Heat and Mass Transfer in U-Bend of a Pneumatic Conveying Dryer

HEAT AND MASS TRANSFER IN U-BEND OFA PNEUMATIC CONVEYING DRYER

M. Hidayat1,2 and A. Rasmuson1,�

1Chemical Engineering Design, Department of Chemical and Biological Engineering, Chalmers

University of Technology, Goteborg, Sweden.2Chemical Engineering Department, Engineering faculty, Gadjan Mada University, JL Gratika No 2,

Yogyakarta, Indonesia.

Abstract: Computational fluid dynamics (CFD) modelling with the Eularian–Eularianformulation is used to describe the drying phenomena occurring in pneumatic conveyingdrying particularly in the U-bend. Two user defined scalar equations (UDSs) are inserted intothe solution to take into account the solid particle moisture content and the mass fraction ofwater in the gas phase, respectively. The drying kinetics cover the two periods of drying: theconstant drying rate and the falling drying rate. The investigation emphasized influences ofthe parameters (solid loading ratio, gas velocity, bend radius ratio, feed moisture content andgeometry arrangement of a U-bend) on the drying rate and moisture content. A validation ofthe drying model is accomplished by comparing calculation results with experimental data.In general, the drying rate decreases along the axial direction of pipe due to the decrease in driv-ing force (the air humidity increases). The mass-weighted average drying rate shows a slightdecrease in and just after the U-bend, which is mainly due to the high accumulation of solid par-ticles at the outer U-bend wall. Solid particles disperse and the slip velocities are high in the areaafter the U-bend. This causes the mass-weighted average drying rate to slightly increase.

Keywords: pneumatic conveying drying; U-bend; computational fluid dynamics (CFD).

INTRODUCTION

Pneumatic conveying dryers are widely usedin industry. In such a dryer, the external (temp-erature, humidity, mass/heat transfer coeffi-cients) conditions for particles vary along theflow path. A typical dryer is depicted inFigure 1. It consists of erect sections withuprisers and downcomers connected withU-bends. In a study by Fyhr and Rasmuson(1997) it is found that U-bends significantlyinfluence drying behaviour since they enhancevelocity differences (slip) between suspendedmaterial and the drying medium. This slip willincrease external heat and mass transferrates, thereby enhancing drying conditions.In contrast, the bend will increase the pressuredrop of the system. Thus, choosing the appro-priate bend shape can be utilized in the overalloptimization of a pneumatic conveying dryer.The U-bends may cause problems for stickymaterials or if the material is very wet in combi-nation with too low drying rates, our experi-ence though is that this mainly givesproblems in the feeding section of the dryer.Pneumatic drying involves simultaneous

momentum, heat and mass transfer between

drying gas, solid particles and walls. Thegas and particles exchange heat and massthrough drying, and momentum is exchangedin order to convey particles. The gas andparticles interact with the walls through wallfriction and heat convection (radiation). Thedrying times are typically short, in order ofseconds, due to limited conveying distances(Stoess, 1983) and the fact that the dryinggas becomes saturated. For this reason,many of these dryers are utilized as pre-dryers ahead of longer residence time fluidbed and rotary dryers, for example, in polymerdrying operations (Kirk-Othmer, 1993). How-ever, some pneumatic conveying dryers arealso applied as main dryers, for instance, fordrying fibres in the pulp and paper industry.A comprehensive study concerning fluiddynamics, heat and mass transfer betweengas and solid particles in the pneumaticdrying system is necessarily needed toobtain better knowledge for the design of apneumatic dryer.Studies of the fluid dynamics of gas and

solid particles through a bend have beenaccomplished by several authors, forexample, Huber and Sommerfeld (1994),

307 Vol 85 (A3) 307–319

�Correspondence to:Dr A. Rasmuson, ChemicalEngineering Design,Department of Chemical andBiological Engineering,Chalmers University ofTechnology, SE-41296.Goteborg, Sweden.E-mail: [email protected]

DOI: 10.1205/chered06162

0263–8762/07/$30.00þ 0.00

Chemical EngineeringResearch and Design

Trans IChemE,Part A, March 2007

# 2007 Institutionof Chemical Engineers

Levy and Mason (1998), Yilmaz and Levy (2001), Akilli et al.(2001) and Tu and Fletcher (1995). Huber and Sommerfeld(1994) have investigated the role of centrifugal forces in seg-regating solid particles from a carrier gas and they havefound the presence of particle size segregation due to cen-trifugal forces at a 908-bend. The phenomena of secondaryflows and of the formation and dispersion of ropes are usuallystudied simultaneously. Huber and Sommerfeld (1994), Levyand Mason (1998) and Yilmaz and Levy (2001) have studiedthe distribution of particles in a pipe cross-section affected bya 908-bend. Levy and Mason (1998) have concluded that thepaths taken by the particles after the bend are stronglydependent on the diameter of the particles. The ropes aredispersed due to secondary flow and flow turbulence (Akilliet al., 2001). In previous papers by the authors (Hidayatand Rasmuson, 2004, 2005, 2007), the influence of a U-bend on particle velocity, slip velocity, particle concentrationdistribution, pressure profile and heat transfer phenomenabetween gas and solid particles have been studied.Kemp et al. (1991) carried out drying experiments to find

particle velocities, heat transfer and drying rates in a verticalunit. They have reviewed models for pneumatic conveyingdryers and have concluded that none have been entirely suc-cessful. They also noticed that effective drying occurs in theinlet zone. Levy and Borde (1999) and Skuratovsky et al.(2005) have simulated vertical pneumatic conveying dryersin one- and two-dimensional models, respectively. In thedrying modelling, they have considered that solid particlesexperience two drying stages. During the first stage, heattransfer controls the evaporation process from the saturatedouter surface of a particle to the surrounding gas (a constantdrying rate period). During the second stage, diffusion ofmoisture through the particle crust and convection into thegas medium control the evaporation process. Fyhr andRasmuson (1997) have presented a model for a pneumaticconveying dryer employing a one-dimensional hydrodyna-mic plug flow model coupled to a comprehensive two-dimensional model for drying single wood chips. In thisstudy it is found that U-bends significantly influence dryingbehavior since they enhance velocity differences (slip)between suspended material and the drying medium.The present study examines heat and mass transfer (i.e.,

drying) between gas and solid particles in a U-bend.

Influences of important parameters (gas velocity, solid load-ing ratio, bend radius ratio and moisture content of solid par-ticles entering the system) on heat and mass transfercoefficients and the drying rate are studied numerically. Thecommercial software package Fluent 6.1 is used in the calcu-lations. The Eularian–Eularian modelling approach is appliedto predict flow behaviour. A drying model is added using twouser defined scalar equations (USDs) to take into account thegas humidity and moisture content of the solid particles. Thisis necessary since the standard multiphase feature of Fluent6.1 is not able to handle this complex system. Source termsfor both UDSs and the energy equation for the solid particlesare also introduced. The results obtained from the simu-lations are compared with experimental data from a pilotdryer.

MATHEMATICAL MODEL

The Eulerian–Eularian model is presented in this section.The model expands the definition of continuum assumptionto the dispersed phase and employs the Navier–Stokesequation to both continuous (gas) and dispersed (solid par-ticles) phases. Both phases are assumed to be incompressi-ble. The condition is steady-state and involves heat andmass transfer between phases. However, in order to avoiddivergence problems, the numerical solution is iterated atunsteady-state conditions.In the momentum equation the gas and solid are linked

using a drag force. The drag force model employs the corre-lation proposed by Gidaspow et al. (1992). This correlationcombines the Wen and Yu model (Wen and Yu, 1966) forthe dilute system and the Ergun equations (Ergun, 1952)for the dense system. The heat and mass transfer coeffi-cients between gas and solid use the correlation developedby Gunn (1978). He proposes Nusselt and Sherwood corre-lations which are valid for a system having the porosityrange of 0.35–1.0 and a Reynolds number up to 105. TwoUDSs are inserted into the solution to take into account thesolid particle moisture content and the mass fraction ofwater in the gas phase, respectively. The moisture evapor-ation rate of solid particles and the humidification rate ofgas are treated in the source terms of the correspondingUDS equations. The evaporation energy of moisture is trea-ted in the source term of the solid energy equation. Moredetails about heat and mass transfer are given in the heatand mass transfer model formulation section. The realizablek–1 epsilon model is used to capture turbulence phenomenain both phases. The granular theory for the gas–solid flow ofthe Eulerian model is introduced (Ding and Gidaspow, 1990).The set of governing equations was solved by using the

commercial Fluent 6.1 software package. The discretisedequations, along with the initial condition and boundaryconditions, were solved using the segregated solutionmethod. Using the segregated solver, the conservation ofmass and momentum were solved iteratively and apressure–correction equation was used to ensure consist-ency of the conservation of momentum and the conservationof mass (continuity equation). To assist in obtaining a con-vergent solution, Fluent allows one to solve the discretizedequations using a step-by-step solution by activating anddeactivating the discretised equations in the numericalsolution window.

Figure 1. Schematic drawing of the pneumatic conveying dryer devel-oped at Chalmers University of Technology (Fyhr and Rasmuson,1997).

Trans IChemE, Part A, Chemical Engineering Research and Design, 2007, 85(A3): 307–319

308 HIDAYAT and RASMUSON

Governing Equations

The conservation equation of the mass of phase i (i ¼ gasor solid) is

@

@t(airi)þ r � (airiui) ¼ 0 (1)

with the constraintX

ai ¼ 1: (2)

The conservation equation of the momentum of phase i(i ¼ gas or solid) is

@

@t(airiui)þ r � (airiuiui) ¼ �rpi

þ r � ti � r � (airiu0iu

0i )þ airigþ Kji(uj � ui) ð3Þ

where the index j is a pair of the index i (if the index i rep-resents the gas phase then the index j represents the solidphase, and vice versa). The pressure gradients of gas andsolid phase are �rpi ¼ �agrp and �rpi ¼ �asrp� rps,respectively. The Kji ¼ Kij in the drag force term representsthe inter-phase gas–solid momentum exchange coefficientwhich uses correlations derived by Gidaspow et al. (1992).The Reynolds stresses of phase i, �riu

0iu0

i employ theBoussinesq hypothesis (Hinze, 1975) to relate the Reynoldsstresses to the mean velocity gradients. The turbulencekinetic energy and turbulence dissipation rate employ therealizable k–1 model proposed by Shih et al. (1995).Equation (3) needs additional information for the solidphase (i ¼ s) which is mainly obtained from the granulartemperature equation:

3

2

@

@t(asrsus)þ r � (asrsusus) ¼ (� psIþ ts):rus

þ r � (kusrus)� gus þ fgs (4)

The conservation equation of the energy of phase i(i ¼ gas or solid) is

@

@t(airiHi)þr� (airiuiHi)¼�ai

@pi@t

þti:ruiþQjiþSh,i (5)

where Qji is the intensity of heat exchange between gas andsolid phases and Sh,i is the source term of the conservationequation of the energy of phase i. The intensity of heatexchange (Qji) employs the Nusselt correlation developedby Gunn (1978) to calculate the heat transfer coefficientbetween gas and solid phases. The source term for gasphase (Sh,i) is zero and the source term for the solid phase(Sh,i) is due to moisture evaporation from solid phase togas phase. More details regarding the source term of thesolid phase are given in the heat and mass transfer modelformulation section.The transport equation of the UDS of phase i (i ¼ gas or

solid) is

@airici

@tþ r � (airiuici) ¼ r � (aiGirci)þ Sc,i (6)

where c is the scalar variable which represents the massfraction of water in the gas or in the solid particles. Themass fraction of water in the solid particles is the moisturecontent itself.

Constitutive equations play the role of closing governingequations. The following section describes the constitutiveequations for the heat and mass transfer between gas andsolid in the conservation equation of the energy of the solidphase and the transport equation of the UDSs of bothphases. Additional constitutive equations are given in the pre-vious paper (Hidayat and Rasmuson, 2005).

Heat and Mass Transfer

Drying involves coupled heat and mass transfer. The inletgas, which is the drying medium, is hotter than the inletsolid. The energy transfer is mainly governed by externalconvection from gas to solid phase. The internal energytransport (mainly conduction) is usually rapid. This energyis used to increase solid temperature and to evaporate themoisture from the solid material. The moisture transportoccurs mainly by means of external convection at highermoisture contents and internal transport (capillary flow, diffu-sion) at lower moisture contents. Due to the complexity of themultiphase flow problem, the drying model has to be simplebut comprehensive, which means that it must include a con-stant drying rate and a falling drying rate as the generalcharacteristics of the drying process.The standard multiphase flow feature of Fluent 6.1 is not

able to solve these phenomena. The continuous and the dis-persed phases represent only the gas and solid phases,respectively. The mass fraction of water in the gas phaseand the moisture content of the solid phase have to be mod-eled in two additional UDSs.For the convective heat and mass transfer between gas

and solid we use the correlations proposed by Gunn(1978), here written for heat transfer:

Nus ¼ (7� 10ag þ 5a2g)(1þ 0:7Re0:2s Pr1=3)

þ (1:33� 2:4ag þ 1:2a2g)Re

0:7s Pr1=3 (7)

hsg ¼kgNusds

(8)

The mass transfer analogue is obtained by substituting Shfor Nu and Sc for Pr.The transition between the constant and the falling drying

rate periods occurs when the solid particle surface becomesunsaturated and internal mass transfer resistance becomessignificant. Due to the fact that the studied particle diameteris small and a simple drying model is desired, the dryingrate in the falling drying rate period is assumed to decreasein a linear fashion. This assumption was also utilized by Sza-fran and Kmiec (2004) in their CFD modelling of a spoutedbed dryer. The transition point in their case is defined by com-paring values of the mass flux calculated using the externalmass transfer equation and the internal mass transferequation. The equilibrium moisture content is taken as a con-stant value using the value at the inlet. In the present study,the transition point and the equilibrium moisture content istaken locally, considering the influence of gas and solidphase local conditions.In our case we use wood as a model material. The moist-

ure equilibrium is obtained by doing a polynomial regressionon the experimental data of the sorption isotherm of wood atdifferent temperatures and humidities of gas as given by


HEAT AND MASS TRANSFER IN U-BEND OF A PNEUMATIC CONVEYING DRYER 309

Siau (1984).

Xc ¼ Aþ BHc þ CH2c þ DH3

c (9a)

Xme ¼ Aþ BHme þ CH2me þ DH3

me (9b)

where Hc and Hme are the saturated humidity of gas (Hc ¼ 1)and the local gas humidity, respectively and A, B, C and D arepolynomial coefficients as function of the solid temperatureand given in Table 1.The mass flux of moisture evaporated from the solid

material during the constant drying rate is

NIc,s ¼

kg,cMc

RTs(Pc,s � Pc,g) (10)

where R is the gas constantThe mass flux of moisture evaporated from the solid

material during the falling drying rate is modelled as

NIIc,s ¼

X � Xme

Xc � XmeNI

c,s (11)

where Xme � X � Xc.The two UDSs take into account the mass transfer of

water between the solid and gas phases. The dryingrate of solid particles and the humidification rate of gasare treated in the source terms of their respective UDSequations.Mass transfer:

Sc,s ¼ �6asNc,s

ds(12)

Sc,g ¼ �Sc,s (13)

where Nc,s represents to NIc,s and NII

c,s in the constant andfalling drying rate, respectively.Heat transfer:

Qsg ¼6asaghsg(Ts � Tg)

ds(14)

The source term for the conservation equation of theenergy for solid phase is

Sh,s ¼ Nc,sHvap,c (15)

where Hvap,c is the evaporation energy of water obtained bydoing a polynomial regression from available steam tables(Hellsten, 1992).

Hvap,c ¼ 3 006300� 1428:1Ts � 1:5534T2s (16)

NUMERICAL SOLUTION

Geometry

Calculations are conducted for U-bend pipes with the samelength, i.e., 5 m, regardless of different bend radius ratios.The calculation domain is constructed of three parts,i.e., the upstream pipe, the U-bend and the downstreampipe. The length of the upstream pipe is 0.5 m for all vari-ations. The different lengths of pipe in the bend due to differ-ent bend radius ratios are compensated for by adapting thelength of the downstream pipe (Table 2). Figure 2 showsa sketch of the geometry of the calculation domain of theU-bend. The pipe diameter is 0.1 m. The dimensions ofthe experimental equipment are given in the experimentalsetup section.The computational grids are approximately 48 000 cells

(Figure 3). This number was generated by applying thesame cross-sectional meshes of pipe obtained from the opti-mum cross-sectional meshes of pipe in the single-phase flowcase (Hidayat and Rasmuson, 2004). The grid was gener-ated using Gambit 2.0, which is compatible with Fluent 6.1.A boundary layer, which contains four cells with a distanceof the cell adjacent to the wall at 2% of the diameter of thepipe and a growth factor of 1.2, was employed at the wallto improve the performance of the wall function and to fulfillthe requirement of y þ, the dimensionless wall distance, for

Table 1. The polynomial coefficients for equation (9) as function of thesolid temperature.

Polynomial coeff. Equations

A 20.010688þ 2.7619 � 1025� Ts

B 1.17092 2.6459 � 1023� Ts

C 22.2111þ 4.9748 � 1023� Ts

D 1.77142 3.7579 � 1023� Ts

Table 2. Summary of parameter values for calculations.

Parameter

SLR, kg kg21 ug, m s21

Bend variation The feed moisturecontent, kg water/kg

sawdustBR, m m21 L1, m B, m L2, m

0.1 10 3 0.5 0.4712 4.0288 0.1750.25 15

�

4 0.5 0.6283 3.8717 0.2000.5

�

20 6�

0.5�

0.9425�

3.5575�

0.2251.5 25 8 0.5 1.2566 3.2434 0.2507.5 30 10 0.5 1.5708 2.9292 0.275

12 0.5 1.8850 2.6150 0.3000.3251.41

�

�

Base case.



the cell adjacent to the wall. The y þ is defined by

yþ ¼rutypm

(17)

Further considerations regarding this meshing system aregiven in the previous paper (Hidayat and Rasmuson, 2004).

Boundary Conditions

The calculation domain (Figure 2) contains three bound-aries: the inlet boundary, the wall boundary and the outletboundary. A fully developed flow was introduced at the inletboundary of the calculation domain (Figure 2). The fullydeveloped flow was obtained from the separate calculationdomain of a straight vertical pipe with a length of 40 timesthe pipe diameter. This straight pipe calculation domain is

not shown in the paper. A flat profile of each parameterwas introduced at the inlet of this pipe and they resulted ina fully developed flow at the outlet. The fully developedflow obtained at the outlet was used as the inlet boundarycondition for the actual calculation domain, as depicted inFigure 2. The gravitation direction is downward or in theopposite direction of the inlet velocity.The outlet boundary condition of the latter was set up as a

pressure outlet boundary instead of as an outflow boundaryto avoid difficulties with backflow. No slip was used tomodel gas velocity at the wall and wall functions were usedas described in the previous paper (Hidayat and Rasmuson,2005). The solid phase used a generalized Eularian solid sur-face boundary condition model developed by Tu and Fletcher(1995). The derivation of this model is similar to the Lagran-gian treatment of wall-particles interaction. The generalizedwall boundary condition for the particulate phase can be writ-ten in a generic form.

awþ b@w

@h

��w

¼ c; where w ¼ ½uNs , u

Ts �,

a ¼ ½aN ,aT �, b ¼ ½bN ,bT �and c ¼ ½cN ,cT � (18)

The detailed derivation and the coefficient values are givenby Tu and Fletcher (1995).

Solution Strategy and Convergence

To enhance convergence, a calculation of a multiphaseflow in a complex geometry situation (like a U-bend) usinga two-fluid model needs an appropriate numerical strategy.Instead of using a steady-state solution strategy for this pro-blem, a transient solution with quite small time steps wasused and gave convergent solutions and reasonable results.Initiating a solution from a simple case and then step-by-stepincreasing the complexity of the solution is a good strategy tobreak-down the complexness of the problem. This strategycan be accomplished by activating and deactivating the dis-cretised equations in the numerical solution window. Redu-cing the values of the under relaxation factor of thesensitive variables often assists in reducing a jumping fluctu-ation of their residual values. When the solution advancessmoothly, the values are turned back to the previous ones.

Figure 2. Sketch of the geometry of the calculation domain.

Figure 3. (a) Mesh system for the cross-sectional area of circular pipe; (b) mesh system for the longitudinal plane of the U-bend.



A good initial guess of each variable is, of course, importantto promote convergence.A second order upwind discretization scheme was used for

the momentum equation while a first order upwind discretiza-tion was used for volume fraction, energy, turbulence kineticenergy and turbulence dissipation rate. These schemesensured, in general, satisfactory accuracy, stability andconvergence.The convergence criterion is based on the residual value of

the calculated variables, i.e., mass, velocity component,energy, turbulence kinetic energy, turbulence dissipationrate and volume fraction. In the present calculations, thethreshold values were set to a ten thousandth of the initialresidual value of each variable except the residual value ofenergy which was a millionth. The residual value of energyrequires a very small value to ensure accuracy of the solution(Fluent, 2001). In pressure–velocity coupling, the phase-coupled SIMPLE algorithm (Vasquez and Ivanov, 2000)was used, which is an extension of the SIMPLE algorithm(Patankar, 1980) to multiphase flows.

EXPERIMENTAL SETUP AND VALIDATION

Experimental Apparatus

A schematic diagram of the pilot dryer is shown in Figure 4.The dryer consists of five basic components: a pipelineincluding bends; a manual solid feeder; a cyclone; a heater;and a fan which is positioned after the cyclone to producenegative pressure on the system. The pipeline is insulatedand the total length of pipe is 25.7 m and the pipe diameteris 0.072 m.A pressure drop indicator (PI), which is engaged on the

pipe before the heater, utilizes the dryer to determine thegas flow rate entering into the system. Dry temperature indi-cators are located at three positions: at the inlet near thepressure drop indicator (TI-1), after the heater (TI-3) and atthe outlet after the cyclone (TI-4). A wet bulb temperatureindicator is located at one position only, at the inlet near the

pressure drop indicator (TI-2). The detailed positions of thepressure drop and temperature indicators are given inFigure 4.

Experimental Method

Heat loss determinationIn order to determine the performance of the system insu-

lation, a heat loss test was performed by flowing air throughthe system and turning the heater on. This test was done atsteady-state conditions: before and after feeding particlesinto the system. The steady-state condition was obtained inabout 30 min. Heat loss can be determined from the air temp-erature difference between the TI-3 and the TI-4. Heat lossdata was used to estimate the heat flux through the wall inthe simulations with the assumption that there is no signifi-cant change in heat loss in air flow only, as compared toair–solid particle flow.

Air mass flow rate measurementThe air mass flow rate is indirectly determined by using the

values indicated by the PI and the temperature indicators (TI-01 and TI-02). The PI is used to predict the air velocity flowingthrough the pipe and TI-01 and TI-02 are used to predict thedensity of air. The air mass flow rate can be easily calculatedwhen the air velocity, the pipe diameter and the density of airare available.

Solid particles preparationSawdust was used as the solid particles to be dried. For

simulation purposes, the sawdust particles were assumed tobe spherical with an average diameter of 0.00075 m. Thissize was obtained from measurements using SEM. Rawmaterial sawdust taken from a storage room was weighed.The moisture content of the raw material was measured inorder to determine how much water should be added toobtain the stipulated initial moisture content. The raw materialwas fed into a rotary mixer and after that water was pouredslowly into the rotary mixer to obtain better mixing. When theraw material sawdust and water were well mixed, after about15 min, several samples from different positions were ana-lysed for the initial moisture content of the feed. The moisturecontent of the feed was 1.41 kg water kg21 dry wood and thetotal wet weight of the feed was 10 kg.

Drying the sawdust feedFeeding the sawdust into the pilot dryer was carried out at

a steady-state air flow condition. To achieve this condition,initially the TI recorder and printer were turned on and per-mitted to work properly for few minutes. Then, the fan wasturned on. It is recommended to start the fan at a low rpmand increase the flow-rate gradually. If there was no problemwith the air flow, the heater was activated. The steady-stateair flow condition was normally achieved within 30 min. Tenkilograms of wet sawdust was fed constantly into the pilotdryer. The time needed to feed all the wet sawdust was52 min and 22 s. The temperatures of feed and productwere measured frequently and were 20 and 348C, respect-ively. The air mass flow rate entering to the system was0.041 kg s21 and the inlet dry air temperature before andafter entering the heater was 20 and 1258C, respectively.

Figure 4. Schematic diagram of the pilot dryer for validationpurposes.



The humidity of inlet air before entering the heater was 45%or 0.007 of water content in air (kg water kg21 air). The moist-ure content of the feed was 1.41 kg water kg21 dry wood. Theprocess continued to perform the heat loss determination.The moisture content of the samples was analyzed byusing the Mellter LP16 electronic moisture analyser.

Validation

A simulation using the data of drying process in the pilotdryer was conducted in the calculation domain, as shown inFigure 5. The pilot dryer was divided into six parts. Theinlet condition for the first part was obtained from the exper-imental data. The outlet of the previous part was used asthe inlet for the next one. The drying process in the cyclonewas not simulated. Table 3 summarizes the values of severalvariables obtained from the experiment and the simulation.Simulation results show that the moisture content is some-

what slightly overpredicted. A major reason for this may bedue to the absence of a cyclone in the simulation. Anotherreason may be the lack of detailed modelling of sawdustproperties. The uniform solid particles assumption in termsof size, structure and physical properties could not beavoided because of the limitation of the code itself. Over-esti-mated moisture content of sawdust influences the sawdusttemperature as well. Due to less water evaporated from thesawdust, less energy is needed. The evaporating energy ofwater is taken from the sawdust. This causes the temperatureestimation of the sawdust to be higher than the temperature

of the sawdust obtained from the experimental data. How-ever, the calculation of air temperature shows very goodagreement with experimental data.

RESULTS AND DISCUSSION

This study simulates the mechanisms of pneumatic con-veying drying in a U-bend. Several important parameters:solid loading ratio (SLR); inlet gas velocity; bend radiusratio (BR); feed moisture content and geometry arrangement;are investigated and the effect of each parameter on dryingrate behaviour and particle moisture content is studied. Vali-dation of the model used is given in the validation section andin the previous papers (Hidayat and Rasmuson, 2005, 2007).

General

In a drying process, the drying rate and particle moisturecontent are the two most relevant parameters. Other relevantparameters are pressure and the temperature of the dryingmedium and the temperature of the dried material. Fordetailed discussions of the latter see the previous papersby Hidayat and Rasmuson (2005, 2007).A general overview of the drying rate and solid moisture

content through the U-bend is given in Figures 6 and7. Figure 6 shows the local drying rate and the local moisturecontent parameters in the longitudinal plane [Figure 3(b)].The longitudinal plane is acquired at the symmetry plane ofthe system. Figure 7 gives the mass-weighted and area-weighted average values of the drying rate and moisture con-tent calculated at several cross-sectional planes along theaxial direction. The cross-sectional planes were acquired atseveral positions (including eight positions in the 4 m of thevertical straight pipe not shown in this paper), i.e., in theupstream pipe at LD ¼ 25; in the U-bend at u8 ¼ 0, 45, 90,135 and 180; and in the downstream pipe at LD ¼ 0.575 to35.575 with an interval of 5.Figure 6(a) shows that the local drying rate slightly

decreases along the upstream pipe. However, a drasticincrease in the local drying rate occurs in the U-bend andin the downstream near the U-bend outlet. After this, thelocal drying rate decreases gradually along the downstream

Figure 5. Sketch of the calculation domain geometry of the pilot dryerpipe for validation purposes.

Table 3. The summary of the value of several variables obtained fromthe experiment and the simulation.

Variable Experiment Simulation

Gas flow velocity, m s21 11.4 11.4The averaged effective sawdust

diameter, m7.5 � 1024 7.5 � 1024

Solid loading ratio at inlet, kgsawdust/kg air

7.86 � 1022 7.86 � 1022

Moisture content of sawdust atinlet, kg water/kg dry sawdust

1.41 1.41

Moisture content of sawdust atoutlet, kg water/kg dry sawdust

0.94 1.04

Water content of air at inlet, kgwater/kg air

7 � 1023 7 � 1023

Water content of air at outlet, kgwater/kg air

2.2 � 1022 1.9 � 1022

Air temperature at inlet, 8C 125 125Air temperature at outlet, 8C 75 73Sawdust temperature at inlet, 8C 20 20Sawdust temperature at outlet, 8C 34 43



pipe. This behaviour apparently indicates that the U-bendincreases the drying rate. However, it should be noted thatsolid particle distribution is also of importance.When solid particles flow through a curvature, i.e., a

U-bend, they experience centrifugal forces which causesolid particles to accumulate at the outer bend wall (Hidayatand Rasmuson, 2005). In fact, the high drying rate takesplace at locations where the solid volume fraction is low. Inthe area where the solid particles accumulate, the localdrying rate tends to be slightly lower than the area wheresolid particles do not accumulate. An accumulation of par-ticles around the outer bend causes much more energy tobe transferred from the gas to solid particles. This causesthe solid temperature in this area to be slightly lower than inareas where the solid volume fraction is lower. A lower temp-erature of solid and a more humid surrounding air decreasethe driving force of the drying rate and of course the dryingrate decreases as well. As a result, the mass-weight averagedrying rate slightly decreases in the U-bend and just after theU-bend. This behaviour is clearly shown in Figure 7(a).The behaviour of moisture content is presented in Figures

6(b) and 7(b). The moisture content decreases gradually inthe upstream pipe, the U-bend and in the downstream pipe.In the U-bend and just after the U-bend, the decrease ofmoisture content is slightly slower than in the upstream andin the downstream directions, located far from the U-bendexit. This is understandable since the drying rate in thatarea is slightly lower. A higher drying rate, of course,causes a faster decrease in the moisture content.

Influence of Studied Parameters

Solid loading ratioThe solid loading ratio influences the flow regime occurring

in the system. In the present study, the solid loading ratio wasvaried from 0.1 to 7.5 kg s21 of solid particles flow per kg s21

of air flow (Table 2). In this range the flow is considered to bedilute (Crowe et al., 1998) which is suitable for a pneumaticsystem.Figures 8(a) and (b) show the effect of varying solid loading

ratios on the mass-weighted average values of the drying rateand moisture content, respectively. As seen in Figure 8(a), thedrying rate decreases with increased solid loading ratio. Thedecrease is clearly seen at solid loading above 1.5. A majorreason for this is a strong decrease in the driving force. Forthe higher solid loading ratio, the increase in solid tempera-ture is less than the lower solid loading ratio. As a result,the water vapor pressure at the surface of solid particles islower. Also, for the higher solid loading ratio, the drying airbecomes more humid. This means that the driving force ofthe drying rate decreases. In the axial direction, the dryingrate tends to decrease slowly due to mainly the increase inair humidity.Figure 8(b) shows that an increase in the solid loading ratio

causes a lower reduction of the moisture content. At the high-est solid loading ratio 7.5, the reduction in moisture contentoccurs only in the inlet area where the air is still at low humid-ity. As soon as the solid particles come in contact with air, theair humidity increases drastically since its capacity is limited.

Figure 6. (a) The local drying rate and (b) the local moisture content on the longitudinal plane of the base case. This figure is available in colouronline via www.icheme.org/cherd



Later along the axial pipe, the drying rate is very low and themoisture content remains almost constant throughout the restof the pipe. A sign of limited air appears already at the solidloading ratio of 1.5. It shows up as a slower decrease in themoisture content.In pneumatic conveying drying, dilute conditions are

necessary since the process is limited by the humidity ofthe drying medium. A higher solid loading ratio causes afaster saturated drying medium. Based on the current results,a solid loading ratio of 0.5 seems to give better operating con-ditions in terms of drying rate and even operating capacity.

Gas velocityThe gas velocity and solid loading ratio are major factors

dictating the flow characteristic and the flow regime of thesystem. In the present study, gas velocity was varied from10 to 30 m s21, normally the operating velocity of pneumaticconveying. The effect of varying gas velocity on the mass-weighted average values of the drying rate and the moisturecontent is shown in Figures 9(a) and (b), respectively.The role of gas velocity in changing the drying rate is

mainly due to the presence of the mass transfer coefficientin equation (10). The mass transfer coefficient was calculatedfrom the mass transfer analogue of equations (7) and (8). TheSherwood number (Sh) increases with increased Reynoldsnumber (slip velocity indirectly). It is obvious that an increasein the gas velocity will increase the slip velocity; so that the

drying rate increases with increased gas velocity, as clearlydepicted in Figure 9(a).In contrast, an increase in gas velocity will give a shorter

residence time for drying. This is seen in Figure 9(b) wherean increase in gas velocity gives less reduction in moisturecontent.

Bend radius ratioTo study the influence of the bend radius ratio (BR) on the

mass-weighted average values of the drying rate and themoisture content, calculations were performed for variationsin the bend radius ratio from 4 to 12 m m21. The effect ofvarying bend radius ratios on the mass-weighted averagevalues of the drying rate and the moisture content is shownin Figures 10(a) and (b), respectively.As can be seen, the mass-weighted average values of the

drying rate and moisture content are the same for all vari-ations before entering the U-bend, since the flow propertiesare the same. In the general section, above, it was explainedthat the mass-weighted average drying rates slightlydecrease in the U-bend and just after the U-bend. Thebend radius ratio plays a role in altering the distribution ofsolid particles around the U-bend and the dispersion ofsolid particles after the U-bend. Due to improved dispersalof solid particles after the U-bend and the fact that slip vel-ocities are high in this area, the mass-weighted averagedrying rate slightly increases.

Figure 7. (a) The mass-weighted and area-weighted average valuesof the drying rate and (b) the mass-weighted average values ofmoisture content behaviors along the axial direction of the base case.

Figure 8. (a) The mass-weighted average drying rate and (b) themass-weighted average moisture content of sawdust along theaxial direction of pipe for different solid loading ratios.



The different bend radius ratios slightly alter the mass-weighted average values of the drying rate and moisture con-tent in and after the U-bend. At higher bend radius ratios, solidparticles experience higher centrifugal forces and thus theaccumulation of solid particles at the outer bend wall and justafter the bend exit will be higher. This causes the mass-weighted average drying rate for the higher bend radius to beslightly lower. As a result, the reduction in the mass-weightedaverage moisture at higher bend radius ratios is alsolower than the reduction at lower bend radius ratios. Aminor discrepancy occurs at the low bend radius ratios(at BR ¼ 3, 4 and 6). At BR ¼ 6, the mass-weighted averagedrying rate in the U-bend and after the U-bend is slightlyhigher than the mass-weighted average drying rate of BR 3and 4.

Feed moisture contentAs mentioned before pneumatic conveying dryers have

short drying times so many of these dryers are utilized aspre-dryers ahead of main dryers. However, some pneumaticconveying dryers are also applied as main dryers. Theprevious variations were calculated at high feed moisturecontent (1.41 kg water per kg solid particles) where the exter-nal convection mainly controls the drying. When the moisturecontent is low enough (reaching the critical point between theconstant and falling drying rates), both the external convec-tion and the internal transport become important. To studythe drying mechanism at low moisture contents, the feed

moisture content was varied from 0.175 to 0.325 kg waterper kg solid particles. This interval covers the range of criticalor transition point between the constant and falling drying ratethat is 0.245 to 0.285 kg water per kg solid particles.Figures 11(a) and (b) show the effect of the feed moisture

content on the mass-weighted average values of the dryingrate and the moisture content. As seen in Figure 11(a), themass-weighted average drying rate slightly decreases witha decrease in feed moisture content, and also gives alower reduction in moisture content [Figure 11(b)]. If themoisture content reaches the critical point, the drying mech-anism shifts from the constant drying rate to the fallingdrying rate mechanism.

Geometry arrangementA pneumatic dryer usually consists of uprisers and down-

comers connected with U-bends. The effect of geometryarrangement of a U-bend on drying behavior is thus of inter-est. The study of geometry arrangement of a U-bend wasconducted using base case geometry by simply changingthe sign of the gravitational force. In this way, the inlet pos-ition becomes located in the downcomer and the outlet pos-ition is located in the upriser. For purposes of simplification,the current case is called down-case and the usual case iscalled up-case.The effect of changing the geometry arrangement of a

U-bend on the mass-weighted average values of the dryingrate and moisture content is shown in Figure 12.

Figure 9. (a) The mass-weighted average drying rate and (b) themass-weighted average moisture content of sawdust along theaxial direction of pipe for different gas velocities.

Figure 10. (a) The mass-weighted average drying rate and (b) themass-weighted average moisture content of sawdust along theaxial direction of pipe for different bend radius ratios.



As can be seen, the drying rate for the up-case tends to behigher than the drying rate for the down-case in the regionbefore U-bend. In the U-bend, the drying rates for bothcases show almost the same values, and in the region afterthe U-bend, the drying rate for the up-case tends to belower than the drying rate for the down-case. These differentresults are due to the effect of the gravitational force direction.When the gas-solid flows through the upriser section, the flowdirection is opposite to the gravitational force. This, of course,creates higher slip velocity and eventually increases thedrying rate. In the U-bend, the centrifugal force still seemsto dominate. High accumulation of particles at the outerU-bend wall is the main reason for having almost the samedrying rate.The up-case shows a slightly better performance than the

down-case. The solid particles coming out of the outlet of theup-case are slightly drier than at the outlet of the down-case.Different lengths of upriser and downcomer can be thereason for the difference in performance. The up-case hasupriser and downcomer lengths of 4.50 and 3.56 m, andthe down-case has upriser and downcomer lengths of 3.56and 4.50 m. Another reason for this could be the fact thatthe initial drying process gives the highest drying rate. Forthe down-case, the initial drying process occurs in the down-comer where the drying rate is less than in the upriser.

CONCLUSIONS

The phenomena of pneumatic conveying drying werestudied numerically by using the extended Fluent 6.1. Theinvestigation emphasized influences of the parameters(solid loading ratio, gas velocity, bend radius ratio, feed

moisture content and geometry arrangement of a U-bend)on two variables: drying rate and moisture content. Incom-pressible, Eularian–Eularian gas–solid phase model, non-isothermal and steady-state conditions were considered.Two UDSs were inserted into the solution to take into accountthe solid particle moisture content and the mass fraction ofwater in the gas phase, respectively. The moisture evapor-ation rate of solid particles and the humidification rate ofgas were treated in the source terms of the correspondingUDS equations. The evaporation energy of moisture wastreated in the source term of the solid energy equation.The drying model was validated by drying sawdust using

the pilot pneumatic conveying dryer. Simulation resultsshowed that the moisture content is slightly overpredicted.A major reason for this may be due to the absence of acyclone in the simulation and another reason may be thelack of detailed modelling of sawdust properties. The esti-mated temperature of the sawdust was higher than the temp-erature of sawdust obtained from experimental data.However, the calculation of air temperature showed verygood agreement with experimental data.The mass-weighted average drying rate occurring in the

U-bend showed slightly undesired results. The slightdecrease in the mass-weighted average drying rate occurredin the U-bend and just after the U-bend, which was mainlydue to the high accumulation of solid particles at the outerU-bend wall. In the area after the U-bend, the solid particlesdispersed and the slip velocities were high, causing the

Figure 11. (a) The mass-weighted average drying rate and (b) themass-weighted average moisture content of sawdust along theaxial direction of pipe for different feed moisture content ratios.

Figure 12. (a) The mass-weighted average drying rate and (b) themass-weighted average moisture content of sawdust along theaxial direction of pipe for the up-case and down-case.



mass-weighted average drying rate to slightly increase. Anincrease in the solid loading ratio caused a decrease in thedrying rate. A major reason for this was a strong decreasein the driving force. An increase in gas velocity basically aug-ments the drying rate, since the mass transfer coefficient inequation (10) increased due to the increased Reynoldsnumber (slip velocity indirectly). Different bend radius ratiosslightly altered the mass-weighted average values of thedrying rate and moisture content in and after the U-bend.The feed moisture content was varied to evaluate the per-formance of the drying model. Lower feed moisture contentcaused a lower drying rate. Changing the U-bend positionhad small effect on drying behaviour.

NOMENCLATUREBR a bend radius ratio (a bend radius divided by a pipe

radius), m m21

D pipe diameter, mds diameter of solid particle, mg the acceleration due to gravity, m s22

H the specific enthalpy, m2 s22 in equation (5) or humidityin equation (9)

h the heat transfer coefficient, kg s23 K21

Hvap,c the evaporation energy of moist or water, m2 s22

I the tensor unitK inter-phase momentum exchange coefficient,

kg m23 s21

k the thermal conductivity, kg m s23 K21

ku the solid diffusion coefficient, kg m23 s21

kg,c the mass transfer coefficient of moisture, m s21

LD the normalized axial direction, m m21

Mc the molecular weight of moisture, kg mole21

Nc the drying rate, kg m22 s21

Nu the Nusselt numberp the static pressure, PaPr the Prandtl numberps the solid pressure, PaPc the moist or water vapour pressure, kg ms22

Q the intensity of heat exchange, kg ms23

R bend radius, mRe the Reynolds numberSc the Schmidt numberSh the Sherwood numberSh the source term of the conservation equation of the

energy, kg ms23

Sc the source term of the transport equation of the UDS,kg ms23

SLR the solid loading ratio, kg solid particles kg21 airT the temperature, Kt the time unit, su the mean velocity, m s21

u the fluctuating velocity, m s21

ut the shear velocity, m s21

X the moisture content of sawdustyp the wall distance of the first cell, m

Greek symbolsa the volume fraction, volume of particles, m3 / volume of

gas, m3

f the energy exchange, kg ms23

gu the collisional energy dissipation, kg ms23

m the shear viscosity, kg ms21

t the stress-strain tensor, kg ms22

u the granular temperature, m2 s22

r density, kg m23

h the normal direction in general coordinate, kg ms22 (Tuand Fletcher, 1995)

c the scalar variable which is the mass fraction of water inthe gas or in the solid particles

G the diffusion coefficient of scalar variable, kg ms21

SuperscriptsN the normal direction in equation (16)T the transpose sign in equation (12) or the tangential

direction in equation (16)

Subscriptsc criticalg the gas phasei the subscript i represents either the gas phase (subscript

g) or the solid phase (subscript s)j the pair of the index i (if the index i represents the gas

phase then the index j represents the solid phase, viceversa)

me moisture equilibriums the solid phasew the position at a wall

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Heat and Mass Transfer in U-Bend of a Pneumatic Conveying Dryer

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