SIMULATION OF HEAT TRANSFER AND FLUID FLOW IN A POROUS BED OF IRON ORE PELLETS DURING UP- DRAUGHT DRYING

Transcription

1 Fith International Conerence on CFD in the Proce Indutrie CSIRO, Melbourne, Autralia December 006 SIMULATION OF HEAT TRANSFER AND FLUID FLOW IN A POROUS BED OF IRON ORE PELLETS DURING UP- DRAUGHT DRYING Anna-Lena LJUNG 1, T. Staan LUNDSTRÖM 1 and Kent TANO 1 Diviion o Fluid Mechanic, Luleå Univerity o Technology, SE , Luleå, Sweden LKAB, Reearch and Develoment, SE , Malmberget, Sweden ABSTRACT Iron ore ellet i one o the mot reined roduct or comanie uch a LKAB and it i thereore a global need or reearch in the area in order to otimize the roduction and imrove quality. Thi work aim at modelling and otimizing the drying zone o a travelling grate elletizing lant and to tart with, a model o velocity and temerature ditribution in the u-draught drying zone i develoed with aid o comutational luid dynamic. The velocity ditribution in the orou bed i decribed by law o luid dynamic in orou media. The dominating heat traner mechanim i convection and two energy equation are required ince the orou media region contain both luid and olid. Reult rom imulation how a raid cooling o air due to the high eciic urace area in the orou material. Concluion are that it i oible to imulate convective heat traner within a orou media in ANSYS CFX There are however ome limitation when uing the diuive tranort equation a the olid hae energy equation that need urther invetigation. Moiture content and condenation in the bed are not included in the reent model and i thereore ubject to uture work. NOMENCLATURE a eciic urace area o the acked bed [m -1 ] α thermal diuivity [m - -1 ] A area erendicular to low direction [m ] c eciic heat at contant reure [J kg -1 K -1 ] D here article diameter [m] ε oroity h convective heat traner coeicient [W m - K -1 ] k thermal conductivity [W m -1 K -1 ] K ermeability [m ] ρ denity [kg m -3 ] reure [Pa] Q volume low [m 3-1 ] t time [] T temerature [ºC] u velocity [m -1 ] U uericial luid velocity [m -1 ] μ dynamic vicoity [kg m -1-1 ] Subcrit luid olid concentrate are very ine grained and agglomeration i thereore neceary. Agglomeration can be achieved by elletizing and intering. Ore containing large quantitie o contamination mut be very ine-grained, and can thereore only be ued or ellet. Due to advantage uch a good tranortability and mechanical trength, ellet are ometime roduced rom good iron ore a well. Pellet are thu intered here with high iron content. The average diameter or iron ore ellet i about 1 mm and 99 % o all ellet have a diameter in the range mm and 70 % o thee are, in their turn, within the interval mm. Pellet can be indurate in hat urnace, in grate-kiln and on travelling grate. The rincile o intering ellet i almot the ame in grate-kiln and on travelling grate. The roce tart with u- draught drying (UDD), ollowed by down- draught drying (DDD), a reheating zone, a burn zone and a cooling zone. The zone or burning i called iring on travelling grate and in great kiln or kiln. In the burning zone, magnetite i tranormed to hematite through oxidation. Beore entering the drying zone, green ball are acked in a continuou bed. There are, a already mentioned, two oible low direction or the drying air. Oten a combination o thee two tye o drying are ued, in order to make the lower layer more reitant to reure. In UDD, hot air will make the lower art o the bed dry quickly but the air will oon cool rom it inlet temerature to it evaoration temerature, which may lead to condenation in the uer art o the bed. The green ball are weakened when water condenate in the bed and thi i one o the reaon why there i a limitation in bed height. When the green ball reach DDD, their trength ha imroved enough to avoid roblem due to condenation. The heat ulied ha to be controlled o that the moiture exiting in the ore can ecae through the caillarie without any over-reure which would weaken the ellet tructure. Thi henomenon when overreure occur i called chock drying and i one o the greatet limitation in inlet air temerature. Another reaon to kee the temerature airly low i the rik or early oxidation [1]. THEORY The governing equation or luid low are given a ollow []: INTRODUCTION Beore iron ore enter the blat urnace, it i neceary to remove a great ortion o the mineral ballat comonent by graining. To remove thee contamination, Continuity equation ρ + u ( ρ ) = 0 (1) 1

2 Momentum equation u ρ = + μ u + ρ F. () There are variou orm o the momentum equation orou medium analogue to the Navier-Stoke equation. The commonly ued Darcy' law i in reined and one dimenional orm exreed a [3] d μ Q =. (3) dx K A The coeicient K, called ermeability in ingle hae low, i indeendent o the nature o the luid and i excluively given by the geometry o the medium. Darcy law i valid a long a Reynold number baed on average grain diameter doe not exceed ome value, oten between 1 and 10 [4]. A the velocity increae, the tranition to nonlinear drag i quite mooth. Thi tranition i to tart with not rom laminar to turbulent low ince at uch comaratively mall Reynold number the low in the ore i till laminar. The breakdown in linearity i rather due to increaed inertia and i thereore a conequence o the tortuoity o the oreace. An equation that quite oten it data well over the entire range o Reynold number i the Ergun equation [5] Δ = 150 y 1.75 ( 1 ε ) 3 ε ( 1 ε ) 3 ε ρu D μu + D. (4) Regarding heat traner, convection i the mode o energy traner between a olid urace and the adjacent liquid or ga in motion and it involve the combined eect o conduction and luid motion. Since motion o luid i involved, heat traner by convection i artially governed by the law o luid mechanic. Since the region with the orou media contain both luid and olid, two energy equation are required. The energy equation can be reented in ollowing orm by taking average over an elemental volume o the medium [6]. Fluid hae energy equation: ε ( ρc ) + ( ρc ) v T ( εk T ) + a h T T ) δt Solid hae energy equation: ( 1 ε )( c ) ( (( 1 ε ) k T ) + a h ( T T ) T = =. (5). (6) The lat term in Eq. 5 and 6 have their origin in Newton law o cooling. The convective heat traner coeicient, h, i an exerimentally determined arameter whoe value deend on all variable inluencing convection uch a the urace geometry, the nature o luid motion, the roertie o the luid and the bulk luid velocitie [7]. Seciic urace area, a, i tated by the ollowing exreion which i develoed rom geometrical conideration [6] a 6(1 ε ) =. (7) D COMPUTATIONAL FLUID MECHANICS CFX 10.0 ue the Finite Volume (FV) method a dicretization aroach. The olution domain i thereore ubdivided into a inite number o contiguou control volume (CV), and the conervation equation are alied to each CV. Numerical olution or luid low roblem have variou tye o unavoidable error, mainly modelling error, dicretization error and iteration error. Since the irt one require exeriment to be determined in thi cae, ocu i et on the latter error [8]. Dicretization error can be deined a the dierence between the exact olution o the governing equation and the exact olution o the dicrete aroximation. Dicretization error can be etimated by retrieval o an extraolated value when meaurement rom dierent grid are available [8]. Iteration error can be deined a the dierence between the exact and the iterative olution o the dicretized equation. The iteration error hould be o an order o magnitude lower than dicretization error. I the error level at the tart o comutation i known, the error will all -3 order o magnitude i the norm o reidual ha allen 3-4 order o magnitude. Thi would imly that the irt two or three mot igniicant digit will not change in urther iteration, and that the olution i accurate within %. The dimenionle arameter Courant number i one o the key arameter in tranient CFD imulation and i deined a c uδt Δx = (8) being the ratio o time te Δt to the characteritic convection time u/δx that i the time required or a diturbance to be convected a ditance Δx. When uing exlicit method a tranient cheme, the criterion to be atiied i c < 1. Larger courant number are allowed when uing the backward or imlicit Euler method a tranient cheme, but uing too large value can lead to lo o numerical accuracy and each time te mut have iterative convergence [8]. MODELLING The ollowing aumtion are now introduced: Pellet are regarded a incomreible olid here with uniorm diameter o 1 mm. The low i aumed to be two dimenional with no regard taken to thermal- or ma low rom the bed urrounding. Eect due to movement o the bed are alo neglected. Moiture content in the bed i not taken into account. Material arameter uch a denity and conductivity are baed on intered ellet

3 and are aigned contant value rom Meyer [1] and earlier work at LKAB (See Aendix A). A bed o green ball i exected to have greater variation in oroity than a bed o ired ellet. Meaurement o natural variation in acking o green ball are however not available and the variation i thereore etimated to be around 15% with a mean value o The layer o ired ellet i aroximately 0.1 m and i given a ix oroity o 0.39 which i an average oroity calculated rom ellet denity and bulk denity. Since heat in a bed o ellet i u to 90% tranerred by convection, all other heat traner mechanim will be let out o calculation. Only u- draught drying i invetigated. The inlet air temerature i 300 ºC and the initial temerature o the air and ellet in the bed i 35 ºC in UDD. Thermal diiation i not taken into account. With thee aumtion a orou domain i ued to account or the orou material. When imulating heat traner in orou media with ANSYS CFX 10.0, the luid energy equation (Eq. 5) i automatically taken into account. However, a ource term equal to the lat term in Eq. 5 divided by ε mut be added in order to olve or the convective heat traner between olid and luid. The olid energy equation (Eq. 6) i not taken into account automatically, but may be included a a diuive tranort equation by the ue o an additional variable. A ource mut be added here a well to account or the interaction between olid and luid. Additional Variable (AV) are non-reacting, calar comonent which are tranorted through the low and ANSYS CFX 10.0 tyically interret additional variable a concentration within the luid domain. In thi cae, the additional variable hould rovide a local average temerature in the olid material. The diuive tranort equation on eciic orm ha the aearance ( ερ φ) = ( ερ α φ) + εs Since Eq. 9 i uoed to rereent Eq. 6, the additional variable Φ and the thermal diuivity α are tated a ollowing: ( 1 ε ) T olid ρ c φ = ερ k (9) (10) α =. (11) ρ c By ubtituting Eq. 10 and Eq. 11 with Eq. 9, the ollowing tranort equation i obtained: (1 n) ρ c k nρ ρ c T olid = ns + (1 n) ρ c nρ T olid. (1) Eq. 1 imlie ome limitation in oroity and luid denity variation. Fluid denity mut be indeendent o temerature, reure and location and the luid ued in calculation i thereore given contant material arameter value baed on the mean temerature in the model. Poroity mut, in the ame way a denity, have a contant value in the energy equation. It i however oible to let low through the bed be a unction o thi variation in oroity, ince the exreion o the linear and quadratic coeicient o Eq. 4 are eciied in the orou lo model. Layer o dierent oroity due to dierence in ize and acking or green ball and ired ellet are imlemented in the model with aid o te unction. To account or natural variation, randomly elected value o oroity within the interval are interolated over the whole region o green ball. A oroity value baed on a volume average o the decribed variation i ued in the energy equation. A value o normal eed i alied at the inlet or tability reaon. The magnitude o the velocity i aroximated rom available roce value o ma low and velocitie. The inlet uericial velocity i rom thi aroximation given a value o 3.8 m/. Since the value o velocity i baed on a temerature o 300 ºC, the velocity ued a inlet boundary condition i recalculated with reect to denity change and et to.7 m/. The outlet boundary condition i et to tatic reure with zero a relative reure. By taking the traner coeicient a zero or the olid temerature inlet boundary condition, the only heat traner between olid and luid i done by the convective term in Eq. 5 and Eq. 6. Thermal energy i choen a heat traner model and gravity i neglected in the model. The low i aumed to be turbulent, baed on the theory by Nield [3], ince the ore Reynold number or the condition decribed above i 300. There are numerou turbulence model under invetigation or low in orou media. For examle, Mauoka and Takatu [9] rooed the 0- equation model, Antohe and Lage [10] a macrocoic turbulence k-ε model and Kuwahara et al. [11] erormed a large eddy imulation (LES) tudy. Simulation in thi work are carried out with a tandard k- ε turbulence model with deault intenity and length cale and automatic eddy diiation ince thi model i exected to rovide a good comromie in comutational eort, robutne and accuracy. It i imortant to note that uch a turbulence model only will take macrocoic turbulence eect into account and turbulence due to the orou matrix in a microcoic ene will be let out o calculation. Since only two dimenional low eect are taken into account, the geometry o the bed i imliied in order to ave comutational time. By uing a ymmetry condition, only one hal o the width o the geometry ha to be included. Since the low i aumed to be two dimenional, only one element in z- direction i ued and ymmetry condition on the two boundarie are alied. A no li boundary wall condition i imoed at the leaning wall. The bed height i 0.55 m and the to and bottom width o thi bed i m and 3.5 m, reectively. The imliied geometry together with boundary condition i reented in Figure 1. 3

4 extra [Pa] Error Grid 1 Error Grid 3 (%) (%) Table : Reult rom dicretization error analyi. The oroity ditribution in the bed i reented in Figure 3. The natural variation o oroity i interolated rom ten randomly elected oint and the correonding low ditribution i reented in Figure 4. Figure 1: Simliied geometry with boundary condition. Seciied blend actor 1.0 i ued a advection cheme and econd order backward Euler a tranient cheme. RESULT A grid convergence tet baed on reult rom iothermal, teady tate imulation with three conecutive grid i done in order to etimate the magnitude o the dicretization error. Value o area average inlet reure are ued or the error analyi and the reult i reented in Table 1. The RMS reidual target i et to 1e-7 a convergence criteria, which in thi cae rereent a reduction o iteration error with at leat -3 order o magnitude. Grid No. No. o node Normalized number o node Area average inlet reure [Pa] Table 1: Reult rom grid reinement tudy. The reult o the grid reinement tudy how monotone convergence. The olynomial curve in Figure indicate that the reult are in the aymtotic range and an extraolated value o reure or an ininitely ine meh i thu obtained. Figure 3: Poroity ditribution. 5131,00 Area average inlet reure [Pa] 5130, ,00 519,50 519,00 518,50 y = 0,01x + 0,6x + 519,31 518,00 0,0 1,0,0 3,0 4,0 5,0 Normalized number o node Figure : Area average inlet reure a a unction o normalized number o node. The extraolated value and the correonding etimated error are hown in Table. The coaret grid i ued in all urther imulation in order to ave comutational time. Figure 4: Velocity ditribution. For illutration o temerature ditribution in luid and olid, a tranient imulation i carried out with iterative convergence criteria ulilled ince a reduction o RMS reidual o at leat three decade i achieved or every timete. Evaluation o luid temerature i illutrated in Figure 5 and the correonding alteration in olid temerature in Figure 6. The grah reent temerature deendence on height or dierent time te. 4

5 high imortance to make validating exeriment to comare with the imulation model in the uture. Flow eect due to movement o the bed and other inluence rom the roce need to be urther invetigated a well a eect on heat traner due to microcoic and macrocoic turbulence. In order to ully clariy drying o ellet, heat and moiture tranort hould alo be invetigated on a maller cale ince the reent model doe not take mall cale eect into account. Due to the comlex oroity ditribution in the bed, it i imortant to ue aroriate aroximation in order to make the ermeability a unction o both time and location. In thi work, an invetigation i made on how to imlement uch variation in CFX It i however imortant to tre that the value ued in the model are baed on rough aroximation and hould not be conidered otherwie. Thi work, however, acilitate urther invetigation on how to decribe the bed in a roer way. Figure 5: Fluid temerature ditribution at x=0 m reented at t=0, t=15, t=30 and t=45. Figure 6: Solid temerature ditribution at x=0 m reented at t=0, t=15, t=30 and t=45. DISCUSSION AND CONCLUSION Thi work demontrate the oibility o doing heat traner model in ANSYS CFX 10.0 that calculate olid and luid temerature. Current limitation are limitation in denity and oroity variation. The reented model how heat traner tendencie, but to get a roer etimation o velocity and temerature ditribution in the orou bed, urther imrovement are needed. It i alo o Both iteration error and dicretization error hould be negligible in comarion to modelling error, ince the aumtion in the model are arbitrary and convergence i achieved in all imulation. ACKNOWLEDGEMENTS The author exre their gratitude to Magnu Malm, Simon Töyrä and Mat Strömten at LKAB and Ul Sjötröm at MEFOS or valuable dicuion and LKAB or inancially backing u thi work. REFERENCES [1] MEYER, K., Pelletizing o iron ore, Sringer- Verlag, Berlin, Heidelberg, 1980 [] KUNDU, PIJUSH K., COHEN, IRA M., Fluid Mechanic, Academic Pre, San Diego, nd ed., 00 [3] NIELD, DONALD A., BEJAN, ADRIAN, Convection in Porou Media, Sringer-Verlag, New York, nd ed., 1999 [4] BEAR, JACOB, Dynamic o Fluid in Porou Media, Dover ublication Inc., New York, 1988 [5] ERGUN, S., Fluid low through acked column, Chemical Engineering Progre, Vol. 48, 89-94, 195 [6] AMIRI, A.,VAFAI, K., Analyi o dierion eect and non-thermal equilibrium, non-darcian, variable oroity incomreible low through orou media, Int. J. Heat Ma Traner, Vol. 37, No. 6, , 1994 [7] ÇENGEL, YUNUS A., Introduction to thermodynamic and heat traner, McGraw-Hill Inc., New York, 1997 [8] FERZIGER, J.H., PERIĆ, M., Comutational Method or Fluid Dynamic, Sringer-Verlag, Berlin, 3 rd ed., 00 [9] MASUOKA, T., TAKATSU, Y., Turbulence model or low through orou media, Int. J. Heat Ma Traner, Vol. 39, No. 13, , 1996 [10] ANTOHE, B. V., LAGE, J. L., A general twoequation macrocoic turbulence model or incomreible low in orou media. Int. J. Heat Ma Traner, Vol. 40, No. 13, ,

6 [11] KUWAHARA, F., YAMANE, T., NAKAYAMA, A., Large eddy imulation o turbulent low in orou media. International Communication in Heat and Ma Traner, Vol. 33, , 006 APPENDIX A Parameter Value Dimenion Denity 3700 Kg m -3 Bulk denity 00 Kg m -3 Convection heat 190 W m - K traner coeicient Average diameter 0.01 m Poroity 0.39 Seciic heat 560 J kg -1 K -1 caacity Thermal conductivity 0.4 W m -1 K -1 Table A.1: Material arameter or ired ellet 6