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준형 하
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1 연료전지및고체수소저장용기전산모사 유하늘 인하대학교기계공학과 에코스마트파워연구실 (eco-smart Power Lab.)

2 발표순서 연료전지 ㅅ 1 연료전지소개 연료전지모델 3 연료전지해석결과 수소 저장용기 ㅅ 1 금속수소화물소개 수소흡 탈장모델 3 수소흡 탈장모델해석결과

3 Introduction of Eco Smart Power Lab. (ESPL) High performance computing cluster Large scale PEFC simulation High-Temperature PEMFC model Master PC.66GHz x 4core cpu x. Sub node.66ghz x 4core cpu, Current density, water contents distribution IV curve validation GDL deformation Fuel cell model development & structural analysis FSI(fluid-structure interaction) approach HCM DMFC simulation Performance curve and methanol crossover validation, Johan Ko et al., JPS 011 3D DMFC simulation result 3

4 Polymer Electrolyte Fuel Cell 고분자전해질연료전지 (PEFC) 관련모델 -phase, steady state, non-isothermal model (Large scale simulation > 13.5M cells) PEFC cold start(cs-pefc) model (with HMC) Single phase transient model Anode Cathode 1 Hydrogen oxidation reaction (HOR) H H e Oxygen reduction reaction (ORR) O H e H O Reference: Ju H. Investigation of the effects of the anisotropy of gas-diffusion layers on heat and water transport in polymer electrolyte fuel cells. J Power Sources 009;191:59-68 외 SCI급 11편 4

5 Fuel cell modeling : 3-D, two phase PEFC 질량보존식 운동량보존식 화학종보존식 ( u) Sm Flow channels (Navier-Stokes equation) Porous media (Darcy s equations) Flow channels and porous media Water transport in the membrane mem mem Sm Si M w. Dw EW i uu K u p p ( m u) D m m m j S g g, eff g g l l i i i i i i i mem mem mem I K l Dw M w nd M w P 0 l EW F For water in the CLs: For other species in the CLs Si M i. nd F I si j nf S M s j nf i i i 전하보존식 Proton transport Electron transport eff e S 0 eff s S 0 In the CLs: S j Reference: Ju H. Investigation of the effects of the anisotropy of gas-diffusion layers on heat and water transport in polymer electrolyte fuel cells. J Power Sources 009;191:

PEFC large-scale simulations Mesh configuration Cell dimensions Channel [EA] 4 4 Cathode Inlet Channel width [mm] 1 1 Channel Depth [mm] 0.6 0.

53 GHz Each processor memory : GB Anode outlet Rib width [mm] 1 1 Thickness of GDL/CL/MEM [mm] Active Area (cm ) 00 Operating cell voltage 0.

6 PEFC large-scale simulations Mesh configuration Cell dimensions Channel [EA] 4 4 Cathode Inlet Channel width [mm] 1 1 Channel Depth [mm] Anode Inlet Cathode outlet Total number of cells (~ 13.5 million) Number of iterations required for convergence : 5000 CPU time / iteration : 7.81 minutes Intel core i7 with.53 GHz Each processor memory : GB Anode outlet Rib width [mm] 1 1 Thickness of GDL/CL/MEM [mm] Active Area (cm ) 00 Operating cell voltage V H Concentration (%) 30 Anode Stoichiometry 1.33 Cathode Stoichiometry.0 Anode/Cathode/Coolant Outlet Pressure 0.5/0.01/ /0.01/0.03 Total channel area [m ] 1.44E-5 1.9E-5 Reaction area [cm ] Operating conditions Atmospheric Cell operating temperature 60 o C 6

7 PEFC large-scale simulations Pressure distribution (Pa) Hydrogen concentration distribution In the anode (mol/m 3 ) Anode Gas Channel Cathode Gas Channel Oxygen concentration distribution In the cathode (mol/m 3 ) 7

8 PEFC large-scale simulations Liquid saturation contours Current distribution in the membrane (A/m ) Cathode inlet Water content distribution in the membrane 8

9 PEFC large-scale simulations Mesh configuration Overall polarization curves for Cases 1-3 Two-dimensional cross-sectional view Liquid saturation curves in different regions of the cathode GDL at 1.5 A cm - 9

10 PEFC large-scale simulations Liquid saturation contours at 1.5 A cm - Current density contours at 1.5 A cm - Case 1 Case Case 3 10

11 Fuel cell modeling : 3-D, transient CS-PEFC 질량보존식 1 u 1 t K Anode : s uu u p g u u eff s d dt Cathode : j ie Sm, a M H M ( w Dw, m Cw) ( nd ) F F j j ie Sm, c M O M ( HO M w Dw, m Cw) ( nd ) 4F F F 화학종보존식 i C i i i i t uc D eff C S c Water : Other species : j I S s n q nf F HO HO e HO c d sg S i c i s j nf 에너지보존식 C T C pt p t cell t g HO C put k eff T ST energy : S T U o j T T i e eff e S sg h sg 전하보존식 eff S 0 e e Proton: Electron: S S j j Reference: J. Ko, Comparison of numerical simulation results and experimental data during cold-start of PEFCs, Applied Energy 01; 94:

12 CS-PEFC simulations Ice evolution contours in the cathode catalyst layer Cell voltage evolution curve Current density evolution contours in the membrane (A/m ) 1

13 Fuel cell modeling : 3-D, two phase DMFC 직접메탄올연료전지 (DMFC) 관련모델 -phase, steady state, nonisothermal model (Large scale simulation > 1.M cells) Anode Cathode 1 Methanol oxidation reaction (MOR) CH OH H O 6H 6e CO 3 Oxygen reduction reaction (ORR) O H e H O Reference: H. Ju et. al, Effects of serpentine flow-field designs with different channel and rib widths on the performance of a direct methanol fuel cell, J. Power sources, 05, 01, 3-47 외 SCI급 4편 13

14 Fuel cell modeling : 3-D, two phase DMFC 질량보존식 ( u) Sm l C j i MeOH S S M a n e mem cata m k MeOH 6 d, MeOH D F F MeOH mem k j mem a mem i M D n e w w d 6F EW F Anode CL : Cathode CL : jc jc Sm Sk MO M w 4F F k mem xover mem ie MMeOH nmeoh M w Dw n d EW F CL 운동량보존식 Flow channels (Navier-Stokes equation) uu K Porous media (Darcy s equations) u p p 전하보존식 Proton transport Electron transport eff e S 0 eff s S 0 Anode CL : Cathode CL : S j S j c j xover 화학종보존식 Flow channels and porous media Water transport in the membrane g l l g g, eff g l l, eff l ( imi u) Di m i Di m i mi mi j Si mem mem mem I K l Dw M w nd M w P 0 l EW F l ja i C e mem MeOH cata SMeOH M MeOH. n d,meoh. D MeOH 6F F mem MeOH : O : xover c MeOH SO M O 4F CL j 3 n Reference: H. Ju et. al, Effects of serpentine flow-field designs with different channel and rib widths on the performance of a direct methanol fuel cell, J. Power sources, 05, 01,

3-D, two-phase DMFC simulations Flow channel geometry and numerical procedures Cell properties and operating conditions Description Channel / rib width Thickness of anode GDL Thickness of anode CL

$7 Porosity of CLs 0.7 Volume fraction of ionomer in CLs 0.3 Permeability of GDLs 1.0 10-1 m Total number of cells : 1. million CPU time / iteration : 16 sec Intel core i7 with.$

15 3-D, two-phase DMFC simulations Flow channel geometry and numerical procedures Cell properties and operating conditions Description Channel / rib width Thickness of anode GDL Thickness of anode CL Thickness of cathode GDL Thickness of cathode CL Thickness of membrane Thickness of bipolar plate Value 1.0/0.5 mm m m m m m 10-3 m Porosity of GDLs 0.7 Porosity of CLs 0.7 Volume fraction of ionomer in CLs 0.3 Permeability of GDLs m Total number of cells : 1. million CPU time / iteration : 16 sec Intel core i7 with.53 GHz Permeability of GDLs m Hydraulic permeability of MEM m Contact angle of GDLs and CLs 9 Anode /cathode stoichiometry.5 / 3.0 Cell operating temperature Anode/cathode inlet pressure 60 o C Atmospheric Inlet methanol concentration 1000 mol m -3 15

16 3-D, two-phase DMFC simulations Methanol concentration contours (mol/m 3 ) Anode flow channel [mol/m 3 ] Anode GDL [mol/m 3 ] Anode CL [mol/m 3 ] Oxygen concentration contours (mol/m 3 ) at 400 ma/cm Cathode flow channel Cathode GDL Cathode CL [mol/m 3 ] [mol/m 3 ] [mol/m 3 ] 16

17 3-D, two-phase DMFC simulations Liquid saturation contours at 400 ma/cm Anode GDL Cathode CL Anode CL Cathode GDL 17

18 3-D, two-phase DMFC simulations Flow field design and optimization 18

Fuel Cell modeling : HT-PEMFC 질량보존식운동량보존식화학종보존식전하보존식에너지보존식전기화학반응 u Sm 1 uu p for flow channels ( Navier Stokes equations) K u p for porous media ( Darcy ' s equations) eff uc D C S i i i i eff e S 0

19 Fuel Cell modeling : HT-PEMFC 질량보존식운동량보존식화학종보존식전하보존식에너지보존식전기화학반응 u Sm 1 uu p for flow channels ( Navier Stokes equations) K u p for porous media ( Darcy ' s equations) eff uc D C S i i i i eff e S 0 for proton transport eff s S 0 for electron transport eff p C ut k T S s M z k i i ne ja Sm MH for anode catalyst layer F jc jc Sm Sk M O M HO for cathode catalyst layer k 4F F T ja SH for anode catalyst layer F jc jc SO, S H for cathode catalyst layer 4F F Ie ST ja for anode catalyst layer eff Ie ST for membrane eff I du dt e O ST jc j eff c T for cathode catalyst layer M i chemical formula of species i si stoichiometry coefficient n number of electrons transferred H H e Hydrogen oxidation reaction at the anode side H O O 4H 4e Oxygen reduction reaction at the cathode side S ja for anode catalyst layer S jc for cathode catalyst layer 19

$HT-PEFC simulations Cell dimensions and base operating conditions Physiochemical and transport properties Description Value Porosity of GDL, CL 0.6, 0.4 Volume fraction of ionomers in CL 0.$ 8 m Anode/cathode channel/rib width 1 10-3 m Anode/cathode channel height 0.7 10-3 m Coolant channel width 0.5 10-3 m Coolant channel height 0.

8 m Anode/cathode channel/rib width 1 10-3 m Anode/cathode channel height 0.7 10-3 m Coolant channel width 0.5 10-3 m Coolant channel height 0.

20 HT-PEFC simulations Cell dimensions and base operating conditions Physiochemical and transport properties Description Value Porosity of GDL, CL 0.6, 0.4 Volume fraction of ionomers in CL 0.3 Permeability of GDL, CL , m Electronic conductivity in the GDL, CL, BP 150, 300, S m -1 Description Value Cell length 0.8 m Anode/cathode channel/rib width m Anode/cathode channel height m Coolant channel width m Coolant channel height m Thickness of the anode/cathode GDLs m Thickness of the anode/cathode CLs m Thickness of the membrane m Anode/cathode inlet pressure 1.0 atm Anode stoichiometry 1.5 (70% H ) Specific heat capacities of GDL, CL, membrane, and BP, respectively Specific heat capacities of species (H, O, N, H O) Thermal conductivities of GDL, CL, membrane, BP Thermal conductivities of species (H, O, N, H O) Volumetric reference exchange current density in anode, Volumetric reference exchange current density in cathode, 568, 3300, 1650, 930 J kg -1 K , 99, 104, 1968 J kg -1 K -1 1., 1.5, 0.95, 0 W m -1 K , 0.096, 0.093, W m - 1 K A m A m -3 Cathode stoichiometry.0 (Air) Anode/cathode inlet temperature 383K RH of the anode/cathode inlet 0.0% Phosphoric acid doping level 6. Anode transfer coefficient 0.5 Cathode transfer coefficient 0.65 Reference H /O molar concentration mol m -3 0

21 HT-PEFC simulations Model validation Gas crossover effects 1

22 Modeling of the hydrogen absorption / desorption 질량보존식 평형압력 t g g u S for hydrogen m n n H H 1 1 Peq a0 an exp 1 M Rg T T0 1 t s S m for metal 에너지보존식 where, Ea P g s s Sm Ca exp ln sat for absorption RT P eq, a Ed Pg P eq, d s s Sm Cd exp emp for desorption RT Peq, d P : Equlibrium pressure eq s sat s emp : Saturated metal density : Empty metal density C : Rate constant E : Activation energy R : Gas constant c t p p g g eff c ut k T S 운동량보존식 1 g u 1 g uu P Su where, Su u t K T where, c 1 c c k 1 k k : Dynamic viscosity : Permeability s s g g p p p eff s g S S H T c c o g s T m p p

23 Metal hydride : LaNi 5 Hydrogen absorption LaNi 5 + 3H LaNi 5 H 6 Model validation Reference: J. Nam, Three-dimensional modeling and simulation of hydrogen absorption in metal hydride hydrogen storage vessels, Applied energy, 89, 01, 외 SCI 1편 3

24 Metal hydride : LaNi 5 Hydrogen desorption Model validation LaNi 5 H 6 LaNi 5 + 3H 4

x (0 x 3 ) Absorption : exothermic reaction Desorption : endothermic reaction Layer

25 Metal hydride simulations outer diameter Computational domain, mesh and dimensions of numerical geometry inner diameter Absorption / desorption formula x ZrCo H ZrCoH x (0 x 3 ) Absorption : exothermic reaction Desorption : endothermic reaction Layer thickness Model assumption 수소는이상기체 베드는동종다공성미디어 금속과수소사이에는국부적온도평형 부피팽창, 비열의변화는무시 inlet 5

26 3D hydrogen absorption/desorption simulations in the ZrCo bed Curve fitting for equilibrium pressure S. Konishi, Journal of Nuclear Materials 3, 94p, 1995 x ZrCo H ZrCoH x 0 x 3 n n H H 1 1 Peq a0 an exp 1 M Rg T T0 where, T =433K (absorption) 0 T =53K (desorption) 0 absorption desorption a a a ` a a a a a a a 최소자승법을이용하여실험적으로측정한평형압력을온도와 H/M atomic ratio 의다항식으로근사 흡장 9 차다항식, 탈장 7 차다항식 6

27 3D hydrogen absorption/desorption simulations in the ZrCo bed Reaction kinetics, thermal physical properties, and operating conditions Description absorption desorption Initial/ inlet temperature, T 0 / T in 5/5 ºC 350 /350 Initial pressure, P i 71 kpa 3 kpa Pre-exponential factor, C a 0. s s-1 Activation energy, E a 13.0 kj mol kj mol-1 Specific heat of hydrogen gas, C g p kj(mol K) -1 Thermal conductivity Specific heat of the metal, C s p kj(mol K) kj(mol K)-1 Thermal conductivity of hydrogen gas, k g W(m K) W(m K)-1 k M Thermal conductivity of ZrCo, k ZrCo W(m K) -1 Thermal conductivity of ZrCo hydride, k ZrCoH W(m K) -1 Thermal conductivity of the SUS 16. W(m K) -1 k MH Porosity of the metal, ε 0.69 Permeability of the metal, K 10-8 m Heat transfer coefficient, h 165 W(m K) -1 Hydrogen-free metal density, ρ s emp 760 kg m -3 Saturated metal density, ρ s sat kg m -3 Reference pressure, P ref 1 bar s kmh km k ( H / M ) k ( H / M) sat (H/M) sat M 7

28 3D hydrogen absorption/desorption simulations in the ZrCo bed kg kg kg H H, initial H, abs R T V H P P MW H i M M g i H Vi MWM M 90% desorbed, 3.7min 99% desorbed, 13.5min 금속수소화물에수소가저장됨에따른수소공급탱크의압력변화를적용 실험적으로측정한온도 profile과모델을이용하여계산한온도 profile을비교함으로써모델의정확성을검증 수소흡장반응은발열반응으로반응초기급격히온도가상승하지만시간이지남에따라용기외부에서의냉각으로인하여온도가감소 계산결과 H/M atomic ratio 1.8 기준 90% 흡장되는시간이약 3.7분, 99% 흡장되는시간은약 13.5분으로나타남 ( 실험결과 : 90% - 4분, 99% - 14분 ) 8

29 3D hydrogen absorption/desorption simulations in the ZrCo bed temperature H/M ratio 반응초기활발한흡장반응으로인하여온도가급격히상승 (53.5K 까지상승함 ) 시간이지남에따라용기외부에서의냉각으로인하여외벽의온도가감소하여용기벽면부근에서우선적으로흡장반응이일어남 ZrCo 층이얇게설계되어 radial 방향으로큰편차를보이지않음 9

30 3D hydrogen absorption/desorption simulations in the ZrCo bed temperature 실험에서측정한용기온도 profile과계산한결과를비교함으로써모델을검증 탈장반응은흡열반응으로반응초기온도가급격히감소하나시간이지남에따라용기외벽에서의가열로인하여온도가상승 계산결과 H/M atomic ratio 1.8기준 90% 탈장도달시간이 19.6분으로실험에서측정한 18분과근사한결과 를나타냄 H/M atomic ratio 30

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(2) : :, α. α (3)., (3). α α (4) (4). (3). (1) (2) Antoine. (5) (6) 80, α =181.08kPa, =47.38kPa.. Figure 1.

Continuous Distillation Column Design Jungho Cho Department of chemical engineering, Dongyang university 1. ( ).... 2. McCabe-Thiele Method K-value. (1) : :, K-value. (2) : :, α. α (3)., (3). α α (4) (4).