AIRFLOW PATTERNS IN A LABORATORY BATCH-TYPE, TRAY AIR DRYER

Transcription

1 5 th Internatonal Conference From Scentfc Computng to Computatonal Engneerng 5 th IC-SCCE Athens, 4-7 July, 2012 IC-SCCE AIRFLOW PATTERNS IN A LABORATORY BATCH-TYPE, TRAY AIR DRYER Dmtros A. Tzempelkos 1, Alexandros P. Vouros 2, Achlleas V. Bardakas 2, Andronkos E. Flos 2 and Donssos P. Margars 1 1 Flud Mechancs Laboratory, Department of Mechancal Engneerng and Aeronautcs, Unversty of Patras, GR Patras, Greece. e-mal: margars@mech.upatras.gr 2 Laboratory of Flud Mechancs and Turbomachnery, Department of Mechancal Engneerng Educators, School of Pedagogcal and Technologcal Educaton (ASPETE), GR Athens, Greece. e-mal: aeflos@meed-aspete.net Keywords: Batch dryer, Arflow, CFD, Smulaton. Abstract. The batch-type dryer s one of the most popular equpment for frut dryng. However, the optmzaton of the ar dstrbuton nsde the dryng chamber remans a very mportant ssue, due to ts strong mpact on effcent dryng and unformty of mosture content of products. A new scale laboratory batch-type, tray ar dryer has been desgned, constructed and evaluated for dryng several hortcultural and agrcultural products. The flow feld nsde the dryer s studed through computatonal flud dynamcs (CFD). A three-dmensonal model for laboratory dryer has been created and the steady state ncompressble, Reynolds-Averaged Naver- Stokes (RANS) equatons that formulate the flow problem are solved, ncorporatng standard and RNG k-ε turbulence models. The smulatons are conducted for testng chamber average velocty of 2,9 m/s at ambent temperature. The CFD models are evaluated by comparng arflow patterns and velocty dstrbutons to measured data. Numercal smulatons and measurements convnce that the new scale laboratory batch-type dryer s able to produce a suffcently unform ar dstrbuton throughout the testng chamber of the dryer. 1 INTRODUCTION One of the most mportant factors n desgnng conventonal batch-type ar dryers s the arflow desgn. In ndustral ar dryers the effect of flow heterogenety s partcularly dffcult to resolve. The dstrbuton of arflow depends on the process of dryng, the dryng medum, the geometry and the equpment of the dryng chamber. These factors determne the unformty of dryng and qualty of fnshed products. Even though the performance of a dryng chamber can be studed expermentally, the tme and cost lmts of research restrcts the generalzaton of the results and certanly cannot be appled to the orgnal desgn of the dryng chamber. In contrast, wth the help of computatonal flud dynamcs (CFD), spannng a wde range of ndustral and non ndustral applcatons, the complexty of the flow feld can be solved numercally. Mathoulaks et al [1] smulate the flow of ar n an ndustral batch-type, tray ar dryer. The dstrbuton of pressure and velocty over the product were found to have a lack of spatal homogenety leads to varatons n dryng rates and mosture contents. Margars and Ghaus [2] smulated the arflow n an ndustral drer and provded parameters for dfferent confguraton helped to optmze the dryng space wth sgnfcant mprovement n the qualty of the dred product and the reducton of energy consumpton. Mrade [3] used a twodmensonal CFD model wth tme dependent boundary condtons, studyng the dstrbuton unformty of ar velocty n an ndustral dryer meat for low and hgh levels of ventlaton cycle. Hoang et al [4] smulated the arflow nto a cold store solvng the steady state ncompressble, Reynolds-averaged Naver-Stokes (RANS) equatons, applyng the standard k-ε and the RNG k-ε turbulence models. The results showed that the RNG k-ε model does not help to mprove the predcton of recrculaton and any mprovement requres fner grd wth enhanced smulaton of turbulent flow. Amanlou and Zomordan [5] desgned a new frut cabnet wth dfferent geometres and smulated them usng CFD. The expermental results and the predcted data from CFD revealed a very good correlaton coeffcent for dryng ar temperature and ar velocty n the dryng chamber. Norton and Sun [6] n a revew paper show the wdely use of CFD for predctng the ar velocty and temperature n dryng chambers and Scott and Rchardson [7] and Xa and Sun [8] present the commercal CFD packages that have been ncreasngly deployed n the food ndustry. Recent studes show that lmted research on the predcton and measurements of flow and pressure felds n batch-type ar dryers has been performed. The absence of experments can be attrbuted to the dffculty of drect measurement of local ar velocty and flow n a dryng chamber of hortcultural and agrcultural products.

2 The present study concerns the desgn, constructon and evaluaton of a new scale laboratory batch-type, tray ar dryer whch can serve thermal dryng studes n fully controllable envronment. The velocty and pressure felds are analyzed wth the ad of CFD commercal code Fluent. For the numercal smulatons the steady state RANS equatons are solved n combnaton wth the standard k-ε and the RNG k-ε turbulence models. The effect of the turbulence modelng s dstngushed through drect comparsons of the derved arflow patterns. The purposes of the current research are: a) the study of the velocty felds n the dryng chamber of new scale laboratory batch-type, tray ar dryer buldng a CFD method that s affordable n terms of computaton tme and b) the comparson of the numercal outcomes wth expermental measurements performed wth a sensor velocty. 2 EXPERIMENTAL SETUP AND MEASUREMENTS 2.1 Descrpton of the dryer The lab scale batch-type, tray ar dryer whch has been desgned and constructed n the Laboratory of Flud Mechancs and Turbomachnery n ASPETE, s shown n Fgures 1 and 2. The overall dmensons of the faclty are 4,7 m (length), 2,5 m (wdth) and 2,5 m (heght). The constructon of the ar ducts are made from steel of 0,8 mm thckness. All the ducts are nsulated wth 10 mm Alveolen (Frelen) wth thermal conductvty of 0,032 W/mK and water absorpton of 0,011 kg/m 2. Fgure 1. Schematc dagram of the lab-scale batch-type, tray ar dryer Fgure 2. Photo of the lab-scale ar dryer, equpped wth measurng nstrumentaton and data acquston system The square secton dryng chamber (0,5m x 0,5m) s of tower (vertcal) type and s equpped wth a metal tray whch s supported on four, sde walls mounted, load cells. A set of four refractory glasses 10 mm thckness are avalable to replace the sde steel walls when optcal clarty and precse vsual observatons are requred. Upstream of the dryng chamber, the long rectangular dffuser wth total dvergence angle 6,7 o, the tube heat exchanger n whch the hot water s provded through a boler of 58 kw ( kcal/h) thermal power, the transtonal duct wth observaton wndow that ncludes the sprayer for humdfyng purposes, the corner duct that ncorporates four gude vanes and the flow straghteners secton, are located. The flow straghteners consstng from an alumnum honeycomb (made form 3003 alumnum alloy fol) wth cell sze of 1/4 and 38 mm thckness and screen wres located downstream of the honeycomb, are consdered necessary amng to the

3 flow unformty n the dryng secton. The flow rate s observed and controlled wth a custom made and calbrated rake of ptot tubes, namely ptot rake, located at the nlet of the dryng chamber. Downstream of the vertcal dryng chamber, the second corner duct wth gude vanes, the elevated horzontal modular constructed duct, the outlet dumper and the ext dffuser, are located. The modular desgn of the faclty permts the easy place of two or three horzontal dryng chambers n tandem arrangement, on the elevated return or ext flow leg. The ar flow s establshed and controlled through a centrfugal fan drectly drven by a 3 phase electrc motor of 3 kw wth ts speed regulated by an ac nverter. Adjustng the ar dampers, the laboratory dryer would be used for thermal dryng expermental studes n both open crcut and close crcut operatons. 2.2 Measurements Ar velocty surveys nto the dryng chamber under ambent condtons,.e. atmospherc pressure at 18,4 o C were carred out for constant speed the nduced centrfugal fan at 690 rpm n 23 Hz. The volumetrc flow rate was m 3 /h, resultng to a mean velocty 2,9 m/s and Reynolds number 9,9x10 4 (based on hydraulc dameter of the dryng chamber). The mean speed of the ar flow at the nlet s the weghted average velocty of the 12 ponts collected from the ptot rake arrangement as shown n Fgure 3 and the four pressure taps (same level wth the contact tp of the ptot tube) n the sde wall of the nlet of the dryng chamber. Fgure 3. The rake of the ptot tubes Fgure 4. A 3D vew secton of the dryng chamber wth the locaton of the measured veloctes (dmensons n mllmeter) Each ptot s connected va plastc tubng to a custom made pressure collector system equpped wth solenod valves (Tekmatc 24VDC, 6W) permttng ts operaton and control wth the use of custom software developed n Labvew. A dfferental pressure transmtter (Dwyer, model MS-121-LCD) wth a calbrated accuracy ± 2% of the selected range of 25 Pa was used to measure each of the 12 ponts wth automatcally open-close the proper solenod valve. Amng to the cross check of the veloctes measured by ptot tubes and statc pressure holes, a velocty reference transducer (54T29, Dantec Dynamcs wth 54N81Multchannel CTA) was used whch s the best balance between cost and accuracy. The velocty range of the sensor s 0 30 m/s. The calbrated accuracy s ± 2% of readng ± 0,02 m/s or 2,6 % of the selected range of 3 m/s, whch s assured by a certfcate provded by the manufacturer. The measurement of the velocty was done nsde the duct at dstance 510 mm from the nlet of the dryng chamber. For measurng the ar velocty durng each test, at dfferent locatons of the dryng chamber, 4 holes on the sde wall of the dryng chamber were perced (Fgures 2 and 4). All holes except the one through whch velocty transducer was nserted for ar velocty measurement, were flled tghtly by conc plastc washers. Inlet ar velocty was kept constant durng the experment. For readng velocty at each pont nsde the dryng cabnet, the velocty transducer was nserted through a sde wall proxmty hole and adjusted at eght dfferent locatons along the depth of the dryng chamber. At each pont the tme averaged velocty was determned from measurement wth frequency of 200 Hz (200 samples/sec) and averaged over a 10 sec perod. The expermental values are drectly compared wth the numercal predctons at the same locatons. Both the dfferental pressure transmtter and the velocty transducer are connected to a PC wth a PCIe-6321 DAQ devce (Natonal Instruments ) va NI SCXI-1000 and NI SCXI-1302 modules. Custom software through Labvew was used to nterface wth the data acquston. The overall accuracy of the CFD calculatons s calculated as the average of the absolute dfferences between the tme-averaged velocty magntude for the CFD calculaton and the measurement at each poston, dvded by

4 the average velocty magntude n the dryng chamber obtaned from the measurements and s expressed as: n Ucfd Uexp 1 E 1 n Uexp 1 00 (1) where U cfd s the average velocty at poston from the CFD calculaton, U exp s the average velocty at poston from the measurement and n s the number of measurement ponts. 3 NUMERICAL SIMULATION Numercal computaton of flud transport ncludes conservaton of mass, momentum and turbulence model equatons. The preprocessor Gambt was used to create geometry, dscretze the flud doman nto small cells to form a volume mesh and set up the approprate boundary condtons. The flow propertes were then specfed, the equatons were solved and the results were analyzed by Fluent Governng equatons The governng equatons based on the conservaton of mass and momentum of a newtonan flud flow whch appled to an nfntesmal small volume n a cartesan co-ordnate system (x, y, z) and usng the Reynolds averaged formulaton [9], are: dvu 0 t (2) u t p dv Uu dv gradu S (3) eff x p,t (4) eff T (5) In these formulae, U s the velocty vector, consstng of three components u x, u y, u z (m/s), p s the pressure (Pa), T s temperature ( o C). The densty ρ (kg/m 3 ) and the lamnar vscosty μ (kg/ms) are the only flud propertes nvolved; μ Τ and μ eff are the turbulent and effectve vscosty, respectvely. The sources S contan further contrbutons of the vscous stress term and can contan addtonal body forces. The arflow at a constant temperature n the ar dryer s consdered (ρ = 1,225 kg/m 3 and μ = 1,7894 x 10-5 Ns/m 2 ) Turbulence models The k-ε models are the most wdely valdated turbulence models n lterature and are the standard models to use n the commercal codes. The k-ε model uses an eddy-vscosty hypothess for the turbulence, expressng the turbulent stresses as an addtonal vscous stress term [Eq. (5)]. In the k-ε model, the turbulent vscosty s expressed n terms of two varables: the turbulence knetc energy k and ts dsspaton rate ε. In ths model, the k and ε equatons are of a smlar conservaton format, contanng convectve and dffusve terms The standard k-ε model In the standard k-ε model, the producton and destructon terms n the ε equaton contan emprcal constants. The resultng equatons are smlar to the governng flow equatons [9] : k 2 T C (6) k dv Uk dv grad k P (7) t k 2 dvudv grad C1 P C2 t k k where P s a term contanng the turbulence producton due to the stresses n the flow. The standard k-ε model contans fve emprcal constants (C μ, C 1ε, C 2ε, σ k and σ ε ) and durng ths study these constants were not (8)

5 changed: Dmtros A. Tzempelkos, Alexandros P. Vouros, Achlleas V. Bardakas, Andronkos E. Flos and Donssos P. Margars. C μ = 0,09, C 1ε = 1,44, C 2ε = 1,92, σ k = 1,0 and σ ε = 1,3 (9) Near walls the equatons do not hold and standard logarthmc wall profles are mplemented. An mportant varable s y +, a dmensonless dstance normal to the wall. The value of y + determnes n whch regon of the boundary layer the frst node s stuated. The log-law s vald only for y + > RNG k-ε model The RNG k-ε model s obtaned va a statstcal mechancs approach, n whch small scale motons are systematcally removed from the governng equatons by expressng ther effects n terms of larger scale motons and a modfed vscosty. Furthermore, a new term appears n the ε-equaton, whch account for ansotropy n strongly straned turbulent flows. Ths term s ncorporated through a modeled constant n the producton term, based on the equlbrum assumpton that producton equals dsspaton, restrctng the RNG k-ε model to a coarse grd approach near walls. The same default wall functons as n the standard k-ε model are vald n ths case. The ε equaton s [9] : 2 dvudv grad C1 C1RNG P C2 (10) t k k C n 1 n 0 1n 1RNG 3 (11) n Ps 0,5 k where n 0 and β are addtonal model constants, whch are equal to 4,38 and 0,012 respectvely and P s s the shear part of the producton. The standard values of the other constants are regarded as sutable for ths applcaton: C μ = 0,0845, C 1ε = 1,42, C 2ε = 1,68, σ k = 0,7179 and σ ε = 0,7179 (13) The k equaton s the same format as n the standard k-ε model and the same wall profles are appled Model of the tray A source term was added to k-ε and RNG k-ε turbulence models equatons to estmate the pressure drop across the tray nto the dryng chamber. The tray was calculated as a screen and n the CFD smulaton, the screen was modeled as a thn porous meda of fnte thckness over whch the pressure change was defned as a combnaton of Darcy's Law and an addtonal nertal loss term and s gven by [10] : 1 2 p UC2 U m 2 (14) where μ s the lamnar flud vscosty, α s the permeablty of the medum, C 2 s the pressure-jump coeffcent, U s the velocty normal to the porous face, and Δm s the thckness of the medum Model of the ar dryer The flow feld nto the dryng chamber of empty laboratory batch-type, tray ar dryer, operated n open crcut mode s numercally studed. The structure of the modeled dryer s depcted n Fgure 5. The dryer s 4,7 m n length, 0,5 m n wdth and 1,38 m n heght. The dmensons of the dryng chamber are 0,5 x 0,5 x 0,66 m. The ar dryer s modeled wth the tray located n a dstance 0,29 m from the nlet of the dryng chamber. The tray has a length of 0,48 m, wdth of 0,48 m and thckness 2,8 mm. The shape of the tray has been modeled as a screen wth orthogonal holes. The dmensons of the orthogonal holes are 23,74mm x 10,9mm. A gap of 10 mm exsted between the tray and the wall of the dryng chamber. (12)

6 Fgure 5. Geometry of the ar dryer wth tray Fgure 6. Computatonal grd of the ar dryer model The velocty profle at the entrance of the dryng chamber was measured by 12 ponts (Fgure 3). These ponts were used as an nlet boundary condton for the smulaton performed and for that reason the geometry of the fan, the dffuser, the tube heat exchanger, the down gude vanes and the flow straghteners are not modeled Descrpton of the numercal smulaton The calculatons have been performed wth Fluent. In the steady RANS smulatons of the arflow nto the batch-type tray ar dryer, the standard k-ε and the renormalzaton group RNG k-ε turbulence models have been used. The standard k-ε model whch vald only for fully turbulent flows s a sem-emprcal model based on model transport equatons for the turbulence knetc energy (k) and ts dsspaton rate (ε). The model transport equaton for the turbulence knetc energy s derved from the exact equaton, whle the model transport equaton for the dsspaton rate s obtaned usng physcal reasonng and bears lttle resemblance to ts mathematcally exact counterpart. In the dervaton of the k-ε model, t was assumed that the flow s fully turbulent, and the effects of molecular vscosty are neglgble. The RNG k-ε model employs a dfferental form of the relaton for the effectve vscosty, yeldng an accurate descrpton of how the effectve turbulent transport vares wth the effectve Reynolds number. Ths allows accurate extenson of the model to near-wall flows and low-reynoldsnumber or transtonal flows. The standard logarthmc wall functons, whch are a collecton of sem-emprcal formulas and functons were appled to brdge the vscosty affected regon between the wall and the fully turbulent regon. The SIMPLE algorthm has been used together wth the solver of Fluent to solve the pressurevelocty couplng equatons. In order to mprove numercal accuracy, the second-order-upwnd scheme has been used to dscretze the RANS equatons Numercal soluton control For the numercal smulatons, a desktop PC (Intel Core 7 CPU at 2,67 GHz) was used. The number of teratons has been adjusted to reduce the scaled resdual below the value of 10-5 whch s the crtera. For each run, the observaton of the ntegrated quanttes of total pressure, at sucton as well as at dscharge surface was apponted for the convergence of the soluton. In many cases ths drves the resduals n lower values than the ntally set value. Dependng on the case, the convergence was acheved at dfference teratons, as the result at a specfc mass-flow was used to ntalze the computatons at another mass-flow. Amng to smooth convergence, varous runs were attempted by varyng the under-relaxatons factors. In that way, a drect control regardng the update of computed varables through teratons was acheved. Intalzng wth low values for the frst teratons steps and observng the progress of the resduals, ther values were modfed amng to the acceleraton of the convergence Boundary condtons and mesh cells The nlet boundary condton of the model was set as an nlet velocty profle by usng a set of velocty measured at 12 ponts nsde the ar dryer (Fg 3). The drecton of the velocty was normal to the nlet boundary and the average velocty was 2,89 m/s. The turbulent ntensty, whch s defned as the rato of the root-meansquare of the velocty fluctuatons, to the mean flow velocty can be estmated from the followng formula derved from an emprcal correlaton for ppe flows [10], u 0,16Re 18 Dh (15) u avg The turbulent ntensty at the nlet boundary was set as 3,8%, based on Re=9,9x10 4. An atmospherc pressure boundary located downstream of the outlet duct was specfed as pressure outlet. The no slp boundary condton was used n all the walls. Porous jump boundary condton was used for the tray and approprate values for

7 pressure jump coeffcent, C 2, and permeablty α, were then calculated from the lterature [11]. The CFD model of new scale laboratory batch-type dryer conssts of about 8x10 5 computatonal nodes (Fgure 6). A body ftted structured grd was used. The grd was refned closed to the walls, n between the wall and the tray and nsde the tray. The y + was n the range of 30 to 50. The grd ndependence was checked and a converged soluton was obtaned after approxmately teratons. 4 RESULTS AND DISCUSSIONS The predcted veloctes wth k-ε and RNG k-ε at heght z=0,51m, as shown n Fgure 4, are compared wth the correspondng expermental values. Fgure 7 shows a comparson between the measured and the smulated values of ar velocty dstrbuton, whch gve an overall accuracy of the CFD calculatons, E n equaton (1), 2,79 % for the k-ε and 2,72 % for the RNG k-ε turbulence model. The dfference of the absolute between the smulated and expermental values vares from 0,002 to 0,227 m/s for k-ε and 0,002 to 0,213 m/s for RNG k-ε turbulence model. The relatve error between the smulated and expermental values vares from 0,08 to 7,38 % for k-ε and 0,08 to 6,93 % for RNG k-ε turbulence model. The average velocty of the expermental values s 3,22 m/s wth a standard devaton 0, The average velocty and standard devaton for the k-ε and RNG k- ε turbulence model s 3,274 m/s, 0,09367, 3,267 m/s and 0,10503 respectvely. The overall accuracy of the CFD calculatons ndcates the CFD smulaton scheme s practcal for the analyss of the velocty feld n the dryng chamber. Fgure 8 llustrates the turbulent ntensty predcted wth k-ε and RNG k-ε at poston z=0,51m. The average turbulent ntensty s about 4%. At the edges of the dryng chamber (5 cm for the wall) the turbulent ntensty reaches almost 14%. Ths dfference could be explaned by the presence of the tray and ts geometry. In Fgure 9, the velocty contours chosen for ther relevance concernng the assessment of the arflow calculatons are shown. It can be seen that hgh veloctes are encountered at the center of the chamber. Near the four walls the ar moves at lower veloctes due to the presence of the tray whch located 200 mm below the level where measurements were taken. Both the two turbulence models predct almost the same ar flow dstrbuton. Fgures 8 and 9 verfy that at the core of the dryng chamber, the turbulent ntensty of the velocty feld s relatvely low and the flow s homogenous. Fgure 7. Velocty dstrbutons at z =0,51m. Comparson between the measured data and CFD predcton wth k-ε and RNG k-ε turbulence model: (a) y=163mm, (b) y=223mm, (c) y=283mm and (d) y=343mm

8 Fgure 8. Turbulent ntensty n z = 0,51m. Comparson between numercal predctons wth k-ε and RNG k-ε turbulence models: (a) y=163mm, (b) y=223mm, (c) y=283mm and (d) y=343mm Fgure 9. Velocty contours (m/s) at z = 0,51m predcted wth k-ε (left) and RNG k-ε (rght) turbulence models The velocty contours at the ar dryer of the developed CFD model are presented n Fgure 10. The velocty contours reveal the presence of hgh veloctes regons especally at the mddle of the dryng chamber and above the tray dsk. In Fgure 11, the statc pressure contours n the ar dryer reflects the presence of low veloctes regme especally at the nlet of the dryng chamber and at the upper gude vanes. At a dstance 310 mm from the nlet of the dryng chamber, there s a pressure drop from 6 to 1 Pa n terms of gauge pressure. Ths drop of the statc pressure s due to the presence of the tray dsk at ths locaton. In Fgure 12, δ represents the relatve dfference of velocty magntude wth k-ε and RNG k-ε turbulence model wth respect to the k-ε turbulence model and defned as: Uk U 100 (16) U RNGk k Near the wall of the dryng chamber the parameter δ reaches almost 10% and n contrary at the mddle of the chamber, the velocty predctons are ndependent of the turbulence model.

9 Fgure 10. Contours of velocty magntude (m/s) predcted wth k-ε (left) and RNG k-ε (rght) model at y=0,25 m Fgure 11. Statc pressure contours (Pa) predcted wth k-ε (left) and RNG k-ε (rght) model at y=0,25 m Fgure 12. Comparson of δ between k-ε and RNG k-ε turbulence model: (a) y=163 mm, (b) y=223 mm, (c) y=283 mm and (d) y=343 mm 5 CONCLUDING REMARKS A flud flow model of a new scale laboratory batch-type, tray ar dryer, ncludng ts major physcal features, s developed usng CFD code Fluent. Standard k-ε and RNG k-ε turbulence models were used for computng turbulence parameters nsde the ar dryer. Numercally predcted velocty profles nsde the dryng chamber are compared wth the measured data. These predctons are found to be n reasonable agreement wth measured data. The turbulence ntensty s low and the homogenety of the dryng chamber s acceptable. There s a slghtly dfference between the k-ε and the RNG k-ε turbulence model predctng the velocty profles and the model developed s found useful to predct the arflow pattern nsde the dryng chamber. Further work wll focus on valdatng CFD results wth dryng experments wth organc and norganc products n the dryng chamber of the ar dryer.

10 ACKNOWLEDGMENTS The measurng equpment and the data acquston of the lab batch-type dryer n the Laboratory of Flud Mechancs and Turbomachnery has partally funded from publc and prvate sponsors. The authors gratefully acknowledge Specal Account for Research of ASPETE, Delta P S.A., Α.A. Robas & Co., Mr. Donsos Tsepenakas (EKO S.A.) and Mr. Mchals Petrolekas (Natonal Instruments, Hellas) for ther knd contrbuton and support. REFERENCES [1] Mathoulaks, E., Karathanos, V.T. and Belessots, V.G. (1998), Smulaton of ar movement n a dryer by computatonal flud dynamcs: Applcaton for the dryng f fruts, Journal of Food Engneerng, Vol. 36, pp [2] Margars, D.P. and Ghaus, A.G. (2006), Dred product qualty mprovement by ar flow manpulaton n tray dryers, Journal of Food Engneerng, Vol. 75, pp [3] Mrade, P.S. (2003), Predcton of the ar velocty feld n modern meat dryers usng unsteady computatonal flud dynamcs (cfd) models, Journal of Food Engneerng, Vol. 60, pp [4] Hoang, M.L., Verbonen, P., Baerdemaeker, J. and Ncola, B.M. (2000), Analyss of the ar flow n a cold store by means of computatonal flud dynamcs, Internatonal Journal of Refrgeraton, Vol. 23, pp [5] Amanlou, Y. and Zomordan, A. (2010), Applyng CFD for desgnng a new frut cabnet dryer, Journal of Food Engneerng, Vol. 101, pp [6] Norton, T. and Sun, D.W. (2006), Computatonal flud dynamcs (CFD) an effectve and effcent desgn and analyss tool for the food ndustry: a revew, Trends n Food Scence and Technology, Vol. 17, pp [7] Scott, G. and Rchardson,P. (1997), The applcaton of computatonal flud dynamcs n the food ndustry, Trends n Food Scence and Technology, Vol. 8, pp [8] Xa, B. and Sun, D.W. (2002), Applcatons of computatonal flud dynamcs (CFD) n the food ndustry: a revew, Computers and Electroncs n Agrculture, Vol. 34, pp [9] Tu, J., Yeoh, G.H. and Lu, C. (2008), Computatonal Flud Dynamcs, A Practcal Approach, 1 st ed., Butterworth-Henemann. [10] Fluent 6.3 User s Gude (2006), Fluent Inc. [11] Idelchk, I.E. (1994), Handbook of hydraulc resstance, 3 rd ed., CRC Press Inc.