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Influence of Air Humidity on Drying of Individual IronOre PelletsAnna-Lena Ljung a , T. Staffan Lundström a , B. Daniel Marjavaara b & Kent Tano ba Luleå University of Technology, Division of Fluid Mechanics , Luleå, Swedenb LKAB , Luleå, SwedenPublished online: 27 Jun 2011.

To cite this article: Anna-Lena Ljung , T. Staffan Lundström , B. Daniel Marjavaara & Kent Tano (2011) Influence of AirHumidity on Drying of Individual Iron Ore Pellets, Drying Technology: An International Journal, 29:9, 1101-1111, DOI:10.1080/07373937.2011.571355

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Influence of Air Humidity on Drying of Individual IronOre Pellets

Anna-Lena Ljung,1 T. Staffan Lundstrom,1 B. Daniel Marjavaara,2 and Kent Tano21Lulea University of Technology, Division of Fluid Mechanics, Lulea, Sweden2LKAB, Lulea, Sweden

The influence of air humidity on drying is investigated at four inletair dew points; Tdp¼ 273, 292, 313, and 333K. A numerical modeltaking into account capillary transport of liquid and internal evapor-ation is applied to a spherical geometry representative for an individ-ual iron ore pellet. Drying simulations are carried out withcommercial computational fluid dynamic (CFD) software and theboundary conditions are calculated from the surrounding fluid flow.The results indicate that the effect of air humidity arises from the startof the first drying period, that is, the surface evaporation period,whereas the difference is reduced at the end of the period due to a pro-longed stage of constant rate drying attained at high saturations. Atlow saturations, there is no constant drying stage because the surfacebecomes locally dry before the pellet temperature has stabilized at thewet bulb temperature. The magnitudes of the drying rates and moist-ure contents are rather similar at the time when internal dryingbecomes dominating (i.e., when the total surface evaporation rate iszero) for the respective dew points, yet the drying time is increasedat high saturations. It was also found that the moisture gradients atthe surface and inside the pellet increased with drying rate.

Keywords CFD; Convective drying; Heat and mass transfer;Mathematical modeling; Porous media

INTRODUCTION

Iron ore pellets are a highly refined product supplied tothe steel-making industry. The use of pellets offers manyadvantages such as customer-adapted products, transport-ability, mechanical strength, and quality control yet itsproduction is time and energy consuming. There is thus anatural driving force to enhance the process in order tooptimize production and improve quality.

Induration of pellets is generally performed by straightgrate or grate-kiln processes. Typical for both types ofprocesses is that balled pellets made from a mixture of ironore, additives, and water (so-called green pellets) are trans-ported through a drying zone, a preheating zone, a firingzone, and a cooling zone. In the drying and preheat zones,pellets are packed on a moving grate while warm air isconvected through the bed. A rotary kiln is used in the

firing zone of a grate-kiln furnace, whereas the grate iscontinued through firing in a straight grate process. Anoverview of drying methods currently used in the mineralprocessing industry was presented by Wu et al.[1] In thedrying zone of a straight grate process, warm air isconvected through the bed first from below (up-draughtdrying, UDD) and then from above (down-draught drying,DDD). The reason for using two drying directions is to firstmake the lower layers more resistant to pressure in UDD.Hence, hot air driven from below will make the lower partof the bed dry quickly but the air will soon cool from itsinlet temperature to its dew point, which may lead torecondensation in the upper part of the bed. The greenballs are weakened when water condenses in the bed,resulting in a limitation in the bed height. When the greenballs reach DDD, their strength should have improvedenough to avoid problems due to condensation. Dryingof an individual pellet is generally divided into four stagesconcerning evaporation of free water: (1) evaporation ofliquid moisture at the pellet surface, (2) surface evapor-ation coexisting with internal drying as the surface islocally dry, (3) internal evaporation with a completelydry surface, and (4) internal evaporation at boiling tem-peratures.[2,3] It has been debated whether or not the dryingrate in the surface evaporation stage is constant.[4–6]

Mathematical description of the drying of iron ore pelletshas previously been considered by Huang et al.,[7] who pro-posed a mathematical model for the whole drying processbased on mass balance and energy conversions. Alternativeroutes were applied by Sadrnezhaad et al.,[8] Tsukermanet al.,[3] and Barati,[9] all describing drying of individual pel-lets by the use of shrinking core models. The surface evapor-ation period of an individual iron ore pellet placed in infinitespace was investigated by Ljung et al.,[4] in which a diffusivemodel with constant diffusivity of internal liquid was appliedto a two-dimensional cylindrical geometry representative foran iron ore pellet. In their work, the asymmetric influence ofthe heat and mass transfer from the surrounding flow fieldwas taken into account by the use of computational fluiddynamics (CFD). Considering both the liquid and vapor

Correspondence: Anna-Lena Ljung, Lulea University ofTechnology, Division of Fluid Mechanics, SE-971 87, Lulea,Sweden; E-mail: anna-lena.ljung@ltu.se

Drying Technology, 29: 1101–1111, 2011

Copyright # 2011 Taylor & Francis Group, LLC

ISSN: 0737-3937 print=1532-2300 online

DOI: 10.1080/07373937.2011.571355

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phases, and with the diffusivity of liquid as a function ofsaturation, etc., a three-dimensional model including all fourstages of drying was compared against experimental resultsin Ljung et al.[2] with very good agreement.

A review of applications of CFD in drying processes ingeneral was provided by Jamaleddine and Ray.[10] Zili[11]

adopted the finite volume method when simulating dryingof a granular material, an approach also used by Wuet al.[12] who simulated drying of a three-dimensional moistobject. Two-dimensional simulations were performed byCarmo and Lima,[13] who investigated drying of an oblatespherical solid. Janjai et al.[14] used a finite element–basedmethod to model two-dimensional moisture diffusion ina mango. Simulations of diffusive moisture transport in atwo-dimensional cylindrical object were conducted by Kayaet al.[15] The coupling of heat and mass transfer between aporousmediumand its surroundingswas investigated byErri-guible et al.[16] and three-dimensional simulations of dryingshowing the importance of taking the surrounding flow fieldinto account were conducted by Mohan and Talukdar,[17]

promoting the approach in Ljung et al.[2,4] The effect ofhumidity on drying of porous materials in fluidized bedswas previously studied by Tatemoto et al.,[18] who found thatthe temperature at the sample center increased with humidityat high pressures. Fritzell et al.[19] concluded from experi-mental investigation of drying of medium density fiberboard(MDF) fibers that the drying rate decreased with humidity,and a constant drying rate was observed in all studied cases.

As previously stated, the relative humidity in a bed ofpellets can be high, leading to condensation when the airis cooled by the pellets. It is therefore of interest to investi-gate how the level of surrounding air saturation affects dry-ing. Using the drying model developed and validated inLjung et al.[2] for individual pellets, we aim to apply themodel to some special cases important for the drying of abed of iron ore pellets with humidity of the surroundingair in focus. Together with detailed data regarding the localmoisture content, drying rate, and temperature as well asthe transition between drying periods, it is also of interestto examine the existence of a constant rate drying period(see Fritzell et al.[19]) at boundary conditions relevant forpellet drying. Pellets at different positions in a bed can besubjected to rather different boundary conditions, with,for example, lower temperature and higher humidityfurther up in the bed in the UDD zone. The focus of thiswork is, however, the particular effect of humidity, andall simulations are therefore carried out with an individualspherical pellet placed in infinite space. Even though thedistribution of the heat and mass transfer coefficients atthe surface can be expected to vary significantly from pel-lets packed in a bed, simulations of a single pellet are per-formed to show trends and tendencies that are also validfor pellets in packing. Pellets with fixed initial pellet andair temperatures are thus compared for four dew points,

Tdp¼ 273, 293, 313, and 333K, representing differentpositions in the bed or stages in time of the drying.

THEORY

The drying model used for simulations is here rendered inbrief. For a more thorough description of the model, thereader is referred to Ljung et al.[2] The model is applied toan individual iron ore pellet placed in a stream of air andthe surrounding aswell as the internal fluid flows aremodeled.

Surrounding Fluid Flow

The following continuity, momentum, and energyequations hold for the surrounding fluid flow:

@q@t

þr � quð Þ ¼ 0; ð1Þ

qDu

Dt¼ �rpþ lr2u ð2Þ

and

qcp� �

f

@Tf

@tþ qcp� �

fu � rTf ¼ r � kfrTf

� �þ uf ; ð3Þ

respectively.

Porous Domain

The continuity equations for the flow of liquid andvapor phases inside the porous medium are

@Ml

@t�r � DslrMlð Þ ¼ � _mml

qs 1� eð Þ ð4Þ

and

@Mv

@t�r � qg/gDav;effr

Mv

qg/g

!¼ _mml

qs 1� eð Þ : ð5Þ

The volume fractions,/; porosity, e; liquid-phase saturation,S; and moisture contents, M, are related as

/g þ /l þ /s ¼ 1 ð6Þ

e ¼ 1� /s ð7Þ

S ¼ /l

eð8Þ

Mtot ¼ Mv þMl ¼qv/v

qs/s

þ ql/l

qs/s

: ð9Þ

The effective diffusivity, Dsl, in the second term of Eq. (4)may be expressed as[2,20]

Dsl ¼ KKrl2

r2ccðrcÞrll: ð10Þ

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The permeability, K, is estimated by Ljung et al.[2] asK¼ 2.501e-14m2 for an iron ore pellet. The relativepermeability, Krl, is a function of the saturation, S, and theirreducible saturation, Sir,

Krl ¼S � Sir

1� Sir

� �3

: ð11Þ

The irreducible saturation is the saturation for which theliquid is no longer a continuous phase. A value of Sir¼ 0.150.15 is assumed, following the work of Plumb.[21] WithcðrcÞ ¼ pr2ca=A, the distribution function a(r) can be determ-ined from the expression[22]

eA ¼Z rmax

rmin

pr2a rð Þdr: ð12Þ

A constant distribution of particle sizes [a(r) ¼ const] withrmin¼ 3.5mm and rmax¼ 22.5mm is assumed. The criticalradius, rc, can be derived in a similar way as

rc ¼3/l

p a A=ð Þ þ r3min

� �1=3

: ð13Þ

For water, r=ll is a linear function of temperature accordingto the following relationship[20]:

rll

¼ 1:604T � 394:3ðm=sÞ: ð14Þ

The effective binary diffusion coefficient, Dav,eff, in thesecond term of Eq. (5) is related to the ordinary binary dif-fusion by a Bruggeman-type correlation in order to accountfor the pore tortuosity

Dv;eff ¼ /3 2=g Dav: ð15Þ

By applying a total energy equation where the materialproperties are a combination of iron ore, water, and airproperties, the temperature distribution inside the pelletmay be calculated from the following expression:

@

@t1� eð Þ qcð Þsþ/l qcð Þlþ/g qcð Þg

� �Ts

¼ r � kmrTsð Þ þ us:

ð16Þ

The overall thermal conductivity, km, is taken as the arithme-tic mean of the conductivities.

Internal Evaporation

The internal drying process is driven by temperature andlimited by the relative saturation, RS, of vapor in air. Onlytemperatures below the boiling point are considered here.

The mass flux originating from evaporation can be derivedfrom

_mml ¼ hmsfasf qv;satðTÞ 1�RSð Þ ð17Þ

where hm,sf is an interstitial mass transfer coefficient. Con-vection heat and mass transfer at a surface is analogous,and the heat and mass transfer coefficients can be relatedby the heat and mass transfer analogy[23] as

h

hm¼ k

DavLe1=3ð18Þ

where Le is the ratio of the thermal and mass diffusivities(Le¼ k=qcpDav). Because the heat and mass transfer for aparticular geometry is interchangeable, the interstitial heattransfer coefficient, hsf, and interstitial mass transfer coef-ficient, hm,sf, are comprised by Eq. (18). The value of theinterstitial heat transfer coefficient hsf depends, in its turn,on all variables influencing convection such as the surfacegeometry, the nature of fluid motion, the properties ofthe fluid, and the bulk fluid velocities.[23] An appropriatevalue for the interior of an iron ore pellet where theReynolds number is very low is approximated to 0.55Wm�2K�1.[2] The specific surface area, asf, is developedfrom geometrical considerations and stated by

asf ¼6ð1� eÞ

dp: ð19Þ

The relative saturation RS is defined as

RS ¼ pvpv;sat

¼ Mvqs/sRT

pv;sat/gmlð20Þ

where pv,sat(T) is the vapor pressure corresponding tosaturation at temperature T as calculated from Antonie’sequation[24] according to

lnpsat

1:333 � 102� �

¼ A� B

C þ Tð21Þ

with A¼ 18.3036, B¼ 3,816.44, and C ¼�46.13. Thedecrease of temperature corresponding to the evaporation is

us ¼ � _mmlhlg: ð22Þ

Boundary Conditions

For a pellet subjected to evaporation, the source ofenergy may be expressed as

us ¼ hðT1 � TsÞ � _mmlhlg: ð23Þ

The mass flux, _mml , is determined from the difference inconcentration between the saturated vapor at the surface

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(as the interface between gas and liquid is regarded to be ata thermodynamic equilibrium) and the surrounding rela-tive saturation. The mass flux is thus determined from[23]

_mml ¼ hmml

R

pv;sat Tsð ÞTs

� pv;sat T1ð ÞRS

T1

� �: ð24Þ

The convective mass transfer coefficient, hm, and the satu-rated pressure, pv,sat, are calculated from Eqs. (18) and (21),respectively, with the convective heat transfer coefficient, h,determined from simulations. The convective heat trans-ferred from the air to the pellet will thus be used for bothincreasing the temperature and evaporation of water. Thebalance between convective heat transfer and the evaporativeheat loss will eventually reach an equilibrium, resulting in aconstant pellet temperature, the so-called wet bulb tempera-ture Twb, provided that the whole surface is covered in water.Originating from Eq. (23), the balance is expressed as

ðT1 � TsÞ ¼ hlgDABLe

1=3

k

Ml

R

pv;sat Tsð ÞTs

� pv;sat T1ð ÞRS

T1

� �ð25Þ

where Ts is equal to Twb at equilibrium. From Eq. (25) it isapparent that the external variables influencing the surfacetemperature at which equilibrium occurs are the temperatureand relative saturation at the inlet. The relative saturation RSis related to the dew point, Tdp, according to the followingrelationship:

RS ¼psat;Tdp

T1

psat;T1Tdp: ð26Þ

Although not explicitly given in Eq. (26), the relative satu-ration will increase with dew point due to a relatively largeincrease of the saturated vapor pressure with Tdp. If the pel-let surface temperature is below the dew point of the sur-rounding air, there will be condensation instead ofevaporation. This phenomenon is taken into account byEq. (24), which will show a positive contribution to the pellettotal moisture content if the temperature is below the dewpoint temperature. Because the latent energy in the vaporis released at condensation, a positive contribution of heatwill also be added by the energy equation source term.

The magnitude of the vapor flux at the surface is limitedby the internal mass transfer and the diffusivity of vapor inair. The highest possible vapor flux is assumed equal to _mml

and is limited by the relative saturation and liquid moisturecontent. There will thus only be a flux of vapor if the liquidmoisture surface content is approaching zero and if there isvapor in the region. This is controlled by Heaviside stepfunctions, H, as

_mmv ¼ _mmlHðRSÞHð�MlÞ: ð27Þ

Equation (27) will thus be zero when the relative saturationis zero or if there is liquid moisture at the surface.

MODELING

The simulations were divided into two parts. The sur-rounding fluid flow was first simulated to determine appro-priate boundary conditions at the pellet surface. Becausethe heat transfer coefficient is regarded as independent oftemperature, and the mass transfer can be calculated fromEq. (18), the pellet domain was thereafter simulated inde-pendently of the surrounding domain by applying valuesof the heat transfer coefficient at a large number of discretepoints (>15,000) located on the pellet surface. The spheri-cal pellet was placed in a cylinder to enable simulations ofthe surrounding fluid flow (see Fig. 1), and the simulationswere carried out with an inlet velocity of the fluid flow of7.3m=s, which was appropriate for the interstitial velocityin a bed of pellets. The inlet temperature was set to423K and the pellet initially had a uniform temperatureof 308K. The pellet was spherical with a diameter of12mm and was fully saturated with water at the beginning.With a porosity of 0.325, this corresponds to an initialmoisture content of 0.09126. Properties of the pelletmaterial are presented in Table 1.

The simulations were carried out with the CFD softwareANSYS CFX 12.1, which is a hybrid control volume–basedfinite element method (CV-FEM), on a 150-node PC-clusterwith excellent parallelization.[25] For the discretization ofthe advection term, the numerical advection correctionscheme (NACS) as used with blend factor b set to 1 for

FIG. 1. Spherical pellet domain and surrounding fluid flow domain with

coordinate system.

TABLE 1Material properties of the iron ore

Parameter Value Reference

Density 5,262 (kg=m3) [32]Thermal conductivity 5.27 (W=m K) [33]Specific heat capacity 586 (J=kg K) [34]Porosity 0.325 [32]Average particle size of rawmaterial

26e-6 (m) [35]

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the transport equations. The robust, implicit, andunbounded second-order backward Euler (SOBE) schemewas applied for the time discretization and shape functionsapproximating the pressure gradient and the diffusionterm.[26] Simulations of the surrounding fluid flow were con-ducted with the shear stress transport (SST) turbulencemodel. The SST turbulence model is an evolved version ofthe two-equation k-x turbulence model where the largefree-stream dependency present in the original Wilcoxmodel is avoided. SST also shows better agreement withexperiments when adverse pressure gradient boundary-layer flows are simulated.[27]

In the simulations, the surface evaporation period andthe first stage of the falling rate period are considered.The simulations for drying are therefore divided into twoperiods for numerical reasons. In period 1 the capillary

moisture transport within the pellet was large enough tocontinually supply the surface of it with liquid water forsurface evaporation to the surrounding air. It was thereforeassumed that no internal vapor escaped from the pellet atthis stage and only heat and liquid mass transfer fromthe pellet was considered due to the fact that /g wasinitially very small. Period 2 is a transitional period wherethe liquid moisture content is locally approaching zero dueto low capillary transport. The influence of internal evapor-ation was thus increasing and the vapor phase was there-fore taken into account. To avoid negative values of themoisture content, the evaporation was stopped when amoisture content of 0.05% was reached.

Error Estimation

Two domains were constructed and meshed, one for thesurrounding fluid flow and one for the spherical pellet. Themesh of the surrounding was designed to fit yþ< 1, ensuringthat the boundary layer close to the pellet surface wasresolved correctly as yþ relates the distance from the wallto the first node with the wall shear stress. The meshes wereunstructured tetrahedral meshes with high-density regionsand surface prisms at the no-slip sphere wall. The boundaryof the cylinder wall surrounding the pellet was regarded as afree-slip wall. The tetrahedral meshes are displayed in Fig. 2,where a section of the sphere domain and surroundingdomain close to the sphere wall is presented. A grid conver-gence test based on results from simulations of three con-secutive grids of each domain was carried out to estimatethe magnitude of the discretization error. For steady-statesimulations of heat transfer between a pellet and the

FIG. 2. Mesh of the pellet domain and fluid flow domain in the interface

region.

TABLE 2Discretization error estimation in the fluid domain with the area average heat transfer

coefficient as key variable. The coefficient is evaluated at a surface temperature of 308K

Meshno. No. of cells h (W=m2 K)

Extrapolated value(W=m2 K)

Apparentorder

Error(%)

1 10,456,552 94.9844 92.37 1.53 2.832 8,157,799 95.338 3.213 5,265,927 96.082 4.02

TABLE 3Discretization error estimation in the pellet domain with a local moisture content at t¼ 32 s

as key variable

Mesh no. No. of cellsMoisture

content (kg=kg)Extrapolatedvalue (kg=kg)

Apparentorder Error (%)

1 951,168 0.0740409 0.0740422 2.57 0.00172 421,543 0.07403923 191,646 0.0740371 0.0069

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surrounding flow field, the average wall heat transfer coef-ficient was chosen as a key variable. Following the procedureof Richardson extrapolation recommended by Celic et al.,[28]

the results show monotone convergence and an extrapolatedvalue for an infinitely fine mesh was obtained (see Table 2).Meshes of the pellet were also compared with internal moist-ure content as a key variable at t¼ 32 (see Table 3). The pelletdomain was represented by mesh no. 3 in all further simula-tions. Iteration errors should be negligible because all simula-tions fulfill the convergence criteria of max residuals less than1e-5 for the fluid domain and 5e-5 for the pellet domain.Notice that the apparent order in the fluid domain is reason-able because it is between 1 and 2. In the pellet domain theapparent order is too high. The reason for this might be thatother errors than those accounted for in Richardson extra-polation become important when the overall error is verysmall, as is the case for the moisture content.

RESULTS AND DISCUSSION

Now we discuss the importance of the dew point, Tdp, ofthe surrounding air from a theoretical point of view. If thesurface temperature of the pellet, Ts, is below Tdp, there willbe condensation until the surface has reached Tdp; see Eqs.(25)–(26). Hence, for a certain preheating of a pellet or bedof pellets there will be no condensation. At equilibriumbetween heat transfer and evaporative heat loss, Ts

becomes equal to the wet bulb temperature, Twb, andEqs. (25)–(26) then yield that Twb increases with Tdp (seeFig. 3), where Twb is presented for four dew point tempera-tures (Tdp¼ 273, 293, 313, and 333K). A result of this isthat the drying rate decreases with Tdp becauseDT¼T1�Ts decreases with surface temperature.

The convective heat transfer coefficient at the pelletsurface is, as stated before, determined from simulationsof the surrounding fluid flow (see Figs. 4 and 5) wherethe velocity and temperature distribution around the pelletin planes alongside the fluid flow are displayed. Time-averaged transient simulation of the fluid flow past thesphere provides a value of the average heat transfercoefficient of h¼ 96.07W=m2K, to be compared toh¼ 96.082W=m2K retrieved from steady-state simula-tions. A maximum value of the local heat transfer coef-ficient is observed at the upstream stagnation point andthe minimum value is observed at the vortex side of thepellet where the boundary layer separates. This results inan asymmetric distribution of h in the flow direction as seenin Fig. 6. The corresponding local mass transfer coefficientis determined by Eq. (18). The averaged heat transfer coef-ficient corresponds to an average Nu� 42. For a solidsphere, an estimation of the average Nu (Nu¼ hd=k) canbe stated as[29]

Nud ¼ 2þ 0:27Re0:62d Pr0:33 ð28Þ

FIG. 3. Wet bulb temperature, Twb, is plotted for four dew points

(Tdp¼ 273, 293, 313, and 333K), at an inlet temperature of T1¼ 423K.

The corresponding relative saturation at T1¼ 423K is RS¼ 0.0019,

0.007, 0.0209, and 0.0531.

FIG. 4. Time-averaged velocity distribution.

FIG. 5. Time-averaged temperature distribution.

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where Red is the Reynolds number (Red¼ qvd=l) and Pr isthe Prandtl number (Pr¼ cpl=k). This provides a value ofNu� 37. Correlations of Nu are usually reasonable overa certain range of conditions, yet accuracy much betterthan 20% is generally not expected[23] and the verificationof the surrounding flow can therefore be consideredsuccessful.

Drying simulations were performed with inlet air dewpoint temperatures of Tdp¼ 273, 293, 313, and 333K,and the simulations were run until the surface was com-pletely dry. Overall, the moisture content of the pelletdecreased as a function of time. An increase in moisturecontent due to condensation was, however, observed inthe case of Tdp¼ 313 and 333K, as seen in Fig. 7 wherethe pellet moisture content is displayed as a function oftime. The increase is expected from the theoretical dis-cussion above because the initial temperature of the pelletis 308K. The corresponding drying rates show a surfaceevaporation period succeeded by a falling rate period. Aprolonged surface evaporation stage with constant dryingrate was obtained at high relative saturations of the air;see Fig. 8, where the drying rates are presented as a func-tion of time. The initial increase in average temperature

of the pellet is more rapid if the saturation is high, andthe temperatures will stagnate at the respective wet bulbtemperature at the end of the surface evaporation period(see Fig. 9). The increase in temperature in the falling ratestage of drying will be more rapid at low saturations. Thesetemperatures are the same as those derived from Fig. 3,verifying the simulations. From Figs. 7–9 it is apparent thatthe differences in drying due to inlet air humidity arisefrom the beginning of drying. The effect is damped at theend of the surface evaporation period and the falling ratedrying period will in its turn also reduce the differencesbecause the rate of decrease in the drying rate is slightly lessfor high inlet air dew point temperatures. The magnitudesof the drying rates and moisture contents are nearly ident-ical at the time when internal drying becomes dominant

FIG. 6. Local heat transfer coefficient at upstream side (left) and side

view (right).

FIG. 7. Pellet moisture content as a function of time for dew points

Tdp¼ 273, 293, 313, and 333K.

FIG. 8. Drying rate as a function of time for dew points Tdp¼ 273, 293,

313, and 333K.

FIG. 9. Average pellet temperature as a function of time for dew points

Tdp¼ 273, 293, 313, and 333K.

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FIG. 10. Surface max, min, and average pellet moisture contents for (a) Tdp¼ 273K, (b) Tdp¼ 293K, (c) Tdp¼ 313K, and (d) Tdp¼ 333K.

FIG. 11. Surface liquid evaporation and surface vapor flux plotted with the total drying rate for (a) Tdp¼ 273K, (b) Tdp¼ 293K, (c) Tdp¼ 313K, and

(d) Tdp¼ 333K.

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(i.e., when the total surface evaporation rate is zero) for therespective dew points. This is at time t¼ 126.9, 129.6,140.9, and 164.3 s, respectively.

The transition between drying periods is clearly shownin Fig. 10, where the surface maximum and minimummoisture contents together with the average pellet moisturecontent are displayed for the specified dew points. The sur-face evaporation period is extended with relative saturationand the first stage of the falling rate period could actuallybe shortened; see Fig. 11, where the surface vapor andliquid fluxes are presented. Comparison between Figs. 10and 11 indicates that some surface liquid evaporation is

present even though the moisture content is approachingzero. This phenomenon is foremost observed at high dryingrates and is being controlled by the internal water transporttoward the surface. The appearance of the drying ratecurves is thus influenced by both the asymmetric distri-bution of the heat transfer coefficients at the surface andthe diffusion of moisture inside the pellets, explaining thesharp transitions in drying rate.

The influence of the distribution of heat and mass trans-fer coefficients at the surface is clearly presented in Fig. 12,where the local surface moisture contents are displayed forall dew points. The moisture contents are presented at thetimes when the internal drying period is initiated forthe respective dew point. The asymmetric distribution ofmoisture on the surface is also reflected within the pelletas exemplified with planes alongside the fluid flow inFig. 13. From Figs. 12 and 13 it is apparent that a high dry-ing rate, that is, low dew point temperature, will increasethe moisture gradients at the surface.

CONCLUSIONS

In this work, drying of an individual iron ore pellet issimulated at various inlet air dew point temperatures(Tdp¼ 273, 293, 313, and 333K). The results indicate thatthe effect of air humidity stems from the start of the firstdrying period, that is, the surface evaporation period,and the difference is reduced at the end of the period dueto a prolonged stage of constant rate drying attained athigh relative saturations. At low saturations, there is noconstant drying stage because the surface becomes locallydry before the pellet temperature has stabilized at the wet

FIG. 12. Distribution of moisture at the surface at Mmin¼ 0.001 for (a)

Tdp¼ 273K, t¼ 30.8 s; (b) Tdp¼ 293K, t¼ 35.3 s; (c) Tdp¼ 313K,

t¼ 48.9 s; and (d) Tdp¼ 333K, t¼ 76.4 s. The surface is lightened in order

to visualize the three-dimensional shape.

FIG. 13. Distribution of moisture in the middle of the pellet in a plane

parallel with the external fluid flow at Mmin¼ 0.001 for (a) Tdp¼ 273K,

t¼ 30.8 s; (b) Tdp¼ 293K, t¼ 35.3 s; (c) Tdp¼ 313K, t¼ 48.9 s; and (d)

Tdp¼ 333K, t¼ 76.4 s.

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bulb temperature. The existence of a constant drying rateperiod is thus dependent on the specific relative saturation.As expected, the simulations show that the wet bulbtemperature is increased with the relative saturation inair, and condensation will occur if the pellet surface tem-perature is below the dew point. The initial increase intemperature will be more rapid if the saturation is high,and the increase in temperature in the falling rate dryingperiod is faster at low saturations. The magnitudes of thedrying rates and moisture contents are rather similar atthe time when internal drying becomes dominant (i.e., whenthe total surface evaporation rate is zero) for the respectivedew points, yet the drying time is increased for high satura-tions. The gradients of moisture at the surface and insidethe pellet are, however, increased with drying rate.

Regarding the surrounding fluid flow, steady-state simu-lations with the SST turbulence model have proven to besufficient for simulations of the turbulent fluid flow sur-rounding the spherical pellet. More advanced turbulencemodels should, however, be considered in the future inorder to fully capture vortex shedding and unsteady effects.In addition, studies of systems of pellets will be done usingappropriate methodologies.[30,31] With the results obtainedfrom simulations, it is clear that the numerical model canserve as a valuable tool for further investigation andoptimization of drying of iron ore pellets.

NOMENCLATURE

A Area (m2)asf Specific surface area (m�1)c Specific heat (J=kg K)cp Specific heat at constant pressure (J=kg K)d Pellet diameter (m)D Diffusivity (m2=s)dp Diameter of grain (m)H Heaviside step functionh Convection heat transfer coefficient (W=m2 K)hlg Latent heat of vaporization (J=kg)hm Convection mass transfer coefficient (m=s)K Permeability (m2)Krl Relative permeabilityk Thermal conductivity (W=m K)km Thermal conductivity of the porous medium

(W=m K)M Moisture content (kg=kg)m Molecular weight (kg=kmol)_mm Mass flux (kg=m2 s), mass generation (kg=m3s)p Pressure (Pa)R Universal gas constantRS Relative saturationr Radius (m)rc Critical radius (m)S SaturationSir Irreducible saturation

T Temperature (K)Tdp Dew point temperature (K)Twb Wet bulb temperature (K)t Time (s)u Velocity (m=s)

Greek Symbols

e Porosityl Dynamic viscosity (kg=ms)q Density (kg=m3)r Surface tension (N=m)/ Volume fractionu Energy source term (W=m2)

Subscripts

a Airf Fluidg Gasl Liquids Solidsat Saturatedv Vapor

ACKNOWLEDGMENTS

The authors express their gratitude to the HjalmarLundbohm Research Center (HLRC) and LKAB for finan-cially supporting the work.

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