cfd modeling of rotary cement kilns

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERINGAsia-Pac. J. Chem. Eng. 2008; 3: 106–118Published online in Wiley InterScience(www.interscience.wiley.com) DOI:10.1002/apj.123

Research ArticleCFD modeling of rotary cement kilns

Kaustubh S. Mujumdar1,2 and Vivek V. Ranade1*1Industrial Flow Modeling Group, National Chemical Laboratory, Pune-411 008, India2Department of Chemical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai-400 076, India

Received 22 May 2007; Revised 8 July 2007; Accepted 12 July 2007

ABSTRACT: Rotary cement kilns are widely used to convert calcineous raw meal into cement clinker, and are keycomponents in the cement industry. In this article, we report a comprehensive computational fluid dynamics (CFD)-based model to capture key transport processes in rotary cement kilns. Separate but coupled computational modelswere developed for the bed and the freeboard regions of the rotary kiln. The complex swirling airflow produced bykiln burners, coal combustion, gas-phase combustion of volatile matter and radiative heat transfer in the freeboardregion were modeled. The clinkerization reactions in the bed region were modeled assuming solids as pseudo fluids.Coating formation in cement kilns (for both bed and freeboard regions) was considered. Appropriate source and sinkterms were developed to model transfer of CO2 from the bed to the freeboard region due to calcination reaction inthe bed region. The developed bed and freeboard models were coupled by mass and energy communication throughcommon interface. These coupled computational models were able to quite satisfactorily predict the available data fromindustrial kilns and previously published results. The computational models were also able to capture the intricacies ofthe burning zones of rotary cement kilns for changing burner-operational parameters like axial to swirl ratio and oxygenenrichment. The developed approach, computational models and simulation results will not only help in developingbetter understanding of cement kilns but also provide quantitative information about influence of burner design andother design parameters on kiln performance. 2008 Curtin University of Technology and John Wiley & Sons, Ltd.

KEYWORDS: rotary cement kiln; CFD; coal combustion; burner

INTRODUCTION

The formation and manufacture of clinker in cementindustry has been a focus of considerable attentionworldwide because of the high energy usage and highenvironmental impact of the process. Typically, forproducing one ton of cement, a well-equipped plantconsumes nearly 3 GJ of energy.[1] For each ton ofclinker produced, an equivalent amount of greenhousegases is emitted. Rotary kilns have the ability toprovide the desired energy and residence time fordriving solid–solid and solid–liquid reactions and aremost suitable as reactors for clinker formation. Rotarykilns used for carrying out clinkerization reactions in acement plant not only consume a major portion of totalenergy supplied but are also one of the main sourcesof CO2 emission in a cement plant. Considering theimpetus on reduction in emission of greenhouse gasesand reduction in energy consumption for quite sometime now, it is essential to understand the characteristics

*Correspondence to: Vivek V. Ranade, Catalysis, Reactors &Sepatations Unit, National Chemical Laboratory, Pune - 411 008,India. E-mail: [email protected]

of cement kilns in detail and use this understanding forperformance enhancement.

A schematic of the rotary cement kiln is shown inFig. 1. Partially calcined raw meal is fed slowly intothe rotary kiln (∼0.05 m/s) from one end. The solidsin the kiln move forward in a complicated path alongthe kiln length due to gravity, and simultaneously ina transverse direction due to the rotating kiln walls.As the solids move forward in the kiln, solid–solidand solid–liquid reactions occur in a bed region toform clinker. The energy required for the clinkerizationreaction is provided by the combustion of coal inthe freeboard region in a counter-current mode withrespect to the solids. Primary air and fuel are suppliedin appropriate quantities through burner nozzles alongwith secondary air and swirling air to produce a stableflame in the freeboard region. The coal combustionin the freeboard region transmits energy mainly viaradiation to the solids bed. The burner configuration,swirling air and other operating parameters influencethe flame characteristics, heat transfer to the bed region,and temperature profiles in the bed and the freeboardregions. Part of the solids melt and a coating is formedinside the kiln, which protects the refractory and kilnshells from extreme temperatures. Clinker composition

2008 Curtin University of Technology and John Wiley & Sons, Ltd.

Asia-Pacific Journal of Chemical Engineering CFD MODELING OF ROTARY CEMENT KILNS 107

Partially CalcinedRaw Meal

Exhaust gases

Clinker

Secondary Air

Coating

Entrainment Radiation

FlameClinker Reactions

Rotating kiln

Melt

Coal +Primary Air

Figure 1. Schematic of rotary cement kiln. This figure isavailable in colour online at www.apjChemEng.com.

and overall energy consumption in the kiln is controlledby temperature profiles and residence time of raw mealwithin the kiln.

Since the important reactions involved in clinkerformation occur in the rotary kiln, performance of therotary kiln controls the quality of the product andgoverns the overall performance of the plant. However,in spite of being the key equipment in a cement plantand being in practice for decades, there is a lack ofrealistic computational models for rotary cement kilns.The reason for this can be attributed to involvementof complex physics, multiple phases and occurrenceof several simultaneous processes with significantlydifferent time scales during clinker formation. In ourrecent work[2] we have developed a comprehensive one-dimensional model for rotary cement kilns. In this work,the computational models developed not only predictedthe behavior of industrial cement kilns satisfactorilybut also provided useful clues for reducing energyconsumption in rotary cement kilns. The numericalexperiments using the computational models could alsopredict the influence of the kiln’s operating parameterson net energy consumption in kilns. Such guidelinescan provide useful hints to operating engineers for kilnoptimization.

Unfortunately, due to its one-dimensional nature, thedeveloped computational model[2] cannot adequatelycapture the influence of burner design and key operat-ing parameters like ratio of swirling to axial air, oxygenenrichment, etc. on flame characteristics and perfor-mance of cement kilns. The knowledge of influence ofthese parameters on coal combustion, flame characteris-tics and temperature profiles within the kiln is essentialto ensure optimum performance of the kilns. In orderto ensure the quality of the product without jeopardiz-ing energy efficiency, it is essential to have a tool thatprovides detailed quantitative guidelines for manipu-lating burner operations. Computational fluid dynamics(CFD) framework offers promise of becoming such atool. Development of a comprehensive CFD framework,which can provide an insight and quantitative guidelinesfor burner design and optimization for cement kilns, was

therefore undertaken in this work. The complexity andcoexistence of a wide range of spatiotemporal scales andprocesses in rotary cement kilns demand different andunconventional approaches for developing CFD models.Some attempts at developing CFD models for rotarycement kilns have been made (for example, Refs [3and 4]). These models were limited to predicting theoverall behavior of cement kilns. These models did notconsider some important processes like coating forma-tion or modeling clinkerization reactions. Our earlierattempts at modeling a cement kiln[5] showed promis-ing results. This article reports the development of CFDmodels, which adequately accounts for most of the rele-vant processes occurring in cement kilns and provides atool to capture the influence of burner design and oper-ational parameters on the overall performance. In thiswork, however, we have not included a quantitative dis-cussion on energy saving and greenhouse gases reduc-tion in cement kilns for the reasons explained below.

It is important to note that, in a cement plant, a rotarycement kiln is closely coupled to the clinker cooler onone side and calciner on the other, which in turn, iscoupled to the preheater assembly. The quantitative pre-dictions on energy saving and greenhouse gas reductionwould require to simulate the entire train from preheaterto cooler.[6] However, simultaneous modeling of theentire suite in a CFD framework is almost an impos-sible task. Hence, the scope of the present work waslimited to discussing the development of a CFD modelfor a rotary cement kiln with the motive of capturing theinfluence of burner design and operating parameters onflame characteristics and performance of cement kilns.Some comments on the energy savings for differentburner-operational parameters are, however, included inthis article together with a general discussion on themanufacture of cement.

The next section discusses the computational modelin detail. Previously published CFD models were crit-ically reviewed before presenting the approach andmodel developed in this work. A solution methodol-ogy and simulated results are discussed thereafter. Thecomputational model was then used to understand theinfluence of various burner operating parameters on thekiln’s performance. Key conclusions based on this workare discussed at the end.

COMPUTATIONAL MODEL

Cement kilns are complex systems that involve occur-rence of several simultaneous processes in both thebed and freeboard regions. It is thus essential to firstidentify key issues and use appropriate methodologyto develop tractable computational models for rotarycement kilns. Key issues which need to be consideredwhile developing a comprehensive model for cementkilns are discussed in detail in our recent publication[2]

2008 Curtin University of Technology and John Wiley & Sons, Ltd. Asia-Pac. J. Chem. Eng. 2008; 3: 106–118DOI: 10.1002/apj

108 K. S. MUJUMDAR AND V. V. RANADE Asia-Pacific Journal of Chemical Engineering

and will not be repeated in this article. It is impor-tant to note that most of the previously published CFDmodels do not consider these key issues. The previousCFD models of cement kilns are briefly reviewed in thefollowing section.

CFD models for cement kilns

Due to the complexity of the physics involved, andthe occurrence of multiple phases with a large num-ber of reactions in the bed/freeboard regions, very fewCFD models have been published for rotary cementkilns.[3,4,7] Most of these computational models do notaccount for the main key issues simultaneously in asingle framework.[2] Mastorakos et al .[7] developed aCFD-based model for cement kilns, which includedcombustion, radiative heat transfer, conduction in thebed/walls and chemical reactions. The bed and free-board models were thus treated as separate domains,and coupling between them is handled explicitly. Thegeometry of the kiln was assumed to be axisymmetric inthis work, and therefore, the boundary conditions wereapplied only in an approximate manner. Moreover, thiswork assumed a formation of coating throughout thekiln length. Karki et al .[4] developed a 3D CFD-basedmodel for simulating simultaneous combustion and heattransfer in cement kilns. They have used an effectivethermal conductivity to define degree of mixing in thebed region, developing a single computational modelfor simulating cement kilns. Different values of effec-tive thermal conductivities at different locations in thekiln were used. However, there are no proper guidelinesto choose proper effective thermal conductivity, andthe values used are based on experience. Moreover, thework was mainly focused on modeling fluid dynamics,while heat transfer and clinkerization reactions were notmodeled. The model predictions thus gave only qualita-tive agreement with industrial observations, which areconsidered reasonable for global quantities of interest.Kolyfetis and Markatos[3] also focused on coal combus-tion and heat transfer in the freeboard region and didnot account for clinker reactions. Their computationalmodel did not consider any coating formation inside thekiln. The above discussion clearly points out the needfor developing better and more realistic CFD models ofcement kilns by accounting for key issues.

It is also important to note that along with physicalissues that need to be captured, there are numericalissues involved in cement kiln modeling. The freeboardregion of the kiln in which combustion of coal takesplace and the bed region of the kiln where clinkerizationreactions take place are strongly coupled with eachother. However, the characteristic time-and-space scalesof the freeboard and bed regions are significantlydifferent. The typical velocities of the gas phase inthe freeboard region are about 10 m/s while typical

velocities of solid particles in the bed region areof the order of about 0.05 m/s. In addition to thetime scales of the freeboard and bed regions, actualchemical reactions occur at the scale of the particles,which is much smaller than the length scale of akiln. Considering these vastly different characteristictime-and-length scales of processes, building a singleCFD-based model with the objective of capturing allthe relevant space-and-time scales might either failor become excessively computation-intensive. Earlier,Spang[8] has reported convergence difficulties whilesolving flow, heat transfer and reactions in the freeboardand bed regions simultaneously. Hence, in the presentwork, we have developed separate but coupled modelsfor the bed and the freeboard regions. The strategywas to simulate different regions with similar timescales separately, and then couple them by mass andenergy communication via common boundaries.[2] Themethodology adopted is pictorially shown in Fig. 2 andwill be explained in detail in the next section. Beforethat, we shall discuss the individual model equations forthe bed and freeboard regions in what follows.

Bed model

Several solid–solid and liquid–solid reactions occurin the bed region of rotary cement kilns. The fivemajor reactions considered by most of the researchersare given in Table 1. It can be seen that these reac-tions involve components like CaCO3, CaO, C2S, C3S,C3A and C4AF. While formation of some of the minorphases, viz. C12A7, C2AS, CS, C3S2, CS2, CF, C2F havebeen reported[9], they are generally present in insignifi-cant amounts and hence are usually neglected for mod-eling purposes.[7,8,10] We also consider only five majorreactions occurring in cement kilns during clinker for-mation (as given in Table 1) in the present study. Oneof the important issues in modeling these reactions isthe availability of the relevant kinetics. In our recentwork,[10] we have critically analyzed the modeling of

Heat Flux(bc* to bed)

Temperature(bc* to freeboard)

CO2 from CalcinationReaction in bed

common surface(bed/freeboard)

Heat Loss(Radiation + convection)

Conduction heattransfer (walls)

*boundary condition

Bed

Freeboard

Figure 2. Coupling methodology.



Table 1. Reactions, kinetics and heat of reactions.[9]

Reaction k0 E (kJ/mol) �H (kJ/mol)

Bed

1. CaCO3 = CaO + CO2 1.18 × 103 (kmol/m2/s) 185 179.42. 2CaO + SiO2 = C2S 1.0 × 107 (m3/kg/s) 240 −127.63. C2S + CaO = C3S 1.0 × 109 (m3/kg/s) 420 16.04. 3CaO + Al2O3 = C3A 1.0 × 108 (m3/kg/s) 310 21.85. 4CaO + Al2O3 + Fe2O4 = C4AF 1.0 × 108 (m6/kg2/s) 330 −41.3

clinkerization reactions in cement kilns. The kineticparameters used in this work for clinkerization reactionswere shown to work reasonably well for three differentindustrial kilns covering a wide range of operationalconditions. Therefore, these parameters were used tomodel kinetics in the present work.

In our one-dimensional model of a rotary cementkiln, the height variation of bed along the kiln lengthwas modeled using Krammer’s model[10,30,31,32]. Thesame bed height profile can in principle be includedin the CFD model. However, since the focus wason understanding flame characteristics, the bed heightvariation along the kiln was ignored in the presentwork to simplify the grid generation. The developedframework, however, can accommodate variation of thebed height in a straightforward manner.

The motion of solids in the rotating cylinder exhibitscomplex motion and various flow regimes. Severalattempts have been made to simulate motion of solids inthe transverse section of rotating cylinders.[11,12] Eventhe state-of-the art CFD models were not able to accu-rately capture the details of solids in motion.[12] Thesepreliminary studies on simulations of the motion ofsolids in a transverse plane of a rotating cylinder how-ever, indicated that the flow generated in a transversesection of the kiln might be approximated by treatingsolids as pseudohomogeneous fluids. The constant vis-cosity as well as the power-law viscosity models wereevaluated. Based on these studies we have treated solidsas pseudohomogeneous fluids with constant viscosity(2 kg/m/s) in this work.

Another important aspect of cement kilns is theformation of a coating which has a significant influenceon shell temperature profile and heat transfer. Formationof a coating in cement kilns is a complex function ofliquid formation in the bed, flow/reactions occurring inthe bed and freeboard regions, kiln r.p.m. and energyexchange between bed and freeboard regions. Thephenomenon of coating formation in cement kilns is notyet well understood. In our recently developed reactionengineering-based model[2] the location of the coatingformation was calculated as a part of the solution ofmodel equations. Nevertheless, such an approach isdifficult to use with the CFD framework since it willinvolve dynamic meshing. Our model predictions forthree industrial kilns with varying operating conditions

and dimensions showed that the coating formationoccurred only after half the kiln length from the entrypoint of solids. This also seems to be consistent withshell temperature measurements reported by Kolyfetisand Markatos.[3] However, there is no data/modelthat gives inputs regarding the beginning of coatingformation in cement kilns. In the absence of anyinformation, the location of coating formation wasassumed to be formed at the midpoint of the kiln lengthfrom the feed end.

It was essential to formulate appropriate boundaryconditions for the kiln walls to estimate heat lossesthrough the kiln shell. The outer wall of the kiln wasgiven a rotational boundary condition (5.5 r.p.m., seeTable 2) and heat loss through the shell was modeledusing convection and radiation. Ambient temperaturewas assumed to be 300 K. The convective heat trans-fer coefficient was considered to be 30 W/m2 K, assuggested by Mastorakos et al .[7], for industrial cementkilns. Mass, momentum and energy conservation equa-tions for the bed region are given below.

Mass conservation equation:

∂ρ

∂t+ ∇ · (ρu) = Sm,b (1)

Table 2. Dimensions and operating conditions of akiln.[2]

Sr. no. Variable Industrial kiln

1. Length (m) 502. Inner refractory diameter (m) 3.43. Coating thickness (m) 0.134. Speed of rotation (rpm) 5.55. Solids inflow (kg/s) 38.886. Height at solids entry (m) 0.467. Secondary air 13.469 kg/s; 1373 K8. Axial air 1.17926 kg/s; 313 K9. Coal air 0.943 kg/s; 328 K8. Swirl air 0.5266 kg/s; 313 K10. Coal fraction (kg/s) 1.2511. Char 0.6412. Volatiles 0.2713. Ash content 0.0914. Calorific value (kcal/kg coal) 620015 Coal particle size (µm) 100



Momentum conservation equation:

∂(ρu)

∂t+ ∇ · (ρuu) = −∇p − ∇ · σ + ρg (2)

Energy conservation equation:

ρCp∂T

∂t+ ρCpu · ∇T = ∇ · ((keff ∇T + τeff · u)

)

+Nc∑

i=1

Ri (−�Hr,i ) + Se,b (3)

Species conservation equation:

∂(ρYi )

∂t+ ∇ · (ρuYi ) = ∇ · (ρDi∇Yi ) + Ri (4)

In the above equations u is velocity, ρ is density, Tis temperature and Yi is mass fraction of species, i .Di is the diffusion coefficient of species i . The rate ofreaction Ri was based on simple Arrhenius law withactivity coefficients and energy of activation given inTable 1.[10] Sm,b and Se,b are the volumetric mass sinkterm (kg/m3/s) and volumetric heat sink term (W/m3)respectively, due to loss of CO2 caused by calcinationreaction occurring on the bed. The calculation of theseterms is discussed later in this section.

Freeboard model

A computational model based on the Eulerian-Lagran-gian approach was developed to simulate a pulverizedcoal burner in a cement kiln. Since the volume fractionof coal particles in the freeboard region is not expectedto go beyond 10%, the motion and burning of coal par-ticles was modeled using the Lagrangian approach.[13]

The standard k –ε model was seen to predict the gas-phase turbulence for the freeboard region of cementkilns quite satisfactorily and therefore was used in thiswork.[4,7] Gas-phase combustion was modeled usingfinite rate chemistry. Radiation was modeled using theP1 approach. The reasons for choosing these modelsare discussed in the individual subsections later on. Themodel equations for the continuous (Eulerian frame) andfor the dispersed particles (Lagrangian frame) are givenbelow.

Continuous phaseMass conservation equation:

∂ρ

∂t+ ∇ · (ρv) = Sm,comb + Sm,calc (5)

where, Sm,comb (kg/m3/s) is the mass source added tothe continuous phase from dispersed phase (i.e. due todevolatilization, char reaction) due to coal combustion

in the freeboard region, and Sm,calc (kg/m3/s) is the masssource added due to CO2 addition from the bed regiondue to calcination reaction.

Momentum conservation equation:

∂(ρv)

∂t+ ∇ · (ρvv) = −∇p + ∇ · (τ) + ρg + F (6)

where, p is the static pressure, τ is the stress tensor,ρg is the gravitational force and F is the external bodyforce that arises due to interaction of the dispersed phaseand other model-dependent source terms.

Energy equation:

∂(ρE )

∂t+ ∇ · (v(ρE + p)) = ∇ · (keff∇T − �hj Jj

+ (τeffv)) + Se,comb + Se,calc (7)

The first three terms on the righthand side of the equa-tion represent heat transfer due to conduction, speciesdiffusion and viscous dissipation, respectively. Se,combrepresents the heat source due to char combustion, andSe,calc is the heat source due to CO2 addition from thebed due to calcination reaction.

Discrete phaseThe motion of the coal particles was simulated using theLagrangian frame of reference by solving the followingequations

dup

dt= FD(u − up) + gx(ρp − ρ)

ρp+ Fx (8)

where uP is a particle velocity and u is a continu-ous phase velocity. The additional force Fx includesthe forces on the particles that arise due to rotationof the reference frame. FD(u − up) is the drag forceper unit mass of the particle. The present computa-tional model assumes coal particles to be comprisedof char, volatiles and ash. The computational modelsfor coal devolatilization, gas-phase mixing and combus-tion used in our recent work[2] were shown to predictthe performance of three different kilns with differentcoal composition and calorific values quite reasonably.Therefore, the same models were used in the presentwork. The coal particle first gets heated by absorbingenergy from the gas. The energy is received by con-vection and radiation. Due to heating the coal particlestarts to devolatilize. Some approaches use correlationsof volatile yield with particle temperature, or definedevolatilization rates using one- or two-step Arrehe-nius schemes.[4] The present model assumes a con-stant rate of devolatilization for coal combustion.[14]

The devolatilization constant recommended as 12.0 forcoal combustion[14] was used in the simulations.[2] Thecoal particle density was assumed to decrease in pro-portion to the volatiles released in the gas phase.[15]



On devolatilization, gas-phase combustion occurs. Theinvestigations of coal devolatilization have given rise toa number of models for volatiles and kinetics of theirgas-phase combustion (see, for example, Ref. [16]). Inmany cases, assumption of a generalized single global-step reaction of volatile fuel (and assumption of CH4 asvolatile matter in coal) has reproduced temperature pro-files for gas in the freeboard region reasonably well forcommercial coal combustors.[16–19] Our recent work[2]

on simulation of three different industrial cement kilnsfed with coal of different physical compositions alsolends an indirect justification for using the assumptionof single-step gas-phase combustion reaction. Hence,we have used a global single-step reaction of volatilefuel to model gas-phase combustion in this work as:

CH4 + 2O2 −−→ CO2 + 2H2O (9)

However, the framework developed is general enoughthat more complicated volatile combustion reactionscan be included as required. The kinetics and heat ofreaction for the assumed gas-phase reaction are givenin Table 1. It should be noted that the characteristicreaction time scales at temperatures prevailing in kilns(>1500 K) are less than 1 ms. Therefore, at such hightemperatures, the reaction will be limited by turbulentmixing rather than reaction kinetics. Two approaches,i.e. generalized finite rate formulation (eddy breakup(EBU) model) and mixture fraction/PDF formation aregenerally used to model-mixing of limited turbulentgas-phase combustion.[20] The main advantage of theEBU combustion model of Magnussen–Hjertager[21]

lies in its simplicity and robustness for its wide rangeof operating conditions. Hence, it is widely used forpredicting gas-phase combustion in coal combustors(Refs [4,16,17] and references cited therein), and hence,was used in this work. This model compares the kineticrate with the turbulence mixing rate and selects thelower rate for further calculations as:

Rcombg = min(RS,EBU, RS,Arr) (10)

where

RS,EBU = CRρk

εmin

(yF,

yox

b

),

RS,Arr = Bsρ2yFyOX exp

(− Es

RT

) (11)

yF is the mass fraction of the fuel and yOX is the massfraction of oxygen. The values for Arrhenius kineticconstants BS and ES are specified in Table 1. CR isa parameter of the EBU turbulent combustion model,which is usually set to 4. Char combustion was modeledusing a diffusion-limited surface-reaction model derivedfrom the model of Baum and Street.[22] This model is

extensively used for modeling char combustion in coal-fired furnaces[23] and was used in the present work.The model assumes that the surface reaction proceedsat a rate determined by the diffusion of the gaseousoxidant to the surface of the particle ignoring the kineticcontribution to the surface reaction rate.

Radiation modelingThe radiation was modeled using the P1 radiationmodel. The P1 radiation model is recommended foruse when the optical thickness aL >1, where ‘a’ is theabsorption coefficient of gas, and L is the characteristiclength of the system (Fluent 6.2 user manual). For theoperating conditions prevailing in the cement kilns, theoptical thickness is generally >1 (∼1.2–1.8 for the kilnunder study), and thus the P1 model was used to designradiation in the present work. The P1 model is thesimplest case of the more general P-N model, whichis based on the expansion of the radiation intensity intoan orthogonal series of spherical harmonics. When onlyfour terms in the series are used, the radiation heat fluxis given by:

qr = −�∇G (12)

where, � = 1

3(a + σs) − Cσs(13)

in which G is the incident radiation, a is the absorptioncoefficient, σs is the scattering coefficient and C is thelinear anisotropic phase function coefficient.

From the transport equation of G and combining theabove equation, we get

−∇qr = aG − 4aσT 4 (14)

When the effect of the coal particles in the P1 radiationmodel is included, the incident radiation is written as,

−∇qr = (a + ap)G − 4π

(aσT 4

π+ Ep

)(15)

where, ap is the equivalent absorption coefficient andEp is the equivalent emission of the particles. The localabsorption coefficient for the gas–particle mixture wascalculated using the following expression[4,24]

a = 0.32 + 0.28 e−Tg/1135 (16)

where T is the temperature in Kelvin. In the vicinityof the burner region, the absorption coefficient wasaugmented by 0.4 m−1 to account for soot.[4,24] Aconstant value of 0.13 m−1 was used for isotropicscattering coefficient.[4,24]

Mass transfer from bed to freeboard region

As calcination reaction takes place in the bed region,CO2 is released from the bed to the freeboard region.



The release of CO2 from the bed to the freeboard regionwas modeled in each region individually. For the bedregion, volumetric sink terms for mass (kg/m3/s) andenergy (W/m3) were applied to each cell through user-defined functions (UDFs) as

Sm,b = −RCO2 (17)

Where RCO2 is rate of CO2 produced in each cell andSm,b (kg/m3/s) is the volumetric mass sink in eachcell (in Eqn (1)). The mass sink in each cell was thuscalculated proportional to the amount of CO2 produceddue to calcination reaction. The corresponding heat sinkin each cell was calculated as

Se,b = −RCO2 × CP,CO2 × (TCO2,avg − Tbase) (18)

where Se,b (W/m3) is the volumetric heat sink in eachcell (see Eqn (3)). As a first approximation, we use anaverage temperature of the bed in the calcination region(i.e. TCO2,avg = 1000 K) to evaluate the heat sink fromthe bed. This mass and sink were passed as sources tothe freeboard region as described below.

In this model, we implemented the transfer of CO2from the bed to the freeboard as a function of axialposition. It is possible to transfer CO2 lost from thebed to the freeboard at every cell interfaces appearingon the bed-freeboard boundary (cell to cell couplingor 2D coupling). CO2 transfer from the bed to thefreeboard can also be implemented in the CFD modelby averaging over the chord of the bed at every axialposition (1D coupling, for example see Mujumdar andRanade[10]). Since the difference in the results predictedwith the 1D and 2D coupling was not significant (aswill be discussed later) we used 1D coupling for masstransfer from the bed to the freeboard. From the bed runthe averaged loss of mass at different axial locations wascalculated. From this information mass flux Fz(Kg/m2s)at different axial locations could be calculated. Themass source was passed to freeboard region as

Sm,calc =∫ L

0

Fz (z )

VdA (19)

where Sm,calc (kg/m3/s) is the mass source of CO2 to thefreeboard region, Fz (z ) is the mass flux profile obtainedalong the kiln length, V is the volume of the cell, anddA is the cross-sectional area through which CO2 entersthe freeboard region. A corresponding heat source termwas written for the freeboard model to account for heataccompanied by CO2 from the bed, and was written as

Se,calc =∫ L

0

(Fz(z )

V

)× CP,CO2×(TCO2,avg−298.0) dA

(20)

where Se,fb (W ) is the heat source due to CO2 enter-ing the freeboard region, and TCO2,avg is the averagetemperature of CO2 as discussed previously.

With these model equations, we now discuss themethodology adopted to simulate a rotary cement kiln.

Solution methodology

Though separate computational models were used forthe bed and the freeboard region, the computational gridwas generated for the whole kiln. Different componentsand the generated grid are shown in Fig. 3. The compu-tational grid for the bed, freeboard and shell regions wasextracted from this single computational grid. The com-mercial grid generation code, GAMBIT 2.0, was usedto model the geometry and to generate a computationalgrid for the entire kiln. All the simulations were carriedout using commercial FLUENT 6.2.9 solver. The over-all methodology is shown schematically in Fig. 2 andexplained below.

The bed model was first simulated independently.A pseudohomogeneous approximation was used tosimulate the motion of solids in the bed region. Inthe first phase, a constant viscosity was specified forthe bed material as discussed earlier. Simulation ofthe bed region was initiated by assuming a heat fluxat the bed–freeboard common interface (consideredas the wall for these simulations). The bed flow andthe reactions occurring were solved simultaneously toget the temperature profile for the common interfacebetween the freeboard and bed regions. The obtainedbed temperature was then used to initiate simulationsof the freeboard region. Combustion of coal particles inthe freeboard region was modeled using the Eulerian-Lagrangian approach. The freeboard was then simulatedusing the temperature profile from the bed run toget the heat flux profile for the common interface.This heat flux was then passed as boundary conditionto simulate the bed region again. This process wascontinued till the temperature and the heat flux throughthe interface did not change with further iterations.For the initial simulations, 1D coupling was initiated.Thereafter, some simulations were also carried outwith 2D coupling between freeboard and bed regions.This is discussed in the next section. Exchange ofCO2 from bed to freeboard region due to calcinationwas accounted for by appropriate source/sink terms.Suitable under-relaxation factors were identified forfaster convergence of a coupled solution.

RESULTS AND DISCUSSION

The computational model described in the previous sec-tion was used to understand the details of the burning



Figure 3. Computation grid. (a) Kiln burner, 12 axial air portsi, coal airinletii, swirl air inletiii; (b) bed region grid; (c) cross-sectional view of kiln (kilninternal diameter: 3.14 m); (d) burner grid; and (e) freeboard region grid.This figure is available in colour online at www.apjChemEng.com.

zone and overall behavior of rotary cement kilns. Ahexahedral grid of 18 100 (∼12 nodes in the radialdirection and 150 nodes in the axial direction) and5 85 000 cells (∼35 nodes in the radial direction and150 nodes in the axial direction) was used to simu-late the bed and freeboard regions of the kiln, respec-tively. Care was taken to resolve the region near theburner using a finer grid in order to capture swirl-ladenhigh-velocity flows produced by the kiln burner. Gridsof similar magnitude were found to be adequate forcement kiln simulations [see Ref. [7] and referencescited therein]. The discretization scheme for convec-tion and heat transfer terms of governing equations isquite important. Although second-order schemes canachieve higher accuracy and capture finer details forcomplex flow fields and multiple phase problems, theygenerally suffer from deteriorating convergence. Oursimulations also indicate that first-order schemes werefound to be much more stable. Because of complexityof the current problem and the need to couple swirlingflow, combustion, heat transfer and species transport,all the governing equations were discretized using first-order upwind scheme (see Ref. [25] and references citedtherein). To avoid large oscillations and divergence ofsolutions under relaxations for momentum, k , ε, energy,radiation and species in individual CFD simulationswere initially started with 0.1 for the first 1000 simula-tions and then gradually increased to 0.5 as the solutionprogressed. During simulations of bed and freeboardregions, the temperatures at different locations weremonitored. The individual runs for bed and freeboardregions were simulated till the temperatures at these

locations did not change beyond 0.1%. For this levelof accuracy, the residual values for a convergence runreached well below 10−4 for all the equations. Typi-cally, one bed run required a CPU time of ∼5 h, and thefreeboard required a CPU time of ∼20 h to convergencewith this grid on a dual processor machine of 2 GHzprocessor speed and 2 GB memory. The results for cou-pling of bed and freeboard regions are discussed below.

Coupling of bed and freeboard regions

The computational model was used to simulate a typicalindustrial kiln in which the dimensions and operatingconditions are specified in Table 2.[2] The properties ofgas and solids used for these simulations are specifiedin Table 3. The bed and freeboard regions of thekiln were simulated separately and communicated viamass and energy communication through a commoninterface. To accelerate the convergence typically forfirst few iterations, 1D coupling was done. For this1D coupling the temperature and heat fluxes wereaveraged radially at each axial location and were passedto freeboard and bed runs, respectively (see SolutionMethodology section). An under-relaxation of 0.5 wasused in these simulations. The iterative procedure wascarried out till the temperature and heat flux of commoninterface did not change further within an error of±1%. Once 1D coupling was converged, 2D couplingwas initiated. For these simulations, coupling the heatflux and temperature values between common interfaceof bed and freeboard regions were not averaged in



Table 3. Physical properties used in simulations.

Sr. No. Variable Value

1. Bed density (kg/m3) 1046b

2. Bed heat capacity(kJ/kg K)

1.088c

3. Bed thermalconductivity(W/m K)

0.5a

4. Gas heat capacity(J/kg K)

(0.106TG + 1173)d

5. Gas viscosity (kg/m/s) (0.1672 × 10−5√

TG −1.058 × 10−5)d

a Ref. [26].b Ref. [4].c Ref. [8].d Ref. [17].

the radial direction. A cell-to-cell correspondence oftemperature and heat flux at a common interface wascarried out. Since 1D runs were already converged,no under-relaxation was used in these simulations. Theiterations with 2D coupling were carried out till thebed temperature in the kiln did not change further(within ±0.1%). Typically, 10 iterations of 1D couplingand three iterations for 2D coupling were required forcomplete convergence.

However, it was observed that the difference in resultsof converged 1D-coupled simulations and 2D-coupledsimulations were insignificant. The comparison of tem-perature contours for converged 1D-and 2D-coupledsimulations are shown in Fig. 4(a) and (b). The area-weighted average temperature of the gas in the free-board region is shown in Fig. 4(c). It can be seenfrom Fig. 4(c) that the difference in averaged predic-tions was also insignificant. Moreover, the percentageerror in total amount of heat flux given to the bed regionby the two methods was less than ∼0.5%. Therefore,all the subsequent simulations were carried out usinga 1D-coupling methodology. This saves CPU time byapproximately 20%.

Simulations of rotary cement kilns

The converged simulations of bed and freeboard modelswere analyzed to gain insights into flame characteristicsand three-dimensional flow, temperature and composi-tion distribution with the kiln. Unfortunately, there wereno temperature and composition measurements avail-able inside the kiln. Hence, the model results wereinitially compared with available data at the kiln exitend. The results were also compared with results of theone-dimensional model of Mujumdar et al .[2] A com-parison of bed and freeboard region temperatures bythe present CFD model (temperature in central x -plane)and the 1D model[2] for the same kiln with the sameoperating conditions are shown in Fig. 5(a) and (b). A

(a)

(b)

(c)

1200

1400

1600

1800

2000

2200

2400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Normalized kiln lengthG

as T

empe

ratu

re, K

1D Coupled

2D Coupled

Figure 4. (a) Temperature contours in central x-plane(1D coupled). (b) Temperature contours in central x-plane(2D coupled). (c) Comparison of area-weighted averagedfreeboard gas temperature. This figure is available in colouronline at www.apjChemEng.com.

deviation in temperature predictions by CFD and 1Dmodel, as can be seen from these figures, could be dueto difference in assumption of internal coating formationin both the models. This is explained later in this sec-tion. The mass fraction profiles of C3S and C4AF alongthe kiln length by the CFD and 1D models are shown inFig. 5(c) and (d). These results seem to be reasonable.

The temperature distribution by the kiln wall controlsthe net loss to the environment, which is one ofthe major contributors in the net energy consumptionin the kiln. Thus, it is essential to calculate theshell temperatures accurately. The comparison of shelltemperatures by the two models is shown in Fig. 6(a).It is important to note that the CFD model wasable to capture the temperature dip (∼200 ◦C) asobserved in industrial data (see Fig. 6(b)). This wasdue to additional resistance to heat transfer causedby the coating formation. Such dips in the shells’temperatures have not been presented in previouslypublished CFD models due to inconsistent modelingof coating formation.[3,7] The quantitative difference intemperature predictions of the two models could bedue to difference in location of coating formation inthe CFD and 1D models, respectively. The 1D modelwas able to calculate the coating formation based onoperating conditions (the coating was calculated to beformed at around one-fourth of the kiln length from thesolid’s exit end). However, in the CFD approach, due



0

500

1000

1500

2000

2500

3000

0 0.2 0.4 0.6 0.8 1

Normalized kiln length

Tem

pera

ture

, K

CFD1D Model

0 0.2 0.4 0.6 0.8 1

Normalized kiln length

0

500

1000

1500

2000

2500

3000

Tem

pera

ture

, K

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Normalized Kiln Length

C3S

Mas

s F

ract

ion

CFD

1D Model

0 0.2 0.4 0.6 0.8 1

Normalized Kiln Length

0

0.2

0.4

0.6

0.8

1

C4A

F M

ass

frac

tion

CFD

1D

(a)

(c)

(b)

(d)

Figure 5. (a) Comparison of the bed temperature with published results.[2] (b) Comparisonof the freeboard temperature with published results.[2] (c) Comparison of clinkercomposition (C3S) with published results.[2] (d) Comparison of clinker composition (C4AF)with published results.[2]

to a prior meshing requirement, one has to assume thecoating length in the kiln before the simulations (thecoating formation was assumed to be formed at aroundthe halfway point of the kiln length from the solid’s exitend in the present work).

The quantitative comparison of the temperature andclinker composition by the model with the industrialdata and 1D model is given in Table 4. In general, thepresented CFD model was able to capture the overallbehavior of the kiln reasonably well when comparedwith industrial observations and published results.

Table 4. Comparison of model predictions withindustrial data and published literature.

Sr.no. Variable

Industrialdata CFD 1D[2]

1. Mass fraction C3S 0.483 0.501 0.4872. Mass fraction C2S 0.239 0.225 0.2773. Mass fraction C3A 0.051 0.052 0.0524. Mass fraction

C4AF0.143 0.129 0.144

5. Mass fraction CaO 0.084 0.087 0.046. Temperature of

solids (K)1673 1632 1636

On obtaining reasonable agreement with industrialobservations and previously published results, the CFDmodel was used to understand the intricacies of theburning zone in cement kilns which cannot be cap-tured by a 1D model. Typical results obtained by theCFD model for coal devolatilization, char burnout andCO2 mass fractions in the central plane of the freeboardregion are shown in Fig. 7. Information regarding thelocation of release of volatiles in the freeboard region(see Fig. 7(a)) and char burnout (see Fig. 7(b)) in theradial direction can be obtained from such simulations.The simulation results can help identify various zones ofcoal combustion. The possibility of coal particles hit-ting the walls or bed due to improper burner designor operating conditions can be identified. CO2 massfraction in the central plane of the freeboard region isshown in Fig. 7(c). The CO2 mass fraction was highernear the solid’s entrance due to calcination reaction.Figure 7(d) represents the temperature contours in thecentral plane of the freeboard region. The possibility oftemperature zones beyond acceptable limits due to tilt-ing of the flame and possible damages to the refractorycan be examined using such results. If the simulationsindicate undesired flame characteristics, the CFD modelcan be used to understand the influence of various



(a) (b)

Figure 6. Comparison of shell temperatures with published literature.[2] (a) Predictionsby computational model Abscissa 1 corresponds to burner location. (b) Reported shelltemperature measurements from an industrial kiln[3]. Kiln Length: 75 m, Inner diameter:4.35 m. Abscissa 0 corresponds to burner location.

(a)

(b)

(c)

(d)

Figure 7. (a) Coal devolatilisation, Kg/s ( = 1.52 × 10−5;= 0). (b) Char burn out, Kg/s ( = 1.24 × 10−4; = 0).

(c) CO2 mass fraction ( = 1.0; = 0). (d) Temperaturecontours in central vertical plane of freeboard region, K (= 2330K; = 300K). This figure is available in colour onlineat www.apjChemEng.com.

burner design parameters and operating protocols onflame characteristics. The figures predicted by the devel-oped model for temperature and mass fraction for coaland air in the freeboard region seem to be reasonablewhen compared with industrial observations. Thus, thedeveloped model was not only able to envisage thebehavior of cement kilns as reported in previously pub-lished results but was also able to provide informationregarding burning zone intricacies quite satisfactorily.

Effect of burner-operational parameters onthe kiln performance

Numerical experiments were then carried out using themodel to investigate the influence of burner-operational

parameters on the kiln behavior. The burner of cementkilns forms one of the most important components ofthe entire system, which controls the flame charac-teristics in the freeboard region and subsequently theperformance. Predetermined quantities of primary airand secondary air are passed through the burners alongwith swirl air and fuel to get the desired flame charac-teristics. For industrial cement kilns, typically primaryair is passed through the burner as high-momentumjets (∼200–250 m/s) along with relatively slow sec-ondary air (∼15–20 m/s). The swirl air passed throughthe burner opens the primary jet and influences therate of entrainment of secondary air in the primaryair. The relationship between jet momentum and theswirl/secondary component of air has significant effecton flame length and heat transfer in cement kilns.[27]

It is observed that kilns with low jet momentum suf-fer from poor air-fuel mixing, with long flames leadingto more fuel consumption.[27] The developed computa-tional model was used to analyze the effect of variationof axial to swirl ratio through the burner (consequenteffect of axial jet) on the flame characteristics in thefreeboard region and corresponding effect on clinkercomposition.

The base case simulation (explained earlier) wascarried out at an axial to swirl ratio of 2 with a veryhigh primary jet velocity (∼245 m/s). To capture thefreeboard region temperature profiles at low-momentumjets, the ratio of axial to swirl air was reduced from2 to 1 (with axial velocity reduced to ∼100 m/s).The consequent change in the temperatures due toreduced axial jet momentum in the central plane ofthe freeboard region is shown in Fig. 8(a) and (b).As the primary air jet momentum is reduced, theflame (shown by temperature contours) tends to becomelarger (see Fig. 8(b)). Consequently, for low axial jet



simulation, C3S composition decreased to 0.45 from0.5 by reducing axial to swirl ratio from 2 to 1. Boththese results seem to be in reasonable agreement withprevious results for cement kiln coal burners.[27] Thereduction in axial velocity and consequent increasein swirl component causes expansion of primary jet(i.e. enhanced jet entrainment, see Fig. 8(a) and (b))which is also in agreement with published results.[28]

Moreover, the temperature profiles obtained in thefreeboard region (see Fig. 8(a) and (b)) for differentaxial to swirl ratios seems to be reasonable, at leastqualitatively, when compared with published resultsfor burners operated with different fuels.[29] Thus, thedeveloped computational model was able to capture theinfluence of the ratio of swirl to axial air on the flamecharacteristics, and the performance of cement kilns.

The computational model was also analyzed to pre-dict the temperature profiles in the freeboard regionof the kiln for different burner-operational parameters.For example, influence of changing inlet coal parti-cle size, coal flow rate, ash content of coal at thesame energy input (by changing coal flow rate) andoxygen enrichment of the primary air on temperatureprofiles in the kiln is shown in Fig. 9(a).[5] It can beseen that, at the same levels of energy input by coal,the temperatures are more or less similar (no signifi-cant influence of particle size or ash content) exceptwith oxygen-enriched air. As expected, decreasing thecoal flow rate from 1.5 to 1 kg/s decreases the overallenergy supplied to the kiln and therefore the freeboardtemperature decreases. With coal particles containingmore ash, the position of maximum temperature shiftsslightly away from the burner. When oxygen-enrichedair was used, a significant increase in the maximum tem-perature was observed. This was because of enhancedcombustion rates due to availability of more oxygen inoxygen-enriched air. The comparison of mass fractionof volatiles for this case with the base case is shown inFig. 9(b). It can be seen that with enriched oxygen, therate of consumption of volatiles was significantly higher

(a)

(b)

Figure 8. (a) Temperature contours in central vertical planeof freeboard region Axial to swirl ratio = 2 ( = 2330K;= 300K). (b) Temperature contours in central vertical planeof freeboard region, K Axial to swirl ratio = 1 ( = 2280K;

= 300K). This figure is available in colour online atwww.apjChemEng.com.

0

500

1000

1500

2000

2500

3000

3500

0 0.2 0.4 0.6 0.8 1

Dimensionless Kiln Length

Gas

Tem

pera

ture

, K

Kiln-normal-operationLow-coal-flow-rateOxygen-enriched-airLow-coal-Particle-sizeLow-Coal-Grade

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.1 0.2 0.3 0.4

Dimensionless Kiln Length

Vol

atile

s M

ass

Fra

ctio

n in

Fre

eboa

rd,

O2 enriched

Base

(a)

(b)

Figure 9. (a) Predicted gas temperature profiles. (b) Pre-dicted profiles for volatile mass.

than the base case. Thus, the developed CFD model canprovide guidelines for ensuring the desired flame sizeand position for different coal grades either by manip-ulating coal particle size, swirl to axial air ratio, orpossible use of oxygen enrichment of primary air.

Further work on modeling of melting and using betterconstitutive equations for solids phase[12] is in progressand may enhance the utility of models and frameworkdeveloped in this work.

CONCLUSIONS

A comprehensive framework of a CFD-based modelwas developed to simulate coal combustion, radiationand clinkerization reactions occurring in rotary cementkilns. Due to significantly different physical time scales,separate but coupled models were developed for the bedand freeboard regions of cement kilns. The Eulerian-Lagrangian approach-based model was developed forcombustion of pulverized coal in the freeboard region ofkilns. The radiation was modeled using the P1 radiation



model. The solid–solid reactions in the bed region weresimulated using a pseudohomogeneous approximation.The bed and the freeboard region models were coupledtogether by mass and energy communication throughcommon boundaries. The developed CFD model wasable to predict the data at the exit end of industrialkilns and the published data in the literature was quitesatisfactory. The model provided qualitative as well asquantitative information about the key parameters likeregions of devolatilization, char combustion, burningzone position, clinker reactions, etc. The developedmodel was also able to capture the influence of burnerdesign and key operating parameters like ratio of swirlto axial air, oxygen enrichment, etc. on the flamecharacteristics in the freeboard region and performanceof cement kilns. The following specific conclusions aredrawn from the present study:

• The presented coupling methodology to solve modelequations representing processes occurring in rotarycement kilns worked well and can be extended toother similar complex reactors. It was observed thataveraged coupling methodology (i.e. 1D coupling)saves computational resources compared to the cell-to-cell coupling methodology (i.e. 2D coupling) with-out jeopardizing accuracy of predicted results.

• The simulation results indicate that reducing burnerprimary jet velocities produces longer flames in thefreeboard region and consequently increases energyrequirements of rotary cement kilns.

The developed model and presented results will helpin providing detailed information, and in developingoptimum operating protocols for cement kiln operations.

Acknowledgments

The authors would like to acknowledge many helpfuldiscussions with Professor Anurag Mehra, IITB, duringthe course of this work. One of the authors (K.S.M.)is grateful to the Council of Scientific and IndustrialResearch (CSIR), India, for providing financial support.

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