The Padulles dynamic model can predict the transient response of cell voltage, temperature of the cell, hydrogen/oxygen out flow rates and cathode and anode channel temperatures/pressures under sudden change in load current. Hence, a dynamic fuel cell simulation is developed in this model, which incorporates the dynamics of flow and pressure in the anode and cathode channels and mass/ heat transfer transient features in the fuel cell body. This model based on some assumption such; the gases are ideal, the stack is fed with hydrogen and air, temperature is stable at all times, the ratio of pressures between the interior and exterior of the channel is large, The channels that transport gases along the electrodes have a fixed volume, only source of losses is ohmic and Nernst equation can be applied too.
This model is an integration of Padulles-Hauer dynamic model with Amphlett static model. The advantage of this dynamic model is using Amphlett equation for simulating the polarization values. Amphlett model as the most complicated and preferable static model, but the most precise. Based on this model, the obtained polarization voltage is identical to the experimental results.
Fig1. Padulles-Amphlett Dynamic Model Block Diagram
from opem.Dynamic.Padulles_Amphlett import *
qH2=qH2_Calc(qMethanol=0.0002,CV=2,t1=2,t2=2)
qH2
3.6363636363636364e-05
Kr=Kr_Calc(N0=5)
Kr
1.2955435375179044e-08
qO2=qO2_Calc(qH2=qH2,rho=1.168)
qO2
3.113325031133251e-05
PH2=PH2_Calc(KH2=0.0000422,tH2=3.37,Kr=Kr,I=1,qH2=qH2)
PH2
0.19704428889827239
PO2=PO2_Calc(KO2=0.0000211,tO2=6.74,Kr=Kr,I=1,qO2=qO2)
PO2
0.1905549730945132
PH2O=PH2O_Calc(KH2O=0.000007716,tH2O=18.418,Kr=Kr,I=1,qH2O=qH2)
PH2O
0.2425275190047356
Enernst=Enernst_Calc(E0=0.6,N0=5,T=343, PH2=PH2, PO2=PO2,PH2O=PH2O)
Enernst
2.9234016588243374
Eta_Act=Eta_Act_Calc(T=343,PO2=PO2 , PH2=PH2, i=2, A=50.6)
Eta_Act
0.38390602046791616
Relectronic
Should be approximately constant over the relatively narrowtemperature range of PEM fuel cell operation. Therefore, the parameter Relectronic can be taken as a constant, but is generally difficult to predict and, therefore, is initially an unknown.
Eta_Ohmic=Eta_Ohmic_Calc(i=2, l=0.0178, A=50.6, T=343, lambda_param=23, R_elec=0)
Eta_Ohmic
0.003531492225469087
Eta_Conc=Eta_Conc_Calc(i=2, A=50.6, B=0.016, JMax=1.5)
Eta_Conc
0.0004272617031588504
Loss=Loss_Calc(Eta_Act=Eta_Act,Eta_Conc=Eta_Conc,Eta_Ohmic=Eta_Ohmic)
Loss
0.38786477439654415
FC_Voltage=Vcell_Calc(Enernst=Enernst, Loss=Loss, N=5)
FC_Voltage
0.9840777868416166
Power=Power_Calc(Vcell=FC_Voltage,i=2)
Power
1.9681555736832332
Efficiency_Calc(Vcell=FC_Voltage,N=5)
0.1261638188258483
i
=0 to i
=4 with step
=0.1Test_Vector={"A":50.6,"l":0.0178,"lambda":23,"JMax":1.5,"T":343,"E0":1.229,"N0":5,"KO2":0.0000211,"KH2":0.0000422,"KH2O":0.000007716,"tH2":3.37,"tO2":6.74,"t1":2,"t2":2,"tH2O":18.418,"B":0.016,"R":0,"rho":1.168,"qMethanol":0.0002,"CV":2,"i-start":0.1,"i-stop":4,"i-step":0.1,"Name":"Test"}
Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=False,ReportMode=True)
{'I': [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3.0, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9], 'P': [0.5139571050565013, 0.9818293974271133, 1.4321830622295815, 1.871089991478542, 2.3014338158615835, 2.72491286817189, 3.142649276570101, 3.555440520606415, 3.9638828203358005, 4.368438911998416, 4.769478416867183, 5.167303402108664, 5.562165360323403, 5.954276933375901, 6.343820269580719, 6.7309531426037355, 7.115813534854511, 7.4985231388582365, 7.8791900782642434, 8.257911054514981, 8.634773063176024, 9.009854782655777, 9.383227709947201, 9.754957098504613, 10.12510273955794, 10.493719618233213, 10.860858468594623, 11.226566246354942, 11.590886533977079, 11.953859889838787, 12.315524150794642, 12.675914695660513, 13.035064675732759, 13.393005217342077, 13.74976560055816, 14.105373417455501, 14.459854712781162, 14.813234109404705, 15.165534920554036], 'V': [5.139571050565013, 4.909146987135566, 4.773943540765272, 4.677724978696355, 4.602867631723167, 4.54152144695315, 4.489498966528716, 4.444300650758018, 4.404314244817556, 4.368438911998416, 4.335889469879257, 4.306086168423887, 4.27858873871031, 4.253054952411358, 4.229213513053812, 4.2068457141273345, 4.185772667561477, 4.165846188254576, 4.146942146454865, 4.1289555272574905, 4.1117966967504875, 4.095388537570807, 4.0796642217161745, 4.0645654577102555, 4.050041095823176, 4.036046007012774, 4.022540173553564, 4.009487945126765, 3.996857425509338, 3.9846199632795956, 3.9727497260627875, 3.96122334239391, 3.9500195987068967, 3.9391191815711992, 3.9285044573023313, 3.918159282626528, 3.9080688412922058, 3.8982195024749227, 3.888598697577958]}
Data=Dynamic_Analysis(InputMethod=Test_Vector,TestMode=True,PrintMode=True,ReportMode=True)
########### Padulles-Amphlett-Model Simulation ########### Analyzing . . . I : 0.1 E : 6.0684154992732005 V Eta Activation : 0.18557231242539243 V Eta Concentration : 2.109426805213159e-05 V Eta Ohmic : 0.00017548304819292376 V FC Efficiency : 0.6589193654570529 FC Power : 0.5139571050565013 W FC Voltage : 5.139571050565013 V Loss : 0.1857688897416375 V PH2 : 0.19717074233280188 atm PH2O : 0.2426831613626925 atm PO2 : 0.1906263686382979 atm ########### I : 0.2 E : 6.068413961701556 V Eta Activation : 0.23146009851376736 V Eta Concentration : 4.221638333089875e-05 V Eta Ohmic : 0.0003510800160998837 V FC Efficiency : 0.629377818863534 FC Power : 0.9818293974271133 W FC Voltage : 4.909146987135566 V Loss : 0.23185339491319815 V PH2 : 0.1971566919511875 atm PH2O : 0.24266586776736396 atm PO2 : 0.1906184358000996 atm ########### I : 0.3 E : 6.068412424065923 V Eta Activation : 0.2583036192079603 V Eta Concentration : 6.336641945755048e-05 V Eta Ohmic : 0.0005267910327125488 V FC Efficiency : 0.6120440436878553 FC Power : 1.4321830622295815 W FC Voltage : 4.773943540765272 V Loss : 0.25889377666013036 V PH2 : 0.19714264156957312 atm PH2O : 0.24264857417203542 atm PO2 : 0.1906105029619013 atm ########### I : 0.4 E : 6.068410886366294 V Eta Activation : 0.27735002084480426 V Eta Concentration : 8.454445034568427e-05 V Eta Ohmic : 0.0007026162388380664 V FC Efficiency : 0.5997083306020967 FC Power : 1.871089991478542 W FC Voltage : 4.677724978696355 V Loss : 0.278137181533988 V PH2 : 0.19712859118795872 atm PH2O : 0.24263128057670688 atm PO2 : 0.19060257012370302 atm ########### I : 0.5 E : 6.068409348602667 V Eta Activation : 0.2921240370409447 V Eta Concentration : 0.00010575055020278165 V Eta Ohmic : 0.0008785557847524419 V FC Efficiency : 0.5901112348363035 FC Power : 2.3014338158615835 W FC Voltage : 4.602867631723167 V Loss : 0.2931083433758999 V PH2 : 0.19711454080634436 atm PH2O : 0.24261398698137834 atm PO2 : 0.1905946372855047 atm ########### I : 0.6 E : 6.0684078107750326 V Eta Activation : 0.3041956781419353 V Eta Concentration : 0.00012698479353178086 V Eta Ohmic : 0.0010546098289093816 V FC Efficiency : 0.582246339352968 FC Power : 2.72491286817189 W FC Voltage : 4.54152144695315 V Loss : 0.3053772727643765 V PH2 : 0.19710049042472996 atm PH2O : 0.2425966933860498 atm PO2 : 0.1905867044473064 atm ########### I : 0.7 E : 6.068406272883388 V Eta Activation : 0.31440243547871893 V Eta Concentration : 0.000148247255132642 V Eta Ohmic : 0.0012307785370829418 V FC Efficiency : 0.5755767905806046 FC Power : 3.142649276570101 W FC Voltage : 4.489498966528716 V Loss : 0.3157814612709345 V PH2 : 0.19708644004311557 atm PH2O : 0.24257939979072127 atm PO2 : 0.19057877160910808 atm ########### I : 0.8 E : 6.068404734927729 V Eta Activation : 0.3232442167420945 V Eta Concentration : 0.00016953801010392253 V Eta Ohmic : 0.0014070620817435461 V FC Efficiency : 0.5697821347125663 FC Power : 3.555440520606415 W FC Voltage : 4.444300650758018 V Loss : 0.32482081683394204 V PH2 : 0.19707238966150117 atm PH2O : 0.24256210619539273 atm PO2 : 0.1905708387709098 atm ########### I : 0.9 E : 6.068403196908046 V Eta Activation : 0.3310434726426763 V Eta Concentration : 0.00019085713384438152 V Eta Ohmic : 0.0015834606415773538 V FC Efficiency : 0.564655672412507 FC Power : 3.9638828203358005 W FC Voltage : 4.404314244817556 V Loss : 0.332817790418098 V PH2 : 0.19705833927988675 atm PH2O : 0.24254481260006414 atm PO2 : 0.19056290593271147 atm ########### I : 1.0 E : 6.068401658824337 V Eta Activation : 0.33802037026202836 V Eta Concentration : 0.00021220470205456714 V Eta Ohmic : 0.0017599744011013664 V FC Efficiency : 0.5600562707690275 FC Power : 4.368438911998416 W FC Voltage : 4.368438911998416 V Loss : 0.3399925493651843 V PH2 : 0.19704428889827239 atm PH2O : 0.2425275190047356 atm PO2 : 0.1905549730945132 atm ########### I : 1.1 E : 6.068400120676597 V Eta Activation : 0.3443319458183834 V Eta Concentration : 0.0002335807907384422 V Eta Ohmic : 0.0019366035503462617 V FC Efficiency : 0.5558832653691355 FC Power : 4.769478416867183 W FC Voltage : 4.335889469879257 V Loss : 0.34650213015946807 V PH2 : 0.197030238516658 atm PH2O : 0.24251022540940706 atm PO2 : 0.19054704025631486 atm ########### I : 1.2 E : 6.068398582464819 V Eta Activation : 0.35009414904739194 V Eta Concentration : 0.00025498547620500224 V Eta Ohmic : 0.002113348284589288 V FC Efficiency : 0.5520623292851136 FC Power : 5.167303402108664 W FC Voltage : 4.306086168423887 V Loss : 0.35246248280818626 V PH2 : 0.1970161881350436 atm PH2O : 0.24249293181407852 atm PO2 : 0.19053910741811658 atm ########### I : 1.3 E : 6.068397044188998 V Eta Activation : 0.35539503345654255 V Eta Concentration : 0.0002764188350699048 V Eta Ohmic : 0.0022902088041253615 V FC Efficiency : 0.548537017783373 FC Power : 5.562165360323403 W FC Voltage : 4.27858873871031 V Loss : 0.3579616610957378 V PH2 : 0.19700213775342923 atm PH2O : 0.24247563821874998 atm PO2 : 0.19053117457991825 atm ########### I : 1.4 E : 6.06839550584913 V Eta Activation : 0.36030304442922906 V Eta Concentration : 0.00029788094425712723 V Eta Ohmic : 0.0024671853140681515 V FC Efficiency : 0.5452634554373536 FC Power : 5.954276933375901 W FC Voltage : 4.253054952411358 V Loss : 0.36306811068755435 V PH2 : 0.19698808737181484 atm PH2O : 0.24245834462342142 atm PO2 : 0.19052324174171997 atm ########### I : 1.5 E : 6.068393967445208 V Eta Activation : 0.3648724409731032 V Eta Concentration : 0.00031937188100060893 V Eta Ohmic : 0.002644278024175193 V FC Efficiency : 0.5422068606479247 FC Power : 6.343820269580719 W FC Voltage : 4.229213513053812 V Loss : 0.367836090878279 V PH2 : 0.19697403699020044 atm PH2O : 0.24244105102809288 atm PO2 : 0.19051530890352164 atm ########### I : 1.6 E : 6.068392428977227 V Eta Activation : 0.36914696409844006 V Eta Concentration : 0.0003408917228459314 V Eta Ohmic : 0.0028214871486926026 V FC Efficiency : 0.539339194118889 FC Power : 6.7309531426037355 W FC Voltage : 4.2068457141273345 V Loss : 0.3723093429699786 V PH2 : 0.19695998660858605 atm PH2O : 0.24242375743276434 atm PO2 : 0.19050737606532336 atm ########### I : 1.7 E : 6.068390890445182 V Eta Activation : 0.3731623911228729 V Eta Concentration : 0.00036244054765199196 V Eta Ohmic : 0.0029988129062160497 V FC Efficiency : 0.5366375214822406 FC Power : 7.115813534854511 W FC Voltage : 4.185772667561477 V Loss : 0.376523644576741 V PH2 : 0.19694593622697168 atm PH2O : 0.2424064638374358 atm PO2 : 0.19049944322712503 atm ########### I : 1.8 E : 6.068389351849069 V Eta Activation : 0.3769483587657406 V Eta Concentration : 0.00038401843359268825 V Eta Ohmic : 0.003176255519565377 V FC Efficiency : 0.5340828446480225 FC Power : 7.4985231388582365 W FC Voltage : 4.165846188254576 V Loss : 0.3805086327188987 V PH2 : 0.19693188584535729 atm PH2O : 0.24238917024210727 atm PO2 : 0.19049151038892673 atm ########### I : 1.9 E : 6.068387813188879 V Eta Activation : 0.38052969267197334 V Eta Concentration : 0.00040562545915863245 V Eta Ohmic : 0.0033538152156708046 V FC Efficiency : 0.5316592495454955 FC Power : 7.8791900782642434 W FC Voltage : 4.146942146454865 V Loss : 0.38428913334680276 V PH2 : 0.1969178354637429 atm PH2O : 0.24237187664677873 atm PO2 : 0.19048357755072845 atm ########### I : 2.0 E : 6.0683862744646095 V Eta Activation : 0.3839273955127959 V Eta Concentration : 0.0004272617031588504 V Eta Ohmic : 0.003531492225469087 V FC Efficiency : 0.5293532727253193 FC Power : 8.257911054514981 W FC Voltage : 4.1289555272574905 V Loss : 0.3878861494414239 V PH2 : 0.19690378508212852 atm PH2O : 0.2423545830514502 atm PO2 : 0.19047564471253012 atm ########### I : 2.1 E : 6.068384735676256 V Eta Activation : 0.38715939375662295 V Eta Concentration : 0.00044892724472251814 V Eta Ohmic : 0.0037092867838082735 V FC Efficiency : 0.5271534226603188 FC Power : 8.634773063176024 W FC Voltage : 4.1117966967504875 V Loss : 0.39131760778515373 V PH2 : 0.19688973470051413 atm PH2O : 0.24233728945612165 atm PO2 : 0.19046771187433184 atm ########### I : 2.2 E : 6.068383196823811 V Eta Activation : 0.39024111055794025 V Eta Concentration : 0.00047062216330069346 V Eta Ohmic : 0.0038871991293599716 V FC Efficiency : 0.5250498125090778 FC Power : 9.009854782655777 W FC Voltage : 4.095388537570807 V Loss : 0.3945989318506009 V PH2 : 0.19687568431889974 atm PH2O : 0.2423199958607931 atm PO2 : 0.1904597790361335 atm ########### I : 2.3 E : 6.068381657907269 V Eta Activation : 0.39318591119501267 V Eta Concentration : 0.0004923465386680586 V Eta Ohmic : 0.004065229504538212 V FC Efficiency : 0.5230338745789967 FC Power : 9.383227709947201 W FC Voltage : 4.0796642217161745 V Loss : 0.3977434872382189 V PH2 : 0.19686163393728537 atm PH2O : 0.24230270226546458 atm PO2 : 0.19045184619793523 atm ########### I : 2.4 E : 6.068380118926627 V Eta Activation : 0.3960054536369255 V Eta Concentration : 0.0005141004509246927 V Eta Ohmic : 0.004243378155424144 V FC Efficiency : 0.5210981356038789 FC Power : 9.754957098504613 W FC Voltage : 4.0645654577102555 V Loss : 0.40076293224327436 V PH2 : 0.19684758355567097 atm PH2O : 0.242285408670136 atm PO2 : 0.1904439133597369 atm ########### I : 2.5 E : 6.068378579881878 V Eta Activation : 0.39870996749954657 V Eta Concentration : 0.0005358839804978295 V Eta Ohmic : 0.00442164533169592 V FC Efficiency : 0.5192360379260482 FC Power : 10.12510273955794 W FC Voltage : 4.050041095823176 V Loss : 0.4036674968117403 V PH2 : 0.19683353317405658 atm PH2O : 0.24226811507480747 atm PO2 : 0.19043598052153862 atm ########### I : 2.6 E : 6.068377040773017 V Eta Activation : 0.40130847825734167 V Eta Concentration : 0.0005576972081436541 V Eta Ohmic : 0.004600031286563196 V FC Efficiency : 0.5174417957708685 FC Power : 10.493719618233213 W FC Voltage : 4.036046007012774 V Loss : 0.40646620675204853 V PH2 : 0.19681948279244216 atm PH2O : 0.2422508214794789 atm PO2 : 0.1904280476833403 atm ########### I : 2.7 E : 6.068375501600038 V Eta Activation : 0.4038089891176398 V Eta Concentration : 0.0005795402149490941 V Eta Ohmic : 0.004778536276705824 V FC Efficiency : 0.5157102786607133 FC Power : 10.860858468594623 W FC Voltage : 4.022540173553564 V Loss : 0.4091670656092947 V PH2 : 0.19680543241082776 atm PH2O : 0.24223352788415034 atm PO2 : 0.190420114845142 atm ########### I : 2.8 E : 6.068373962362936 V Eta Activation : 0.40621862980268425 V Eta Concentration : 0.0006014130823336223 V Eta Ohmic : 0.004957160562216277 V FC Efficiency : 0.5140369160418929 FC Power : 11.226566246354942 W FC Voltage : 4.009487945126765 V Loss : 0.4117772034472342 V PH2 : 0.1967913820292134 atm PH2O : 0.2422162342888218 atm PO2 : 0.19041218200694368 atm ########### I : 2.9 E : 6.068372423061707 V Eta Activation : 0.4085437792118771 V Eta Concentration : 0.0006233158920510905 V Eta Ohmic : 0.005135904406545483 V FC Efficiency : 0.5124176186550433 FC Power : 11.590886533977079 W FC Voltage : 3.996857425509338 V Loss : 0.4143029995104737 V PH2 : 0.196777331647599 atm PH2O : 0.24219894069349326 atm PO2 : 0.1904042491687454 atm ########### I : 3.0 E : 6.0683708836963435 V Eta Activation : 0.4107901672807063 V Eta Concentration : 0.0006452487261915484 V Eta Ohmic : 0.005314768076451755 V FC Efficiency : 0.5108487132409738 FC Power : 11.953859889838787 W FC Voltage : 3.9846199632795956 V Loss : 0.4167501840833496 V PH2 : 0.1967632812659846 atm PH2O : 0.24218164709816473 atm PO2 : 0.19039631633054707 atm ########### I : 3.1 E : 6.068369344266841 V Eta Activation : 0.4129629601316751 V Eta Concentration : 0.0006672116671831024 V Eta Ohmic : 0.0054937518419525275 V FC Efficiency : 0.5093268879567676 FC Power : 12.315524150794642 W FC Voltage : 3.9727497260627875 V Loss : 0.41912392364081075 V PH2 : 0.19674923088437024 atm PH2O : 0.2421643535028362 atm PO2 : 0.1903883834923488 atm ########### I : 3.2 E : 6.068367804773196 V Eta Activation : 0.41506683170178466 V Eta Concentration : 0.0006892047977937692 V Eta Ohmic : 0.005672855976278701 V FC Efficiency : 0.5078491464607577 FC Power : 12.675914695660513 W FC Voltage : 3.96122334239391 V Loss : 0.42142889247585713 V PH2 : 0.19673518050275585 atm PH2O : 0.24214705990750765 atm PO2 : 0.19038045065415046 atm ########### I : 3.3 E : 6.0683662652154 V Eta Activation : 0.417106024344736 V Eta Concentration : 0.0007112282011333409 V Eta Ohmic : 0.005852080755831333 V FC Efficiency : 0.5064127690649867 FC Power : 13.035064675732759 W FC Voltage : 3.9500195987068967 V Loss : 0.42366933330170065 V PH2 : 0.19672113012114145 atm PH2O : 0.2421297663121791 atm PO2 : 0.19037251781595219 atm ########### I : 3.4 E : 6.06836472559345 V Eta Activation : 0.4190844003836543 V Eta Concentration : 0.0007332819606552831 V Eta Ohmic : 0.0060314264601405215 V FC Efficiency : 0.5050152796886153 FC Power : 13.393005217342077 W FC Voltage : 3.9391191815711992 V Loss : 0.42584910880445015 V PH2 : 0.19670707973952706 atm PH2O : 0.24211247271685057 atm PO2 : 0.19036458497775385 atm ########### I : 3.5 E : 6.068363185907339 V Eta Activation : 0.42100548618901656 V Eta Concentration : 0.0007553661601586168 V Eta Ohmic : 0.006210893371826288 V FC Efficiency : 0.503654417602863 FC Power : 13.74976560055816 W FC Voltage : 3.9285044573023313 V Loss : 0.4279717457210015 V PH2 : 0.1966930293579127 atm PH2O : 0.24209517912152204 atm PO2 : 0.19035665213955555 atm ########### I : 3.6 E : 6.068361646157063 V Eta Activation : 0.4228725100457559 V Eta Concentration : 0.000777480883789843 V Eta Ohmic : 0.006390481776561363 V FC Efficiency : 0.5023281131572472 FC Power : 14.105373417455501 W FC Voltage : 3.918159282626528 V Loss : 0.43004047270610707 V PH2 : 0.1966789789762983 atm PH2O : 0.2420778855261935 atm PO2 : 0.19034871930135727 atm ########### I : 3.7 E : 6.068360106342617 V Eta Activation : 0.4246884348310017 V Eta Concentration : 0.0007996262160448594 V Eta Ohmic : 0.00657019196303564 V FC Efficiency : 0.501034466832334 FC Power : 14.459854712781162 W FC Voltage : 3.9080688412922058 V Loss : 0.4320582530100822 V PH2 : 0.1966649285946839 atm PH2O : 0.24206059193086493 atm PO2 : 0.19034078646315894 atm ########### I : 3.8 E : 6.068358566463993 V Eta Activation : 0.4264559863331208 V Eta Concentration : 0.0008218022417708932 V Eta Ohmic : 0.006750024222922298 V FC Efficiency : 0.4997717310865285 FC Power : 14.813234109404705 W FC Voltage : 3.8982195024749227 V Loss : 0.43402781279781405 V PH2 : 0.19665087821306954 atm PH2O : 0.2420432983355364 atm PO2 : 0.19033285362496066 atm ########### I : 3.9 E : 6.068357026521189 V Eta Activation : 0.42817767789163225 V Eta Concentration : 0.0008440090461684635 V Eta Ohmic : 0.006929978850845375 V FC Efficiency : 0.49853829456127663 FC Power : 15.165534920554036 W FC Voltage : 3.888598697577958 V Loss : 0.4359516657886461 V PH2 : 0.19663682783145514 atm PH2O : 0.24202600474020786 atm PO2 : 0.19032492078676233 atm ########### Done!
Inputs, Constants & Middle Values
$$Parameter$$ | $$Description$$ | $$Unit$$ | $$Value$$ |
$$T$$ | FuelCell temperature | $$K$$ | $$User$$ |
$$N_0$$ | Number of cells | $$--$$ | $$User$$ |
$$E_0$$ | No load voltage | $$V$$ | $$User$$ |
$$K_{H_2}$$ | Hydrogen valve constant | $$kmol.s^{-1}.atm^{-1}$$ | $$User$$ |
$$K_{H_2O}$$ | Water valve constant | $$kmol.s^{-1}.atm^{-1}$$ | $$User$$ |
$$K_{O_2}$$ | Oxygen valve constant | $$kmol.s^{-1}.atm^{-1}$$ | $$User$$ |
$$\tau_{H_2}^{(s)}$$ | Hydrogen time constant | $$s$$ | $$User$$ |
$$\tau_{H_2O}^{(s)}$$ | Water time constant | $$s$$ | $$User$$ |
$$\tau_{O_2}^{(s)}$$ | Oxygen time constant | $$s$$ | $$User$$ |
$$l$$ | Membrane Thickness | $$cm$$ | $$User$$ |
$$A$$ | Active area | $$cm^2$$ | $$User$$ |
$$\tau_{1}^{(s)}$$ | Reformer time constant | $$s$$ | $$User$$ |
$$\tau_{2}^{(s)}$$ | Reformer time constant | $$s$$ | $$User$$ |
$$CV$$ | Conversion factor | $$--$$ | $$User$$ |
$$B$$ | An empirical constant depending on the cell and its operation state | $$V$$ | $$User$$ |
$$R_{electronic}$$ | R-Electronic | $$\Omega$$ | $$User$$ |
$$\lambda$$ | An adjustable parameter with a possible minimum value of 14 and a maximum value of 23 | $$--$$ | $$User$$ |
$$J_{Max}$$ | Maximum current density of the cell | $$Acm^{-2}$$ | $$User$$ |
$$r_{h-o}$$ | Hydrogen-oxygen flow ratio | $$--$$ | $$User$$ |
$$q_{methanol}$$ | Molar flow of methanol | $$kmol.s^{-1}$$ | $$User$$ |
$$i_{start}$$ | Cell operating current start point | $$A$$ | $$User$$ |
$$i_{step}$$ | Cell operating current step | $$A$$ | $$User$$ |
$$i_{stop}$$ | Cell operating current end point | $$A$$ | $$User$$ |
$$P_{H_2}$$ | Hydrogen partial pressure | $$atm$$ | $$System$$ |
$$P_{H_2O}$$ | Water partial pressure | $$atm$$ | $$System$$ |
$$P_{O_2}$$ | Oxygen partial pressure | $$atm$$ | $$System$$ |
$$K_r$$ | Modeling constant | $$kmol.s^{-1}.A^{-1}$$ | $$System$$ |
$$q_{O_2}^{(inlet)}$$ | Molar flow of oxygen | $$kmol.s^{-1}$$ | $$System$$ |
$$q_{H_2O}^{(inlet)}$$ | Molar flow of water | $$kmol.s^{-1}$$ | $$System$$ |
$$q_{H_2}^{(inlet)}$$ | Molar flow of hydrogen | $$kmol.s^{-1}$$ | $$System$$ |
$$J$$ | Actual current density of the cell | $$Acm^{-2}$$ | $$System$$ |
$$C_{O_2}$$ | Concentration of oxygen in the catalytic interface of the cathode | $$molcm^{-3}$$ | $$System$$ |
$$C_{H_2}$$ | Concentration of hydrogen in the catalytic interface of the anode | $$molcm^{-3}$$ | $$System$$ |
$$R_{Proton}$$ | Resistance to proton flow | $$\Omega$$ | $$System$$ |
$$\xi_2$$ | Parametric coefficients for cell model | $$--$$ | $$System$$ |
$$\xi_1$$ | Parametric coefficients for cell model | $$--$$ | $$-0.948$$ |
$$\xi_3$$ | Parametric coefficients for cell model | $$--$$ | $$7.6\times10^{-5}$$ |
$$\xi_4$$ | Parametric coefficients for cell model | $$--$$ | $$-1.93\times10^{-4}$$ |
$$\mu_F$$ | The fuel utilization | $$--$$ | $$0.95$$ |
$$HHV$$ | Higher Heating Value Potential | $$V$$ | $$1.482$$ |
$$R$$ | Universal gas constant | $$J.kmol^{-1}.K^{-1}$$ | $$8314.47$$ |
$$F$$ | Faraday’s constant | $$C.kmol^{-1}$$ | $$96484600$$ |
1- J. Padulles, G.W. Ault, J.R. McDonald. 2000. "An integrated SOFC plant dynamic model for power systems simulation." Journal of Power Sources (Elsevier) 86 (1-2): 495-500. doi:10.1016/S0378-7753(99)00430-9
2- Hauer, K.-H. 2001. "Analysis tool for fuel cell vehicle hardware and software (controls) with an application to fuel economy comparisons of alternative system designs." Ph.D. dissertation, Transportation Technology and Policy, University of California Davis.
3- J. C. Amphlett, R. M. Baumert, R. F. Mann, B. A. Peppley, and P. R. Roberge. 1995. "Performance Modeling of the Ballard Mark IV Solid Polymer Electrolyte Fuel Cell." J. Electrochem. Soc. (The Electrochemical Society, Inc.) 142 (1): 9-15. doi: 10.1149/1.2043959.