USER MANUAL. Model validation can be done at performance and / or water balance level through trial and error procedure:

Transcription

1 USER MAUA he purpose of the model is to predit performne of single ell of whih the geometri prmeters mteril properties trnsport prmeters nd the operting onditions re speified by the user. he pbility of the model inludes multiple flow field rhitetures (lnd-hnnel flow field or open flow field) flow rrngements (oflow or ounterflow) oidnts (ir or helio). Importnt mteril nd trnsport prmeters (wter ontent tivity orreltion ioni ondutivity dissolved wter diffusion oeffiient) n be tilored by user input. Model vlidtion n be done t performne nd / or wter blne level through tril nd error proedure:. if performne is the only onern: voltge n be found by tril nd error until the output urrent density mthes the input trget urrent density.. If wter blne is onerned s well: in the se of oflow opertion follow the sme proedure s finding out voltge; in the se of ounterflow opertion it is suggested tht voltge be found out first by tril nd error nd then the wter flow rte t eit be found by tril nd error until urrent density mthes the input trget urrent density nd wter molr flow rte mthes the inlet flow rte by b-of-envelope lultion. hree elements to run the progrm:. input file input.dt opied & psted from input worsheet input.ls.. eeutble progrm ES.ee.. n empty folder nmed out where ll the output files will be. Steps to run the progrm:. prepred input.dt from input.ls. Me sure ll input.dt ES.ee nd folder out re under the sme diretory.. double li ES.ee

2 IU he eel file input.ls is the input worsheet. he boed region in User Input tb s highlighted is where user input is required. he Input File Generted tb s highlighted is generted ording to the informtion provided in User Input tb nd loed.

3 hen you n opy nd pste the ontents into input.dt whih is the input file required to run the progrm. ilorble input prmeters inlude (ll in SI units):. for eh lyer in the fuel ell sndwih: thiness hydrophobiity (FE weight perentge or ontt ngle) porosity through-plne nd in-plne hydruli permebility through-plne nd in-plne therml ondutivity through-plne nd inplne eletroni ondutivity through-plne nd in-plne ioni ondutivity through-plne nd in-plne diffusion oeffiient through-plne nd in-plne diffusion oeffiient through-plne nd in-plne diffusion oeffiient number of grids in through-plne diretion. tive re in-plne width lnd/hnnel width rtio number of grids in in-plne diretion

4 4. for est / west / north / south boundries in the - sub-model (see Appendi A: Computtionl omin) boundry onditions re speified for solved-for vribles: temperture eletri potentil ioni potentil onentrtion onentrtion onentrtion gs pressure nd liquid pressure. Eh boundry ondition is speified by four numbers: boundry type ( st ind nd ind or rd ind of boundry ondition?) onvetion oeffiient for rd ind of boundry ondition onstnt vlue for st ind of boundry ondition / mbient vlue for rd ind of boundry ondition onstnt flu for nd ind of boundry ondition 4. operting urrent density stoihiometry of stoihiometry of molr flow rte of in thode strem molr flow rte of in node strem oolnt temperture grdient flow rrngement (ounterflow or oflow?) oidnt (ir or helio?) 5. funtionl form of prmeters: pillry pressure liquid sturtion orreltion ( everett [] / Kumbur []) eletro-osmoti drg oeffiient ( Zwodzinsi [] / Springer [4]) wter ontent wter tivity orreltion Weber [5] ustomiztion: R E ref u ioni ondutivity wter ontent orreltion Jing [6] ustomiztion: R E ref u wter diffusion oeffiient in eletrolyte phse with respet to hemil potentil grdient wter ontent orreltion Weber [5] ustomiztion: R E ref u whether to onsider thermo-osmoti drg? eletril ontt resistne therml ontt resistne ehnge urrent density for R ehnge urrent density for RR ionomer volume frtion in thode tlyst lyer

5 UU here is summrizing file nmed summry.out to ontin the informtion bout temperture nd wter blne in eh segment in the long-flow diretion (y). he lulted verge urrent density nd FR re listed in the end. summry.out Segment I # emperture nd wter molr flow rte informtion in orresponding segment Current density net wter trnsport ross membrne hmi resistne in orresponding segment (in SI units) Globl urrent density nd FR verged in long flow diretion (y) here re seprte output files nmed s solved-for-vrible_result.out for eh solved-for vrible (temperture eletri potentil Ve ioni potentil Vp onentrtion Co onentrtion Ch onentrtion Cho gs 5

6 pressure gs nd liquid pressure liq). he five olumns represent inde in through-plne diretion (z) inde in in-plne diretion () oordinte in through-plne diretion (z) 4 oordinte in in-plne diretion () 5 vlue. here re seprte output files nmed s flu_solved-for-vrible_result.out for the flu of eh solved-for vrible. he si olumns represent inde in through-plne diretion (z) inde in in-plne diretion () oordinte in through-plne diretion (z) 4 oordinte in in-plne diretion () 5 flu in through-plne diretion (z) 6 flu in inplne diretion (). 6

7 7

8 Appendi A: Computtionl omin - Sub-Model R W WES M M C MEM C M M EAS z SU + Simplifition Anode outlet Cthode inlet y Anode strem sweep diretion Cthode strem 8 Anode inlet Cthode outlet

9 Appendi B: hysis In porous medi (inluding mro-porous G substrte miro-porous lyer nd tlyst lyer) onvetive trnsport of gs speies diffusive trnsport of gs speies liquid wter trnsport phse trnsfer between wter vpor nd liquid wter onvetive trnsport of het ondutive trnsport of het ltent het relese / bsorption by phse hnge eletron trnsport In MEA (inluding tlyst lyer nd membrne) diffusive trnsport of dissolved wter hydruli permetion of wter eletro-osmosis thermo-osmosis ondutive trnsport of het Joule heting ion trnsport elusive in tlyst lyer hydrogen oidtion retion oygen redution retion phse trnsfer between wter vpor / liquid wter nd dissolved wter reversible nd irreversible retion het relese / bsorption 9

10 Appendi C: Governing Equtions - sub-model rmeter iffusion Medi Miro-orous yer C onv diff C onv diff C onv diff Svl d Ctlyst yer Membrne J gen onv diff / onv diff i dc d E F q q S 4F J gen F onv diff Svl gen i C / C qonv qond vl S vl G K G C G Svl G s W K S M W vl where S e / gen s gen s J F d d / / E F onv ond i S i q J gen( ) vls ond vl nf K J G gen C G Svl / G nf s W K W K Svl M W M W e J e s J / i onv i u where i= GCi i j diff ji diff where i j= eff C ji i j

11 R: R F R F C C s i J u u ref ref gen ep ep / RR: s r r A r r A E C F J gg gg gg W gg gg W gg W W r C gen 4 st vl vl R C S u C u C q G onv q th ond G G G G K u K u + Simplifition F A i n n F A i n n 4 n n

12 n n n n net i A F net. 5 i A m p E th E i A F ell

13 Appendi : Boundry Conditions - sub-model z= z=m C z=c EM z=mem C z=c M z= = & =W C / / / C / speified C C C C C speified C / C / / / C C speified C C / / / / speified C C C speified speified / / / / G speified G G / / / / speified G G G speified / / / / speified / / / / e e e e s speified s / / / / s s

14 + Simplifition in ia n F n in n in st st R R n in ia 4F n n in in n in 79% % ia 4F in in st n n st 79% % R R for the under-sturted gs flow in the flow field n where j represents or j C j Ru n n j C j Ru n n n n where j represents or for the sturted gs flow in the flow field C ( ) / st j where j represents Ru 4

15 5 u st j R C where j represents j u st j n n n R C where j represents or

16 Appendi E: rmeters retion rte onstnt: referene [7] F i ref ep F ref C Ru 4 [s - ] effetiveness ftor: referene [7] E r tnh [/] hiele modulus: referene [7] r gg eff [/] gg effetive oygen diffusion oeffiient inside gglomerte: referene [8] eff gg gg.5 [m /s] dissolved wter onentrtion: defined dry Cd [mol/m ] EW over-potentil: defined s e for R; s e Erev for RR [V] 6

17 tlyst loding: referene [mnufturer] =.5.4 [mg t /m ] essible speifi t surfe re: referene [9] A t =5.4 [m t/g t ] roughness ftor: referene [] t / A t / [m t/m ] C/ C hrge trnsfer oeffiient: referene [] = [/] retion order: referene [] =.5 [/] referene onentrtion: referene [] ref C / = 4 [mol/m ] volumetri ehnge urrent density ref i =.7 [A/m ] for R referene [] ref i =fitting for RR enry s onstnt for oygen into eletrolyte: referene [] 7

18 ep 666 R 5. / [/] enry s onstnt for hydrogen into eletrolyte: referene [] 4.56 [/] R enry s onstnt for oygen into liquid wter: referene [4] ep 5 R / W [/] gglomerte prtile rdius: referene [ 5] r gg =.5-6 [m] ionomer volume frtion inside gglomerte prtile: referene [5] gg =.5 [/] thiness of ionomer thin film surrounding gglomerte prtile: referene [5] =5-8 [m] thiness of wter thin film surrounding gglomerte prtile: referene [6] C s W [m] A gg effetive surfe re for oygen to dissolve into gglomerte prtile: referene [6] 8

19 A gg r C gg [m - ] oygen diffusion oeffiient in ionomer: referene [7].88 ep9 [m /s] oygen diffusion oeffiient in liquid wter: referene [6] W =.4-9 [m /s] wter ontent ~ wter tivity orreltion: referene [5] ep ep K ep ep K K.7 * * E E E EW * * E E EW * E EW * E 4.7[ g / mol] * E 5.[ g / mol] * E 7.6[ g / mol] * K diffusion oeffiient of dissolved wter with regrd to hemil potentil grdient: referene [5] 9

20 .8 9 f V ep R where f V [m /s] V m V V diffusion oeffiient of dissolved wter with regrd to onentrtion grdient: referene [8] d ln d [m /s] d ln eletro-osmoti drg oeffiient: referene []. 4 E [/].5 eletro-osmoti drg oeffiient: referene [4].5 E [/] ioni ondutivity in membrne referene [6].67 R ep [S/m] R 5 ioni ondutivity in thode tlyst lyer [9] C R.67 ep R 5 thermo-osmoti drg oeffiient referene [] ep [mol/m s K] Knudsen diffusion oeffiient referene [] [S/m]

21 Kn 4r p Ru M [m /s] effetive binry diffusion oeffiient referene [8 ] s.5.5 eff i j Kn i j s i j Kn s. 5 sturtion pressure: referene [] [m /s] st [] in ⁰ C wter tivity: defined C Ru [/] st pillry pressure ~ liquid sturtion orreltion referene [] p /.46s.4s.56ln s wt%.469.5wt% K [] pillry pressure ~ liquid sturtion orreltion referene [] p os K / J s [] s. s.6 s.47 J s.47s.s.6s effetive permebility: defined if 9 if 9

22 K KK r [m ] reltive permebility referene [] K for non-wetting phse K s. 6.6 r s nw entropy hnge of retion: referene [4] S S =.4 for R [J/mol K] =-6.6 for RR [J/mol K] r for wetting phse [/] nw binry diffusion oeffiient between wter vpor nd oygen: referene [5] =.8-5 [m /s] binry diffusion oeffiient between wter vpor nd nitrogen: referene [5] =.9-5 [m /s] binry diffusion oeffiient between oygen nd nitrogen: referene [5] =. -5 [m /s] binry diffusion oeffiient between wter vpor nd helium: referene [5] e e =9.8-5 [m /s] binry diffusion oeffiient between oygen nd helium: referene [5] e e =8. -5 [m /s]

23 binry diffusion oeffiient between hydrogen nd wter vpor: referene [5] =9.5-5 [m /s] density of dry membrne: referene [6] dry =98 [g/m ] equivlent weight of membrne: referene [mnufturer] EW =. [g/equiv] ionomer volume frtion in thode tlyst lyer: referene [9] C =. [/] density of liquid wter: referene [7] W = [g/m ] moleulr weight of wter: referene [7] M W =8 - [g/mol] dynmi visosity: referene [7] =.65-4 for liquid.5-5 for gs [ s] molr ltent het of vporiztion: referene [7] vl =4.65 [J/mol] surfe tension: referene [7]

24 =.65 [/m] therml voltge: referene [] E th =.5 [V] reversible voltge referene [] Ru E rev log [V] 4F universl gs onstnt: referene [7] R u =8.4 [J/mol K] Frdy onstnt F =96485 [C/mol] 4

25 Appendi F: Referene. everett M. Cpillry Behvior in orous Solids. rns. Am. Inst. Min. Metll. et. Eng Kumbur E. C.; Shrp K. V.; Menh M. M. Vlidted everett Approh for Multiphse Flow in EFC iffusion Medi. I. ydrophobiity Effet. J Eletrohem So 7 54 () B95.. Zwodzinsi. A.; vey J.; Vlerio J.; Gottesfeld S. he wter ontent dependene of eletro osmoti drg in proton onduting polymer eletrolytes. Eletrohimi At () Springer. E.; Zwodzinsi. A.; Gottesfeld S. olymer eletrolyte fuel ell model. J Eletrohem So Weber A. Z.; ewmn J. rnsport in polymer eletrolyte membrnes II. Mthemtil model. J Eletrohem So 4 5 () A A5. 6. Jing R.; Mittelstedt C. K.; Gittlemn C. S. hrough plne proton trnsport resistne of membrne nd ohmi resistne distribution in fuel ells. J Eletrohem So 9 56 B ewmn J. S. Eletrohemil Systems. nd ed.; rentie ll: Englewood Cliffs J Bruggemn V.. A. G. Berehnung vershiedener physilisher Konstnten von heterogenen Substnzen. I. ieletrizitätsonstnten und eitfähigeiten der Mishörper us isotropen Substnzen. Annlen der hysi (7) Gsteiger. A.; Gu W.; Mhri R.; Mthis M. F.; Somplli B. Beginning of life MEA performne effiieny loss ontributions. In ndboo of Fuel Cells Fundmentls ehnology nd Applitions Vielsth W.; Gsteiger. A.; mm A. Eds. John Wiley & Sons: ew Yor ; Vol. p 59.. Yoon W.; Weber A. Z. Modeling ow ltinum oding Effets in Fuel Cell Ctlyst yers. J Eletrohem So 58 B7.. Meng.; Wng C. Y. Eletron trnsport in EFCs. J Eletrohem So 4 5 A58.. eyerlin K. C.; Gu W.; Jorne J.; Gsteiger. A. Study of the ehnge urrent density for the hydrogen oidtion nd evolution retions. J Eletrohem So 7 54 B6.. Bernrdi. M.; Verbrugge M. W. Mthemtil model of gs diffusion eletrode bonded to polymer eletrolyte. AIChE Journl 99 7 (8) Mnn R. F.; Amphlett J. C.; eppley B. A.; hurgood C.. enry's w nd the solubilities of retnt gses in the modelling of EM fuel ells. J ower Soures 6 6 () Sun W.; eppley B. A.; Krn K. An improved two dimensionl gglomerte thode model to study the influene of tlyst lyer struturl prmeters. Eletrohimi At 5 5 (6 7) in G.; e W.; guyen. V. Modeling liquid wter effets in the gs diffusion nd tlyst lyers of the thode of EM fuel ell. J Eletrohem So 4 5 A rthsrthy A.; Srinivsn S.; Appleby A. J.; Mrtin C. R. emperture dependene of the eletrode inetis of oygen redution t the pltinum/nfion interfe miroeletrode investigtion. J Eletrohem So Zwodzinsi. A.; eemn M.; Sillerud..; Gottesfeld S. etermintion of wter diffusion oeffiients in perfluorosulfonte ionomeri membrnes. J hys Chem (5)

26 9. iu Y.; Murphy M. W.; Ber. R.; Gu W.; Ji C.; Jorne J.; Gsteiger. A. roton Condution nd ygen Redution Kinetis in EM Fuel Cell Cthodes: Effets of Ionomer to Crbon Rtio nd Reltive umidity. J Eletrohem So 9 56 B97.. Kim S.; Menh M. M. Investigtion of temperture driven wter trnsport in polymer eletrolyte fuel ell: hermo osmosis in membrnes. J Membrne Si 9 8 ( ).. Knudsen M.; rtington J. R. he Kineti. heoryof Gses. Some Modern Aspets. J hys Chem 95 9 () Menh M. M. Fuel Cell Engines. John Wiley & Sons: ew Yor 8.. Kumbur E. C.; Shrp K. V.; Menh M. M. n the effetiveness of everett pproh for desribing the wter trnsport in fuel ell diffusion medi. J ower Soures 7 68 () mpinen M. J.; Fomino M. Anlysis of Free Energy nd Entropy Chnges for lf Cell Retions. J Eletrohem So Cussler E.. iffusion: Mss rnsfer in Fluid Systems. rd ed.; Cmbridge University ress: Cmbridge Morris. R.; Sun X. Wter sorption nd trnsport properties of fion 7. Journl of pplied polymer siene 99 5 (8) Cengel Y. A.; Boles M. A. hermodynmis: n engineering pproh. MGrw ill igher Edution: 6. 6