Ebrhi Afshri nd Seyed Ali Jzyeri Het nd Wter Mngeent in PEM Fuel Cell EBRAHIM AFSHARI, SEYED ALI JAZAYERI Deprtent of Mehnil Engineering K.N. Toosi University of Tehnology Prdis Ave, Vn squre, Tehrn IRAN efshri@lborz.ntu..ir Abstrt: - Proton exhnge ebrne (PEM) fuel ells re proising power-genertion soures for obile nd sttionry pplitions. In this pper non-isotherl, single-doin nd two-diensionl oputtionl fluid dynis odel is presented to investigte het nd wter trnsfer in PEM fuel ell. A set of governing equtions, onservtion of ss, oentu, speies, energy nd hrge for gs hnnels, gs diffusion lyers, tlyst lyers nd the ebrne regions re onsidered. These equtions re solved nuerilly in single doin, using finite-volue-bsed oputtionl fluid dynis tehnique. This odel ounts for the jor trnsport phenoen in PEM fuel ell: onvetive nd diffusive het nd ss trnsfer, eletrode inetis, nd potentil fields. The results re shown to be in good greeent with previous wor nd it is vlidted with reent experientl dt vilble Key-Words: - PEM Fuel ell; Het; Non-isotherl, Single-Doin; CFD 1 Introdution The high power density nd rpid djustent to power dends e proton exhnge ebrne fuel ells one of the best ndidtes for len lterntive energy soures for the 1st entury. The high ost nd reltively low relibility of fuel ell re the liiting ftors for their widespred use. A better understnding of operting onditions in PEM fuel ell is essentil to the developent nd optiiztion of fuel ells, the introdution of heper terils nd fbrition tehniques, nd the design nd developent of novel rhitetures. The diffiult experientl environent of fuel ell systes hs stiulted orts to develop odel tht ould siulte nd predit ulti-diensionl oupled trnsport of retnts, het nd hrged speies using oputtionl fluid dyni ethods. At present, uh odeling wor hs been done [1-7]. He et l. [1] developed two-phse nd twodiensionl odel of wter trnsport in GDL of PEM fuel ell. U et l. [] proposed trnsient, single-phse, single-doin nd two-diensionl odel for eletroheil nd trnsport proesses in PEM fuel ell. The het ngeent ws negleted by ssuing isotherl opertion Siegel et l. [, 4] investigted Single doin PEM fuel ell odel bsed on ggloerte tlyst geoetry. These odels re two-diensionl nd inludes the trnsport of liquid wter within the porous eletrodes Liu et l.[ 7] hve eployed the ixture odel for two-phse behvior in PEM fuel ell, whih n desribe the liquid wter behvior in GDL nd gs hnnel with the dvntges of sipliity nd low ost of the lultion. Wng et l. [8] lso introdued the ixture odel to desribe two-phse behvior in PEM fuel ell, nd they predited tht the liquid wter sturtion within the thode will reh 6.% t1.4a for dry inlet ir. In the ontinution of this wor, Wng nd oworers [9] siulted the funtion of iroporous lyer between thode GDL nd tlyst lyer with the ixture odel. Nguyen et l. [1] presented oputtionl fluid dynis odel of PEM fuel ell with serpentine flow field hnnels. The odel ounts for detiled speies ss trnsport, het trnsfer, nd eletroheil inetis. In order to set up tool for the dyni predition of ell behviour nd void the probles involved in other pprohes, novel pproh to the proble presented by Frneso et l. [11]. The Hwng [1] odel illustrtes the behviors of the two-phse flow nd het trnsfer in porous eletrode. This odel only investigted the thode side nd the boundry onditions in the interfes were used in nueril solution. Rowe nd Li [1], lso Mishr et l. [14] perfored study on the wter nd therl ngeent on PEM fuel ell using stedy-stte, one-diensionl pproh. They used the boundry onditions in the interfes of different regions. ISSN: 179-87 17 Issue, Volue, April 8
Ebrhi Afshri nd Seyed Ali Jzyeri In this odel, the oputtionl doin onsist two hnnels, two gs diffusion lyers, two tlyst lyers, nd polyer eletrolyte ebrne (PEM). The ell is onsidered to be two-diensionl nd stedy stte. Then, the governing equtions re solved nd theoretil perforne of PEM fuel ell is investigted by looing t preters suh s pressure, teperture, urrent density nd speies onentrtion in single-doin region. Mthetil Model Figure 1 shows sheti of two-diensionl setion of the PEM fuel ell orresponding to the geoetry of the odel onsidered in this study, whih onsists of seven different regions: node nd thode gs hnnels (GH, GH), node nd thode diffusion lyers (GDL, GDL), node nd thode tlyst lyers (CL, CL), nd the ebrne (PEM). Inside the fuel ell, hydrogen gs nd ir re supplied to the ell through the node nd thode hnnels, respetively, nd the gses diffuse ross the respetive gs diffusion lyers towrd the ebrne eletrode ssebly, whih inludes the two tlyst lyers nd the ebrne. In the node tlyst lyer, hydrogen is onsued to generte protons nd eletrons, while in the thode tlyst lyer, oxygen rets with protons nd eletrons generting wter. Bsed on ss onservetion, the ss of hydrogen onsued in the node side should be equl to the ss of wter generted in the thode side less the ss of oxygen onsued in the thode side. Fig 1. Sheti of two-diensionl setion of the PEM fuel ell In this study oprehensive two-diensionl, non-isotherl, one phse, stedy stte odel is dopted. The other ssuptions used in this odel re s follows: idel retnt gs ixtures; linr nd inopressible gs flow; ipereble to gses ebrne; unifor nd fully hydrted thode tlyst lyer; isotropi nd hoogenous gs diffusion lyers, nd does not extend into the gs hnnels; negligible ohi potentil drop in the eletronillyondutive solid trix of porous eletrodes nd tlyst lyers; the single-phse ssuption for wter trnsport. In ontrst to usul pproh whih eploys seprte differentil equtions for different regions, we hve ten single-doin pproh in whih single set of governing equtions vlid for ll regions. As result, no interfil onditions re required to be speified t internl boundries between these regions. Considering stedy stte opertion of the ell, the governing equtions for the physil phenoen re surized below. Conservtion of ss ross the entire ell is governed by the ontinuity eqution.( ρ u r ) = (1) Where ρ nd u r re the density of the gs ixture nd the veloity vetor, respetively. The density of the ixture is lulted using: 1 ρ = y / ρ () Where y is the ss frtion of speies. The density of eh speies, ρ is obtined fro the perfet gs lw reltion: ρ = pm () In whih p orresponds to the node or thode side pressure, M is the oleulr weight, T is the teperture nd R is the universl gs onstnt. The flow field is governed by the stedy stte Nvier Stoes equtions, whih express oentu onservtion for Newtonin fluid. A onvenient forultion for CFD is: 1 r r.( ρu u) = p + μ. τ + S Dr (4) Where, u r nd p re the porosity, veloity nd pressure vetors, τ is the visous stress tensor trix nd S Dr is the Dry soure nd tht is tive only in the GDL nd tlyst lyers. ISSN: 179-87 18 Issue, Volue, April 8
Ebrhi Afshri nd Seyed Ali Jzyeri μ r S Dr = u () K Where μ nd K re the dyni visosity, nd hydruli perebility. The stedy stte speies trnsport eqution tes the for: r.( u C ) =.( D C ) + S (6) Where C is the olr onentrtion of speies D nd is the etive speies diffusivity. The soure ters for hydrogen nd oxygen speies ount for onsuption due to retion in the tlyst lyers. s j S = (7) nf Also the soure ter for wter vpor ounts for prodution of wter t the thode in the tlyst lyers. n s j S =.( d I ) (8) F nf Where nd is eletro-osoti drg oiient, s is stoihioetry oiient in eletroheil retion of speies, n is nuber of eletrons in eletroheil retion, F is Frdy onstnt (96487C/ole), j is trnsfer urrent density, nd I is urrent density. The trnsfer urrent densities nd Surfe overpotentil re expressed s follows: j C ref H 1/ α + α = ( i ) ( ) (. F. η) (9) ref C H C ref O α j = ( i ) ( )exp(. F. η) (9b) ref CO Where η = (1) φ η = V φ (1b) ell U U = 1..9 1 ( T 98.1) (11) Where C is olr onentrtion, α is trnsfer oiient, η is overpotentil, φ is phse potentil, Vell is ell potentil nd U is therodyni equilibriu potentil. The supersript ref indites referene stte nd Subsripts,,,, H, O indite node, thode, stndrd ondition, ebrne, hydrogen nd oxygen, respetively. Eletroheil retions in the PEM fuel ell re: M heil forul z s M = ne, s stoihietry oiient (11) n = nuber of eletrons Hydrogen oxidtion retion in node side is: H Oxygen redution retion in thode side is: + H = e (1) + H O O 4H = 4e (1b) The potentil distribution n be lulted by pplying the generi trnsport eqution without the onvetive ters..( σ ϕ ) + S = (1) Where σ is the proton ondutivity on the ebrne, nd the soure ter, S represents the prodution/onsuption of protons due to eletroheil retions in the tlyst lyers. The rte of the eletroheil retion is desribed by the Butler Voler reltion, where the eletril potentil is ssued to be onstnt in eh eletrode. It is set to zero on the node side, nd in the thode side is the differene between the ell voltge nd open iruit voltge. S = j (14) The energy eqution is presented in Eq. (14) nd ontins soures for ohi heting due to ioni resistne, reversible het, het produed due to tivtion losses. r.( ρ C ut ) =.( T ) + S p T (1) Where C p is het pitne nd is eted therl ondutivity. The soure ters S T in tlyst lyers nd ebrne re given by respetively. S T du I = j( η + T ) + (16) dt σ I ST = (17) σ The ss diffusion oiient of speies, D, in the node nd thode gs hnnels is ISSN: 179-87 19 Issue, Volue, April 8
Ebrhi Afshri nd Seyed Ali Jzyeri lulted s funtion of teperture nd pressure For the porous regions, the expression is odified into the etive speies diffusivity, using Bruggn orreltion []. D 1. 1. T 1. P D = i D = i D ( ) ( ) (18) T P The proton ondutivity, σ, nd the eletroosoti drg oiient, n d, for wter in the ebrne re orrelted with the wter ontent of the ebrne, λ, whih is in turn funtion of the wter tivity,. g CW = (18) st P.4 + 17.81 9.8 + 6. for < 1 = 14 + 1.4( 1) for1 < λ (19).λ n d = () 1 1 σ = σ = (.19λ.6) 1 1 exp(168.( )) T (1) Nueril Proedures The governing equtions were disretized using finite volue bsed finite differene ethod nd solved using oputtionl fluid dyni ode. In this ode the pressure nd veloity fields is treted with the SIMPLER pressure orret-ion lgorith, where single-doin odel is used. It should be entioned tht by using this odel lthough soe speies dose not exist prtilly in ertin regions of fuel ell, the speies trnsport eqution n still be pplied throughout the entire oputtionl doin by using the lrge soure ter tehnique []. For instne, no hydrogen or oxygen virtully exist in the ebrne nd in this region suffiiently lrge soure ter is ssigned to the hydrogen or oxygen trnsport eqution, whih freezes the hydrogen or oxygen ole frtion t zero. Stringent nueril tests were perfored to ensure tht the solutions were independent of the grid size. The oupled set of equtions ws solved itertively, nd the solution ws onsidered to be onvergent when the reltive error in eh field between two onseutive itertions ws less thn. The CPU 1 6 tie rnged fro 1 to inute on Pentiu IV PC (. GHz, 1GB RAM). 4 Results nd Disussion Model vlidtion is heed using nueril nd experientl results in literture. The experientl setup input dt shown in tble 1, were used in this odel fro Ref 1. In Fig.. the lulted results for polriztion urve re opred nd vlidted with the experientl results. The ury of this odel is so tht there is no djustent required for retive surfe re or the exhnge urrent density nd porosity is required to redjust the present odel predition with the experientl results. Tble 1 Physil properties Desription Unit Vlue T K. ell P t P t t GDL 4 1 t CL 6 7 1 t PEM 4 1.8 1 ξ - 1. ξ - GDL -.6 CL -.6 MC -.6 K 1 ref H ref O 1 ol / 4.88 ol / 4.88 R J / ol K 8.4 GDL W /. K 1.6 CL W /. K 1. PEM W /. K.4 F C / ol 96487 μ p s 1 μ p s 1 1 / 1.18 1 D, H, s 4 D, H O, / s 1.18 1 4 D, O, / s.48 1 D, H o, / s 7. 1 ISSN: 179-87 14 Issue, Volue, April 8
6.4948E-1 WSEAS TRANSACTIONS on FLUID MECHANICS Ebrhi Afshri nd Seyed Ali Jzyeri Cell Potentil (V) 1. 1.1 1.9.8.7.6..4 Nueril odel Experientl [1]..1...4..6.7.8.9 1 Current Density(A/ ) Fig. Coprison between the nueril odel nd experientl results Ref 1. Fig. shows the flow-veloity vetors for I =.7A.. Two rs on eh plot represent the lol xiu nd iniu veloities in the odule. It is seen tht the xiu veloities our t the outlet hnnel. The veloity in the GDLs nd ebrnes is lost zero; therefore gs retnts inter these regions only by diffusion........4.8 lyer, whih is uh lrger thn het genertion in the node side. On other hnd, exhnge urrent density of the nodi retion is severl orders of gnitude higher thn the thodi retion. The het gener-tion in the tlyst lyers is trnsferred by both onvetion nd ondution in ll regions within the PEM fuel ell nd uses to inrese the ell teperture. The xiu teperture ours in the thode tlyst lyer sine jor het gener-tion tes ple in this region. The teperture distribution within the ebrne is not liner due to signifint het genertion of Joule heting. The non-unifor teperture distribution y beoe even worse for fuel ell sts nd thus, therl ngeent is very ritil in PEM fuel ell perforne. Teperture (K) 4. 4.8.6.4.1 6.4948E-1.7E-1..7E-1.1.... 6.4948E-1.7E-1 1.4.7E-1.1...4.47.48.49. b Fig. the flow-veloity vetors, () inlet ross- setion, (b) outlet ross-setion The teperture rises within PEM fuel ell is due to het genertion used by exotheri nture of retions nd Joule heting. The teperture hnges ross the entire ell for I =.7A. re shown in Fig. 4. The thode side teperture is higher thn the node side. This is due to het genertion by the retion in the thodi tlyst.8.4 1 4 6 Distne *1^6 () Fig. 4 Teperture distribution ross the entire ell, orrespond to the preter obintion given in tble 1. Fig. shows the wter flux ross the ebrne s funtion of the lol urrent density where reltive huidity is 1% in the node gs stre. At low urrent densities, the wter flux is negtive. Beuse wter is trnsported fro the thode to the node due to b diffusion rising fro the wter onentrtion grdient, but t high urrent densities it beoes positive, signifying the doinnt et of eletro-osoti drg of wter trnsport. Also by onsidering the se urve in the thode tlyst lyer, the influene of eletro-osoti drg is redily pprent. At low urrent density, there is very little hnge in wter ontent ross the ebrne eletrode ssebly. This is due to reltively low ount of drg nd the ft tht vpor tivity t node nd thode is lost identil. At high urrent density, the wter ontent urve beoes steeper s the node dehydrtes nd the thode wter ontent inreses. Also, the totl ount of wter ontined in the MEA dereses. This ours beuse the vpor tivity of the node stre hs dropped due to wter reovl upstre ISSN: 179-87 141 Issue, Volue, April 8
Ebrhi Afshri nd Seyed Ali Jzyeri leving less wter vilble to hydrte the node. Wter flux/h+ 1. -. -1-1. -..4.6.8 1 Current density (A/^) Fig. Net wter flux ross the ebrne 4- Conlusion A Two-diensionl, single-doin nd nonisotherl odel of PEM fuel ell hs been developed to investigte therl nd wter trnsport nd ets on ell perforne. Therl response nd wter trnsport hve been investigted. The therl ngeent nd wter ngeent is oupled. A study ws perfored for four ritil preters: urrent density, operting teperture, reltive huidity nd therl ondutivity of gs diffusion lyer. The results show tht, the gs retnts inter the GDLs nd ebrnes only by diffusion. Also, the the xiu veloities our t the outlet hnnel nd xiu teperture ours in the thode tlyst lyer sine jor het genertion tes ple in this region. At low urrent densities, the wter flux is negtive but t high urrent densities it beoes positive, signifying the doinnt et of eletro-osoti drg of wter trnsport Referenes: [1] J. S. Yi. He, T. Vn Nguye, Two-phse flow odel of the thode of PEM fuel ell using interdigited flow fields, J. AICHE, Vol. 1,, pp. 64. [] S. U, C. Y. Wng, K. S. Chen, Coputtionl fluid dynis odeling of PEM fuel ells, J. Eletrohe. So, Vol.147,, pp. 448 449. [], N. P. Siegel, M. W. Ellis, D. J. Nelson, M. R. Spovsy, Single doin PEMFC odel bsed on ggloerte tlyst geoetry, J. Power Soures., Vol. 11,, pp. 81 89. [4] N. P. Siegel, M. W. Ellis, D. J. Nelson, R. Spovsy, A two-diensionl oputtionl odel of PEMFC with liquid wter trnsport, J. Power Soure., Vol.18, 4, pp. 17 184. [] L. You, H. Liu, A two-phse flow nd trnsport odel for the thode of PEM fuel ells, Int. J. Het Mss Trnsfer, Vol. 4,, pp.77 87. [6] L. You, H. Liu, A two-phse flow nd trnsport odel for PEM fuel ells, J. Power Soures Vol.1, 6, pp.19. [7] H. Sun, H. Liu, L.-J. Guo, PEM fuel ell perforne nd its two-phse ss trnsport, J. Power Soures, Vol. 14,, PP.1 1. [8] Z.H. Wng, C.Y. Wng, K.S. Chen, Two-phse flow nd trnsport in the ir thode of proton exhnge ebrne fuel ells, J. Power Soures, Vol. 94, 1, PP.4. [9] U. Psogullri, C.Y. Wng, K.S. Chenb, Twophse trnsport in polyer eletrolyte fuel ells with bilyer thode gs diffusion edi, J. Eletrohe. So, Vol.1,, pp.a174 A18. [1] P. T. Nguyen, T. Berning, N. Djilli, Coputtionl odel of PEM fuel ell with serpentine gs flow hnnels, J. Power Soures Vol.1, 4, pp.149 17. [11] M. De Frneso, E. Arto, P. Cost, Trnsport phenoen in ebrnes for PEMFC pplitions: n nlytil pproh to the lultion of ebrne resistne, J. Power Soures, Vol. 1, 4, pp.17 14 [1] J. J. Hwng, A oplete two-phse odel of porous thode of PEM fuel ell, J. Power Soures, Vol.164, 7, pp. 174 181. [1] A. Rowe, X. Li, Mthetil odelling of proton exhnge ebrne fuel ells, J. Power Soures, Vol.1, 1, pp. 8 96. [14] V. Mishr, F. Yng, R. Pithuni, Anlysis nd design of PEM fuel ells, J. Power Soures, Vol.141,, pp.47 64. ISSN: 179-87 14 Issue, Volue, April 8