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1 Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007, pp so j i ns l l 3yk ÇValeri A. DanilovÇmp *Ç m l ne e 134 *GS d te re o v ( o 15p r, o 9p }ˆ) Development of 3D DMFC Model for Flow Field Design Hongseong Kim, Valeri A. Danilov, Jongkoo Lim* and Il Moon Department of Chemical Engineering, Yonsei University, 134, Sinchon-dong, Seodaemun-gu, Seoul , Korea *GS Caltex Corporation, 104-4, Munji-dong, Yusung-gu, Daejeon , Korea (Received 15 November 2006; accepted 9 January 2007) k l l vr ˆm l rvp r pl p p ˆ m p srp o ~ p p 3 o p m. yl ~p srp vr ˆm l rv tn rp, l rvp l ƒ m p t. o ~p sr kt r p p k o e l rp qpp } p l p p p p l p np n. p r o r o~l p p m. r o~l p p l two-fluid p pn l o~p Ž p e l p f e p tp pl, rp 4 v l rv o p serpentine, zigzag, parallel, semi-serpentine ˆl p rn l, k, ˆm p, ~ p p m. pn l ˆp q rp Žk m, p ˆp d prp r p r o m. h Abstract The objective of this study is to develop a 3D DMFC model for modeling gas evolution and flow patterns to design optimal flow field for gas management. The gas management on the anode side is an important issue in DMFC design and it greatly influences the performance of the fuel cell. The flow field is tightly related to gas management and distribution. Since experiment for the optimal design of various flow fields is difficult and expensive due to high bipolar plate cost, computational fluid dynamics (CFD) is implemented to solve the problem. A two-fluid model was developed for CFD based flow field design. The CFD analysis is used to visualize and to analyze the flow pattern and to reduce the number of experiments. Case studies of typical flow field designs such as serpentine, zigzag, parallel and semi-serpentine type illustrate applications of the model. This study presents simulation results of velocity, pressure, methanol mole fraction and gas content distribution. The suggested model is verified to be useful for the optimal flow field design. Key words: Direct Methanol Fuel Cell, Flow Field, 3D Model, CFD p n pp n p. l v k pr v p l n l l p rp l v rp p r p n pp, p l e l v p r n kv p. l svp vl tep r l p To whom correspondence should be addressed. ilmoon@yonsei.ac.kr l v p l vo p 21 p pe p. p pep ˆp v p l p e vop k v k kp l rv kp p q, n p rl p v k op m p ˆ l p me p e rm o qop p rp r n p p l rv edš p n re n l. l rv p, p p v l r n, r q p op p en l rl p. 93

2 94 ËValeri A. DanilovËps Ë p pl q n p l rv tp kv l pp, l rv r edšp p o p n erp. q l rv l ƒ PDA n r op n o l p lv pp, tl q m k p m k l p lv vr ˆm l rv q r p l p. vr ˆm l rv p p r, r v, vr~ rv n q p rvp m, p p o, k p nr s, l p } l v npl p rp m p. l l rv nr l e r r, rk p d(ac impedence) rk r (voltametry) p r r r l. l rvl l l rvp p o l rvp n l l t mp, l rv p r p n l rp nr s p l rv l, r p p n p r l. er e p l rvp r nr s p r o p e np k l rv p v p r r p p l p r kp. vr ˆm l rv ˆmp l n l rvp y p p p o l p ˆ ~ l l p o p. l p p o v rvp p r p p p o l rv l n tn l p p. n ol pn l k ˆp o r l p n e p rk, l r vp n p rvp m, l p o, k p nr s, l, p ˆ p l r p f rp o m. 2. m n 2-1. so j i nsm k (anode)p o ˆm nkp p qnl p pm, rq ˆ d p p pl. pmp ~ q r v (solid polymer electrolyte membrane)p rq n r. o (cathode)l le qnp p pm l r v p m pm n l p p km rqm p l p. pmp pmp o pp r v l p m pmp p pl. p p vr ˆm l rvp q o n l rp r. Fig. 1p vr ˆm l rvp q o ˆ p [1, 2]. vr ˆm l rvl p rv pp p p r p. : CH 3 H+ H 2 C 2 + 6H + + 6e o : H + + 6e 3H 2 r~ p: CH 3 H C 2 + 2H 2 o45 o k Fig. 1. Reaction Schematic and principle of the direct methanol fuel cell. Table 1. Geometry of the flow fields Parameter Value [m] Plate Width 0.05 Plate Height 0.05 Channel Width Channel Depth Rib Width l vr ˆm l rvp p o m backing layermp r l p m p. o p kl r p l l m orp p p p, o p kl o p vr k p, p p p p backing layer ˆ l r l p p p k p. ˆmp l n l rvp y p p p o l p ˆ ~ l l p o p. l p p o v rvp p r, k l p p r ep. p ˆ p p p r p p p p o l rv l n tn. Table 1p l l n o p s p ˆ p s o l l n CFD p rp Navier-Stokes e p, o ~r p p n ol p n m. o ~r p p qp p q l qp p o flux m p p q l o p s re p lv, r~ o mll o p v r ep rp ~r r p. 3 o pl o~r o p q(mesh) r

3 vr ˆm l rv o o 3 o 95 Table 2. Governing equations for anode channel Governing equations Continuity equation a Momentum equation a Stress tensor a Continuity equation for gas phase a Species conservation b Taken from Sokolichin and Eigenberger [1997] Taken from Wang and Wang [2003] a b Mathematical expression ( ρu) 0 ( ρuu) p + T + ρg u i u T ij µ eff j 2 u + n --δ x j x ij i 3 x n ( ε G ρ G u G ) Γ G ( ρuc k k ) ( 1 ε G )ρ L D Leff, C k k k ( L +ε G ρ G D Geff, C G ) (1) (2) (3) (4) (5) p q, p l s s p r l. p n ol p DMFC p r v -r v ~p q r r pp l l np pl, UDF(user defined functions) pn l v rep soruce termp pn n subroutinep l p m. Table 2 tow-fluid l n v rep r p, l p rp p [2]. 1) p p 2 (tow phase)p. 2) p pp (homogeneous), k (incompressible)p. 3) m r(isothermal)p, r ˆ(steady state)p. 4) ˆm dm (methanol crossover) e. v rep two-fluid l n m p p el p. Density ρ ερ G + ( 1 ε)ρ L (6) Concentration ρc C G ερ G + C L ( 1 ε)ρ L (7) Velocity ρu u G ρ G + u L ρ L (8) Diffusion D eff D G ε + D L ( 1 ε) (9) Viscosity µ eff µ G ε + µ L ( 1 ε) (10) 3-2. o s p mll n, o p l p o p k m v pl p. ˆm pp l r pp, p v r p l pl, r pp o l pl. CH 3 H+ H 2 C 2 + 6H + + 6e 2 + 4H + 2H 2 4e l r pp pl v k o~p r p sq. pp s p p ep. N MeH M MeH1 DL 6 -- I F -- p l p ˆ p p N C 2 DL M C I 6F -- p. p (11) (12) N H 2 M DL ep. H 2 1 H 6α 2 ( + ) I F -- (13) 3-3. Source term o~p o l q p rp n ep Navier-Stokes Equationp l rvp n o l pl r pl p r p k. l r pl p vp source terml l ˆ l [2]. Γ G N tg, C Gs, + ρ G β G C G h (14) l, N t,g k l p v r v β G v r C G v r l r pl p p ˆ. p k p r. p l rv p o l mr p r mp, p, v pp k e (15)p [3]. M ( K i 1)C mix i M i 0 i 1 ( K i 1)γ+ 1 (15) l, y K i -k pp i, K i --- x γ v i p, γ V ( V+ L) v pp o l dp v o p. o l dp p r pp p ˆ p. ˆm p p k p p pl, ˆm p p p. (4) el p v r source termp Γ G δg M G δv (16) p, l, δv o p, v pp k m p rp m. Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

4 96 ËValeri A. DanilovËps Ë p δg γ C L 2 M C 2 + ( )δs N anode l, δg k l p p o L o p δvl k p o δs r, δs δv h ep n l source Γ G p rk m. C 2 Γ G M G γ ψ N anode M C 2h (17) (18) l, M G p ψ, ψ L δv o e (18)p p k pl v r ˆ. o l p v v o. ( G in G out ) Γ G V anode l, G in p l o, G in 0 G out l o V anode o p l p o p G out u G, outρ G ε out G S out (19) (20) 3-4. n m r r p, ohmic e, l p l p v r l p p p ep. ( K ) ϕ s j s σε b Fc ( ϕ l + Fc f v) j s f ij ρ nf i ai 0, ref C i C ref, i γ exp α a F ( ϕ s ϕ l ) RF exp α c F ( ϕ s ϕ l ) RF ( D i ε b C i C i v) s ij nf (24) (25) (26) (27) l, ϕ Š, jm j s l o pr m k r p k, a r rp r pq, i 0,ref C ref, im r, α c m α A o p r r, σm K ~ l o r, D i o p. r l d pp r l p Henry sp l m p. p r MeH a i 0 MeH a i 0, ref MeH C L MeH C L, threshold γ α o e (28)p, l, MeH MeH a i 0 ref C m r, L MeH - l ˆm C Ls, (28) p. l, S out p r u G,out S outl p p ε out S out l p -k l p k p l p kp p e (21)p. MeH α I i a F exp η A RF o l r 2 ai 0 2 ai0, ref C Gs, γ c C G, ref (29) (30) ε G out d sep p. l, γ - v γ in, γ out - o p p m l v, γ in 0 o p l v γ out p. o e (22)l d p [4-6]. γ out ρ mol, L γ out ρ mol, L + ( 1 γ out )ρ mol, G C 2 Γ G M G γ ψ N anode M C 2h C 2 N anode ψ G in G out V anode M G γ M C 2h o45 o k (21) (22) (23) o e (30)p, l, 2 2 ai 0 ref - m r, CG, ref - l 2 C Gs, 2 α I i a F 0, ref exp η C RF (31) orp voltage p e (32)p rp [Danilov et al., 2005]. 2 MeH V cell U U0 0 + η A η C I avg σ H 4. y (32) 4-1. l rvl o p r p l m p l p p l p p tn p. l

Table 3. perating conditions Parameter Value perating temperature 80 C perating pressure 1 atm Inlet velocity of anode channel 0.

Physicochemical properties Parameter Value Proton conductivity of membrane 0.123 S/cm Thermodynamic potential of oxygen reduction 1.

239 Reference exchange current density of anode 94.25 A/m 2 Reference exchange current density of cathode 0.04222 A/m 2 Faraday constant 96,487 C Universal constant 8.

Velocity distribution in anode channels for DMFC with serpentine. Fig. 3. Velocity distribution in anode channels for DMFC with zigzag m o p l p l rv p p. o ˆl p l s p ˆ o ˆ k.

5 Table 3. perating conditions Parameter Value perating temperature 80 C perating pressure 1 atm Inlet velocity of anode channel m/s Inlet methanol concentration at anode 1 M Inlet cross sectional area m 2 PEM thickness m vr ˆm l rv o o 3 o 97 Table 4. Physicochemical properties Parameter Value Proton conductivity of membrane S/cm Thermodynamic potential of oxygen reduction 1.24 V Thermodynamic potential of methanol reduction 0.03 V Cathodic transfer coefficient of cathode Anodic transfer coefficient of anode Reference exchange current density of anode A/m 2 Reference exchange current density of cathode A/m 2 Faraday constant 96,487 C Universal constant J/mol K Fig. 4. Velocity distribution in anode channels for DMFC with parallel Fig. 5. Velocity distribution in anode channels for DMFC with semiserpentine Fig. 2. Velocity distribution in anode channels for DMFC with serpentine. Fig. 3. Velocity distribution in anode channels for DMFC with zigzag m o p l p l rv p p. o ˆl p l s p ˆ o ˆ k. Table 3, Table 4 l rvp nr s p ˆ p. Fig. 2, Fig. 3p p p, o pp p. Fig. 4, Fig. 5 o pp p v, p p l zigzagm serpentinep parallel semi-serpentine l sp o p h DMFC edšl o v p ˆ p m p o t l k l p p r eˆ k l rvp l ƒ m p npp. k l p n p r p f DMFC ed Š l pl tn qn. l rvp nr k p v e p d k l nr p. p e l p dp k p Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

Pressure distribution in anode channels for DMFC with parallel Fig. 7.

Pressure distribution in anode channels for DMFC with semiserpentine v o pp

erp rl l rvp r~ edšp p o o p k p l tn. l rv d p rq e o p d l k o l rr o n.

v k l parallel semiserpentinep zigzagm serpentine rpp k p. 4-3.

6 98 ËValeri A. DanilovËps Ë p Fig. 6. Pressure distribution in anode channels for DMFC with serpentine Fig. 8. Pressure distribution in anode channels for DMFC with parallel Fig. 7. Pressure distribution in anode channels for DMFC with zigzag Fig. 9. Pressure distribution in anode channels for DMFC with semiserpentine v o pp r v, p p CV(open circuit voltage)p v rm. k n rp o l n l v n pp plv. erp rl l rvp r~ edšp p o o p k p l tn. l rv d p rq e o p d l k o l rr o n. o l p p Fig. 8, Fig. 9p k Fig. 6, Fig. 7p P q. v k l parallel semiserpentinep zigzagm serpentine rpp k p j DMFCp o r l ˆmp lt, p p p v r l l r p p pl. o l ˆmp p ov l v r p d t, p p v l rvp o45 o k Fig. 10. Methanol mole fraction distribution in anode channels for DMFC with serpentine

vr ˆm l rv o o 3 o 99 p eˆ. Serpentine zigzag ˆm ˆ o p p, ˆm o rp p Fig. 10, Fig.

Semi-serpentinep o rp ˆm, r p ˆm ˆ. serpentine parallelp ˆp Fig.

$Methanol mole fraction distribution in anode channels for DMFC with zigzag 4-4.$ $Methanol mole fraction distribution in anode channels for DMFC with parallel Fig.$ $Methanol mole fraction distribution in anode channels for DMFC with$

7 vr ˆm l rv o o 3 o 99 p eˆ. Serpentine zigzag ˆm ˆ o p p, ˆm o rp p Fig. 10, Fig. 11 l k p. Fig. 12 o t l ˆm r p k p. p ˆmp r pp l p ˆ p p p p pp, Fig. 17p e. Semi-serpentinep o rp ˆm, r p ˆm ˆ. serpentine parallelp ˆp Fig. 13psemi-serpentine ˆ q sp o p. Fig. 11. Methanol mole fraction distribution in anode channels for DMFC with zigzag 4-4. DMFCp o l p p ml p p ˆ p p p p. p d o p l p p, k eˆp f l rv r ~p p r eˆ. l rvp o l Fig. 12. Methanol mole fraction distribution in anode channels for DMFC with parallel Fig. 14. Gas content distribution in anode channels for DMFC with serpentine Fig. 13. Methanol mole fraction distribution in anode channels for DMFC with semi-serpentine Fig. 15. Gas content distribution in anode channels for DMFC with zigzag Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

100 ËValeri A. DanilovËps Ë p Fig. 16. Gas content distribution in anode channels for DMFC with parallel Fig. 18.

Liquid distribution in experiment with parallel p ˆ p m p p o n. Fig. 18p semi-serpentine Fig. 15p zigzag dp o p ˆ o p ltv p n.

15l k pp, l p m dp o p rp v p p. Fig. 16p parallel o ˆ 25 w o l m p p l p v k p p, p p ˆ p p o p p p. Semi-serpentinep r p d p, parallel p d o p.

Characteristics of the different flow fields Flow fields Serpentine Zigzag Parallel Semi-serpentine Average pressure (Pa) 197.2543 44.72826 51.

8 100 ËValeri A. DanilovËps Ë p Fig. 16. Gas content distribution in anode channels for DMFC with parallel Fig. 18. Gas content distribution in anode channels for DMFC with semiserpentine Fig. 19. Comparison of the different flow fields. Fig. 17. Liquid distribution in experiment with parallel p ˆ p m p p o n. Fig. 18p semi-serpentine Fig. 15p zigzag dp o p ˆ o p ltv p n. Serpentinep o ˆl d o p p, o ˆ 0.7p. Serpentinep p k p ˆ p m d o p Fig. 14l lt. Zigzag Serpentinem o o ˆ dp Fig. 15l k pp, l p m dp o p rp v p p. Fig. 16p parallel o ˆ 25 w o l m p p l p v k p p, p p ˆ p p o p p p. Semi-serpentinep r p d p, parallel p d o p. Table 5 p o ˆl r r rp ˆ lp, Fig. 19l o ˆl k,, d o, ˆm m. 5. l serpentine, zigzag, parallel, semi-serpentinep 4 v ˆp o qpp r, CFD ˆp two-fluid Table 5. Characteristics of the different flow fields Flow fields Serpentine Zigzag Parallel Semi-serpentine Average pressure (Pa) Average velocity (m/s) Average gas content (-) Average MeH mole fraction (mol/mol) Total volume (m 3 ) o45 o k

9 p l p ˆ p m p r o m. two-fluid p rn l p o ˆl d o p l l rvl m p m mp, k,, ˆm p l o ˆl p m. l l rn semi-serpentine o ˆ q n pp, p ˆ p m p p o ˆ k q qp, p dp p. ˆ m p mp, p p pp p k p. Two-fluid p r p ˆ p m p p p mlp e m p mp, p p p m l n ˆp o p np p. C : mass fraction [kg kg 1 ] k D eff : effective diffusion coefficient [m 2 s 1 ] F : Faraday constant [C mol 1 ] G : gas flow rate [kg s 1 ] g : acceleration [m s 2 ] k : permeability of porous material [m 2 ] K : distribution of the components [ ] L : molar flow rate [mol s 1 ] H : membrane thickness [m] I : current [A m 2 ] h : channel height [m] M : molecular weight [kg mol 1 ] N : mass flux [kg m 2 s 1 ] P : pressure [Pa] R : gas constant [J mol 1 K 1 ] S : area [m 2 ] T : temperature [K] u : velocity vector [m s 1 ] U 2 0 : thermodynamic potential of oxygen reduction [V] U MeH 0 : thermodynamic potential of methanol oxidation [V] V anode : volume of anode channels [m 3 ] V cell : cell voltage [V] x : molar fraction in liquid phase [mol mol 1 ]; coordinate [m] y : molar fraction in gas phase [mol mol 1 ]; coordinate [m] z : coordinate [m] m m α : transfer coefficient ε G : gas content [m 3 m 3 ] γ γ c : local fractional vaporization; kinetic factor [ ] : advection correction factor [ ] ρ : density [kg m 3 ] Γ G : source of mass in gas phase [kg m 3 s 1 ] vr ˆm l rv o o 3 o 101 σ : ionic conductivity of membrane [m Ω 1 ] ψ : coefficient [mol m 3 ] µ : viscosity [Pa s] η λ : overpotential [V] : feeding ratio of air and methanol [ ] lzm k : component (MeH, C 2, H 2, 2 ) g zm i : component in : inlet out : outlet L : liquid G : gas A : anode C : cathode eff : effective mix : mixture DL : diffusion layer ref : reference t : total s : interface; solid y 1. Sokolichin, A., Eigenberger, G., Lapin A. and Lübbert, A. Dynamic Numerical Simulation of Gas-liquid Two-phase Flows, Chem. Eng. Sci., 52, (1997). 2. Wang, Z. H. and Wang, C. Y. Mathematical Modeling of Liquid-feed Direct Methanol Fuel Cells, J. Elec. Soc., 150(4), A508-A519(2003). 3. Sundmacher, K. and Scott, K., DIrect Methanol Polymer Electrolyte Fuel Cell: Analysis of Charge and Mass Transfer in the Vapor-liquid-solid System, Chem. Eng. Sci., 54, (1999). 4. Danilov, V. A., Lim, J., Moon, I. and Choi, K. H. A CFD-based Two-fluid Model for a DMFC, AIChE Annual Meeting, ctober 30 November 4, Cincinnati, hio(2005). 5. Danilov, V. A., Lim, J. and Moon, I., Three-Dimensional Two- Phase CFD Model for DMFC Design, J. Power Sources, 162(2), (2006). 6. Danilov, V. A. and Moon, I., Gas Management in Flow Field Design Using 3D DMFC Model under High Stoichiometric Feed, Kor. J. Chem. Eng., 23(5), (2006). 7. Arico, A. S., Creti, P., Baglio, V., Modica E. and Antonucci, V., Influence of Flow Field Design on the Performance of a Direct Methanol Fuel Cell, J. Power Sources, 91, 202(2000). 8. Argyropoulos, P., Scott, K. and Taama, W. M., Carbon Dioxide Evolution Patterns in Direct Methanol Fuel Cells, Elec. Acta., 44, 3575(1999). 9. Argyropoulos P., Scott, K. and Taama, W. M., Modeling Pressure Distribution and Anode/Cathode Streams Vapor liquid Equilibrium Composition in Liquid Feed Direct Methanol Fuel Cells, Chem. Eng. J., 78, 29-41(2000). Korean Chem. Eng. Res., Vol. 45, No. 1, February, 2007

10 102 ËValeri A. DanilovËps Ë p 10. Bewer, T., Beckmann, T., Dohle, H., Mergel, J. and Stolten, D. Novel Method for Investigation of Two-phase Flow in Liquid Feed Direct Methanol Fuel Cells Using an Aqueous H 2 2 Solution, J. Power Sources, 125, 1(2004). 11. Baxter, S. F., Battaglia, V. S. and White, R. E., Methanol Fuel Cell Model: Anode, J. Elec. Soc., 146, 437 (1999). 12. Geiger, A., Lehmann, E., Vontobel, P. and Scherer, G. G., Direct Methanol Fuel Cell in situ Investigation of Carbon Dioxide Patterns in Anode Flow Fields by Neutron Radiography, Scientific Report 2000, Volume V, p.86-87, ed. by: C. Daum and J. Leuenberger, Switzerland, Kulikovsky, A. A. Model of the Flow with Bubbles in the Anode Channel and Performance of a Direct Methanol Fuel Cellc, Elec. Com., 7, 237(2005). 14. Lim, J., Danilov, V. A., Cho, Y., Choi, K., Chang, H. and Moon, I., Flow Field Design for Gas Management in a Direct Methanol Fuel Cell with a Bipolar Plate, in: Proceeding of PSE ASIA(2005). 15. Danilov, V.A. and Il Moon, A nonisothermal two-phase model for a DMFC, 17 th International Congress of Chemical and Process Engineering, CHISA 2006, Praha, Czech Republic, Aug., (2006). 16. Ilyong Jeong and Il Moon, The Evaluation of the Feeding Effect on Liquid-Feed Dmfc Using Rigorous Dynamic Simulation, 2006 AIChE Annual meeting, San Francisco, Calrifonia, USA, Nov., 12-17(2006). 17. Sundmacher, K., Schultz, T., Zhou, S., Scott, K., Ginkel, M. and Gilles, E. D., Dynamics of the Direct Methanol Fuel Cell (DMFC): Experiments and Model-based Analysis, Chem. Eng. Sci., 56, 333(2001). 18. Triplett, K. A., Ghiaasiaan, S. M., Abdel-Khalik, S. I., LeMouel, A. and McCord, B. N., Gas-liquid Two-phase Flow in Microchannels Part II: Void Fraction and Pressure Drop, Int. J. Mult. Flow., 25, 395(1999). 19. Yang, H. and Zhao, T. S., Effect of Anode Flow Field Design on the Performance of Liquid Feed Direct Methanol Fuel Cells, Elec. Acta., 50, (2005). 20. Yang, H., Zhao, T. S. and Ye, Q., Pressure Drop Behavior in the Anode Flow Field of Liquid Feed Direct Methanol Fuel Cells, J. Power Sources, 142, (2005). 21. Yang, H., Zhao, T. S. and Cheng, P., Gas-Liquid Two-phase Flow Patterns in a Miniature Square Channel with a Gas Permeable Sidewall, Int. J. Heat and Mass Transfer, 47, 5725(2004). 21. Wang, Z. H., Wang, C. Y. and Chen, K. S., Two-phase Flow and Transport in the Air Cathode of Proton Exchange Membrane Fuel Cells, J. Power Sources, 94, 40-50(2001). o45 o k

44(3)-16.fm

44(3)-16.fm Korean Chem. Eng. Res., Vol. 44, No. 3, June, 2006, pp. 270-276 지능형헬스케어욕조시스템개발을위한온수온도변화 r ~r l o l l e l 561-756 r rte v v 1 664-14 (2006 3o 9p r, 2006 6o 20p }ˆ) Change of the Warm Water emperature for