Iwo Nitt uvi Krvonen lli imnen nd Mikko Mikkol 008 Modeling the effet of inhomogeneous ompression of GL on lol trnsport phenomen in PEM fuel ell Espoo Finlnd 3 pges elsinki University of ehnology Publitions in Engineering Physis KK F A854 Fuel Cells submitted for publition 8th November 007. 008 by uthors
elsinki University of ehnology Publitions in Engineering Physis eknillisen korkekoulun teknillisen fysiikn ulkisu Espoo 008 KK-F-A854 MELING E EFFEC F INMGENEU CMPREIN F GL N LCAL RANPR PENMENA IN A PEM FUEL CELL Iwo Nitt uvi Krvonen lli imnen & Mikko Mikkol
elsinki University of ehnology Publitions in Engineering Physis eknillisen korkekoulun teknillisen fysiikn ulkisu Espoo 008 KK-F-A854 MELING E EFFEC F INMGENEU CMPREIN F GL N LCAL RANPR PENMENA IN A PEM FUEL CELL Iwo Nitt uvi Krvonen lli imnen & Mikko Mikkol elsinki University of ehnology Fulty of Informtion nd Nturl ienes eprtment of Engineering Physis
istribution: elsinki University of ehnology Advned Energy ystems P.. Box 4100 0015 KK Finlnd URL: http://www.tkk.fi/units/ae/ el. +358-9-451 3198 Fx. +358-9-451 3195 Copyright 007 Iwo Nitt uvi Krvonen lli imnen Mikko Mikkol IBN 978-951--918-9 (PF) IN 1459-768 (PF) URL: http://lib.tkk.fi/reports/008/isbn9789519189.pdf Multiprint y Espoo 008
ELINKI UNIVERIY F ECNLGY P Box 1000 FI - 0015 KK http://www.tkk.fi/ Fulty Fulty of Informtion nd Nturl ienes ABRAC eprtment eprtment of Engineering Physis Author(s) Iwo Nitt uvi Krvonen lli imnen & Mikko Mikkol itle Modeling the Effet of Inhomogeneous Compression of GL on Lol rnsport Phenomen in PEM Fuel Cell Abstrt he effets of inhomogeneous ompression of gs diffusion lyers (GLs) on lol trnsport phenomen within polymer eletrolyte membrne (PEM) fuel ell were studied theoretilly. he inhomogeneous ompression indued by the rib/hnnel struture of the flow field plte uses prtil deformtion of the GLs nd signifintly ffets mteril prmeters. he results suggest tht inhomogeneous ompression does not signifintly ffet the polriztion behvior or gs-phse mss trnsport. owever the effet of inhomogeneous ompression on the urrent density distribution is evident. Lol urrent density under the hnnel ws substntilly smller thn under the rib when inhomogeneous ompression ws tken into ount while the urrent density distribution ws firly uniform for the model whih exluded the effet of inhomogeneous ompression. his is used by the hnges in the seletive urrent pth whih is determined by the ombintions of ondutivities of omponents nd ontt resistne between them. espite the highly uneven urrent distribution nd vrition in mteril prmeters s funtion of GL thikness the temperture profile ws reltively even over the tive re for both modeled ses ontrry to preditions in previous studies. owever n bnormlly high urrent density signifintly elertes deteriortion of the membrne nd is ritil in terms of ell durbility. herefore fuel ells should be refully designed to minimize the hrmful effets of inhomogeneous ompression. Keywords (nd lssifition) Inhomogeneous ompression; Gs diffusion lyer; PEM Fuel ell; Mthemtil model Ple Month - Yer Lnguge Number of pges Espoo Finlnd Februry 008 English 3 IBN (print) IBN (eletroni) IN (print) IN (eletroni) 978-951--918-9 1459-768 eril nme eril number or report ode elsinki University of ehnology Publitions in Engineering Physis K-F-A854 istribution of the printed publition Internet ess (URL) http://lib.tkk.fi/reports/008/isbn9789519189.pdf
ble of Contents 1 INRUCIN 6 MEL ECRIPIN 7.1 Model ssumptions 7. Modeling domin 7.3 Equtions 8.3.1 Governing equtions nd soure terms 8.3. Boundry onditions 11.4 Model input prmeters 11.4.1 GL deformtion 11.4. Gs permebility nd porosity 1.4.3 Eletri properties 1.4.4 herml properties 13 3 REUL AN ICUIN 15 3.1 Polriztion behvior nd speies distribution 15 3. Current density distribution 16 3.3 emperture profile 17 3.4 Effet of the ompressed GL thikness 18 4 UMMARY AN CNCLUIN 19 ACKNWLEGEMEN 0 NMENCLAURE 0 REFERENCE 1 5
1 Introdution he proton exhnge membrne (PEM) fuel ell hs been reeiving substntil ttention s potentil power soure for wide rnge of pplitions beuse of its lower opertion temperture ompred to other types of fuel ell flexibility in size quik strt environmentl friendly hrteristis nd high energy density. owever further improvements of its performne life-time nd ost-effetiveness re still needed to hieve lrge-sle ommeriliztion nd deeper understnding of lol phenomen tking ple in the fuel ell is of vitl importne for future development. A mthemtil model is powerful tool for studying the vrious phenomen ourring in fuel ell from lol to system level. An exellent review of fuel ell models is given by Yo et l. [1]. he ury of the modeled results depends highly on the used modeling prmeters nd ssumptions. herefore the experimentl evlution of the physil prmeters used in the models is essentil. he properties of gs diffusion lyers (GLs) ply n espeilly importnt role in fuel ell opertion [] nd mny experimentl studies n be found on subets suh s gs permebility [3-8] eletril properties [9-14] therml properties [15-17] wter trnsport properties [18-8] nd the effet of ompression [179-3]. In ordne with the experimentl studies signifint modeling efforts hve been devoted to exploring the impt of these prmeters on the trnsport mehnisms nd fuel ell performne. Exmples of the systemti prmetri study re found on the eletri nisotropy of GL [33-35] the thikness nd porosity of the GL [36-39] pore size distribution [40-4] gs permebility [334344] wter trnsport prmeters [45-49] nd the effet of ompression [50-53]. ne of the most ommon shortomings in previous modeling studies is tht the effet of inhomogeneous ompression on the GL indued by the rib/hnnel struture of the flow field plte ws not properly onsidered. A typil rbon pper or loth GL is soft nd flexible nd therefore when the GL is ompressed between two flow field pltes it is deformed nd intrudes in to the hnnel s shown in Fig. 1. he vritions in the GL thikness nd porosity due to ompression ffet the lol trnsport phenomen sine gs permebility eletri ondutivity nd eletri nd therml ontt resistnes t the interfes with neighboring omponents ll depend on ompression. o the uthors knowledge only few studies whih onsider this inhomogeneous ompression n be found in literture see e.g. [53-56]. Although their findings re enlightening mny of the dopted modeling prmeters re subet to lrge unertinty. herefore the uthors hve experimentlly evluted the physil properties of GL s funtion of ompressed GL thikness [57-59] s well s onduted modeling study using the experimentl dt [60]. In this pper the erlier model is improved by pplying more relisti geometry of GL deformtion nd the inlusion of thin ontt resistne lyers with newly evluted physil prmeters s well s orreting some inuries. owever due to lk of informtion prtiulrly for those whih desribe liquid wter behvior the model exludes two-phse phenomen nd the study on the subet is left for future work. 6
Fig. 1 Cross-setionl view of the GL (GL 10 BA IGRACE ) tken by optil mirosope (PMG3 LYMPU). Model desription.1 Model ssumptions Mking theoretilly rigorous fuel ell model whih reflets miro- nd mro-sle trnsport proesses is extremely hllenging beuse of lk of experimentlly evluted physil prmeters. herefore the following ssumptions were employed in the model: (1) tedy stte onditions () All gses obey the idel gs lw nd re idelly mixed (3) Wter exists only in gseous form (4) Very fst retion kinetis nd smll mss trnsfer limittions t the node (5) he tlyst lyers (CLs) nd membrne re isotropi nd homogeneous (6) he membrne is fully hydrted (7) Physil properties of GL under the rib re onstnt Beuse of ssumption (3) the model presented here is vlid only when the prtil pressure of wter is below the sturtion pressure. Assumption (4) implies tht the onservtion equtions for mss momentum nd speies t node GL nd CL re not solved. Assumption (7) ws mde sine ll the experimentl work to evlute the physil properties of GL ws onduted by hnging the thikness of the ompressed GL under the ssumption tht the ompression pressure pplied to the GL ws uniform [57-59].. Modeling domin he modeled domin is two-dimensionl prtil ross-setion of unit ell s shown in Fig. whih onsists of hlf of both the grphite rib nd the hnnel in the flow field plte two GLs nd CLs the eletrolyte membrne nd pseudo two thin lyers 1 nd whih represent the ontt resistne between grphite rib nd GL nd GL nd CL respetively. he effets of inhomogeneous ompression re studied by ompring two models. In the bse se Fig. () the GL is ompressed evenly nd its physil properties re ssumed onstnt. he lterntive model Fig. (b) onsiders the inhomogeneous ompression of GL nd the GL prtilly intrudes into the flow hnnel. he shpe of the deformed GL nd the dependene of physil properties on the lol thikness re desribed in sub-hpter.4. 7
.3 Equtions Fig. Modeled domin () bse se (b) inhomogeneous ompression..3.1 Governing equtions nd soure terms he trnsport phenomen ourring within the ell re modeled with onservtion equtions for mss momentum speies hrge nd energy. All the governing equtions re listed in ble 1. ble 1 lso inludes the subdomins where the equtions re solved. he Nvier-tokes eqution tht desribes momentum onservtion ws redued to ry s lw sine the Reynolds number is less thn one nd thus the inerti nd visous terms n be negleted in the GL nd CL. ry s lw ws ombined with the mss onservtion eqution whih gives Eq. (1) in ble 1. he speies onservtion eqution Eq. () is the Mxwell-tefn diffusion eqution nd tkes into ount the onvetive nd diffusive molr fluxes. ine ir is fed to the thode the multiomponent mss trnsfer involves ternry gs mixture (oxygen wter vpor nd nitrogen). he hrge onservtions Eqs. (3 nd 4) desribe eletri urrent in eletrilly ondutive omponents nd ioni urrent in ioni ondutive omponents. he energy onservtion Eq. (5) tkes into ount both ondutive nd onvetive het fluxes. Note tht on the node only the hrge nd energy onservtion equtions were solved. 8
ble 1 Governing equtions Conservtion eqution ubdomins Mss k sd ρ t p (1) thode (GL CL) µ t peies i ( t vx i ) ( t eff X i ) i Chrge (eletri) ( s sd s ) s N () thode (GL CL) σ φ (3) rib 1 GL CL σ φ (4) CL membrne (ioni) ( m sd m ) m Energy ρic p iv ( κ sd ) i (5) ll he soure terms for the governing equtions re listed in ble. he soure terms of the mss nd speies onservtion eqution represent the onsumption of oxygen nd prodution of wter in the thode CL. he number of eletrons involved in the retion (4 for oxygen onsumption for wter prodution) ppers in these equtions. he soure terms in the hrge onservtion eqution desribe the hrge trnsfer urrent density between the eletri nd ioni phses inside the node nd thode CLs. he trnsfer urrent densities re expressed with the Butler-Volmer reltion s follows: ( α ) ref α + F v η for node (6) R α F exp η for thode (7) ref R ref v Anode side hs fst retion kinetis nd low overpotentil ompred to the thode nd thus node trnsfer urrent density n be linerized s in Eq. (6). he referene onentrtion is equl to the onentrtion of oxygen in ir t P onditions nd is the onentrtion of oxygen in the CL. In the model the rtio of frtion of oxygen m s X ref ref to in Eq. (7) ws repled by the molr. η nd η re the overpotentils t node nd thode respetively: η φ φ (8) η φ φ (9) s m E 0 where E 0 is the open iruit voltge. he soure terms in the energy onservtion eqution orrespond to Joule heting irreversible het of eletrohemil retions nd entropi het of retions in CLs but only Joule heting in other subdomins. 9
10 ble oure terms in eh modeling subdomin. Region Mss peies Chrge Energy GL 0 0 0 ( ) s GL φ σ CL (Anode) 0 0 m s ( ) ( ) F m CL m s CL s + + + η φ σ φ σ (Cthode) F M F M 4 + F F 4 m s ( ) ( ) F m CL m s CL s 4 + η φ σ φ σ 1 0 0 0 ( ) s sd s φ σ Membrne 0 0 0 ( ) m m φ σ he onstitutive reltions used for the governing equtions re listed in ble 3. he molr density n be lulted from idel gs lw s in Eq. (10). he molr frtion of nitrogen is lulted from the ft tht the sum of molr frtions is equl to unity Eq. (11). he effetive Mxwell-tefn diffusion oeffiient tensor eff is relted to the non-porous diffusion oeffiient through the Bruggemn orreltion s in Eq. (1). he elements of the for ternry system re lulted from the Mxwell-tefn binry diffusion oeffiients s in Eq. (13). he temperture nd pressure dependene of the binry diffusion oeffiients ws tken into ount with Eq. (14). Also the temperture dependene of exhnge urrent density ws tken into ount with Eq. (15). ble 3Constitutive reltions. Expression Idel gs lw p M M t t t t R ρ (10) Molr mss of gs mixture i i i t M M X (11) Effetive diffusion oeffiient tensor sd eff 1.5 ε (1) Elements of N N N N N N N N N N N X X X X X X X X X 1 1 11 ) (1 ) (1 + + + + (13) emperture nd pressure dependene of binry diffusion oeffiients ) ( 0 0 1.5 0 0 p p p i i (14) emperture dependene of exhnge urrent density R 0 1 1 exp 0 E ex ref ref (15)
.3. Boundry onditions ymmetry boundry onditions were pplied t x 0 nd x x 1 in Fig. i.e. ll the fluxes were set to zero. No eletri urrent psses through the interfe between the GL/hnnel nd CL/membrne. It ws ssumed tht there is no ioni ontt resistne t the CL/membrne interfe nd thus the ioni potentil nd temperture re ontinuous. n the other hnd ioni urrent does not pss through the GL/CL interfe sine the GL is not ionilly ondutive. he onentrtions nd pressure re ontinuous through GL nd CL nd no boundry onditions re required t the interfes. owever there is no mss flux ross the rib/gl nd CL/membrne interfes. At the thode gs hnnel/gl interfe the pressure ws set equl to mbient pressure. he molr frtions of the speies t the hnnel/gl interfe were lulted bsed on the following ssumptions (1) he modeled ross-setion is in the middle of ell nd produed urrent is onstnt long the hnnel. () he stoihiometry of ir is (3) he ir temperture is 35 K nd the reltive humidity or the ir is 40%. (4) here is no wter trnsport through the membrne hus the molr frtions of oxygen nd wter vpor were fixed to 0.143 nd 0.149 respetively. Furthermore het trnsfer from the GL to ir in the hnnel is lulted vi: h ( ) n Q κ (16) GL ir where Q denotes the het flux lulted from Eq. (5) κ h the het trnsfer oeffiient GL the temperture of GL nd ir the temperture of ir. he temperture of the grphite ribs t y 0 nd y y 1 ws set to 330 K. he eletri nd therml ontt resistnes t grphite rib/gl nd GL/CL interfes were onverted to orresponding eletri nd therml ondutivities of 1 nd. herefore the eletri potentil nd temperture through grphite rib GL nd CL re ontinuous through the 1 nd nd no boundry onditions hve to be presribed..4 Model input prmeters ble 4 lists the ell design prmeters nd mteril kineti nd eletrohemil prmeters. When the GL deformtion is tken into ount (see Fig. b) the properties of GL re vried s funtion of the thikness. hese hnges re desribed in the following sub-hpters..4.1 GL deformtion he deformtion urve of GL observed in the photomirogrphs tken with n optil mirosope (Fig. 1) ws fitted with third order polynomil (fitting ury: R 0.947) nd its dimensionless thikness n be expressed s: 1 6 h m x 500 10 m h( (17) 3 3 6 3 1 4 6 1.047 m x 10 +.105 m x 10 1.070 m x + 3.894 10 x > 500 10 m for the se where the ompressed GL thikness h is 50 µm. he sme proess ws used to obtin expressions for the thikness of the GL when the h ws vried from 150 to 300 µm. 11
.4. Gs permebility nd porosity he redution of the GL thikness ws ssumed to be used by the redution of GL porosity. herefore the porosity of the ompressed GL ε is lulted from the eqution see e.g [5] ε h h h( ( 0 0 h h( s 1 ( 1 ε ) (18) where ε 0 denotes the porosity of unompressed GL nd h 0 the thikness of unompressed GL. h s is the thikness of the GL when ll the pores re lost: h s ( 1 ε h (19) ) 0 0 he redution of GL porosity leds into derese in gs permebility. he gs permebility of the ompressed GL k( ws evluted [57] nd the fitted urve (fitting ury: R 0.997) n be expressed s 3 5 8 1 k ( 0.806h( 6.464 10 h( 5.305 10 h( + 7.164 10 [m ] (0) he porosity of CL ε CL dopted by Bernrdi et l. [61] nd permebility of CL k CL reported by imnen et l. [6] were ssumed to be not ffeted by ompression..4.3 Eletri properties he eletri ondutivity of the GL s funtion of ompressed GL thikness ws evluted in previous study [57]. he ondutivity ws found to be nisotropi nd fitted with liner urve (fitting ury: R 0.964 for in-plne nd R 0.975 for through-plne): σ [ m -1 ] for in-plne ondutivity (1) 7 3 GL x 1.159 10 h( + 6.896 10 σ h x [ m -1 ] for through-plne ondutivity () 6 3 GL y 8.385 10 ( ) + 3.85 10 he eletri ontt resistnes between the GL nd other ell omponents depend strongly on the ompression pressure. he eletri ontt resistne between GL nd grphite urrent olletor R GL/GR (h ) ws found to derese exponentilly s GL ws ompressed [57]. he R GL/GR (h ) ws onverted into through-plne eletri ondutivity of 1 σ 1y (. he σ 1y ( ws lulted s funtion of ompressed GL thikness nd exponentil urve ws fitted into the dt (fitting ury: R 0.983) yielding: y 4 [.056 h ] 4 σ 1 ( 1.714 10 exp 10 [ m -1 ] (3) he eletri ontt resistne between the GL nd CL R GL/CL (h ) ws lso evluted experimentlly by the uthors [59]. he R GL/CL (h ) ws onverted to the through-plne eletri ondutivity of σ y ( whih ws fitted with third degree polynomil (fitting ury: R 0.996) giving 11 3 8 4 σ ( 7.76 10 h( 4.943 10 h( +.664 10 h( 18.911 [ m -1 ] (4) y + Aurte experimentl evlution of the R GL/CL (h ) ws found diffiult s the ompression pressure deresed. herefore in ref. [59] the lowest ompression pressure t whih the R GL/CL (h ) ould be evluted ws 0.664 MP. his orresponds to GL thikness of pproximtely 300 µm bove whih the ury of Eq. (4) diminishes. owever the trend is ler the lower the ompression the higher the ontt resistne. It should be noted tht the vlues used for the in-plne eletri ondutivity of 1 nd σ 1x nd σ x were set equl to the in-plne eletri ondutivity of GL nd CL respetively. hese vlues were dopted beuse the lterl urrent flow in the 1 nd n be expeted to follow to tht in the neighboring more ondutive omponents the GL nd CL. n the other hnd the ondutivity of CL evluted previously [57] ws ssumed to be isotropi sine no relible experimentl dt on its nisotropy ws found. 1
.4.4 herml properties Compred to eletri properties reltively little experimentl dt on the therml properties of GL hve been reported in the literture. Aording to the uthors previous study [58] the through-plne therml ondutivity of GL κ GL ws not ffeted by the ompression pressure nd onstnt vlue ws used in this model. he in-plne therml ondutivity of GL ws ssumed to be the sme s the through-plne therml ondutivity. he evluted therml ontt resistne between the grphite urrent olletor nd GL [58] ws onverted to the through-plne therml ondutivity of 1 κ 1y (. he lulted κ 1y ( s funtion of ompressed GL thikness ws fitted with fourth degree polynomil (fitting ury: R 0.993) giving 14 4 11 3 8 4 1 (.91 10 h( + 3.133 10 h( 1.170 10 h( + 1.639 10 h( 0.438 κ [W m -1 K -1 ] (5) y he therml ontt resistne between the GL nd CL ws ssumed to be sme s the therml ontt resistne between grphite nd GL. herefore Eq. (5) ws used lso for the throughplne therml ondutivity of κ y (. he in-plne therml ondutivities of 1 nd κ 1x nd κ x were set equl to the in-plne therml ondutivity of GL nd CL respetively bsed on the sme ssumption of hrge trnsport t the interfe. he therml ondutivity of CL ws lulted from the dt reported by Khndelwl et l. [15]. In their study the ombined therml resistne i.e. therml bulk resistne of the CL plus therml ontt resistne between GL nd CL ws determined to be 1.5 10 4 m K W -1 t ompression pressure of 1.83 MP (ompressed GL thikness of. 50 µm [58]). By subtrting the therml ontt resistne between GL nd CL whih n be lulted from Eq. (5) from the ombined therml resistne the therml bulk resistne of CL ws determined. he therml ondutivity of CL κ CL lulted using the mesured therml bulk resistne of CL ws ssumed to be isotropi nd independent of ompression. ble 4 Cell design prmeters nd mteril properties. ymbol esription Vlue Geometril prmeters w Chnnel nd rib width 500 µm h Compressed GL thikness under rib 150 300 µm h 0 Unompressed GL thikness 380 µm CL thikness 5 µm Membrne thikness 50 µm 1 thikness 10 µm 13
ble 4 Continued ymbol esription Vlue Mteril prmeters ( p0 0 ) diffusion oeffiient 3.98 10-5 m s -1 [60] N ( p0 0) Binry diffusion oeffiient N.95 10-5 m s -1 [60] N ( p0 0) Binry diffusion oeffiient N 4.16 10-5 m s -1 [60] CL σ s CL eletri ondutivity 30 m -1 [57] CL σ m CL ioni ondutivity 5.09 m -1 κ CL CL therml ondutivity 0.476 W m -1 K -1 [15] κ GL GL therml ondutivity 1.18 [58] σ GR Grphite plte eletri ondutivity 69700 m -1 [63] κ GR Grphite plte therml ondutivity 18 W m -1 K -1 [63] σ m Membrne ioni ondutivity 5.09 m -1 [64] κ m Membrne therml ondutivity 0.1 W m -1 K -1 [15] κ h et trnsfer oeffiient from GL to ir 5 W m - K -1 k CL Permebility of CL 1.6 10-13 m [6] ε 0 Porosity of unompressed GL 0.83 [65] ε CL Porosity of CL 0.4 [61] Kineti nd eletrohemil nd other prmeters E ex Ativtion energy (E ell 0.8V) 76.5 kj mol -1 [66] (E ell < 0.8V) 7.7 kj mol -1 [66] p 0 Ambient pressure 101 35 P α + α Anodi nd thodi trnsfer oeffiients in Eq. (33) 1 [34] α Cthodi trnsfer oeffiient in Eq. (34) 1 [34] Entropy hnge of node 0.104 J mol -1 K -1 Entropy hnge of thode -36.36 J mol -1 K -1 ref v ref 0 v Exhnge urrent density rtio of retion surfe to CL volume node Exhnge urrent density rtio of retion surfe to CL volume thode 1.7 10 9 A m -3 [60] 10 4 A m -3 [60] C p et pity of oxygen 93 J kg -1 K -1 C p et pity of wter vpor 1996 J kg -1 K -1 E 0 pen iruit voltge 1.3 V 0 Referene temperture 73 K 14
3 Results nd disussion 3.1 Polriztion behvior nd speies distribution In the following disussion of modeling results the ompressed GL thikness under the rib is 50 µm for the both ses i.e. bse se nd se onsidering inhomogeneous ompression unless stted otherwise. he polriztion urves for the two modeled ses presented in Fig. 3 were obtined by hnging the ell voltge from 1 to 0.45 V. he urves re lmost identil for both the ses exept t lower voltges. ine two-phse flow is not tken into ount here the model is vlid only when prtil pressure of wter p does not exeed the sturtion pressure p. he st lowest limit for voltge ws determined by lulting the reltive humidity under the rib where flooding usully strts see e.g. [67]. Fig. 4 shows the reltive humidity of gs ( p / p ) t the GL/CL interfe t ell voltges of 0.45 nd 0.5 V. In both modeled ses wter strts to ondense when the ell voltge is below 0.5 V. In the following therefore the ell voltge is fixed to 0.5 V. Fig. 5 shows the molr frtion of oxygen t the GL/CL interfe for both the modeled ses. nly slight differene in molr frtion of oxygen is observed between the two ses s disussed in previous work [60] whih suggests tht the mss trnsfer is not signifintly ffeted by GL deformtion s long s no flooding ours. st Fig. 3 Polriztion urves for the bse se nd se onsidering the inhomogeneous ompression. 15
Fig. 4 Reltive humidity (p /p st ) t the GL/CL interfe t the ell voltge of 0.45 (thin line) nd 0.5 V (bold line) for the bse se nd se onsidering the inhomogeneous ompression. Fig. 5 xygen molr frtion t the GL/CL interfe t ell voltge of 0.5 V. 3. Current density distribution Fig. 6 shows the urrent density distribution t the GL/CL interfe. For the bse se the urrent density distribution is firly uniform over the tive re. owever notbly uneven distribution is seen when inhomogeneous ompression is tken into ount. In this se the lol urrent density is signifintly lower in the middle of the hnnel nd inreses in the region lose to the edge of the rib. his is beuse of hnges in the seletive urrent pth whih is lrgely determined by the eletri ontt resistne between the GL nd CL i.e. σ y ( in Eq. (4) nd eletri ondutivities of GL in Eqs. (1 nd ). A lrge portion of the produed urrent flows lterlly under the hnnel where the ontt resistne is high nd rosses over to the GL ner the rib edge (see Fig. 7). he shpe of the urrent density distribution is different from tht observed in the previous study [60]. he differene minly rises from the estimtes used for the ontt resistne between the GL nd CL nd the shpe of the deformed GL whih both differed signifintly from the experimentlly evluted vlues used here. As result the urrent density ws overestimted t the edge of the rib nd under the hnnel in the previous study. 16
Fig. 6 Current density distribution t the GL/CL interfe t ell voltge of 0.5 V. Fig. 7 Current density profile t /CL interfe (rrow plot) nd t thode GL (stremline plot). Note tht the mgnitudes of rrow nd stremline plots re not in sle. 3.3 emperture profile Fig. 8 shows the temperture profile t the GL/CL interfe. It is interesting to note tht when inhomogeneous ompression is tken into ount the temperture profile is more uniform thn tht of the bse se. A possible reson for this is tht the urrent density under the hnnel is substntilly smller when inhomogeneous ompression is tken into ount thn in the bse se (see Fig. 6). All the terms of the het soure eqution inlude urrent density nd thus the urrent density distribution diretly ffets the temperture profile. Among the het soures the irreversible het of eletrohemil retions ounts for mor prt of het prodution. he temperture differene ross the tive re for the se onsidering inhomogeneous ompression less thn 1 C is muh smller thn the vlue more thn 10 C predited in previous study [68]. here the vlues for the therml ontt nd therml bulk resistnes were overestimted nd the vlues of eletri ontt resistne between GL nd CL were underestimted leding into lrger temperture differenes ross the omponents. 17
Fig. 8 emperture distribution t the GL/CL interfe t ell voltge of 0.5 V. 3.4 Effet of the ompressed GL thikness Applying the simultion tehnique desribed bove the effets of ompressed GL thikness on hrge nd het trnsport were investigted. he thikness of the ompressed GL under the rib ws vried from 300 to 150 µm nd orresponding expression for the shpe of the GL intruding into the hnnel ws used. he physil properties of the GL were hnged orrespondingly. Fig. 9() shows the urrent density distribution t the GL/CL interfe for vrious ompressed GL thiknesses under the rib. he totl urrent integrted over the tive re inreses s the GL is ompressed more sine both the eletri ontt nd bulk resistnes of GL re redued. For exmple the se in whih the GL is ompressed to 150 µm produes. 5% more urrent thn the se of 300 µm t the sme ell voltge of 0.5 V. he shpe of the urrent density distribution lso hnges when the ompressed GL thikness is hnged. A urrent density pek is observed t the edge of the rib when the GL is ompressed to 300 µm. n the other hnd when the GL under the rib is ompressed to 150 µm the urrent density hs mximum t round x 0.61 mm. In this se the ontt resistne between GL nd CL is smll enough even under the hnnel so tht lterl urrent flows in the CL hnge the diretion nd enter into the GL. he shpe of urrent density distribution is lrgely determined by the profile of the deformed GL on whih the ontt resistne between the GL nd CL depends. Fig. 9(b) shows the temperture profile t the GL/CL interfe for vrious ompressed GL thiknesses under the rib. As predited in the previous study [58] the temperture under the rib inreses with deresing ompression beuse of n inrese in both therml bulk nd ontt resistne. owever the temperture profile beomes more uniform over the tive re when the GL under the rib is less ompressed. his is due to the lower het prodution under the hnnel in suh se. ine the vlue of oxygen molr frtion depends on the porosity of GL i.e. the shpe of GL lower ompression of GL leds into reltively higher vlue of oxygen molr frtion ompred to the se of higher ompression whih in turn results in lower vlue of overpotentil in CL. Even though the differenes in their vlues re firly smll (. less thn % for both oxygen molr frtion nd overpotentil) hnges in het prodution re notble. For exmple the irreversible het of eletrohemil retions when the ompressed GL thikness is 00 µm is. 3% higher thn tht for the se of 300 µm on n verge over the tive re. he minor irregulrities in the shpe of the urrent density distribution under the hnnel (Fig. 9()) suh s vrition in the vlue of urrent density in the middle of the hnnel nd rossing of the urrent density urves for the GLs ompressed to 150 nd 00 µm t round x 0.81 mm stems from the diffiulty of determining the profile of the GL intrusion into the hnnel h( i.e. 18
the equivlent of Eq. (17) for eh ompressed GL thikness under the rib. ue to the struture of the GL the profile of the deformed prt nd the unompressed GL thikness under the hnnel vried from smple to smple in the photomirogrphs tken t the sme ompressed thikness under the rib. herefore the expressions for h( re unique for eh smple nd ompressed thikness whih is in turn refleted in the urrent density profiles. Fig. 9() Current density distribution nd (b) temperture profile t the GL/CL interfe t ell voltge of 0.5 V with vrious ompressed GL thikness (150 300 µm) under the rib. 4 ummry nd onlusion A two-dimensionl model ws developed to study the effet of inhomogeneous ompression of GL on the lol trnsport phenomen in PEM fuel ell. he results were ompred to those given by bse se model in whih the GL ompression ws ssumed to be homogeneous. he polriztion behvior nd gs-phse mss trnsport predited by the two models were lmost identil but the urrent density profiles were notiebly different. he model whih onsidered the inhomogeneous ompression showed tht the lol urrent density under the hnnel ws substntilly smller thn under the rib nd hd mximum t the edge of the rib while the urrent density for the bse se ws firly uniform over the tive re. his high vrition in lol urrent density my signifintly elerte membrne deteriortion nd ffet the ell durbility. he model predited firly uniform temperture profile over the tive re with mximum vrition of. 1 C. his ontrdits the results of previous study [68] where lrger temperture vrition up to 10 C ws predited within the ell under similr onditions. his differene stems from the dopted modeling prmeters suh s ontt resistne nd ondutivity nd the geometry of the deformed GL. Espeilly the lol urrent density distribution whih signifintly ffets the temperture profile ws found to be very sensitive to the vlue nd vrition of ontt resistne between GL nd CL. herefore the right hoie of modeling prmeters is essentil for urte predition of lol phenomen whih n not be esily interpreted by the modeled polriztion urves only s disussed in literture [69-71]. he ompressed GL thikness under the rib ffets the urrent density distribution nd temperture profile. Although the totl urrent over the tive re inresed s GL ws ompressed more the unevenness of the temperture profiles beme more prominent. Further effort should be mde to mitigte the detrimentl effets of inhomogeneous ompression of GL e.g. by developing rigid GLs or rigid miro porous lyers onto the GL whih do not deform under ompression or implementing pre-tretment whih urbs or ompenstes for the deformtion of the GL. A limittion of the model presented here is tht phse hnge of wter nd liquid wter trnsport re not onsidered. When the ell is flooded by the ondensed wter gs trnsport is signifintly 19
hindered whih in turn ffets the urrent prodution nd temperture distribution. A further study using proper wter trnsport prmeters is left for the future. Aknowledgements he uthors grtefully knowledge the finnil support from the Fortum Foundtion the Ademy of Finlnd (deision #110748) the Wihuri Foundtion nd ekes the Finnish Funding Ageny for ehnology nd Innovtion. Nomenlture v rtio of retion surfe to CL volume (m -1 ) onentrtion (mol m -3 ) C p het pity (J kg -1 K -1 ) diffusion oeffiient (m s -1 ) F Frdy s onstnt 96487 (As mol -1 ) h thikness (m) trnsfer urrent density (A m -3 ) ref exhnge urrent density (A m - ) k permebility (m ) M molr mss (kg mol -1 ) n unit vetor N molr flux (mol m - s -1 ) p pressure (P) Q het flux (W m - ) R gs onstnt 8.314 (J mol -1 K -1 ) soure term temperture (K) v veloity (m s -1 ) X molr frtion Greek letters α trnsfer oeffiient ε porosity η overpotentil (V) κ therml ondutivity (W m -1 K -1 ) µ visosity of ir 1.9 10-5 (kg m -1 s -1 ) ρ density (kg m -3 ) σ eletri ondutivity (Ω -1 m -1 ) φ potentil (V) 0
ubsripts node thode CL tlyst lyer GL gs diffusion lyer GR grphite wter i speies of gs m ioni phse N s st sd t nitrogen oxygen eletri phse sturtion subdomin mixture of gs 1 thin lyer 1 thin lyer x x-diretion in-plne y y-diretion through-plne Referenes 1 K.Z Yo K. Krn K.B. MAuley P. osthuizen B. Peppley. Xie Fuel Cell 4 (1) (004) 3 9. M. Mthis J. Roth J. FlemingW. Lehnert in:w. Vielstih A. Lmm. Gsteiger (Eds.) ndbook of Fuel Cells John Wiley & ons Ltd. New York 003 pp. 517 537. 3. ohle R. Jung N. Kimiie J. Mergel M. Müller J. Power oures 14 (003) 371 384. 4 V. Guru M.J. Bluemle E.. e Cstro Y-M sou.a. Zwodzinski J.A. Mnn. J. Power oures 165 (007) 793 80. 5 J.. Gostik M.W. Fowler M.. Pritzker M.A. Ionnidis L.M. Behr J. Power oures 16 (006) 8 38. 6 J.P. Feser A.K. Prsd.G. Advni J. Power oures 16 (006) 16 131. 7 M.V. Willims E. Begg L. Bonville.R. Kunz J.M. Fenton J. Eletrohem. o. 151 (8) (004) A1173 A1180. 8 J. oler E. ontnon L. z J. Power oures 118 (003) 17 178. 9.A. Freunberger M. Reum J. Evertz A. Wokun F.N. Bühi J. Eletrohem. o. 153 (006) A158 A165. 10. omimur. Nkmur. Nonmi. ito 001 IEEE 7th Interntionl Conferene on olid ieletris (001) 101 104. 11 V. Mishr F. Yng R. Pithumni J. Fuel Cell i. ehnol. 1 (004) 9. 1
1 J. Ihonen F. Jouen G. Lindbergh G. undholm Eletrohim. At 46 (001) 899 911. 13 P. M. Wilde M. Mndle M. Murt N. Berg Fuel Cells 4 (3) (004) 180 184. 14 Cunninghm M. Lefévre G. Lebrun J.P. odelet J. Power oures 143 (005) 93 10. 15 M. Khndelwl M.M. Menh J. Power oures 161 (006) 1106 1115. 16 P.J.. Vie. Kelstrup Eletrohim. At 49 (004) 1069 1077. 17 J. Ihonen M. Mikkol G. Lindbergh J. Eletrohem. o. 151 (8) (004) A115 A1161. 18 J.. Gostik M.W. Fowler M.A. Ionnidis M.. Pritzker Y.M. Volfkovih A. krs J. Power oures 156 (006) 375 387. 19 V. Guru M.J. Bluemle E... Cstro Y-M. sou J.A.Mnn Jr..A. Zwodzinski Jr. J. Power oures 160 (006) 1156 116. 0. Litster. inton N. illi J. Power oures 154 (006) 95 105. 1 A. Bzylk. inton Z.. Liu N. illi J. Power oures 163 (007) 784 79. N. olmström J. Ihonen A. Lundbld G. Lindbergh Fuel Cells 7 (4) (007) 306 313. 3 J. Benziger J. Nehlsen. Blkwell. Brennn J. Itesu J. Membrne iene 61 (005) 98 106. 4 E.C. Kumbur K.V. hrp M.M. Menh J. Power oures 161 (006) 333 345. 5 E.C. Kumbur K.V. hrp nd M.M. Menh Journl of Power oures In Press Aepted Mnusript (007). 6 E.C. Kumbur K.V. hrp M.M. Menh J. Eletrohem. o. 154 (1) B195 B1304 (007). 7 E.C. Kumbur K.V. hrp M.M. Menh J. Eletrohem. o. 154 (1) B1305 B1314 (007). 8 E.C. Kumbur K.V. hrp M.M. Menh 54 (1) B1315 B134 (007). 9 W.K. Lee C.. o J.W.V. Zee M. Murthy J. Power oures 84 (1999) 45 51. 30 J. Ge A. igier. Liu J. Power oures 159 (006) 9 97. 31. Esribno J.F. Blhot J. Etheve A. Morin R. Mosdle J. Power oures 156 (006) 8 13. 3 W.R. Chng J.J. wng F.B. Weng.. Chn J. Power oures 166 (007) 149 154. 33 J.G. Phroh K. Krn W. un J. Power oures 161 (006) 14-4. 34. Zhou. Liu J. Power oures 161 (006) 444 453. 35. Meng C.Y. Wng J. Eletrohem. o. 151 (004) A358-A367. 36 J.. Jng W.M. Yn C.C. hih J. Power oures 156 (006) 44 5. 37 G. Inoue Y. Mtsukum M. Minemoto J. Power oures 154 (006) 8 17. 38. Ntrn.V. Nguyen J. Eletrohem. o. 148 (001) A134 A1335. 39 J.. Jng W.M. Yn C.C. hih J. Power oures 161 (006) 33 33. 40 Z. Liu Z. Mo C. Wng J. Power oures 158 (006) 19 139. 41.. Chu C. Yeh F. Chen J. Power oures. 13 (003) 1 9. 4 J.. Gostik M.A. Ionnidis M.W. Fowler M.. Pritzker J. Power oures 173 (007) 77 90. 43 J.G. Phroh J. Power oures 144 (005) 77 8. 44 A.. Rwool.K. Mitr J.G. Phroh J. Power oures 16 (006) 985 991. 45 X.. Niu. Munekt.A. yodo K. ug J. Power oures 17 (007) 54 55.
46 J.. Nm M. Kviny Int. J. et Mss rnsfer 46 (003) 4595 4611. 47 U. Psogullri C.Y. Wng Eletrohim. At 49 (004) 4359 4369. 48 U. Psogullri C.Y. Wng J. Eletrohem. o. 151 (004) A399 A406. 49 X. Zhu P.C. ui N. illi J. Power oures 17 (007) 87 95. 50 P.C. ui N. illi J. Power oure 161 (006) 94 300. 51 V.P. hulz J. Beker A. Wiegmnn P.P. Mukheree C.Y Wng J. Eletrohem. o. 154 (007) B419 B46. 5 L. Zhng Y. Liu. ong. Wng Y. Zhou.J. u J. Power oures 16 (006) 1165 1171. 53 P. Zhou C.W. Wu G.J. M J. Power oures 159 (006) 1115 11. 54 P. Zhou C.W. Wu J. Power oures 170 (007) 93 100. 55 P. Zhou C.W. Wu G.J. M J. Power oures 163 (007) 874 881. 56 W. un B.A. Peppley K. Krn J. Power oures 144 (005) 4 53. 57 I. Nitt. ottinen. imnen M. Mikkol J. Power oures 171 (007) 6 36. 58 I. Nitt. imnen M. Mikkol herml ondutivity nd ontt resistne of ompressed gs diffusion lyer of PEM fuel ell Fuel Cells submitted for publition. 59 I. Nitt. imnen M. Mikkol Contt resistne between gs diffusion lyer nd tlyst lyer of PEM fuel ell Eletrohem. Commun. In press. 60. ottinen. imnen. Krvonen I. Nitt J. Power oures 171 (007) 113 11. 61.M. Bernrdi M.W. Verbrugge J. Eletrohem. o. 139 (199) 477 491. 6. imnen. ottinen M. Mikkol V. rinen Eletrohim. At 5 (006) 06 14. 63 Mnufture s dt sheet for IEM-3 grphite by vensk nso AB. 64. Cleghorn J. Kolde W. Liu in:w. Vielstih A. Lmm. Gsteiger (Eds.) ndbook of Fuel Cells John Wiley & ons Ltd. New York 003 pp. 566 575. 65 Mnufturer s t heet for igret GL 10 BA by GL Crbon AG. 66 W. un B.A. Peppley K. Krn Eletrohim. At 50 (005) 3359 3374. 67. Ntrn.V. Nguyen J. Power oures 115 (003) 66 80. 68. ottinen. imnen Eletrohem. Commun. 9 (007) 1047 105. 69 W.Q. o C.. Min X.L. Liu Y.L. e B.. Yin W. Jing J. Power oures 160 (006) 359 373. 70 C.. Min Y.L. e X.L. Liu B.. Yin W. Jing W.Q. o J. Power oures 160 (006) 374 385. 71. Ju C.Y.Wng J. Eletrohem. o. 151 (004) A1954 A1960. 3