure, gives poor prediction in thatthe ozone decomposition rate is overestimated significantly. Given that the rate ofozone decomposition is slow compared to that of carbon combustion, we can expect amore significant effect of mass transfer on the overall performance of CFBcombustion.

12.3.2Bed-to-Wall Heat Transfer

As mentioned above, particles in a CFB are heterogeneously distributed in forms ofdynamic clusters. Most dispersed particles are carried upwards through the coreregion of the bed, while dense clusters tend to flow downwards along the wall untilthey are split off by the air and redirected into the dilute core region. The intenseconvection and renewal of particles near the wall as well as particle–wall collisionsrepresents the main contribution to the total bed-to-wall heat transfer. Under thetypical operating temperature of CFB boilers, the contribution of radiation is ofminor importance to the total performance of heat transfer. Obviously, from theabove description, the clustering of particles is of great importance to the bed-to-wallheat transfer.

Figure 12.8 Snapshots of dimensionlessozone concentration x/x0 and related time-averaged profiles of x/x0 with dimensionlessradial position r/R at different heights(Ug¼ 3.8ms�1, Gs¼ 106 kgm�2 s�1,kr¼ 57.21 s�1). Type A: EMMS/matrix for flow

and EMMS/mass for mass transfer. Type B:EMMS/matrix for flow and the conventionalmodel for mass transfer. Type C: conventionalCFD model for both flow and mass transferwithout structural consideration [38].


In general, the bed-to-wall heat transfer coefficient increaseswith the solids densitynear the wall. As the cross-sectionally averaged voidage is proportional to the voidagenear the wall as mentioned above, the bed-to-wall heat transfer coefficient can becorrelated as a function of the cross-sectionally averaged suspension density given inthe literature; for example, in Reference [47] the Nusselt number (Nu) due to gasconvection and conduction reads:

Nucon ¼ 2:85ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDP=ðrp�rgÞð1�emf ÞgDL

qþ 3:28� 10�3RewPr ð12:28Þ

whereRew is the Reynolds number of falling clusters near the wall.When radiation isconsidered, a simple weighted sum was suggested:

Nu ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNu2con þNu2rad

qð12:29Þ

where the Nu due to radiation can be calculated as:

Nurad ¼dplg

ersT4b�T4

w

Tb�Twð12:30Þ

where

lg is the gas conductivityTw is the temperature of the walls is the radiation coefficienter is the emissivity (12.31).

er ¼ 11epþ 1

ew�1

ð12:31Þ

where ep and ew are the emissivity of the dispersed particles and the wall, respectively.Finer particles usually result in higher heat transfer coefficient due to intensifiedconvection along the wall. It was reported that heat transfer coefficients, includingconvection and radiation, reach about 800Wm�2 K�1 for fine particles in the sizerange around 40 microns [7].

One of alternatives to the above correlations is the cluster renewal model [5]. It isassumed that any part of the wall comes in alternate contact with the cluster anddispersed particles. If d is the fraction of the wall contacted with clusters, then theoverall heat transfer coefficient (h) can be written as:

h ¼ hcon þ hrad ¼ dðhc;con þ hc;radÞþ ð1�dÞðhf ;con þ hf ;radÞ ð12:32Þwhere subscripts �con� and �rad� denote convection and radiation contributions,respectively. The cluster fraction (d) can be estimated from empirical correlations orfrom EMMS/matrix model, while the convective heat transfer component due toclusters can be written as:

1hc;con

¼ dp10lg

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

tcp4lcCcrc

sð12:33Þ


and the convective heat transfer component due to dispersed particles can bewritten as:

hf ;con ¼ lg

dp

Cp

Cgð1�egf Þ0:3Fr0:21t Pr ð12:34Þ

where

Frt is the Froude number defined with the terminal velocity of singleparticles,tc is the average residence time of clusters on the wall,lc,Cc, andrc are the thermal conductivity, specific heat, and density of the cluster,respectively,Cp and Cg are the specific heat of particles and gas, respectively.

To account for the radiative heat transfer, the above Nusselt number due to radiationcan be used for each phase, with ep replaced by ef for the dilute phase, that is:

ef ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

epBð1�epÞ

epBð1�epÞ þ 2

� �s� epBð1�epÞ ð12:35Þ

and by ec for the dense phase, that is, ec¼ 0.5(1 þ ep).

12.4Reaction Kinetics

It is well recognized that fuel particles in a CFB furnace normally undergo thefollowing processes [7]:

. heating and drying,

. devolatilization and volatile combustion,

. primary fragmentation,

. combustion of char with secondary fragmentation and attrition.

These processes are related with manifold factors concerning material propertiesand flow dynamics and so on, but only limited information is available. Therefore,many simplifications were made in modeling practices. The rate of heating wasreported to be around 100K s�1 and evenmore, so that wemay neglect this stage for afirst approximation. The primary fragmentation occurs as the volatile released insidecoal particles exerts a high internal pressure that breaks the coal into fragments [7].The size distribution of primary particle size before the steady attrition process maybe considered as an intrinsic property of the feeding coal [48] and thus be inputted atthe start of computation. The secondary fragmentation and attrition occur throughhydrodynamic forces, mechanical contact between colliding particles, and combus-tion. If the particle ash layer due to combustion of char were assumed to be strippedoff particles instantaneously by the mechanical stress owing to frequent collisions

12.4 Reaction Kinetics j451

with other particles as well as with thewalls, onemight assume the shrinking particlemodel to describe the particle size evolution process, as in Reference [32]:

ddtðdpÞ ¼ � 24q

jrCKCO2 ð12:36Þ

where

q is the stoichiometric coefficient of the char combustion reactionj is the carbon content of char particlesrC is the density of char particlesK is the overall reaction rate coefficient in m s�1

CO2 is the molar concentration of oxygen in kmol m�3.

If the shrinking coremodelwas assumed instead, then the particle size is determinedonly by mechanical interactions such as attrition, and then, as in Reference [49]:

ddtðdpÞ ¼ d

dtðdpÞattr ð12:37Þ

The shrinking rate is the link among the overall reaction rate model, the attritionmodel, and population balance modeling. Such a complicated process concernsfactors of material properties and its modeling is still far from maturity. In thefollowing, we mainly focus on char combustion modeling with respect to devola-tilization and char oxidation.

12.4.1Devolatilization

Devolatilization is highly variable, depending strongly on the coal properties. Variousmechanisms have been postulated for devolatilization, which may help understandthe basis of phenomenological models and explain certain aspects of coal combus-tion. However, at present, a comprehensive description of the chemical reactions ofdevolatilization of coal is not possible due to the complexity of the overall process.Based on experimental results, usually we can postulate mechanisms and proposemodels with some simplification of the real process. In general, the following factorsmay affect the devolatilization [50]:

. coal properties

. pressure

. thermal history

. secondary chemistry.

Devolatilization models can be phenomenological, by postulating hypotheticalspecies participating in simple stoichiometric reactions, for example, single firstorder rate (SFOR) reaction, or be complex network models, based on coal structuralnetwork descriptions [51]. The latter can be evaluated with some commercial codes,such as FG-DVC, CPD, and FLASHCHAIN�. The SFORmodels have the advantage


of simplicity, but their use has to be restricted to particular coal and combustionconditions. Its overall rate can be expressed as [52]:

dVdt

¼ ðV1�VÞA � exp � ERT

� �ð12:38Þ

whereVdenotes the total of volatiles evolved up to time t andV1denotes the ultimateyield of volatiles at t¼1. For simplicity, a constant volatile release rate may beassumed for the whole devolatilization process [32], or, rather, the release is assumedto happen immediately across the furnace [53] or below the secondary airdistributors [54].

The mass and components of released volatiles are dependent on the factorsmentioned above; they may be simplified to split up into gas species considered in acombustor model, for example, CO, CO2, CH4, H2, H2O, O2, SO2, and N2 inReference [32], where the net volatile mass flux released was assumed to equal thefuel feedflux times its volatile content as determinedby the proximate analysis, sulfurwas assumed to be converted into SO2, nitrogen converted intoN2, and hydrogen andcarbon were assumed by ratio to form CH4, CO, and H2. The reactions on astoichiometric basis read:

CH4 þ 32O2 !CO þH2O ð12:39Þ

H2 þ 12O2 !H2O ð12:40Þ

CO þ 12O2 !CO2 ð12:41Þ

S þ O2 !SO2 ð12:42ÞWhen provided with necessary kinetics parameters, the species conservation

equations could be defined in a general manner for the volatiles.

12.4.2Char Combustion

After devolatilization, the volatile-free char particles, which consist of fixed carbonand ash, start to burn. Depending on the ash properties and fluid dynamics aroundparticles, the oxidation of char may be described by the shrinking core model orshrinking particle model. In the shrinking core model, the overall process of charcombustion involves the following steps in sequence: transport of oxygen from thebulk stream of gas to the outer surface of char particles, diffusion of oxygen throughthe ash layer, combustion over the inner core of char, and diffusion of reactionproducts back through the ash layer and then to the bulk streamof gas. The shrinkingparticle model concerns the outer mass transfer from and to the char particle surfaceand the reactions over the particle surface.


The overall reaction rate coefficient of the shrinking particlemodel, on the basis ofone particle, is then defined as a combination of the surface reaction rate coefficient(ks) and the mass transfer coefficient:

1K

¼ 1kp

þ 1ks

ð12:43Þ

and for the shrinking core model:

1K

¼ 1kp

þ 1ki

þ z

geDeð12:44Þ

where

ki is the intrinsic reaction rate coefficient over the inner surfacez is the thickness of the ash layerge is the effective diffusion porosityDe is the molecular diffusion coefficient of oxygen.

For the intrinsic rate coefficient, some typical rates have been reported: for example,42exp(�113 kJ/RT) [4] and 52exp(�161.5 kJ/RT) [51]. The key issue in using theintrinsic rate model is that the total inner surface for reaction and the effectivenessfactors have to be determined a priori, which is difficult as the inner structure variesthroughout burnout.

As for the shrinking particle model, according to Reference [37], the carbon of thechar particles reacts with the oxygen at the particle surface to give either to CO or toCO2:

C þ 12O2 !CO ð12:45Þ

C þO2 !CO2 ð12:46ÞThese two equations can be combined by introducing a mechanical factor (q),

which describes the ratio of carbon monoxide to carbon dioxide, as follows:

C þ 1qO2 ! 2� 2

q

� �CO þ 2

q�1

� �CO2 ð12:47Þ

where q varies with the combustion temperature and char particle size, and it can bedetermined with:

q ¼

2sþ 2sþ 2

dp < 0:05mm

2sþ 2�sð100dp�0:005Þ=0:095sþ 2

0:05 dp 1:0mm

1 dp > 1mm

;

8>>>>>>>><>>>>>>>>:

ð12:48Þ


where the splitting factor s is defined as:

s ¼ 2500 exp � 5:19� 104

RT

� �ð12:49Þ

Then, the conversion rate of carbon on the basis of single char particles(rC, kmol s�1) is:

rC ¼ qrO2 ¼ �qpd2pKCO2 ð12:50Þ

and the conversion rate of oxygen due to carbon combustion per unit bed volume(RO2 , kmolm�3 s�1) can be written as:

RO2 ¼6esxCdp

KCO2 ð12:51Þ

where es is the volume fraction of solid particles and xC is themass fraction of carbonof the bed material. A correlation of Field et al. [55] for ks has been used inReference [32] as follows:

ks ¼ 596q

�Tp � exp � 18000KTp

� �ð12:52Þ

The relevant conversion rate of CO and CO2 can be determined accordingly.

12.4.3Pollutant Emission

The main pollutants considered for CFB combustion are SO2 and NOx. Usually,limestone has been used as the SO2 sorbent. The SO2 retention increases with Ca/Smolar ratio. It was reported that the retention efficiency reaches an optimum arounda bed temperature of 850 �C [4]. SO2 retention reactions involve the thermaldecomposition of limestone to calcium oxide and then the transformation intocalcium sulfate, as follows [56]:

CaCO3 !CaOþCO2 ð12:53Þ

CaO þ SO2 þ 12O2 !CaSO4 ð12:54Þ

NOx may be formed through oxidation of atmospheric nitrogen and charnitrogen. For a CFB boiler, the contribution from atmospheric nitrogen is ofminor importance, while the contribution from char nitrogen can be expressed bya complex series of reactions [57, 58]. For the destruction of the formed NOx, twomajor reactions may involve:

C þ 2NO!N2 þCO2 ð12:55Þ2C þ 2NO!N2 þ 2CO2 ð12:56Þ


CFBhelps restrain theNOx emission in the sense that a combination of a reducingzone in the bottom and an oxidizing zone above is set up by the secondary airentrance. Emission of NOx can thus be controlled by changing the secondary-to-totalair ratio. More detailed reaction kinetics concerning pollutant emission and reduc-tion are given in the literature [5, 56–58].

12.5Modeling Approaches

Based on the above description of hydrodynamics, heat/mass transfer, and reactionkinetics, a comprehensive combustionmodel can be proposed for the furnace side ofa CFB boiler. Depending on the level of model details, the following categories ofmodel may be classified.

12.5.1Lumped Parameter Model

For the purpose of design, the complicatedhydrodynamic profiles can be lumped intoseveral parameters to help obtain knowledge of the overall performance of the wholesystem of a boiler. This was the case in Reference [59], in which a lumped parametermodel was developed with a modular solver based on the Newton–Raphson methodand a library of 22modules, each of them representing the steady-state operation of asingle component of the unit, for example, the furnace, cyclones, external heatexchangers and backpass, and so on. The whole model was created by linking thesemodules according to the real topology. As for the furnace of the boiler, itshydrodynamics is described with the lumped two-phase velocities, void fraction inthe upper part of the furnace. The main chemical reactions involve carbon com-bustion, limestone decomposition and sulfur capture, and hydrogen oxidation. Aglobal correlation of bed-to-wall heat transfer was used to calculate the average bedtemperature. This lumped model has been developed on the basis of the analysis ofthe Emile Huchet power plant data. It has proved to be able to simulate the full loadoperation and to validate the design of another plant.

12.5.21D/1.5D Model

To account for the solids distribution in the furnace, Rajan et al. [60] assumed a seriesof compartments to represent the solids mixing behavior in conventional fluidizedbed combustors. The reaction kinetics models therein were widely cited in laterliterature. Based on the simulation method for bubbling fluidized beds for com-bustion and CFB reactors for decomposition of NaHCO3, Weiss et al. [61] haveproposed a generalized cell (compartment) model, where solids were well mixed ineach cell and only axial distribution between cells was taken into account. Demixingphenomena such as bubbles and clusters were neglected, and no back mixing of gas


was assumed. For each cell themass balance of O2, CO, CO2, H2O, SO2, NO, N2, andcarbon and ashes were considered together with the energy balance. There aredifferent divisions of compartments reported in the literature, such as in Refer-ences [62–64], reflecting different understandings of the flow dynamics in thefurnace. To better describe the radial segregation of particles and its influence onheat transfer,Hannes et al. [65] have introduced a 1.5-Dmodular programming frameby taking into account the core-annulus radial structure.

12.5.3Multi-D Model

To grasp the three-dimensional (3D) behavior, Hypp€anen et al. [66] and laterMy€oh€anen et al. [67] reported their three-dimensional, steady state combustionmodels for a CFB furnace. The model contained essential submodels to describethe complex combustion process, which include the hydrodynamics of the bed,devolatilization of fuel, combustion of char, combustion of hydrocarbons, carbonmonoxide and hydrogen, calcination and sulfur retention, fragmentation andattrition of solids, heat transfer, overall mass balance of the furnace, and 3D balanceequations based on the finite volume method. Reliable experiments and measure-ments in commercial boilers, which cover an 80 MWth boiler burning bituminouscoal and a 235MWe subcritical boiler burning lignite, were used for validation of themodel and for tuning themodel parameters. Another example of 3Dmodel based onempirical correlations has been presented [32]. The model basically consists of threesubmodels of hydrodynamics, gas–solidmixing, and reaction kinetics, couplingwiththe mass balances. According to the axial profile of solid concentration, the furnacewas axially divided into four different regions: dense bottom region, splash zone,dilute upper region, and exit region. In the bottom region, a bubbling bed wasassumed. In the dilute upper region, the two-phase flow was subdivided into anupward flowing lean suspension coexisting with descending dense clusters. Theinfluence of mixing on the overall performance was emphasized through validationagainst data from a large-scale combustor of Chalmers University of Technology.

12.5.4CFD Model

CFD simulation of CFB combustion processes is seldom reported. One relevantattempt has been made [68], which focused on CFB coal gasification. Xiao et al. [53]have reported their two-fluid simulation with kinetic theory of granular flow (KTGF)for the solids stress and EMMS model for the drag force. Owing to the limitation ofcomputing capacity, their reaction kinetics only concerned with carbon oxidation.The 2D simulation was applied to a 135 MWe CFB boiler in China. The preliminarycomparison revealed promising agreement with their measured data on the indus-trial unit. This simulation is an attempt to further exploration of CFD simulation ofcomplex processes inCFBboiler, especiallywith the rapid development of computingcapacity and skills.

12.5 Modeling Approaches j457

12.6Multiscale CFD Modeling of Combustion

To account for the clustering phenomenon and its effects on the flow, heat/masstransfer, and reactions in CFB boiler, multiscale CFDmodeling is the right choice. Itsolves hydrodynamics and the balances for mass and heat through a set of Eulerianconservation equations for each phase, and characterizes the clusteringwith sub-gridclosures of drag coefficient as well as heat and mass transfer coefficients. Some keyissues involved in thismultiscale CFDmodeling of combustion have been addressedin the above sections. Here, we summarize the simulation scheme with a modelingexample that is ongoing. The overall computation algorithm can follow that ofEMMS/mass model [35, 38].

12.6.1Governing Equations for Multiphase Flow and Reactions

To account for the effects of wide size distribution of particles on the hydrodynamicsand reactions, themulti-fluid (Nphases in total andn solid phases) Eulerian–Eulerianapproach is used. The gas mixture is assumed to be the only gas phase, such that thegas momentum conservation is written only for the gas mixture, its components,includingN2,O2, CO,CO2,H2O, SO2,NO2, and so on, are transported through scalarconservations. The solid particles can be divided into several phaseswith respect to itssize distribution, and each phase is a mixture of ash and carbon. The volatiles andmoisture in coal are assumed to be released and mixed instantaneously into the air.The variation of carbon contents is determined through scalar conservation equa-tions. Since the carbon content is quite low in a boiler under normal designs andoperations, we can assume the flow is unaffected by reactions so that the reactionsand hydrodynamics are decoupled and the computing load is reduced. Most of thegoverning equations here of continuity, momentum, and energy conservations areadapted from Fluent documentation [69]. The multiscale CFD approach is repre-sented by the EMMS-based drag coefficient [30], scalar transport equations of gascomponents and carbon [35], as well as bed-to-wall heat transfer coefficient [5], assummarized as follows.

12.6.1.1 Continuity Equation for Phase j (j ¼ 1, 2. . .N)

qqtðejrjÞþr � ðejrjujÞ ¼

XNi¼1

ð _mij� _mjiÞ ð12:57Þ

where

subscripts i, j denote i-th and j-th phase, respectively, of the multi-phase flow_mij denotes the mass transfer from phase i to j_mji denotes the mass transfer from phase j to i.


As the carbon content is low, the reaction andmass transfer are considered to have atrivial effect on the flow behavior, and then the right-hand side of the gas continuityequation vanishes as follows:

qqtðegrgÞþr � ðegrgugÞ ¼ 0 ð12:58Þ

The right-hand side of the solid continuity equations involves further the phasetransfer due to attrition and fragmentation and so on. Its closure depends on thepopulation balance modeling.

12.6.1.2 Momentum Equations for Gas Phase (g) and Solid Phase (s)

qqtðegrgugÞþr � ðegrgugugÞ ¼ �egrpg þr � tg þ egrgg

þXNi¼1

ðFig þ _miguig� _mgiugiÞð12:59Þ

qqtðesrsusÞþr � ðesrsususÞ ¼ �esrpg þrps þr � ts þ esrsg

þXNi¼1

ðFis þ _misuis� _msiusiÞð12:60Þ

where the subscript g denotes the gas phase, and s denotes any of the solid phases.The last two terms in the bracket can be neglected for the gas phase as thecontribution of reactions to the flow is assumed to be trivial. The stress tensor ofphase j reads:

tj ¼ ejmjðruj þruTj Þþ ej jj�

23mj

� �r � ujI ð12:61Þ

where I is the unit tensor, and the interphase force mainly consists of the drag forcebetween phase i and j as defined as:

Fij ¼ bijðui�ujÞ ð12:62Þ

For the gas–solid drag coefficient, as discussed above in the section on the EMMS/matrix model, it follows that:

bgs ¼ bEMMS ¼ 34CD

esegrg ug�us

�� ds

e�2:65g �HD ð12:63Þ

where the standard drag coefficient for single particles reads:

CD ¼0:44; Res > 100024Res

ð1þ 0:15 Re0:687s Þ; Res 1000

8><>: ð12:64Þ

12.6 Multiscale CFD Modeling of Combustion j459

where:

Res ¼egrgds ug�us

�� mg

ð12:65Þ

Table 12.1 shows a typical fitting correlation of HD for an industrial boiler [70].The solid–solid drag (or exchange) coefficient follows the definition of Syamlal [71]

as follows:

bls ¼3ð1þ elsÞ p

2 þClsp2

8

� �eselrsrlðdl þ dsÞ2g0;ls

2pðrld3l þ rsd3s Þul�usj j; ð12:66Þ

Table 12.1 Fitting correlation of HD for an industrial boiler; HD¼ a(Res þ b)c, RemfRe 1000,rp¼ 2000 kgm�3, rg¼ 0.301 kgm�3, mg¼ 4.64� 10�5 Pa�s, dp¼ 0.2mm, Ug¼ 5.5m s�1,Gs¼ 1 kgm�2 s�1, emf¼ 0.4 [70].

Fitting parameters (a, b, c) Range of eg

a ¼ 0:01711þ 0:19941

1þ expð�ðeg�0:4813Þ=0:03557Þ

� 1� 11þ expð�ðeg�0:5393Þ=0:01146Þ

0@

1A

c ¼ 0

0:4 eg < 0:52

a ¼ 0:01434þ 0:1519

1þðeg=0:5470Þ36:6602

b ¼ 0:04313þ 981:9191

1þ 10ðeg�0:4656Þ66:4858 þ 0:1345

1þ 10ð0:5949�egÞ34:7267

c ¼ 0:264� 0:2871

1þðeg=0:5610Þ28:6141

8>>>>>>>>>><>>>>>>>>>>:

0:52 eg < 0:616

a ¼ ð6928:05436�6913:7729egÞ�0:5291

b ¼ 14:4274�76:6432eg þ 153:00702e2g�134:5370e3g þ 44:00795e4g

c ¼ ð0:1636�0:1362egÞ0:5533

8>>><>>>:

0:616 eg < 0:988

a ¼ 1= 10:9534�10:2828e202:4751g

� �b ¼ 1= 3:8606�2:8974e280:1335g

� �c ¼ 1= 7:1479�4:3898e1052:8065g

� �

8>>>>><>>>>>:

0:988 eg < 0:9997

a¼ 1, c¼ 0 0:9997 eg 1


where

subscripts l, s denote arbitrary l-th and s-th solid phase, respectivelyels refers to the coefficient of restitutionCls refers to the coefficient of friction between the l-th and s-th solid-phaseparticlesg0,ls refers to the radial distribution coefficient.

The solid stress and pressure are closed by the kinetic theory of granular flow [72], inwhich the core parameter is the granular temperatureHs, whose transfer equation iswritten as follows:

32

qqtðesrsHsÞþr � ðesrsusHsÞ

� �¼ ð�psIþ tsÞ : ðrusÞþr � ðksrHsÞ

�cs�3bgsHs þ bgsCg �Cs

ð12:67Þwhere C denotes the fluctuating velocity and the covariance term of the fluctuatingvelocities can be assumed to vanish for large particles as a first approximation, andthe solid pressure reads:

ps ¼ esrsHs þ 2e2s rsð1þ essÞg0;ssHs ð12:68ÞIn which the radial distribution function reads:

g0;ss ¼ 1�Xnl¼1

el

es;max

!1=324

35�1

þ ds2

Xnl¼1

eldl

ð12:69Þ

and:

g0;ls ¼ dsg0;ll þ dlg0;ssds þ dl

ð12:70Þ

The solid shear viscosity consists of three parts, that is:

ms ¼ ms;kin þ ms;col þ ms;fr ð12:71Þ

where:

ms;kin ¼ 10rsdsffiffiffiffiffiffiffiffiffiHsp

p96asð1þ essÞg0;ss 1þ 4

5g0;ssesð1þ essÞ

� �2ð12:72Þ

ms;col ¼45esrsdsg0;ssð1þ essÞ

ffiffiffiffiffiffiHs

p

rð12:73Þ

ms;fr ¼ps sinw

2ffiffiffiffiffiffiffiI2D

p ð12:74Þ

The solid bulk viscosity:

js ¼43esrsdsg0;ssð1þ essÞ


p

rð12:75Þ


The diffusion coefficient for granular temperature:

ks ¼ 150rsdsffiffiffiffiffiffiffiffiffiHsp

p384ð1þ essÞg0;ss 1þ 6

5asg0;ssð1þ essÞ

� �2þ 2a2

s rsdsg0;ssð1þ essÞffiffiffiffiffiffiHs

p

r

ð12:76ÞThe collisional dissipation of granular temperature:

cs ¼ 3a2s rsg0;ssHsð1�e2ssÞ

4ds


p

r�r �us

" #: ð12:77Þ

12.6.1.3 Mass Conservation Equations for Gas and Solid ComponentsBased on the two-scale resolution of the structure as shown in Figure 12.9, thegas mass conservation equations can be divided into two sub-grid contributions, asfollows:

qqt

ð1�dÞegfrgh i

þr � ð1�dÞegfrgugfh i

¼ Sg;f þCg;i ð12:78Þ

qqt

degcrg

h iþr � degcrgugc

h i¼ Sg;c�Cg;i ð12:79Þ

where Sg,c and Sg,f denote the source terms due to chemical reactions and Cg,i

denotes the interphase exchange of gas between the dense and dilute phases due tocluster renewal and breakup. The relevant mass conservation equations for thesolids read:

qqt

ð1�dÞesfrs½ � þr � ð1�dÞesfrsusf½ � ¼ Ss;f þCs;i ð12:80Þ

qqt

descrs½ � þr � descrsusc½ � ¼ Ss;c�Cs;i ð12:81Þ

It is consistent that the sum of the right-hand-side terms results in the right-hand-side source terms of the relevant continuity equations. Since the sum of the sourceterms due to reactions is trivial compared to the bulk phase, we for simplicity canignore the first term on the right-hand side. The interphase exchange terms can beeasily obtained by solving either the dense or dilute phase conservation equations.

For the gas components, such as oxygen, we can derive mass conservationequations for the dense and dilute phases, respectively, as follows:

qðdegcrgxO2;cÞqt

þr � ðdrgegcugcxO2 ;c�degcDO2rgrxO2;cÞ�SO2 ;c þCO2 ;i ¼ 0

ð12:82Þq½ð1�dÞegfrgxO2;f �

qtþr � ð1�dÞrgegfugfxO2;f�ð1�dÞegfDO2rgrxO2 ;f

h i�SO2;f�CO2;i ¼ 0

ð12:83Þ


where

SO2;c and SO2;f denote the source terms due to chemical reactions with regard tooxygen conversionDO2 denotes the molecular diffusion coefficient of oxygenCO2;i denotes the interphase exchange of oxygen between the dense and dilutephases due to cluster renewal and breakup.

Figure 12.9 Two-scale resolution of the sub-grid conservation equations [35].


For the other reactive components in the gas mixture, the relevant equations can bewritten accordingly. Subtraction of the mass fractions of all reactive componentsfromunity gives that of inert componentN2. Themass fraction of carbon in each solidphase can be derived as follows:

qðdescrsxC;cÞqt

þr � ðdrsescuscxC;c�descDCrsrxC;cÞ�SC;c þCC;i ¼ 0 ð12:84Þ

q½ð1�dÞesf rsxC;f �qt

þr� ð1�dÞrsesf usf xC;f �ð1�dÞesf DCrsrxC;f ��SC;f �CC;i ¼ 0;

ð12:85Þwhere

SC,c and SC,f denote the source terms due to chemical reactions with regard tocarbon conversionDC denotes the pseudo diffusion coefficient of carbonCC,i denotes the interphase exchange of carbon between the dense and dilutephases due to cluster renewal and breakup.

Themass fraction of inert ash can be derived by subtracting that of carbon fromunity.

12.6.1.4 Energy Conservation EquationsThe energy conservation equation for phase j can be derived as follows:

qqtðejrjhjÞþr � ðejrjujhjÞ ¼ �ej

qpgqt

þ tj : ruj�r � qj þVj

þXNi¼1

ðQij þ _mijhij� _mjihjiÞð12:86Þ

where

hj is the specific enthalpy of the j-th phaseqj is the heat fluxVj is a source term due to chemical reactions or radiationQij is the intensity of heat exchange between the i-th and j-th phaseshij is the interface enthalpy.

If one neglects the temperature difference between solid phases and gas and theenergy transfer due to pressure and stress dissipation, the simplified energyconservation equation can be derived for the mixture of gas and solids as follows:

XNj¼1

qqtðejrjhjÞþr � ðejrjujhjÞ

� �¼XNj¼1

r � ðejljrTÞþVj � ð12:87Þ

12.6.2An Example of Simulation

The above model equations were recently used to simulate the furnace side of anindustrial 150MWeCFBboiler constructed inGuangdongprovince inChina [73]; the


boiler is 7.22� 15.32m in furnace depth and width and 36.5m high, with twocyclones 8.08m in inner diameter. As afirst approximation, the particles are assumedto be in one solid phase with mean diameter of 200 mm and density of 2000 kgm�3,and thus the coal attrition and fragmentation are neglected. The geometry of thewhole boiler follows the real settings of the unit, which is meshed with polyhedralgrid as shown in Figure 12.10. The initial solids inventory is determined with thedesigned pressure drop. The superficial gas velocity is around 6ms�1 in the furnace.For simplicity, only the carbon oxidation is considered in themass conservation in thepresent simulation, while the other reactions are taken into account only in theenergy equation. As the reaction has little effect on the flow behavior, the flow issimulatedfirstwithout any reactions, and then the reactions are added to compute theevolution of gas–solid concentrations after the solids flux reaches steady state, whichis around 10 kgm�2 s�1 for this case.

Figure 12.11 gives a snapshot of the isosurface plot of the solids volume fractiondistribution, along with some characteristic streamlines of gas phase. The densebottom, the splash zone, and the dilute top are captured. The huge vortex in thecyclones and the solids recycle in the siphon are also simulated in reasonableagreement with empirical knowledge. More detailed analysis on the flow as wellas the reaction behavior is ongoing. Such a vivid reproduction of theCFB combustionhas not been available until recently with the rapid development of computing andmodeling technologies. In addition, as experiments in such a hot unit are difficult toperform, we can expectmultiscale CFD simulationwith verifiedmodels can improveour understanding of the design and operation.

Figure 12.10 Geometry of a 150 MWe CFB boiler and its polyhedral mesh.


12.7Summary and Prospects

Circulating fluidized bed combustion involves complexmultiphase fluid dynamics aswell as the couplingbetweenflow,heat/mass transfer, andreactionkinetics over awiderange of spatial-temporal scales. Computational fluid dynamics coupled with multi-scale models enable an in-depth investigation of these related processes. Asmeasure-ment inCFBhot units is difficult to perform,we can expect thatmultiscale CFD simu-lationwill improveourunderstandingof the design andoperationofCFBcombustors.

Figure 12.11 Isosurface plot of the solids volume fraction distribution and some characteristicstreamlines of gas phase.

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