Research ArticleModelling the Evaporation Rate in an ImpingementJet Dryer with Multiple Nozzles
Anna-Lena Ljung1 L Robin Andersson1 Anders G Andersson1 T Staffan Lundstroumlm1
andMats Eriksson2
1Division of Fluid and ExperimentalMechanics Department of Engineering Science andMathematics Lulea University of Technology971 87 Lulea Sweden2Relitor Engineering AB Foretagsvagen 9 954 33 Gammelstad Sweden
Correspondence should be addressed to Anna-Lena Ljung anna-lenaljungltuse
Received 22 December 2016 Accepted 5 February 2017 Published 2 March 2017
Academic Editor Sreepriya Vedantam
Copyright copy 2017 Anna-Lena Ljung et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited
Impinging jets are often used in industry to dry cool or heat items In this work a two-dimensional Computational FluidDynamicsmodel is created to model an impingement jet dryer with a total of 9 pairs of nozzles that dries sheets of metal Different methodsto model the evaporation rate are studied as well as the influence of recirculating the outlet air For the studied conditionsthe simulations show that the difference in evaporation rate between single- and two-component treatment of moist air is onlyaround 5 hence indicating that drying can be predicted with a simplified model where vapor is included as a nonreacting scalarFurthermore the humidity of the inlet air as determined from the degree of recirculating outlet air has a strong effect on the waterevaporation rate Results show that the metal sheet is dry at the exit if 85 of the air is recirculated while approximately only 60of the water has evaporated at a recirculation of 925
1 Introduction
Impinging jets are frequently used in industry with thepurpose of drying cooling or heating different artefacts [1]Impingement drying is especially common for continuoussheets such as paper textiles and metals Metal sheets canfor example be transported through an impingement jetdryer after painting to evaporate the water from the surfaceEnergy consumption and environmental issues are naturallyimportant factors in drying processes [2ndash4] and impingementjet drying is no exception It is therefore essential to furtherincrease the knowledge of the drying technique to enable areduction of the energy consumption while still providing aproper drying
Impingement jet heat transfer is an active area of researchand extensive numerical work has been carried out on theheat transfer from single and twin impingement jets (eg[5ndash11]) Prediction of the turbulent fluid flow in a correctmanner is for instance of absolute importance and in thework of Wang and Mujumdar [6] five low Reynolds number
(Re) turbulence models were examined Results show thatalthough corrections increased agreement with experimentaldata none of the turbulence models manages to predict thelocal Nusselt number (Nu) over the whole domain in anadequate manner The more advanced SST-SAS (Shear StressTransport with Scale Adaptive Simulation) model showedin its turn fairly accurate results in a twin-jet impingementstudy [11]
A review on multiple jet impingement was carried out byWeigand and Spring [12] Olsson et al [13] simulated flowaround two and three jets with 119896-120596 SST turbulence modeland results display that both distance and opening betweenthe jets are important for the heat transfer rates in the stagna-tion zone Elliptical and rectangular impingement jets wereexamined both experimentally and numerically by Caliskanet al [14] yielding an enhanced heat transfer coefficients forelliptical jets The detailed study furthermore discloses theformation of upward flow between two adjacent jets LargeEddy Simulations (LES) of multiple circular impingementjets were carried out by Draksler et al [15] resulting in
HindawiInternational Journal of Chemical EngineeringVolume 2017 Article ID 5784627 9 pageshttpsdoiorg10115520175784627
2 International Journal of Chemical Engineering
Metal sheet
Inlets
Out
let
Wall
Wal
l Wal
l
y
L
x
Hd
Figure 1 Schematic picture of the computational domain that comprises nine inlets and one outlet that is symmetry is applied below themetal sheet It is possible for the air to flow between the inlets but the actual geometry of the pipes and nozzles supplying the inlet air is notdisplayed here due to confidentiality
accurate predictions of main flow features Moreover thestudy indicates that two-equation turbulence models canexcept in the near-wall region where adjacent jets interactprovide a good approximation of the flow A good agreementbetween LES and experiments is also found in the study byKharoua et al [16]
Evidently there is comprehensive research on impinge-ment jet heat transfer but the inclusion of moisture inthe numerical models has to the authorsrsquo knowledge beengiven less attention De Bonis and Ruocco [17] numericallyanalyzed local heat and mass transfer in food slabs due to airjet impingement Jet impingement over a moist protrusionwas studied based on conjugate heat and mass exchangeenabling studies of jet height protrusion size and flow rateby De Bonis and Ruocco [18] A single wet particle ina two-dimensional pulsed opposing jet contractor (POJC)was analyzed by Yahyaee et al [19] showing an increaseddrying performance with increased pulsation amplitude andincreased jet Re Moisture was furthermore included in thework by Bai et al [20] where effects of a moving plate wereconsidered Constant boundary conditions were adopted atthe surface of the moving plate and simulations yieldeda detailed distribution of the velocity temperature andmoisture
From a modelling point of view it is of interest to furtherexamine how to include effects of moisture distribution andevaporationThere are several ways to determine the evapora-tion rate in forced convective flows such as impingement jetsThe moisture field may be simulated by the use of separatecomponents of vapor and air or as a scalar distribution wherethe influence of vapor on the fluid flow is neglected andhence the computational effort is decreased Evaporationrate can also be determined from correlations of Nusseltnumber (Nu) and Sherwoodnumber (Sh) found for examplein literature or derived from simulations With the use ofanalogies between Nu and Sh it is furthermore possible toderive a local mass transfer coefficient from the thermalfield alone that is without including moisture The use ofcorrelations is common in various drying applications [2122]Thedrawback of using correlations is that no informationis given about the distribution of moisture inside the dryerSince the listed methods have different pros and cons it is ofinterest to compare the validity and applicability
In the current paper a study of ametal sheet impingementdryer with multiple nozzles is presented with aid of CFDTheSST turbulence model is adopted and the geometry is based
on a dryer with 9 pairs of nozzles Special attention is puton modelling strategies for the evaporation rate and vaporcontent as well as the influence of recirculating air
2 Modelling
The metal sheet dryer selected for this study is shortlyoutlined below followed by a description of the numericalmodel and the governing equations
21 The Dryer Impingement jet dryers can be designed innumerous ways regarding for instance nozzles capacitiesof the fan capacity of the heat exchanger and space limitsfor the setup The nozzles in the dryer chosen for this studyare placed in 9 pairs that is 9 above and 9 below the metalsheet The humid air exiting the dryer is funneled back to thenozzles via a fan and a heat exchanger in order to increasethe energy efficiency of the dryer To overcome problems ofhigh humidity in the inlet air an outtake before the heatexchanger bleeds about 5ndash10 of the total circulated air Theheat exchanger then reheats the mixture of circulated andfresh air to the desired inlet temperature The bleeding of airwill however lead to a loss in efficiency since new air mustbe heated and it is therefore of interest to keep the outtake ofmoist air at a minimum
Rectangular nozzle openings are used to direct air jetsonto the sheet The dryer has a dimensionless nozzle-to-plate distance 119885119861 of around 13 while the aspect ratioof the nozzles is around 300 The rectangular shape andrelatively high aspect ratio of the nozzles enable the useof a two-dimensional numerical model see Figure 1 Thedryer is furthermore symmetrical above and below themetal sheet and only the top half of the dryer is thereforeconsidered see Figure 1 where the external walls and flowdirections of the computational domain is presented Ninenozzles are included to investigate the interaction betweenthe impingement jets A list of input parameters is displayedin Table 1
The following assumptions are introduced
(i) Gravity is not included
(ii) The motion of the sheet is neglected As suggested[23] surface motion may be neglected if the surfacelinear velocity is less than 20 of the jet velocity atimpact
International Journal of Chemical Engineering 3
(iii) The sheet is assumed to have a constant temperaturethroughout the drying process hence effect of platethickness is not accounted for The validity of thisassumption is discussed in the Results and Discus-sion
(iv) Leakage of air at the entrance and exit of the sheet isnot considered in the model
(v) A plug velocity profile is used at the inletsThe nozzleshape is consequently represented with a simplesharped edged slot [24]
(vi) Humidity in the fresh air is not included
22 Theory The following Reynolds averaged Navier-Stokesequations govern the turbulent flow of air inside the dryer
120597120588120597119905 +
120597120588119880119895120597119909119895 = 0
120597120588119880119894120597119905 + 120597 (120588119880119894119880119895)120597119909119895 = minus 120597119901120597119909119894 +120597120597119909119895 (120591119894119895 minus 120588119906119894119906119895)
120597 (120588119867tot)120597119905 minus 120597119901120597119905 +120597120597119909119895 (120588119880119895119867tot)
= 120597120597119909119895 (120582
120597119879120597119909119895 minus 120588119906119895119867) +
120597120597119909119895 [119880119894 (120591119894119895 minus 120588119906119894119906119895)]
(1)
Turbulence models provide closure of the Reynolds averageequations and for eddy viscosity turbulence models theassumptions of eddy viscosity and eddy diffusivity introducethe expressions
120588119906119894119906119895 = 120583119905 (120597119880119894120597119909119895 +120597119880119895120597119909119894 ) minus
where 120583119905 is the turbulent viscosity and Γ119905 is the turbulent dif-fusivity The constitutive equations for density and enthalpyof air are based on the ideal gas equations of state that is
Thematerial variables in (1) will represent dry air or amixtureof air and water vapor depending on the case studied Thematerial variables 119888119901 120583 and 120582 for the mixture of air andwater vapor are derived as a mass fraction weighted averagefollowing the relationship here exemplified for 120583 as
while air is set as the constraint component with its massfraction calculated from
sum119894
120593119894 = 1 (5)
Table 1 Parameters of the reference dryer
Parameter ValueInlet temperature 41815 KMass flow 1338 kgsSheet temperature 31315 KWater film volume 5 sdot 10minus6m3m2Number of nozzles 18
Two methods to determine the flow of water vapor in thedryer are examined moisture included as a scalar in a single-component flow and inclusion of moisture through two-component flow of air and vapor
221 Two-Component Treatment of Moist Air If vapor isincluded in the air composition a mass fraction transportequation is solved in addition to (1) to calculate the transportof vapor in air according to
120597120593V120597119909119895 minus 120588119906119895120601) (6)
222 Single-Component Treatment of Moist Air The con-served quantity per unit mass 120593 = Φ120588 modelled as a scalarwill depend solely on the existing fluid flow and diffusion andan increase in vapor mass density will not influence the flowThe variable is determined from a transport equation see (6)
23 Boundary Conditions No slip boundary conditions areapplied at all walls and inlet temperature and velocity are setaccording to Table 1 The boundary condition at the metalsheet is based on the assumption that the air is fully saturatedwith vapor at the surface where the liquid film exists Thesaturated mass density of vapor is derived from the ideal gaslaw as
120588Vsat = 119908119901Vsat119877119879 (7)
The saturated pressure 119901Vsat is the vapor pressure corre-sponding to saturation at temperature 119879 as derived fromAntoinersquos equation [25] according to
ln( 119901sat1333 sdot 102 ) = 119860 minus119861
119862 + 119879 (8)
with 119860 = 183036 119861 = 381644 and 119862 = minus4613 Theevaporation rate at the surface of the metal sheet is thenobtained from Fickrsquos law as
= minus119863av120588nabla120593V (9)
The expression is used to calculate evaporation rate both forthe variable composition mixture and for the nonreactingscalar For simulations with vapor treated as a scalar vapor isincluded through a boundary condition at the sheet surfaceequal to (7) For the variable composition mixture howeverthe vapor density at the sheet surface cannot be set directly
4 International Journal of Chemical Engineering
according to (7) and the saturation at the surface is insteadcontrolled through a step function A mass flux at thesheet surface is then applied through a source term anda step function controls the saturation at the surface Forconvergence the mass density of vapor is kept in an intervalof maximum 10 from its theoretical value
The heat transfer coefficient ℎ at the sheet surface isderived from
ℎ = 11990210158401015840119899(119879119904 minus 119879infin) (10)
where 11990210158401015840119899 is the local heat flux determined from Fourierrsquos lawas
If the flow is mainly driven by temperature difference and ℎis known the mass transfer coefficient ℎ119898 may be obtainedfrom the heat and mass transfer analogy according to
ℎℎ119898 =
119896119863av11987111989013 (12)
enabling computation of ℎ119898 without including moisture inthe simulations The mass flux may then be determined fromthe difference in concentration between the saturated vaporat the surface and the surrounding relative saturation as [26]
119897 = ℎ119898119908119897119877 (119901Vsat (119879119904)119879119904 minus 119901Vsat (119879infin)RS119879infin ) (13)
Thegas properties in (14) are evaluated at the arithmeticmeantemperature of the thermal boundary layer [26] The relativesaturation RS is determined from
RS = 119901V119901Vsat (14)
Important to note is however that calculation of evaporationrate based on the heat and mass transfer analogy does notprovide any knowledge about the distribution of vapor insidethe dryer that is inlet relative saturation due to recirculatingair cannot be determined using this method
Investigations of the influence of recirculating air arecarried out using single-component treatment of air withvapor modelled as a scalar The moisture content in the inletair is derived from the average outlet moisture content with acorrection factor to account for the outtake of moist air
24 Numerical Method The simulations are carried out withthe CFD software ANSYS CFX 15 that utilises a hybrid FiniteVolumeFinite Element solver [27] The simulations are runin steady state mode except for when vapor is includedas a two-component mixture A steady state simulation ofthe temperature field is then used for initiation and thesimulation is run until a steady state solution is reachedSpecific initial conditions are otherwise disregarded (ievelocities and mass fractions in the computational domain
are set to zero for initiation) All simulations are run withconvergence criteria of Root Mean Square (RMS) residuallt 10minus7 The flow inside the dryer is turbulent and the SSTturbulence model is applied The SST model is regarded tohave a superior near-wall treatment when compared with thestandard k-120576 model since it uses a k-120596 formulation close tothe wall and a k-120576 formulation in the free-stream howeverit is less computational demanding when compared to DES(Detached Eddy Simulation) and LES based turbulencemodels
The geometry is discretized to structured hexagonal gridsone-element thick in the meshing software ANSYS ICEMCFD 14 The grids have O-shaped blocks around the pipeswith local refinements at the nozzle inlets to better resolvethe jets The grids are also refined near the plate and thebounding walls of the dryer in order to benefit from the near-wall treatment of the SST model A Y+ lt 2 is obtained for theplate
3 Results and Discussion
Amesh study is first carried out followed by a validation of ℎThree different methods to calculate the evaporation rate arethen compared and finally the influence of the recirculatingair is addressed
31 Mesh Study Three grids are created with 77 k 123 k and174 k nodes respectively and simulated without the effectof water vapor With initial conditions according to Table 1the area averaged heat transfer along the plate for the threegrids shows good mesh convergence see Figure 2 It shouldbe noted that the interactions of the jets are sensitive to bothnumerical grids and the initial values of the simulationThis ismost likely due to geometrical aspects and the 2D approxima-tion in addition to the large inlet velocity and short distanceto the plate The grid sensitiveness is exemplified in Figure 3where adjacent jets interact differently for the same positionson the different grids The two finest meshes correlate bestwith regard to location and magnitude of the maximumtransfer coefficients at the stagnation points although localdifferences are observed Further refinement of the meshrequires time-resolved simulations and consequently sincethe difference is onlymarginally reflected in values of the areaaveraged heat transfer (see Figure 2) the finest grid is usedin all further simulations The use of advanced turbulencemodels and a transient study are recommended if furtherdetail is needed from the simulations Although care shouldbe taken in the conclusions regarding fluid flow distributionnear the plate the level of detail is considered sufficient forthe present study
32 Validation of ℎ To validate the fluid flow and turbulencemodel in the dryer the heat transfer coefficient in theimpingement zone is compared to experimental data fromHardisty and Can [24] In the present simulations the airis injected into the dryer as a plug velocity profile which isregarded to be representative of a sharped edge slotThe effec-tive nozzle width 1198611015840 can be derived from 1198611015840 = 119862119889119861 where119861 is the real nozzle width and 119862119889 is the discharge coefficient
International Journal of Chemical Engineering 5
08 1 12 14 16 1806Number of nodes
Aver
ageh
on p
late
(Wm
2K)
times105
100
105
110
115
120
125
Figure 2 Grid convergence study
77k123 k174k
02 04 06 08 10xL
0
50
100
150
200
250
300
350
400
Loca
lℎ(W
m2K)
Figure 3 Local ℎ as a function of normalized distance 119909119871 from thesheet entrance region for three resolutions of the grid
With an approximation of 119862119889 = 068 [24] the dimensionlessnozzle-to-plate distance 1198851198611015840 is reapproximated to 1198851198611015840 asymp20 in the dryer Mimicking the experimental setup in [24]with a velocity of119880in = 525ms at an inlet temperature of119879in= 29315 K and a plate surface temperature of 119879119904 = 37315 Ksimulations of the dryer show nine clear maximums of theheat transfer coefficient ℎ along the metal sheet that is onemaximum for each jet see Figure 4
A comparison between the stagnation point heat transfercoefficients ℎ0 from Figure 4 with the value attained from[24] at 119885119861 asymp 20 yields a good agreement even thoughnine jets are considered in these simulations A value ofℎ0 asymp 350Wm2K is retrieved from [24] to be compared
0
50
100
150
200
250
300
350
Loca
lℎ(W
m2s)
02 04 06 08 10xL
Figure 4 Local ℎ at 1000 positions along the sheet as a function ofnormalized distance 119909119871 from the sheet entrance region
with an averagemaximum value of ℎ0 = 331Wm2K retrievedfrom simulations considering all jets The maximum value ofℎ0 attained from simulations ℎ0 = 353Wm2K is found atthe stagnation point of the middle jet being even closer toexperimental data
33 Comparison between Methods to Derive the EvaporationRate Three methods to calculate the evaporation rate arecompared for verification of the simulations vapor treatedas a scalar variable composition mixture of air and vaporand evaporation rate through the heat and mass transferanalogy (HMTA)The boundary conditions are set accordingto Table 1 and the simulations are run without recirculatingmoisture since results from the HMTAwill predict the evap-oration rate without further determination of the distributionof moisture inside the dryer The three methods give similarresults as can be seen in Figure 5 and Table 2 where the localand average evaporation rates are displayed respectivelyThelargest difference approx 20 is seen between the heat andmass transfer analogy and vapor included as a scalar whilethe difference between the scalar and variable compositionmixture is only around 5 From Figure 5 it is furthermoreapparent that the evaporation rate will follow the heat andmass transfer coefficients with maximal values right belowthe impingement jets
The determined evaporation rates can also be used tochallenge the assumption of constant sheet temperatureEstimations show that the combination of latent heat neededto evaporate the water and heating from the jets would affectthe temperature with only a few degrees during drying ifconstant temperature through the sheet is assumed
34 Influence of Recirculating Air Next the influence of recir-culating air is studied Due to the decreased computationaleffort the moisture is here modelled as a scalar Outtakepercentages OP of 75 10 125 15 and 175 areinvestigated Firstly the temperature and velocity fields are
6 International Journal of Chemical Engineering
Table 2 Area average evaporation rates and relative difference compared to simulations where moisture is included as a two-componentmixture of air and vapor
Method Evaporation rate [kgm2s] Relative difference []Scalar 000575 469Two-component mixture 000605Heat and mass transfer analogy 000687 135
Moisture scalarMoisture two-component mixtureHMTA
Loca
l eva
pora
tion
rate
(kg
m2s)
0
0005
001
0015
002
0025
003
02 04 06 08 10xL
Figure 5 Local evaporation rate as a function of normalizeddistance from sheet entrance
examined which are independent of OP A primary stagna-tion point under the jet and a secondary stagnation pointbetween the jets are observed see Figure 6 where the velocityfield and vectors are displayed for the jet located in themiddleof the row (see Figure 1) A recirculation zone is observedbetween the primary and secondary stagnation point andupwash flow is observed above the secondary stagnationpoint This is together with the unsymmetrical positions ofthe secondary stagnation points in correspondence with thefindings by Caliskan et al [14] and Kharoua et al [16] Forthe studied case the asymmetry could be partly due to thelocation of the outlet The corresponding temperature field isdisplayed in Figure 7 showing the same trends as the velocityfield with regard to stagnation points
Secondly the surface average evaporation rate is investi-gated assuming a film of water across the whole sheet thatis initially no regards are taken to whether or not all wateris evaporated before the exit Results show a decelerationof evaporation rate for low OP Only for OP = 15 and175 the sheet is completely dry before the exit see Figure 8where results from simulations are compared to the requiredevaporation rate determined from process values An OP of100 represents dry air at the inlet
The magnitude of the evaporation rate is observed toincrease with OP that is reduced relative saturation while
628
80
000
188
6525
154
314
4237
730
440
1950
307
565
9662
884
691
7275
461
817
49
125
77
Velocity (m sminus1)
Figure 6 Local velocity below the middle jet Three jets aredisplayed in the picture
321
227
329
304
337
381
345
458
353
535
361
612
369
688
377
765
385
842
393
919
401
996
410
073
418
150
313
150
Temperature (K)
Figure 7 Local temperature below the middle jet Three jets aredisplayed in the picture
the locations of the maximum and minimum evaporationrates remains as long as water is present on the sheet seeFigure 9 where the local evaporation rates are displayed forOP = 10 125 and 15 at 119879in = 418K A step function is hereintroduced to account for the zero evaporation rates at dryareas of the sheet As seen in Figure 9 the evaporation rate iszero close to the exit of the metal sheet for the outtake of 15since the drying is completed before the sheet exits the dryerThe two jets closest to the outlet furthermore show a differentbehavior than the rest of the jets possibly due to geometricalconsiderations
To further investigate the efficiency of the dryer the ratioof dried water volume divided by initial water volume iscalculated At an OP of 15 the metal sheet is totally dryat the exit while at 75 only approx 60 of the water hasevaporated see Figure 10
Recondensation of moist air could impose a possible riskof reducing the dryer efficiency especially if the saturation ishigh close to the outlet To examine the risk of condensationthe relative saturation RS is investigated above and belowthe nozzles At OP = 15 the simulations show that thehighest RS above the plate is attained at the entrance regionsee Figure 11 where the local RS inside the dryer is displayedat four normalized heights Results thus show a low risk ofrecondensation as the RS is only a few percent with maximalRS for the positions closest to the plate of around 6 Thefairly low RS is further confirmed in Figure 12 where the local
International Journal of Chemical Engineering 7
SimulatedRequired
times10minus4
15
2
25
3
35
4
45
5
55
Evap
orat
ion
rate
(kg
s)
20 40 60 80 1000Outtake percentage ()
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
Figure 1 Schematic picture of the computational domain that comprises nine inlets and one outlet that is symmetry is applied below themetal sheet It is possible for the air to flow between the inlets but the actual geometry of the pipes and nozzles supplying the inlet air is notdisplayed here due to confidentiality
accurate predictions of main flow features Moreover thestudy indicates that two-equation turbulence models canexcept in the near-wall region where adjacent jets interactprovide a good approximation of the flow A good agreementbetween LES and experiments is also found in the study byKharoua et al [16]
Evidently there is comprehensive research on impinge-ment jet heat transfer but the inclusion of moisture inthe numerical models has to the authorsrsquo knowledge beengiven less attention De Bonis and Ruocco [17] numericallyanalyzed local heat and mass transfer in food slabs due to airjet impingement Jet impingement over a moist protrusionwas studied based on conjugate heat and mass exchangeenabling studies of jet height protrusion size and flow rateby De Bonis and Ruocco [18] A single wet particle ina two-dimensional pulsed opposing jet contractor (POJC)was analyzed by Yahyaee et al [19] showing an increaseddrying performance with increased pulsation amplitude andincreased jet Re Moisture was furthermore included in thework by Bai et al [20] where effects of a moving plate wereconsidered Constant boundary conditions were adopted atthe surface of the moving plate and simulations yieldeda detailed distribution of the velocity temperature andmoisture
From a modelling point of view it is of interest to furtherexamine how to include effects of moisture distribution andevaporationThere are several ways to determine the evapora-tion rate in forced convective flows such as impingement jetsThe moisture field may be simulated by the use of separatecomponents of vapor and air or as a scalar distribution wherethe influence of vapor on the fluid flow is neglected andhence the computational effort is decreased Evaporationrate can also be determined from correlations of Nusseltnumber (Nu) and Sherwoodnumber (Sh) found for examplein literature or derived from simulations With the use ofanalogies between Nu and Sh it is furthermore possible toderive a local mass transfer coefficient from the thermalfield alone that is without including moisture The use ofcorrelations is common in various drying applications [2122]Thedrawback of using correlations is that no informationis given about the distribution of moisture inside the dryerSince the listed methods have different pros and cons it is ofinterest to compare the validity and applicability
In the current paper a study of ametal sheet impingementdryer with multiple nozzles is presented with aid of CFDTheSST turbulence model is adopted and the geometry is based
on a dryer with 9 pairs of nozzles Special attention is puton modelling strategies for the evaporation rate and vaporcontent as well as the influence of recirculating air
2 Modelling
The metal sheet dryer selected for this study is shortlyoutlined below followed by a description of the numericalmodel and the governing equations
21 The Dryer Impingement jet dryers can be designed innumerous ways regarding for instance nozzles capacitiesof the fan capacity of the heat exchanger and space limitsfor the setup The nozzles in the dryer chosen for this studyare placed in 9 pairs that is 9 above and 9 below the metalsheet The humid air exiting the dryer is funneled back to thenozzles via a fan and a heat exchanger in order to increasethe energy efficiency of the dryer To overcome problems ofhigh humidity in the inlet air an outtake before the heatexchanger bleeds about 5ndash10 of the total circulated air Theheat exchanger then reheats the mixture of circulated andfresh air to the desired inlet temperature The bleeding of airwill however lead to a loss in efficiency since new air mustbe heated and it is therefore of interest to keep the outtake ofmoist air at a minimum
Rectangular nozzle openings are used to direct air jetsonto the sheet The dryer has a dimensionless nozzle-to-plate distance 119885119861 of around 13 while the aspect ratioof the nozzles is around 300 The rectangular shape andrelatively high aspect ratio of the nozzles enable the useof a two-dimensional numerical model see Figure 1 Thedryer is furthermore symmetrical above and below themetal sheet and only the top half of the dryer is thereforeconsidered see Figure 1 where the external walls and flowdirections of the computational domain is presented Ninenozzles are included to investigate the interaction betweenthe impingement jets A list of input parameters is displayedin Table 1
The following assumptions are introduced
(i) Gravity is not included
(ii) The motion of the sheet is neglected As suggested[23] surface motion may be neglected if the surfacelinear velocity is less than 20 of the jet velocity atimpact
International Journal of Chemical Engineering 3
(iii) The sheet is assumed to have a constant temperaturethroughout the drying process hence effect of platethickness is not accounted for The validity of thisassumption is discussed in the Results and Discus-sion
(iv) Leakage of air at the entrance and exit of the sheet isnot considered in the model
(v) A plug velocity profile is used at the inletsThe nozzleshape is consequently represented with a simplesharped edged slot [24]
(vi) Humidity in the fresh air is not included
22 Theory The following Reynolds averaged Navier-Stokesequations govern the turbulent flow of air inside the dryer
120597120588120597119905 +
120597120588119880119895120597119909119895 = 0
120597120588119880119894120597119905 + 120597 (120588119880119894119880119895)120597119909119895 = minus 120597119901120597119909119894 +120597120597119909119895 (120591119894119895 minus 120588119906119894119906119895)
120597 (120588119867tot)120597119905 minus 120597119901120597119905 +120597120597119909119895 (120588119880119895119867tot)
= 120597120597119909119895 (120582
120597119879120597119909119895 minus 120588119906119895119867) +
120597120597119909119895 [119880119894 (120591119894119895 minus 120588119906119894119906119895)]
(1)
Turbulence models provide closure of the Reynolds averageequations and for eddy viscosity turbulence models theassumptions of eddy viscosity and eddy diffusivity introducethe expressions
120588119906119894119906119895 = 120583119905 (120597119880119894120597119909119895 +120597119880119895120597119909119894 ) minus
where 120583119905 is the turbulent viscosity and Γ119905 is the turbulent dif-fusivity The constitutive equations for density and enthalpyof air are based on the ideal gas equations of state that is
Thematerial variables in (1) will represent dry air or amixtureof air and water vapor depending on the case studied Thematerial variables 119888119901 120583 and 120582 for the mixture of air andwater vapor are derived as a mass fraction weighted averagefollowing the relationship here exemplified for 120583 as
while air is set as the constraint component with its massfraction calculated from
sum119894
120593119894 = 1 (5)
Table 1 Parameters of the reference dryer
Parameter ValueInlet temperature 41815 KMass flow 1338 kgsSheet temperature 31315 KWater film volume 5 sdot 10minus6m3m2Number of nozzles 18
Two methods to determine the flow of water vapor in thedryer are examined moisture included as a scalar in a single-component flow and inclusion of moisture through two-component flow of air and vapor
221 Two-Component Treatment of Moist Air If vapor isincluded in the air composition a mass fraction transportequation is solved in addition to (1) to calculate the transportof vapor in air according to
120597120593V120597119909119895 minus 120588119906119895120601) (6)
222 Single-Component Treatment of Moist Air The con-served quantity per unit mass 120593 = Φ120588 modelled as a scalarwill depend solely on the existing fluid flow and diffusion andan increase in vapor mass density will not influence the flowThe variable is determined from a transport equation see (6)
23 Boundary Conditions No slip boundary conditions areapplied at all walls and inlet temperature and velocity are setaccording to Table 1 The boundary condition at the metalsheet is based on the assumption that the air is fully saturatedwith vapor at the surface where the liquid film exists Thesaturated mass density of vapor is derived from the ideal gaslaw as
120588Vsat = 119908119901Vsat119877119879 (7)
The saturated pressure 119901Vsat is the vapor pressure corre-sponding to saturation at temperature 119879 as derived fromAntoinersquos equation [25] according to
ln( 119901sat1333 sdot 102 ) = 119860 minus119861
119862 + 119879 (8)
with 119860 = 183036 119861 = 381644 and 119862 = minus4613 Theevaporation rate at the surface of the metal sheet is thenobtained from Fickrsquos law as
= minus119863av120588nabla120593V (9)
The expression is used to calculate evaporation rate both forthe variable composition mixture and for the nonreactingscalar For simulations with vapor treated as a scalar vapor isincluded through a boundary condition at the sheet surfaceequal to (7) For the variable composition mixture howeverthe vapor density at the sheet surface cannot be set directly
4 International Journal of Chemical Engineering
according to (7) and the saturation at the surface is insteadcontrolled through a step function A mass flux at thesheet surface is then applied through a source term anda step function controls the saturation at the surface Forconvergence the mass density of vapor is kept in an intervalof maximum 10 from its theoretical value
The heat transfer coefficient ℎ at the sheet surface isderived from
ℎ = 11990210158401015840119899(119879119904 minus 119879infin) (10)
where 11990210158401015840119899 is the local heat flux determined from Fourierrsquos lawas
If the flow is mainly driven by temperature difference and ℎis known the mass transfer coefficient ℎ119898 may be obtainedfrom the heat and mass transfer analogy according to
ℎℎ119898 =
119896119863av11987111989013 (12)
enabling computation of ℎ119898 without including moisture inthe simulations The mass flux may then be determined fromthe difference in concentration between the saturated vaporat the surface and the surrounding relative saturation as [26]
119897 = ℎ119898119908119897119877 (119901Vsat (119879119904)119879119904 minus 119901Vsat (119879infin)RS119879infin ) (13)
Thegas properties in (14) are evaluated at the arithmeticmeantemperature of the thermal boundary layer [26] The relativesaturation RS is determined from
RS = 119901V119901Vsat (14)
Important to note is however that calculation of evaporationrate based on the heat and mass transfer analogy does notprovide any knowledge about the distribution of vapor insidethe dryer that is inlet relative saturation due to recirculatingair cannot be determined using this method
Investigations of the influence of recirculating air arecarried out using single-component treatment of air withvapor modelled as a scalar The moisture content in the inletair is derived from the average outlet moisture content with acorrection factor to account for the outtake of moist air
24 Numerical Method The simulations are carried out withthe CFD software ANSYS CFX 15 that utilises a hybrid FiniteVolumeFinite Element solver [27] The simulations are runin steady state mode except for when vapor is includedas a two-component mixture A steady state simulation ofthe temperature field is then used for initiation and thesimulation is run until a steady state solution is reachedSpecific initial conditions are otherwise disregarded (ievelocities and mass fractions in the computational domain
are set to zero for initiation) All simulations are run withconvergence criteria of Root Mean Square (RMS) residuallt 10minus7 The flow inside the dryer is turbulent and the SSTturbulence model is applied The SST model is regarded tohave a superior near-wall treatment when compared with thestandard k-120576 model since it uses a k-120596 formulation close tothe wall and a k-120576 formulation in the free-stream howeverit is less computational demanding when compared to DES(Detached Eddy Simulation) and LES based turbulencemodels
The geometry is discretized to structured hexagonal gridsone-element thick in the meshing software ANSYS ICEMCFD 14 The grids have O-shaped blocks around the pipeswith local refinements at the nozzle inlets to better resolvethe jets The grids are also refined near the plate and thebounding walls of the dryer in order to benefit from the near-wall treatment of the SST model A Y+ lt 2 is obtained for theplate
3 Results and Discussion
Amesh study is first carried out followed by a validation of ℎThree different methods to calculate the evaporation rate arethen compared and finally the influence of the recirculatingair is addressed
31 Mesh Study Three grids are created with 77 k 123 k and174 k nodes respectively and simulated without the effectof water vapor With initial conditions according to Table 1the area averaged heat transfer along the plate for the threegrids shows good mesh convergence see Figure 2 It shouldbe noted that the interactions of the jets are sensitive to bothnumerical grids and the initial values of the simulationThis ismost likely due to geometrical aspects and the 2D approxima-tion in addition to the large inlet velocity and short distanceto the plate The grid sensitiveness is exemplified in Figure 3where adjacent jets interact differently for the same positionson the different grids The two finest meshes correlate bestwith regard to location and magnitude of the maximumtransfer coefficients at the stagnation points although localdifferences are observed Further refinement of the meshrequires time-resolved simulations and consequently sincethe difference is onlymarginally reflected in values of the areaaveraged heat transfer (see Figure 2) the finest grid is usedin all further simulations The use of advanced turbulencemodels and a transient study are recommended if furtherdetail is needed from the simulations Although care shouldbe taken in the conclusions regarding fluid flow distributionnear the plate the level of detail is considered sufficient forthe present study
32 Validation of ℎ To validate the fluid flow and turbulencemodel in the dryer the heat transfer coefficient in theimpingement zone is compared to experimental data fromHardisty and Can [24] In the present simulations the airis injected into the dryer as a plug velocity profile which isregarded to be representative of a sharped edge slotThe effec-tive nozzle width 1198611015840 can be derived from 1198611015840 = 119862119889119861 where119861 is the real nozzle width and 119862119889 is the discharge coefficient
International Journal of Chemical Engineering 5
08 1 12 14 16 1806Number of nodes
Aver
ageh
on p
late
(Wm
2K)
times105
100
105
110
115
120
125
Figure 2 Grid convergence study
77k123 k174k
02 04 06 08 10xL
0
50
100
150
200
250
300
350
400
Loca
lℎ(W
m2K)
Figure 3 Local ℎ as a function of normalized distance 119909119871 from thesheet entrance region for three resolutions of the grid
With an approximation of 119862119889 = 068 [24] the dimensionlessnozzle-to-plate distance 1198851198611015840 is reapproximated to 1198851198611015840 asymp20 in the dryer Mimicking the experimental setup in [24]with a velocity of119880in = 525ms at an inlet temperature of119879in= 29315 K and a plate surface temperature of 119879119904 = 37315 Ksimulations of the dryer show nine clear maximums of theheat transfer coefficient ℎ along the metal sheet that is onemaximum for each jet see Figure 4
A comparison between the stagnation point heat transfercoefficients ℎ0 from Figure 4 with the value attained from[24] at 119885119861 asymp 20 yields a good agreement even thoughnine jets are considered in these simulations A value ofℎ0 asymp 350Wm2K is retrieved from [24] to be compared
0
50
100
150
200
250
300
350
Loca
lℎ(W
m2s)
02 04 06 08 10xL
Figure 4 Local ℎ at 1000 positions along the sheet as a function ofnormalized distance 119909119871 from the sheet entrance region
with an averagemaximum value of ℎ0 = 331Wm2K retrievedfrom simulations considering all jets The maximum value ofℎ0 attained from simulations ℎ0 = 353Wm2K is found atthe stagnation point of the middle jet being even closer toexperimental data
33 Comparison between Methods to Derive the EvaporationRate Three methods to calculate the evaporation rate arecompared for verification of the simulations vapor treatedas a scalar variable composition mixture of air and vaporand evaporation rate through the heat and mass transferanalogy (HMTA)The boundary conditions are set accordingto Table 1 and the simulations are run without recirculatingmoisture since results from the HMTAwill predict the evap-oration rate without further determination of the distributionof moisture inside the dryer The three methods give similarresults as can be seen in Figure 5 and Table 2 where the localand average evaporation rates are displayed respectivelyThelargest difference approx 20 is seen between the heat andmass transfer analogy and vapor included as a scalar whilethe difference between the scalar and variable compositionmixture is only around 5 From Figure 5 it is furthermoreapparent that the evaporation rate will follow the heat andmass transfer coefficients with maximal values right belowthe impingement jets
The determined evaporation rates can also be used tochallenge the assumption of constant sheet temperatureEstimations show that the combination of latent heat neededto evaporate the water and heating from the jets would affectthe temperature with only a few degrees during drying ifconstant temperature through the sheet is assumed
34 Influence of Recirculating Air Next the influence of recir-culating air is studied Due to the decreased computationaleffort the moisture is here modelled as a scalar Outtakepercentages OP of 75 10 125 15 and 175 areinvestigated Firstly the temperature and velocity fields are
6 International Journal of Chemical Engineering
Table 2 Area average evaporation rates and relative difference compared to simulations where moisture is included as a two-componentmixture of air and vapor
Method Evaporation rate [kgm2s] Relative difference []Scalar 000575 469Two-component mixture 000605Heat and mass transfer analogy 000687 135
Moisture scalarMoisture two-component mixtureHMTA
Loca
l eva
pora
tion
rate
(kg
m2s)
0
0005
001
0015
002
0025
003
02 04 06 08 10xL
Figure 5 Local evaporation rate as a function of normalizeddistance from sheet entrance
examined which are independent of OP A primary stagna-tion point under the jet and a secondary stagnation pointbetween the jets are observed see Figure 6 where the velocityfield and vectors are displayed for the jet located in themiddleof the row (see Figure 1) A recirculation zone is observedbetween the primary and secondary stagnation point andupwash flow is observed above the secondary stagnationpoint This is together with the unsymmetrical positions ofthe secondary stagnation points in correspondence with thefindings by Caliskan et al [14] and Kharoua et al [16] Forthe studied case the asymmetry could be partly due to thelocation of the outlet The corresponding temperature field isdisplayed in Figure 7 showing the same trends as the velocityfield with regard to stagnation points
Secondly the surface average evaporation rate is investi-gated assuming a film of water across the whole sheet thatis initially no regards are taken to whether or not all wateris evaporated before the exit Results show a decelerationof evaporation rate for low OP Only for OP = 15 and175 the sheet is completely dry before the exit see Figure 8where results from simulations are compared to the requiredevaporation rate determined from process values An OP of100 represents dry air at the inlet
The magnitude of the evaporation rate is observed toincrease with OP that is reduced relative saturation while
628
80
000
188
6525
154
314
4237
730
440
1950
307
565
9662
884
691
7275
461
817
49
125
77
Velocity (m sminus1)
Figure 6 Local velocity below the middle jet Three jets aredisplayed in the picture
321
227
329
304
337
381
345
458
353
535
361
612
369
688
377
765
385
842
393
919
401
996
410
073
418
150
313
150
Temperature (K)
Figure 7 Local temperature below the middle jet Three jets aredisplayed in the picture
the locations of the maximum and minimum evaporationrates remains as long as water is present on the sheet seeFigure 9 where the local evaporation rates are displayed forOP = 10 125 and 15 at 119879in = 418K A step function is hereintroduced to account for the zero evaporation rates at dryareas of the sheet As seen in Figure 9 the evaporation rate iszero close to the exit of the metal sheet for the outtake of 15since the drying is completed before the sheet exits the dryerThe two jets closest to the outlet furthermore show a differentbehavior than the rest of the jets possibly due to geometricalconsiderations
To further investigate the efficiency of the dryer the ratioof dried water volume divided by initial water volume iscalculated At an OP of 15 the metal sheet is totally dryat the exit while at 75 only approx 60 of the water hasevaporated see Figure 10
Recondensation of moist air could impose a possible riskof reducing the dryer efficiency especially if the saturation ishigh close to the outlet To examine the risk of condensationthe relative saturation RS is investigated above and belowthe nozzles At OP = 15 the simulations show that thehighest RS above the plate is attained at the entrance regionsee Figure 11 where the local RS inside the dryer is displayedat four normalized heights Results thus show a low risk ofrecondensation as the RS is only a few percent with maximalRS for the positions closest to the plate of around 6 Thefairly low RS is further confirmed in Figure 12 where the local
International Journal of Chemical Engineering 7
SimulatedRequired
times10minus4
15
2
25
3
35
4
45
5
55
Evap
orat
ion
rate
(kg
s)
20 40 60 80 1000Outtake percentage ()
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
(iii) The sheet is assumed to have a constant temperaturethroughout the drying process hence effect of platethickness is not accounted for The validity of thisassumption is discussed in the Results and Discus-sion
(iv) Leakage of air at the entrance and exit of the sheet isnot considered in the model
(v) A plug velocity profile is used at the inletsThe nozzleshape is consequently represented with a simplesharped edged slot [24]
(vi) Humidity in the fresh air is not included
22 Theory The following Reynolds averaged Navier-Stokesequations govern the turbulent flow of air inside the dryer
120597120588120597119905 +
120597120588119880119895120597119909119895 = 0
120597120588119880119894120597119905 + 120597 (120588119880119894119880119895)120597119909119895 = minus 120597119901120597119909119894 +120597120597119909119895 (120591119894119895 minus 120588119906119894119906119895)
120597 (120588119867tot)120597119905 minus 120597119901120597119905 +120597120597119909119895 (120588119880119895119867tot)
= 120597120597119909119895 (120582
120597119879120597119909119895 minus 120588119906119895119867) +
120597120597119909119895 [119880119894 (120591119894119895 minus 120588119906119894119906119895)]
(1)
Turbulence models provide closure of the Reynolds averageequations and for eddy viscosity turbulence models theassumptions of eddy viscosity and eddy diffusivity introducethe expressions
120588119906119894119906119895 = 120583119905 (120597119880119894120597119909119895 +120597119880119895120597119909119894 ) minus
where 120583119905 is the turbulent viscosity and Γ119905 is the turbulent dif-fusivity The constitutive equations for density and enthalpyof air are based on the ideal gas equations of state that is
Thematerial variables in (1) will represent dry air or amixtureof air and water vapor depending on the case studied Thematerial variables 119888119901 120583 and 120582 for the mixture of air andwater vapor are derived as a mass fraction weighted averagefollowing the relationship here exemplified for 120583 as
while air is set as the constraint component with its massfraction calculated from
sum119894
120593119894 = 1 (5)
Table 1 Parameters of the reference dryer
Parameter ValueInlet temperature 41815 KMass flow 1338 kgsSheet temperature 31315 KWater film volume 5 sdot 10minus6m3m2Number of nozzles 18
Two methods to determine the flow of water vapor in thedryer are examined moisture included as a scalar in a single-component flow and inclusion of moisture through two-component flow of air and vapor
221 Two-Component Treatment of Moist Air If vapor isincluded in the air composition a mass fraction transportequation is solved in addition to (1) to calculate the transportof vapor in air according to
120597120593V120597119909119895 minus 120588119906119895120601) (6)
222 Single-Component Treatment of Moist Air The con-served quantity per unit mass 120593 = Φ120588 modelled as a scalarwill depend solely on the existing fluid flow and diffusion andan increase in vapor mass density will not influence the flowThe variable is determined from a transport equation see (6)
23 Boundary Conditions No slip boundary conditions areapplied at all walls and inlet temperature and velocity are setaccording to Table 1 The boundary condition at the metalsheet is based on the assumption that the air is fully saturatedwith vapor at the surface where the liquid film exists Thesaturated mass density of vapor is derived from the ideal gaslaw as
120588Vsat = 119908119901Vsat119877119879 (7)
The saturated pressure 119901Vsat is the vapor pressure corre-sponding to saturation at temperature 119879 as derived fromAntoinersquos equation [25] according to
ln( 119901sat1333 sdot 102 ) = 119860 minus119861
119862 + 119879 (8)
with 119860 = 183036 119861 = 381644 and 119862 = minus4613 Theevaporation rate at the surface of the metal sheet is thenobtained from Fickrsquos law as
= minus119863av120588nabla120593V (9)
The expression is used to calculate evaporation rate both forthe variable composition mixture and for the nonreactingscalar For simulations with vapor treated as a scalar vapor isincluded through a boundary condition at the sheet surfaceequal to (7) For the variable composition mixture howeverthe vapor density at the sheet surface cannot be set directly
4 International Journal of Chemical Engineering
according to (7) and the saturation at the surface is insteadcontrolled through a step function A mass flux at thesheet surface is then applied through a source term anda step function controls the saturation at the surface Forconvergence the mass density of vapor is kept in an intervalof maximum 10 from its theoretical value
The heat transfer coefficient ℎ at the sheet surface isderived from
ℎ = 11990210158401015840119899(119879119904 minus 119879infin) (10)
where 11990210158401015840119899 is the local heat flux determined from Fourierrsquos lawas
If the flow is mainly driven by temperature difference and ℎis known the mass transfer coefficient ℎ119898 may be obtainedfrom the heat and mass transfer analogy according to
ℎℎ119898 =
119896119863av11987111989013 (12)
enabling computation of ℎ119898 without including moisture inthe simulations The mass flux may then be determined fromthe difference in concentration between the saturated vaporat the surface and the surrounding relative saturation as [26]
119897 = ℎ119898119908119897119877 (119901Vsat (119879119904)119879119904 minus 119901Vsat (119879infin)RS119879infin ) (13)
Thegas properties in (14) are evaluated at the arithmeticmeantemperature of the thermal boundary layer [26] The relativesaturation RS is determined from
RS = 119901V119901Vsat (14)
Important to note is however that calculation of evaporationrate based on the heat and mass transfer analogy does notprovide any knowledge about the distribution of vapor insidethe dryer that is inlet relative saturation due to recirculatingair cannot be determined using this method
Investigations of the influence of recirculating air arecarried out using single-component treatment of air withvapor modelled as a scalar The moisture content in the inletair is derived from the average outlet moisture content with acorrection factor to account for the outtake of moist air
24 Numerical Method The simulations are carried out withthe CFD software ANSYS CFX 15 that utilises a hybrid FiniteVolumeFinite Element solver [27] The simulations are runin steady state mode except for when vapor is includedas a two-component mixture A steady state simulation ofthe temperature field is then used for initiation and thesimulation is run until a steady state solution is reachedSpecific initial conditions are otherwise disregarded (ievelocities and mass fractions in the computational domain
are set to zero for initiation) All simulations are run withconvergence criteria of Root Mean Square (RMS) residuallt 10minus7 The flow inside the dryer is turbulent and the SSTturbulence model is applied The SST model is regarded tohave a superior near-wall treatment when compared with thestandard k-120576 model since it uses a k-120596 formulation close tothe wall and a k-120576 formulation in the free-stream howeverit is less computational demanding when compared to DES(Detached Eddy Simulation) and LES based turbulencemodels
The geometry is discretized to structured hexagonal gridsone-element thick in the meshing software ANSYS ICEMCFD 14 The grids have O-shaped blocks around the pipeswith local refinements at the nozzle inlets to better resolvethe jets The grids are also refined near the plate and thebounding walls of the dryer in order to benefit from the near-wall treatment of the SST model A Y+ lt 2 is obtained for theplate
3 Results and Discussion
Amesh study is first carried out followed by a validation of ℎThree different methods to calculate the evaporation rate arethen compared and finally the influence of the recirculatingair is addressed
31 Mesh Study Three grids are created with 77 k 123 k and174 k nodes respectively and simulated without the effectof water vapor With initial conditions according to Table 1the area averaged heat transfer along the plate for the threegrids shows good mesh convergence see Figure 2 It shouldbe noted that the interactions of the jets are sensitive to bothnumerical grids and the initial values of the simulationThis ismost likely due to geometrical aspects and the 2D approxima-tion in addition to the large inlet velocity and short distanceto the plate The grid sensitiveness is exemplified in Figure 3where adjacent jets interact differently for the same positionson the different grids The two finest meshes correlate bestwith regard to location and magnitude of the maximumtransfer coefficients at the stagnation points although localdifferences are observed Further refinement of the meshrequires time-resolved simulations and consequently sincethe difference is onlymarginally reflected in values of the areaaveraged heat transfer (see Figure 2) the finest grid is usedin all further simulations The use of advanced turbulencemodels and a transient study are recommended if furtherdetail is needed from the simulations Although care shouldbe taken in the conclusions regarding fluid flow distributionnear the plate the level of detail is considered sufficient forthe present study
32 Validation of ℎ To validate the fluid flow and turbulencemodel in the dryer the heat transfer coefficient in theimpingement zone is compared to experimental data fromHardisty and Can [24] In the present simulations the airis injected into the dryer as a plug velocity profile which isregarded to be representative of a sharped edge slotThe effec-tive nozzle width 1198611015840 can be derived from 1198611015840 = 119862119889119861 where119861 is the real nozzle width and 119862119889 is the discharge coefficient
International Journal of Chemical Engineering 5
08 1 12 14 16 1806Number of nodes
Aver
ageh
on p
late
(Wm
2K)
times105
100
105
110
115
120
125
Figure 2 Grid convergence study
77k123 k174k
02 04 06 08 10xL
0
50
100
150
200
250
300
350
400
Loca
lℎ(W
m2K)
Figure 3 Local ℎ as a function of normalized distance 119909119871 from thesheet entrance region for three resolutions of the grid
With an approximation of 119862119889 = 068 [24] the dimensionlessnozzle-to-plate distance 1198851198611015840 is reapproximated to 1198851198611015840 asymp20 in the dryer Mimicking the experimental setup in [24]with a velocity of119880in = 525ms at an inlet temperature of119879in= 29315 K and a plate surface temperature of 119879119904 = 37315 Ksimulations of the dryer show nine clear maximums of theheat transfer coefficient ℎ along the metal sheet that is onemaximum for each jet see Figure 4
A comparison between the stagnation point heat transfercoefficients ℎ0 from Figure 4 with the value attained from[24] at 119885119861 asymp 20 yields a good agreement even thoughnine jets are considered in these simulations A value ofℎ0 asymp 350Wm2K is retrieved from [24] to be compared
0
50
100
150
200
250
300
350
Loca
lℎ(W
m2s)
02 04 06 08 10xL
Figure 4 Local ℎ at 1000 positions along the sheet as a function ofnormalized distance 119909119871 from the sheet entrance region
with an averagemaximum value of ℎ0 = 331Wm2K retrievedfrom simulations considering all jets The maximum value ofℎ0 attained from simulations ℎ0 = 353Wm2K is found atthe stagnation point of the middle jet being even closer toexperimental data
33 Comparison between Methods to Derive the EvaporationRate Three methods to calculate the evaporation rate arecompared for verification of the simulations vapor treatedas a scalar variable composition mixture of air and vaporand evaporation rate through the heat and mass transferanalogy (HMTA)The boundary conditions are set accordingto Table 1 and the simulations are run without recirculatingmoisture since results from the HMTAwill predict the evap-oration rate without further determination of the distributionof moisture inside the dryer The three methods give similarresults as can be seen in Figure 5 and Table 2 where the localand average evaporation rates are displayed respectivelyThelargest difference approx 20 is seen between the heat andmass transfer analogy and vapor included as a scalar whilethe difference between the scalar and variable compositionmixture is only around 5 From Figure 5 it is furthermoreapparent that the evaporation rate will follow the heat andmass transfer coefficients with maximal values right belowthe impingement jets
The determined evaporation rates can also be used tochallenge the assumption of constant sheet temperatureEstimations show that the combination of latent heat neededto evaporate the water and heating from the jets would affectthe temperature with only a few degrees during drying ifconstant temperature through the sheet is assumed
34 Influence of Recirculating Air Next the influence of recir-culating air is studied Due to the decreased computationaleffort the moisture is here modelled as a scalar Outtakepercentages OP of 75 10 125 15 and 175 areinvestigated Firstly the temperature and velocity fields are
6 International Journal of Chemical Engineering
Table 2 Area average evaporation rates and relative difference compared to simulations where moisture is included as a two-componentmixture of air and vapor
Method Evaporation rate [kgm2s] Relative difference []Scalar 000575 469Two-component mixture 000605Heat and mass transfer analogy 000687 135
Moisture scalarMoisture two-component mixtureHMTA
Loca
l eva
pora
tion
rate
(kg
m2s)
0
0005
001
0015
002
0025
003
02 04 06 08 10xL
Figure 5 Local evaporation rate as a function of normalizeddistance from sheet entrance
examined which are independent of OP A primary stagna-tion point under the jet and a secondary stagnation pointbetween the jets are observed see Figure 6 where the velocityfield and vectors are displayed for the jet located in themiddleof the row (see Figure 1) A recirculation zone is observedbetween the primary and secondary stagnation point andupwash flow is observed above the secondary stagnationpoint This is together with the unsymmetrical positions ofthe secondary stagnation points in correspondence with thefindings by Caliskan et al [14] and Kharoua et al [16] Forthe studied case the asymmetry could be partly due to thelocation of the outlet The corresponding temperature field isdisplayed in Figure 7 showing the same trends as the velocityfield with regard to stagnation points
Secondly the surface average evaporation rate is investi-gated assuming a film of water across the whole sheet thatis initially no regards are taken to whether or not all wateris evaporated before the exit Results show a decelerationof evaporation rate for low OP Only for OP = 15 and175 the sheet is completely dry before the exit see Figure 8where results from simulations are compared to the requiredevaporation rate determined from process values An OP of100 represents dry air at the inlet
The magnitude of the evaporation rate is observed toincrease with OP that is reduced relative saturation while
628
80
000
188
6525
154
314
4237
730
440
1950
307
565
9662
884
691
7275
461
817
49
125
77
Velocity (m sminus1)
Figure 6 Local velocity below the middle jet Three jets aredisplayed in the picture
321
227
329
304
337
381
345
458
353
535
361
612
369
688
377
765
385
842
393
919
401
996
410
073
418
150
313
150
Temperature (K)
Figure 7 Local temperature below the middle jet Three jets aredisplayed in the picture
the locations of the maximum and minimum evaporationrates remains as long as water is present on the sheet seeFigure 9 where the local evaporation rates are displayed forOP = 10 125 and 15 at 119879in = 418K A step function is hereintroduced to account for the zero evaporation rates at dryareas of the sheet As seen in Figure 9 the evaporation rate iszero close to the exit of the metal sheet for the outtake of 15since the drying is completed before the sheet exits the dryerThe two jets closest to the outlet furthermore show a differentbehavior than the rest of the jets possibly due to geometricalconsiderations
To further investigate the efficiency of the dryer the ratioof dried water volume divided by initial water volume iscalculated At an OP of 15 the metal sheet is totally dryat the exit while at 75 only approx 60 of the water hasevaporated see Figure 10
Recondensation of moist air could impose a possible riskof reducing the dryer efficiency especially if the saturation ishigh close to the outlet To examine the risk of condensationthe relative saturation RS is investigated above and belowthe nozzles At OP = 15 the simulations show that thehighest RS above the plate is attained at the entrance regionsee Figure 11 where the local RS inside the dryer is displayedat four normalized heights Results thus show a low risk ofrecondensation as the RS is only a few percent with maximalRS for the positions closest to the plate of around 6 Thefairly low RS is further confirmed in Figure 12 where the local
International Journal of Chemical Engineering 7
SimulatedRequired
times10minus4
15
2
25
3
35
4
45
5
55
Evap
orat
ion
rate
(kg
s)
20 40 60 80 1000Outtake percentage ()
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
according to (7) and the saturation at the surface is insteadcontrolled through a step function A mass flux at thesheet surface is then applied through a source term anda step function controls the saturation at the surface Forconvergence the mass density of vapor is kept in an intervalof maximum 10 from its theoretical value
The heat transfer coefficient ℎ at the sheet surface isderived from
ℎ = 11990210158401015840119899(119879119904 minus 119879infin) (10)
where 11990210158401015840119899 is the local heat flux determined from Fourierrsquos lawas
If the flow is mainly driven by temperature difference and ℎis known the mass transfer coefficient ℎ119898 may be obtainedfrom the heat and mass transfer analogy according to
ℎℎ119898 =
119896119863av11987111989013 (12)
enabling computation of ℎ119898 without including moisture inthe simulations The mass flux may then be determined fromthe difference in concentration between the saturated vaporat the surface and the surrounding relative saturation as [26]
119897 = ℎ119898119908119897119877 (119901Vsat (119879119904)119879119904 minus 119901Vsat (119879infin)RS119879infin ) (13)
Thegas properties in (14) are evaluated at the arithmeticmeantemperature of the thermal boundary layer [26] The relativesaturation RS is determined from
RS = 119901V119901Vsat (14)
Important to note is however that calculation of evaporationrate based on the heat and mass transfer analogy does notprovide any knowledge about the distribution of vapor insidethe dryer that is inlet relative saturation due to recirculatingair cannot be determined using this method
Investigations of the influence of recirculating air arecarried out using single-component treatment of air withvapor modelled as a scalar The moisture content in the inletair is derived from the average outlet moisture content with acorrection factor to account for the outtake of moist air
24 Numerical Method The simulations are carried out withthe CFD software ANSYS CFX 15 that utilises a hybrid FiniteVolumeFinite Element solver [27] The simulations are runin steady state mode except for when vapor is includedas a two-component mixture A steady state simulation ofthe temperature field is then used for initiation and thesimulation is run until a steady state solution is reachedSpecific initial conditions are otherwise disregarded (ievelocities and mass fractions in the computational domain
are set to zero for initiation) All simulations are run withconvergence criteria of Root Mean Square (RMS) residuallt 10minus7 The flow inside the dryer is turbulent and the SSTturbulence model is applied The SST model is regarded tohave a superior near-wall treatment when compared with thestandard k-120576 model since it uses a k-120596 formulation close tothe wall and a k-120576 formulation in the free-stream howeverit is less computational demanding when compared to DES(Detached Eddy Simulation) and LES based turbulencemodels
The geometry is discretized to structured hexagonal gridsone-element thick in the meshing software ANSYS ICEMCFD 14 The grids have O-shaped blocks around the pipeswith local refinements at the nozzle inlets to better resolvethe jets The grids are also refined near the plate and thebounding walls of the dryer in order to benefit from the near-wall treatment of the SST model A Y+ lt 2 is obtained for theplate
3 Results and Discussion
Amesh study is first carried out followed by a validation of ℎThree different methods to calculate the evaporation rate arethen compared and finally the influence of the recirculatingair is addressed
31 Mesh Study Three grids are created with 77 k 123 k and174 k nodes respectively and simulated without the effectof water vapor With initial conditions according to Table 1the area averaged heat transfer along the plate for the threegrids shows good mesh convergence see Figure 2 It shouldbe noted that the interactions of the jets are sensitive to bothnumerical grids and the initial values of the simulationThis ismost likely due to geometrical aspects and the 2D approxima-tion in addition to the large inlet velocity and short distanceto the plate The grid sensitiveness is exemplified in Figure 3where adjacent jets interact differently for the same positionson the different grids The two finest meshes correlate bestwith regard to location and magnitude of the maximumtransfer coefficients at the stagnation points although localdifferences are observed Further refinement of the meshrequires time-resolved simulations and consequently sincethe difference is onlymarginally reflected in values of the areaaveraged heat transfer (see Figure 2) the finest grid is usedin all further simulations The use of advanced turbulencemodels and a transient study are recommended if furtherdetail is needed from the simulations Although care shouldbe taken in the conclusions regarding fluid flow distributionnear the plate the level of detail is considered sufficient forthe present study
32 Validation of ℎ To validate the fluid flow and turbulencemodel in the dryer the heat transfer coefficient in theimpingement zone is compared to experimental data fromHardisty and Can [24] In the present simulations the airis injected into the dryer as a plug velocity profile which isregarded to be representative of a sharped edge slotThe effec-tive nozzle width 1198611015840 can be derived from 1198611015840 = 119862119889119861 where119861 is the real nozzle width and 119862119889 is the discharge coefficient
International Journal of Chemical Engineering 5
08 1 12 14 16 1806Number of nodes
Aver
ageh
on p
late
(Wm
2K)
times105
100
105
110
115
120
125
Figure 2 Grid convergence study
77k123 k174k
02 04 06 08 10xL
0
50
100
150
200
250
300
350
400
Loca
lℎ(W
m2K)
Figure 3 Local ℎ as a function of normalized distance 119909119871 from thesheet entrance region for three resolutions of the grid
With an approximation of 119862119889 = 068 [24] the dimensionlessnozzle-to-plate distance 1198851198611015840 is reapproximated to 1198851198611015840 asymp20 in the dryer Mimicking the experimental setup in [24]with a velocity of119880in = 525ms at an inlet temperature of119879in= 29315 K and a plate surface temperature of 119879119904 = 37315 Ksimulations of the dryer show nine clear maximums of theheat transfer coefficient ℎ along the metal sheet that is onemaximum for each jet see Figure 4
A comparison between the stagnation point heat transfercoefficients ℎ0 from Figure 4 with the value attained from[24] at 119885119861 asymp 20 yields a good agreement even thoughnine jets are considered in these simulations A value ofℎ0 asymp 350Wm2K is retrieved from [24] to be compared
0
50
100
150
200
250
300
350
Loca
lℎ(W
m2s)
02 04 06 08 10xL
Figure 4 Local ℎ at 1000 positions along the sheet as a function ofnormalized distance 119909119871 from the sheet entrance region
with an averagemaximum value of ℎ0 = 331Wm2K retrievedfrom simulations considering all jets The maximum value ofℎ0 attained from simulations ℎ0 = 353Wm2K is found atthe stagnation point of the middle jet being even closer toexperimental data
33 Comparison between Methods to Derive the EvaporationRate Three methods to calculate the evaporation rate arecompared for verification of the simulations vapor treatedas a scalar variable composition mixture of air and vaporand evaporation rate through the heat and mass transferanalogy (HMTA)The boundary conditions are set accordingto Table 1 and the simulations are run without recirculatingmoisture since results from the HMTAwill predict the evap-oration rate without further determination of the distributionof moisture inside the dryer The three methods give similarresults as can be seen in Figure 5 and Table 2 where the localand average evaporation rates are displayed respectivelyThelargest difference approx 20 is seen between the heat andmass transfer analogy and vapor included as a scalar whilethe difference between the scalar and variable compositionmixture is only around 5 From Figure 5 it is furthermoreapparent that the evaporation rate will follow the heat andmass transfer coefficients with maximal values right belowthe impingement jets
The determined evaporation rates can also be used tochallenge the assumption of constant sheet temperatureEstimations show that the combination of latent heat neededto evaporate the water and heating from the jets would affectthe temperature with only a few degrees during drying ifconstant temperature through the sheet is assumed
34 Influence of Recirculating Air Next the influence of recir-culating air is studied Due to the decreased computationaleffort the moisture is here modelled as a scalar Outtakepercentages OP of 75 10 125 15 and 175 areinvestigated Firstly the temperature and velocity fields are
6 International Journal of Chemical Engineering
Table 2 Area average evaporation rates and relative difference compared to simulations where moisture is included as a two-componentmixture of air and vapor
Method Evaporation rate [kgm2s] Relative difference []Scalar 000575 469Two-component mixture 000605Heat and mass transfer analogy 000687 135
Moisture scalarMoisture two-component mixtureHMTA
Loca
l eva
pora
tion
rate
(kg
m2s)
0
0005
001
0015
002
0025
003
02 04 06 08 10xL
Figure 5 Local evaporation rate as a function of normalizeddistance from sheet entrance
examined which are independent of OP A primary stagna-tion point under the jet and a secondary stagnation pointbetween the jets are observed see Figure 6 where the velocityfield and vectors are displayed for the jet located in themiddleof the row (see Figure 1) A recirculation zone is observedbetween the primary and secondary stagnation point andupwash flow is observed above the secondary stagnationpoint This is together with the unsymmetrical positions ofthe secondary stagnation points in correspondence with thefindings by Caliskan et al [14] and Kharoua et al [16] Forthe studied case the asymmetry could be partly due to thelocation of the outlet The corresponding temperature field isdisplayed in Figure 7 showing the same trends as the velocityfield with regard to stagnation points
Secondly the surface average evaporation rate is investi-gated assuming a film of water across the whole sheet thatis initially no regards are taken to whether or not all wateris evaporated before the exit Results show a decelerationof evaporation rate for low OP Only for OP = 15 and175 the sheet is completely dry before the exit see Figure 8where results from simulations are compared to the requiredevaporation rate determined from process values An OP of100 represents dry air at the inlet
The magnitude of the evaporation rate is observed toincrease with OP that is reduced relative saturation while
628
80
000
188
6525
154
314
4237
730
440
1950
307
565
9662
884
691
7275
461
817
49
125
77
Velocity (m sminus1)
Figure 6 Local velocity below the middle jet Three jets aredisplayed in the picture
321
227
329
304
337
381
345
458
353
535
361
612
369
688
377
765
385
842
393
919
401
996
410
073
418
150
313
150
Temperature (K)
Figure 7 Local temperature below the middle jet Three jets aredisplayed in the picture
the locations of the maximum and minimum evaporationrates remains as long as water is present on the sheet seeFigure 9 where the local evaporation rates are displayed forOP = 10 125 and 15 at 119879in = 418K A step function is hereintroduced to account for the zero evaporation rates at dryareas of the sheet As seen in Figure 9 the evaporation rate iszero close to the exit of the metal sheet for the outtake of 15since the drying is completed before the sheet exits the dryerThe two jets closest to the outlet furthermore show a differentbehavior than the rest of the jets possibly due to geometricalconsiderations
To further investigate the efficiency of the dryer the ratioof dried water volume divided by initial water volume iscalculated At an OP of 15 the metal sheet is totally dryat the exit while at 75 only approx 60 of the water hasevaporated see Figure 10
Recondensation of moist air could impose a possible riskof reducing the dryer efficiency especially if the saturation ishigh close to the outlet To examine the risk of condensationthe relative saturation RS is investigated above and belowthe nozzles At OP = 15 the simulations show that thehighest RS above the plate is attained at the entrance regionsee Figure 11 where the local RS inside the dryer is displayedat four normalized heights Results thus show a low risk ofrecondensation as the RS is only a few percent with maximalRS for the positions closest to the plate of around 6 Thefairly low RS is further confirmed in Figure 12 where the local
International Journal of Chemical Engineering 7
SimulatedRequired
times10minus4
15
2
25
3
35
4
45
5
55
Evap
orat
ion
rate
(kg
s)
20 40 60 80 1000Outtake percentage ()
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
Figure 3 Local ℎ as a function of normalized distance 119909119871 from thesheet entrance region for three resolutions of the grid
With an approximation of 119862119889 = 068 [24] the dimensionlessnozzle-to-plate distance 1198851198611015840 is reapproximated to 1198851198611015840 asymp20 in the dryer Mimicking the experimental setup in [24]with a velocity of119880in = 525ms at an inlet temperature of119879in= 29315 K and a plate surface temperature of 119879119904 = 37315 Ksimulations of the dryer show nine clear maximums of theheat transfer coefficient ℎ along the metal sheet that is onemaximum for each jet see Figure 4
A comparison between the stagnation point heat transfercoefficients ℎ0 from Figure 4 with the value attained from[24] at 119885119861 asymp 20 yields a good agreement even thoughnine jets are considered in these simulations A value ofℎ0 asymp 350Wm2K is retrieved from [24] to be compared
0
50
100
150
200
250
300
350
Loca
lℎ(W
m2s)
02 04 06 08 10xL
Figure 4 Local ℎ at 1000 positions along the sheet as a function ofnormalized distance 119909119871 from the sheet entrance region
with an averagemaximum value of ℎ0 = 331Wm2K retrievedfrom simulations considering all jets The maximum value ofℎ0 attained from simulations ℎ0 = 353Wm2K is found atthe stagnation point of the middle jet being even closer toexperimental data
33 Comparison between Methods to Derive the EvaporationRate Three methods to calculate the evaporation rate arecompared for verification of the simulations vapor treatedas a scalar variable composition mixture of air and vaporand evaporation rate through the heat and mass transferanalogy (HMTA)The boundary conditions are set accordingto Table 1 and the simulations are run without recirculatingmoisture since results from the HMTAwill predict the evap-oration rate without further determination of the distributionof moisture inside the dryer The three methods give similarresults as can be seen in Figure 5 and Table 2 where the localand average evaporation rates are displayed respectivelyThelargest difference approx 20 is seen between the heat andmass transfer analogy and vapor included as a scalar whilethe difference between the scalar and variable compositionmixture is only around 5 From Figure 5 it is furthermoreapparent that the evaporation rate will follow the heat andmass transfer coefficients with maximal values right belowthe impingement jets
The determined evaporation rates can also be used tochallenge the assumption of constant sheet temperatureEstimations show that the combination of latent heat neededto evaporate the water and heating from the jets would affectthe temperature with only a few degrees during drying ifconstant temperature through the sheet is assumed
34 Influence of Recirculating Air Next the influence of recir-culating air is studied Due to the decreased computationaleffort the moisture is here modelled as a scalar Outtakepercentages OP of 75 10 125 15 and 175 areinvestigated Firstly the temperature and velocity fields are
6 International Journal of Chemical Engineering
Table 2 Area average evaporation rates and relative difference compared to simulations where moisture is included as a two-componentmixture of air and vapor
Method Evaporation rate [kgm2s] Relative difference []Scalar 000575 469Two-component mixture 000605Heat and mass transfer analogy 000687 135
Moisture scalarMoisture two-component mixtureHMTA
Loca
l eva
pora
tion
rate
(kg
m2s)
0
0005
001
0015
002
0025
003
02 04 06 08 10xL
Figure 5 Local evaporation rate as a function of normalizeddistance from sheet entrance
examined which are independent of OP A primary stagna-tion point under the jet and a secondary stagnation pointbetween the jets are observed see Figure 6 where the velocityfield and vectors are displayed for the jet located in themiddleof the row (see Figure 1) A recirculation zone is observedbetween the primary and secondary stagnation point andupwash flow is observed above the secondary stagnationpoint This is together with the unsymmetrical positions ofthe secondary stagnation points in correspondence with thefindings by Caliskan et al [14] and Kharoua et al [16] Forthe studied case the asymmetry could be partly due to thelocation of the outlet The corresponding temperature field isdisplayed in Figure 7 showing the same trends as the velocityfield with regard to stagnation points
Secondly the surface average evaporation rate is investi-gated assuming a film of water across the whole sheet thatis initially no regards are taken to whether or not all wateris evaporated before the exit Results show a decelerationof evaporation rate for low OP Only for OP = 15 and175 the sheet is completely dry before the exit see Figure 8where results from simulations are compared to the requiredevaporation rate determined from process values An OP of100 represents dry air at the inlet
The magnitude of the evaporation rate is observed toincrease with OP that is reduced relative saturation while
628
80
000
188
6525
154
314
4237
730
440
1950
307
565
9662
884
691
7275
461
817
49
125
77
Velocity (m sminus1)
Figure 6 Local velocity below the middle jet Three jets aredisplayed in the picture
321
227
329
304
337
381
345
458
353
535
361
612
369
688
377
765
385
842
393
919
401
996
410
073
418
150
313
150
Temperature (K)
Figure 7 Local temperature below the middle jet Three jets aredisplayed in the picture
the locations of the maximum and minimum evaporationrates remains as long as water is present on the sheet seeFigure 9 where the local evaporation rates are displayed forOP = 10 125 and 15 at 119879in = 418K A step function is hereintroduced to account for the zero evaporation rates at dryareas of the sheet As seen in Figure 9 the evaporation rate iszero close to the exit of the metal sheet for the outtake of 15since the drying is completed before the sheet exits the dryerThe two jets closest to the outlet furthermore show a differentbehavior than the rest of the jets possibly due to geometricalconsiderations
To further investigate the efficiency of the dryer the ratioof dried water volume divided by initial water volume iscalculated At an OP of 15 the metal sheet is totally dryat the exit while at 75 only approx 60 of the water hasevaporated see Figure 10
Recondensation of moist air could impose a possible riskof reducing the dryer efficiency especially if the saturation ishigh close to the outlet To examine the risk of condensationthe relative saturation RS is investigated above and belowthe nozzles At OP = 15 the simulations show that thehighest RS above the plate is attained at the entrance regionsee Figure 11 where the local RS inside the dryer is displayedat four normalized heights Results thus show a low risk ofrecondensation as the RS is only a few percent with maximalRS for the positions closest to the plate of around 6 Thefairly low RS is further confirmed in Figure 12 where the local
International Journal of Chemical Engineering 7
SimulatedRequired
times10minus4
15
2
25
3
35
4
45
5
55
Evap
orat
ion
rate
(kg
s)
20 40 60 80 1000Outtake percentage ()
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
Table 2 Area average evaporation rates and relative difference compared to simulations where moisture is included as a two-componentmixture of air and vapor
Method Evaporation rate [kgm2s] Relative difference []Scalar 000575 469Two-component mixture 000605Heat and mass transfer analogy 000687 135
Moisture scalarMoisture two-component mixtureHMTA
Loca
l eva
pora
tion
rate
(kg
m2s)
0
0005
001
0015
002
0025
003
02 04 06 08 10xL
Figure 5 Local evaporation rate as a function of normalizeddistance from sheet entrance
examined which are independent of OP A primary stagna-tion point under the jet and a secondary stagnation pointbetween the jets are observed see Figure 6 where the velocityfield and vectors are displayed for the jet located in themiddleof the row (see Figure 1) A recirculation zone is observedbetween the primary and secondary stagnation point andupwash flow is observed above the secondary stagnationpoint This is together with the unsymmetrical positions ofthe secondary stagnation points in correspondence with thefindings by Caliskan et al [14] and Kharoua et al [16] Forthe studied case the asymmetry could be partly due to thelocation of the outlet The corresponding temperature field isdisplayed in Figure 7 showing the same trends as the velocityfield with regard to stagnation points
Secondly the surface average evaporation rate is investi-gated assuming a film of water across the whole sheet thatis initially no regards are taken to whether or not all wateris evaporated before the exit Results show a decelerationof evaporation rate for low OP Only for OP = 15 and175 the sheet is completely dry before the exit see Figure 8where results from simulations are compared to the requiredevaporation rate determined from process values An OP of100 represents dry air at the inlet
The magnitude of the evaporation rate is observed toincrease with OP that is reduced relative saturation while
628
80
000
188
6525
154
314
4237
730
440
1950
307
565
9662
884
691
7275
461
817
49
125
77
Velocity (m sminus1)
Figure 6 Local velocity below the middle jet Three jets aredisplayed in the picture
321
227
329
304
337
381
345
458
353
535
361
612
369
688
377
765
385
842
393
919
401
996
410
073
418
150
313
150
Temperature (K)
Figure 7 Local temperature below the middle jet Three jets aredisplayed in the picture
the locations of the maximum and minimum evaporationrates remains as long as water is present on the sheet seeFigure 9 where the local evaporation rates are displayed forOP = 10 125 and 15 at 119879in = 418K A step function is hereintroduced to account for the zero evaporation rates at dryareas of the sheet As seen in Figure 9 the evaporation rate iszero close to the exit of the metal sheet for the outtake of 15since the drying is completed before the sheet exits the dryerThe two jets closest to the outlet furthermore show a differentbehavior than the rest of the jets possibly due to geometricalconsiderations
To further investigate the efficiency of the dryer the ratioof dried water volume divided by initial water volume iscalculated At an OP of 15 the metal sheet is totally dryat the exit while at 75 only approx 60 of the water hasevaporated see Figure 10
Recondensation of moist air could impose a possible riskof reducing the dryer efficiency especially if the saturation ishigh close to the outlet To examine the risk of condensationthe relative saturation RS is investigated above and belowthe nozzles At OP = 15 the simulations show that thehighest RS above the plate is attained at the entrance regionsee Figure 11 where the local RS inside the dryer is displayedat four normalized heights Results thus show a low risk ofrecondensation as the RS is only a few percent with maximalRS for the positions closest to the plate of around 6 Thefairly low RS is further confirmed in Figure 12 where the local
International Journal of Chemical Engineering 7
SimulatedRequired
times10minus4
15
2
25
3
35
4
45
5
55
Evap
orat
ion
rate
(kg
s)
20 40 60 80 1000Outtake percentage ()
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
Figure 8 Area average evaporation rate as a function of OP
1012515
Loca
l eva
pora
tion
rate
(kg
m2s)
times10minus3
0
01
02
03
04
05
06
07
08
09
1
02 04 06 08 10xL
Figure 9 Comparison of local evaporation rates at different out-takes of moist air
vapor density below the middle jet is displayed for OP = 15The maximum moisture content is attained at the surface ofthe sheet and distinct areas of increased moisture content inthe secondary stagnation points is displayed see Figure 12
4 Conclusions
This study shows the potential of using CFD as a mean toimprove the fluid flow in impingement jet dryers By treatingvapor as a scalar the evaporation rate can still be predicted
5 10 15 200Outtake percentage ()
0
02
04
06
08
1
12
Mas
s rat
io (k
gkg
)
Figure 10 Mass ratio of evaporated water as a function of OP
0
001
002
003
004
005
006
007
RS
02 04 06 08 10xL
yHd = 003
yHd = 008
yHd = 06
yHd = 090
Figure 11 RS at normalized heights inside the dryer as a function ofnormalized distance from the entranceThe sheet is located at 119910 = 0(see Figure 1)
001
20
008
001
60
020
004
3
002
40
027
003
10
035
003
9
004
70
051
000
40
000
Vapor density (kg minus3)mFigure 12 Local density of vapor below the middle jet at OP = 15Three jets are displayed in the picture
with good accuracy both compared to results from the heatand mass transfer analogy and with results from a full modelwhere water vapor is included in the composition of the air Acomparison between simulated values of the stagnation pointheat transfer coefficient ℎ0 and experimental results from theliterature also yields a good agreement Results furthermore
8 International Journal of Chemical Engineering
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
show that the evaporation rate in the impingement dryer ishighly dependent on the saturation of vapor in the inlet airThe risk of condensation inside the dryer is in its turn low forthe studied conditions Interestingly the two jets closest to theoutlet show a lower impact than the other nozzles indicatingthat there is a potential of improvement if the fluid flow closeto the nozzles is further investigated Including 3D effectstransient behavior and more advanced turbulence modelswill give even more conclusive results
Nomenclature
119861 Width of nozzle m1198611015840 Effective nozzle width m119862119889 Discharge coefficient119888119901 Specific heat at constant pressure JkgK119863av Diffusivity m
2sℎ Convection heat transfer coefficientWm2 Kℎ0 Stagnation point heat transfer coefficientWm2 K119867 Enthalpy Jkg119867119889 Height of dryer m119896 Turbulence kinetic energy m2s2119871 Length of metal sheet m Evaporation rate kgm2 s
OP Outtake percentage of recirculating air119901 Pressure Pa11990210158401015840 Heat flux Wm2119877 Universal gas constant JmolKRS Relative saturation119905 Time s119879 Temperature K119880 Velocity component ms119906 Fluctuating velocity component in
The authors declare that they have no competing interests
Acknowledgments
The authors would like to acknowledge Norrbottens Forskn-ingsrad for their financial support
References
[1] A Avci andM Can ldquoAnalysis of the drying process on unsteadyforced convection in thin films of inkrdquo Applied Thermal Engi-neering vol 19 no 6 pp 641ndash657 1999
[2] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoInfluence of air humidity on drying of individual iron orepelletsrdquo Drying Technology vol 29 no 9 pp 1101ndash1111 2011
[3] A-L Ljung V Frishfelds T S Lundstrom and B D Mar-javaara ldquoDiscrete and continuous modeling of heat and masstransport in drying of a bed of iron ore pelletsrdquo DryingTechnology vol 30 no 7 pp 760ndash773 2012
[4] A-L Ljung E M Lindmark and T S Lundstrom ldquoInfluenceof plate size on the evaporation rate of a heated dropletrdquoDryingTechnology vol 33 no 15-16 pp 1963ndash1970 2015
[5] Z Q Lou A S Mujumdar and C Yap ldquoEffects of geometricparameters on confined impinging jet heat transferrdquo AppliedThermal Engineering vol 25 no 17-18 pp 2687ndash2697 2005
[6] S JWang and A S Mujumdar ldquoA comparative study of five lowReynolds number k-120576 models for impingement heat transferrdquoApplied Thermal Engineering vol 25 no 1 pp 31ndash44 2005
[7] M Raisee A Noursadeghi B Hejazi S Khodaparast and SBesharati ldquoSimulation of turbulent heat transfer in jet impinge-ment of air flow onto a flat wallrdquo Engineering Applications ofComputational Fluid Mechanics vol 1 no 4 pp 314ndash324 2014
[8] A Abdel-Fattah ldquoNumerical and experimental study of turbu-lent impinging twin-jet flowrdquo Experimental Thermal and FluidScience vol 31 no 8 pp 1061ndash1072 2007
[9] S Qiu P Xu Z Jiang and A S Mujumdar ldquoNumerical mod-eling of pulsed laminar opposed impinging jetsrdquo EngineeringApplications of Computational Fluid Mechanics vol 6 no 2 pp195ndash202 2012
[10] Y Jiang P Xu A S Mujumdar S Qiu and Z Jiang ldquoAnumerical study on the convective heat transfer characteristicsof pulsed impingement dryingrdquo Drying Technology vol 30 no10 pp 1056ndash1061 2012
[11] J Taghinia M M Rahman and T Siikonen ldquoNumerical inves-tigation of twin-jet impingement with hybrid-type turbulencemodelingrdquo AppliedThermal Engineering vol 73 no 1 pp 648ndash657 2014
[12] B Weigand and S Spring ldquoMultiple jet impingementmdashareviewrdquo Heat Transfer Research vol 42 no 2 pp 101ndash142 2011
[13] E E M Olsson L M Ahrne and A C Tragardh ldquoFlow andheat transfer from multiple slot air jets impinging on circular
International Journal of Chemical Engineering 9
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
cylindersrdquo Journal of Food Engineering vol 67 no 3 pp 273ndash280 2005
[14] S Caliskan S Baskaya and T Calisir ldquoExperimental andnumerical investigation of geometry effects onmultiple imping-ing air jetsrdquo International Journal of Heat andMass Transfer vol75 pp 685ndash703 2014
[15] M Draksler B Niceno B Koncar and L Cizelj ldquoLargeeddy simulation of multiple impinging jets in hexagonalconfigurationmdashmean flow characteristicsrdquo International Jour-nal of Heat and Fluid Flow vol 46 pp 147ndash157 2014
[16] N Kharoua L Khezzar and Z Nemouchi ldquoFlow structure andheat transfer inmultiple impinging jetsrdquoHeat Transfer Researchvol 47 no 4 pp 359ndash382 2016
[17] M V De Bonis and G Ruocco ldquoModelling local heat and masstransfer in food slabs due to air jet impingementrdquo Journal ofFood Engineering vol 78 no 1 pp 230ndash237 2007
[18] M V De Bonis andG Ruocco ldquoConjugate heat andmass trans-fer by jet impingement over a moist protrusionrdquo InternationalJournal of Heat and Mass Transfer vol 70 pp 192ndash201 2014
[19] A Yahyaee K Esmailpour M Hosseinalipour and A SMujumdar ldquoSimulation of drying characteristics of evaporationfrom awet particle in a turbulent pulsed opposing jet contactorrdquoDrying Technology vol 31 no 16 pp 1994ndash2006 2013
[20] G-P Bai G-C Gong F-Y Zhao and Z-X Lin ldquoMultiplethermal andmoisture removals from the moving plate oppositeto the impinging slot jetrdquo Applied Thermal Engineering vol 66no 1-2 pp 252ndash265 2014
[21] A-L Ljung T S Lundstrom B D Marjavaara and K TanoldquoConvective drying of an individual iron ore pelletmdashanalysiswith CFDrdquo International Journal of Heat andMass Transfer vol54 no 17-18 pp 3882ndash3890 2011
[22] G Lu Y-Y Duan X-D Wang and D-J Lee ldquoInternal flowin evaporating droplet on heated solid surfacerdquo InternationalJournal of Heat and Mass Transfer vol 54 no 19-20 pp 4437ndash4447 2011
[23] A S Mujumdar ldquoBook review handbook of industrial dryingthird editionrdquo Drying Technology vol 25 no 6 pp 1133ndash11342007
[24] H Hardisty and M Can ldquoAn experimental investigation intothe effect of changes in the geometry of a slot nozzle on theheat transfer characteristics of an impinging air jetrdquo Proceedingsof the Institution of Mechanical Engineers Part C Journal ofMechanical Engineering Science vol 197 no 1 pp 7ndash15 1983
[25] D M Himmelblau and J B Riggs Basic Principles and Calcula-tions in Chemical Engineering Bernard Goodwin Upper SaddleRiver NJ USA 2004
[26] F P Incropera D P Dewitt T L Bergman and A S LavineFundamentals of Heat and Mass Transfer John Wiley amp SonsHoboken NJ USA 2007
![DiestersBiolubricantBaseOil:Synthesis,Optimization ...downloads.hindawi.com/journals/ijce/2012/896598.pdfbiolubricants [2]. Synthetic biolubricant based on renewable resources are](https://static.documents.pub/doc/80x56/5fb2937c9caf334bb4463247/diestersbiolubricantbaseoilsynthesisoptimization-biolubricants-2-synthetic.jpg)
