Modeling of Water Transportation in Dynamic Load Proton Exchange Membrane (PEM) Fuel Cell Power Generator

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Modeling of Water Transportation in Dynamic Load Proton Exchange Membrane (PEM) Fuel Cell Power

Generator

AgungBak ht i ar * Choi ,Kwang-Hwan* * Ki m,Young-Bok * * *

*GraduateSchoolofRegenerationandAirConditioningEngineering,PukyongNationalUniversity,

**Dept.ofRegenerationandAirConditioningEngineering,PukyongNationalUniversity,

***DepartmentofMechanicalSystem Engineering,PukyongNationalUniversity([email protected])

동적부하 PEM 연료전지 발전기에 있어서의 수분전달 모델링

아궁 박티아르* ,최광환* * ,김영복* * *

*냉동공조공학과 대학원,부경대학교,**냉동공조공학과,공과대학,부경대학교,

***기계시스템공학과,공과대학,부경대학교([email protected])

Abst r act

PEM 연료전지에 있어서 수분의 균형이 연료전지의 시스템 성능에 현저한 영향을 미친다.그래서 수분 균형은 가장 중요한 요소 중의 일부가 되었으며,이에 관한 연구가 광범위하게 이루어지고 있다.적절한 수분 균형을 유지하기 위해 서는 적당한 멤브레인 수화작용(membranehydration)이 필요하며,반대로 촉매층(catalystlayer)에서의 익수(water flooding)현상이 없어져야 한다.따라서 이와 같은 동적 상태에서 PEM 연료전지 내의 수분 균형을 유지하기 위해서는, 고도의 동적 수분 조정 기술이 확보되어야 한다.현재의 연구는 이러한 특성을 고려하여 PEM 연료전지에서 동적부하 상태에서의 수분 이동에 관한 일차원 해석 모델에 관한 것이다.금번 모델링의 결과,양극촉매층(CCL,cathode catalystlayer)에서의 수분 상태는 거의 포화 단계에 이르고 있음을 보여주고 있으며,이 모델링은 연료전지가 작동되 는 동안의 CCL에 나타나는 수분의 양상을 예측하는데 활용될 수 있다.본 논문에서는 수분 이동 모델이 국제규격에 따라 다양한 수송기관이 가동될 때,동적부하 상태에서 서로 다른 차이점을 발견하기 위한 시뮬레이션 결과에 초점이 맞추어져 있다.이 모델링을 적용한 결과,수분 포화도가 상태에 따라 상이하게 나타남을 알 수 있었고,또한 정적 수분 조절 요소에 따라 최적 상태가 모든 동적 분포에 따라 달라짐을 알 수 있었다.

Keywords:Fuelcell,Model,Dynamic,Watertransport,DrivingCycle,Membrane

투고일자 :2011년 1월 5일,심사일자 :2011년 2월 25일,게재확정일자 :2011년 4월 13일 교신저자 :최광환([email protected])

[논문] 한국태양에너지학회 논문집 Journal of the Korean Solar Energy Society

Vol. 31, No. 2, 2011 IS S N 1 5 9 8 - 6 4 1 1

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Nomencl at ur e



:mol arr at e( mol . s

^-1

)

_

:e l e c t r oos mot i cdr agc oe f f i c i e nt

ρ

:de ns i t y( kg. c m

^-3

CRF :r

ol l i ngr e s i s t anc ec oe f f i c i e nt

 :c ur r e ntde ns i t y( A. m

^-2

)

 :c r os ss e c t i onar e a,( m

²

)

 :Far adayc ons t ant ( C. mol

^-1

)



:humi di t yr at i o( g/ kg)



:mas s( kg)



:s pe c i f i cvol ume( m

³

/ kg)

 :vol ume( m

³

)

 :f l ow r at e( m

³

/ s )

W

:powe r( Wat t )

Subscr i pt



:c api l l ar i t y



:e vapor at i on

rct

:r e ac t i on

sat

:s at ur at e d

liq

:l i qui d

vap

:vapor

ve

:ve hi c l e

1.I nt r oduct i on

Ge ne r al l y,f l oodi ng ofac at hodec at al ys t l aye r( CCL)i n Fue lc e l li sl i nke dt ohi gh

c ur r e ntde ns i t yope r at i on,whi c hr e s ul t si n t hei nc r e as eofwa t e rpr oduc t i onr at ehi ghe r t han t he r e movalr at e .Howe ve r ,f l oodi ng c an al s o oc c ur at l ow c ur r e nt de ns i t i e s unde rc e r t a i n o pe r a t i ng c o ndi t i o ns ,s uc h a s l o w t e mpe r a t ur e sa ndl o w ga sf l ow r a t e si n whi c hf a s t e rs a t ur a t i onoft hega spha s eby wa t e rva po r[ 1 ]c a noc c ur .The r e f or e ,wa t e r ma na ge me nti sac r i t i c a lde s i gnc o ns i de r a t i o n f orPEM f ue lc e l ls ys t e ms .Theamountand di s pos i t i on ofwat e r wi t hi n t he f ue lc e l l s t r ongl yaf f e c te f f i c i e nc yandr e l i abi l i t y[ 2 ] . Thepur pos eoft hi spape ri st opr opos e t hewat e rt r ans por t at i on mode lt oge tt he advanc e dwat e rmanage me nti n PEM f ue l c e l l .Thi ss t udy al s o s i mul at e st hemode l us i ng dynami cl oadf r om s e ve r als t andar d dr i vi ngc yc l e st ot e s tt hepe r f or manc e s .

2.Model

Wat e rbal anc ei n c at hodec at al ys tl aye r ( CCL)i s bas e d on t he di f f e r e ntamount be t we e n t he r at e ofwat e r addi t i on and r e movalass howni nFi g 1.

Fig1.WaterbalanceinCCL.

The wat e r addi t i on i n CCL c an be

s i mpl i f ye xpr e s s e dast het ot aloft hewat e r

pr oduc t i on f r om oxyge nr e duc t i on r e ac t i on

( ORR)ande l e c t r oos mot i ct r ans por t at i onas

f or mul at e di nEq.1[ 3] .

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_{ } _ 



  ( 1 )

Thei nputai ral s oc ont ai nswat e rt hati s c ar r i e d f r om t he humi di t y.The r e f or e ,t he wat e raddi t i onf r om humi dai ri sgi ve nby Eq.2[ 4] .

_{ } 



_





( 2)

The wat e rr e movalc an be oc c ur r e d i n t wophas e s ,l i qui d a nd va pora ss hown i n Fi g.2 .Themol arf l ow r at eofs a t ur a t e dai r i sgi ve nbyEq.3 .Ot he r wi s er e move dwa t e r t r ough vapor pha s e i s l i mi t e d by t he s a t ur a t i on pr e s s ur e of a i r s t r e am. The a va i l a bl emo l a rf l ow r a t eofa i rs t r e a m

_{}

i sde t e r mi ne dbyEq.4.

_{ }  _



_

_



( 3)

Fig2.Wateroutputphase

Asl o nga st hewa t e ri nputi sno ts at ur a t e d,

t he r e movalofwat e r i n vapor phas e i s de t e r mi ne dbyEq.5.Butt hemagni t udeof

_{ }

i sl i mi t e dbyt he

_{}

t he r e f or et he e xc e s swat e rwi l lt ur ni nt ol i qui d.

_{ } _ _{ }

( 4 )

_{ } _{ } _{ }

( 5 )

Thewat e rl i qui d s at ur at i on l e ve l(

s

)i s de f i ne dast hevol umef r ac t i onoft het ot al voi ds pac eofpor ousme di aoc c upi e dbyt he l i qui dphas e .He nc e ,si sde f i ne di nEq.6 .

  



_



_

( 6)

Af t e r r e c e i vi ng amountofwat e r f r om f ue lc e l lr e ac t i onandme mbr anes i de ,l i qui d s at ur at i onl e ve li nCCLnow i sc hange dby Eq.7andEq.8.I ft he r ei snol i qui dwat e r addi t i on,t hec hangeofsi sz e r o.

∆_{   }  





_{ }



_

( 7 )

_ _ ∆_{   }

( 8 )

Pas aogul l ar ie tal .[ 5]haves t udi e dabout s t e adys t at ewat e rt r ans por t at i oni nGDLof PEM f ue lc e l l .I nt he i rwor k,i ti ss e e nt hat c api l l ar yt r ans por ti st hedomi nantt r ans por t pr oc e s s t o r e move wat e r f r om f l oode d GDLs .

Mol arf l ow r at eoft hewat e rt r ans por t e d

by c api l l ar i t y pr oc e s s i s gi ve n by Eq.9 .

Thel i qui ds at ur at i onc hangebyc api l l ar i t y

pr oc e s si sgi ve nbyEq.1 0.

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_ ^    ^ ×





_ _{  }



 cos_^

( 9)

∆_{ }  





_



_

( 10)

_ _ ∆_{   } ∆_{  }

( 1 1)

Thewat e re vapor at i onr at eofs ys t e m i s de f i ne dbyEq.12andt hel i qui ds at ur at i on c hangebye vapor at i onpr oc e s si sgi ve nby Eq1 3.

_{ }





_

   



^

 ^





_



( 12)

∆_{  }  





_



_

( 1 3)

Thef i nall i qui ds at ur at i onbe c ome s

_ _ ∆_{  } ∆_{  } ∆_{  }

( 14)

The ve hi c l e powe rmode lus e d on t hi s s i mul at i oni sgi ve nbyEq.15unt i lEq.18.



_{ }

, 

  

, 

_{}

, and 

_{}

r e s pe c t i ve l y ar e t he powe r abs or be d by r ol l i ng r e s i s t anc e , ai r r e s i s t anc e , ki ne t i c powe r us e dandt ot alpowe rabs or be d.



_{ } __

 ( 1 5)



    __^ _{ }



_

( 1 6)



_{} ___

( 1 7)

R 8.314

A 0.02m²

_ 1.10^-5m

_{  } 3.10^-4m

N 448



_ _18._0153.₁₀^-3_kg/_mol

ρ 971.8Kg/m³

_ 0.5

κ 1.810^-18m² μ 8.5510^-4N.s/m²

ε 0.6

σ 0.0625N/m

_ 120

h 105.28W/m²K λ 2417.44kJ/kg Table1.Simulationparameters

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Fig3.Speedprofileforalldrivingcycles

4.Resul t sanddi scussi ons

Dur i ng t he ac c e l e r at i on,t he f or c e was t ur ne doutt obepos i t i ve .Si nc et hes pe e di s a l wa yspo s i t i ve ,t hepo we rde ma ndi spo s i t i ve a swe l la ndt hi spo we rde ma nds ho ul dbeme t byt hepo we rge ne r a t i o ns ys t e m.Ont heo t he r ha nd,dur i ng t hede c e l e r a t i o n,t hef o r c ea nd t hepo we rr e que s t e dwe r ene gat i ve .

Fig4.PowerprofilesforJP 10-15Mode

Be c aus et hi swashandl e dbyt hebr aki ng s ys t e m andt he nt hepowe rr e que s t e df r om t h ep o we rge n e r a t i o ns ub s ys t e m wa sa l mo s tz e r o a ss ho wni nFi g4 .Al s o ,t hec ur r e ntde ns i t i e s o fa l ldr i vi ngc yc l e swe r es ho wni nFi g5 .

Fig5.Currentdensityprofilesofalldrivingcycles

The s i mul at i on has s t ar t e d wi t h l ow t e mpe r at ur eandhumi di t yr at i ooft hei nput ai r .Thet e mpe r at ur eunde rt hi sc ondi t i oni s 4 0 ° Ca ndt her e l at i vehumi di t yi s5 0 %.Wi t h t hi s c ondi t i on, t he humi di t y r at i o af t e r be i ngt r ans f e r r e di se qualt o23. 5g/ kg' .At l ow t e mpe r at ur e t he c apabi l i t y oft he ai r s t r e am t o hol d wat e r i s r e l at i ve l y l ow.

He nc e ,t heove r -s at ur at e ds t r e am t e ndst o oc c uraf t e rr e c e i vi ng wat e rf r om t hef ue l c e l lr e a c t i o na ss ho wni nFi g.6 .Asl o nga st he a mo unto fwa t e rr e c e i ve dbyCCLi sno tl a r ge r t ha ni t sma xi mum c a p a bi l i t yt oho l dwa t e r ,t he o ve r -s a t ur a t e ds t r e a m wi l lno to c c ur .

Fl oodi ng phe nome na i s oc c ur r e d i n

al mos t al l pr of i l e s at l ow t e mpe r at ur e ,

ot he r wi s e EUDC has t he hi ghe s t powe r

l oadt hanot he rc yc l e s .The r e f or e ,t hewat e r

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addi t i on i shi ghe rt han i t sr e moval ,whi c h c aus e s EUDC t o have t he hi ghe s tl i qui d s at ur at i onl e ve lpr of i l e .

Fig6.Currentdensityprofileswhenflooding

I nc r e as i ng t he t e mpe r at ur e of t he ai r i nputf r om 40° C t o60° C wi l lde c r e as et he r e l at i vehumi di t y f r om 5 0% t o18. 5% wi t h s ame humi di t y r at i o 23 . 5 g/ kg.I n t hi s c ondi t i on,t hec apabi l i t yoft heai rs t r e am t o hol dmor ewat e ri shi ghe rt ha nt hepr e vi ous c ondi t i on.Thi sc ondi t i on, howe ve r ,make s t hel ow l oad pr of i l ege tdr i e d.Unde rt hi s c ondi t i on,t hec apabi l i t yoft heai rs t r e am t o c ar r youtwat e ri shi ghe rt hanbe f or e ,but t he e vapor at i on r at e i s al s o hi gh.As a r e s ul t ,t hedr yi ngphe nome nonhasha ppe ne d l i keass howni nFi g.7.

Cons e que nt l y, i nc r e as i ng t he humi di t y r at i obe c ome st hec ommonme t hodt oavoi d t hedr yi ngphe nome no n.Thene xts i mul a t i o n c ondi t i on was done by i nc r e as i ng t he humi di t yr at i ooft hei nputai rass howni n Fi g. 8. Thi s f i gur e s hows t he l i qui d s at ur at i onl e ve lwhe nf ue lc e l lwasope r a t e d at6 0° Cofai rwi t h67. 9g/ kghumi di t yr at i o ( 5 0% RH) .I nt hi sc ondi t i on,f l oodi ngi nl ow l oadpr of i l e ss uc hasNYCC andJ P 10-15

c an beavoi de d and ove rf l oodi ng i n hi gh l oadpr of i l e s( EUDC)c anal s ober e duc e d.

Fig7.Currentdensityprofileswhendrying

Fig8.Currentdensityprofileswhenbalancedand flooding

Concl usi ons

Thi s s t udy has made t he wat e r

t r ans por t at i on mode loft hePEM f ue lc e l l

and al s o t he s i mul at i on us i ng dr i vi ng

c yc l e s .Duet ot heobt ai ne dwa t e rbal anc e ,a

f ue lc e l lwi t hdi f f e r e ntdynami cl oadpr of i l e

a l s or e qui r e sdi f f e r e ntc o ndi t i o no ft e mp e r a t ur e

andhumi di t yofai ri nput .Thi sme anst he

pr ope r c ondi t i on f or wat e r manage me nt

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par ame t e r s wi l l be di f f e r e nt i n e ve r y dynami c pr of i l e s .The r e f or e ,t he dynami c wat e r manage me nt s ys t e m i s ne c e s s ar y.

Ther e s ul t sar et hef ol l owi ng;

( 1 )Asl ongast hea mountofwa t e rr e c e i ve d byCCLi snotl ar ge rt hani t smaxi mum c apabi l i t y, t he ove r -s at ur at e d s t r e am wi l lnotoc c ur .

( 2 )A dyna mi cpo we rpr o f i l ewhi c hha smuc h ac c e l e r at i onsne e dsmor epowe r .I nt hi s c as e ,t hewat e rpr oduc t i oni si nc r e as e d t he r e f or et hewat e rr e movalr at es houl d bei nc r e as e d t oavoi d f l oodi ng.I n t hi s pape r ,t hewat e rbal anc ei sobt ai ne di n i nput a i r c ondi t i on 6 0 ° C t e mpe r a t ur e wi t h6 7 . 9g/ kghumi di t yr at i o( 5 0 % RH) .