no slide title - mdx · 2012. 11. 30 유 하 늘 인하대학교 기계공학과...
TRANSCRIPT
2012 11 30
유 하 늘
인하대학교 기계공학과
에코스마트파워연구실(eco-Smart Power Lab)
연료전지 및 고체 수소저장용기 전산모사
2
발표순서
ㅅ 1
2
3
연료전지 소개
연료전지 모델
연료전지 해석 결과
연료전지
ㅅ 1
2
3
금속수소화물 소개
수소 흡middot탈장 모델
수소 흡middot탈장 모델 해석 결과
수소
저장용기
Large scale PEFC simulation High-Temperature PEMFC model
GDL deformation IV curve validation
Current density water contents distribution
Fuel cell model development amp structural analysis rArr FSI(fluid-structure interaction) approach
High performance computing cluster
Master PC
266GHz x
4core cpu x 2
Sub node
266GHz x
4core cpu
Introduction of Eco Smart Power Lab (ESPL)
3
HCM DMFC simulation
Performance curve and methanol crossover validation Johan Ko et al JPS 2011 3D DMFC simulation result
Polymer Electrolyte Fuel Cell
고분자전해질연료전지 (PEFC)
2 2 2H H e Anode
2 2
12 2
2O H e H O Cathode
Hydrogen oxidation reaction (HOR)
Oxygen reduction reaction (ORR)
4
관련 모델
bull 2-phase steady state non-isothermal model
(Large scale simulation gt 135M cells)
bull PEFC cold start(CS-PEFC) model (with HMC)
bull Single phase transient model
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 2009191259-68
외 SCI급 11편
( ) mu S
uu p
Ku p
( ) g g eff g g l l
i i i i i i im u D m m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
5
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 2009191259-68
mem mem
m i w w
i
S S M D EW
i i d iS M n F I s j nF
i i iS M s j nF
S j
질량 보존식
화학종 보존식
전하 보존식
운동량 보존식 Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
Fuel cell modeling 3-D two phase PEFC
For water in the CLs
For other species in the CLs
In the CLs
bull Total number of cells ndash 13538070 (~ 135 million)
bull Number of iterations required for convergence 5000
bull CPU time iteration 781 minutes
bull Intel core i7 with 253 GHz
bull Each processor memory 2 GB
Active Area (cm2) 200
Operating cell voltage 0713 V
H2 Concentration () 30
Anode Stoichiometry 133
Cathode Stoichiometry 20
AnodeCathodeCoolant Outlet Pressure
Atmospheric
Cell operating temperature 60 oC
PEFC large-scale simulations
Mesh configuration
Channel [EA] 24 24
Channel width [mm] 1 1
Channel Depth [mm] 06 08
Rib width [mm] 1 1
Thickness of GDLCLMEM [mm]
025001003 025001003
Total channel area [m2] 144E-5 192E-5
Reaction area [cm2] 200 200
Cell dimensions
Operating conditions
Anode
Inlet
Cathode Inlet
Cathode
outlet
Anode
outlet
6
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
2
발표순서
ㅅ 1
2
3
연료전지 소개
연료전지 모델
연료전지 해석 결과
연료전지
ㅅ 1
2
3
금속수소화물 소개
수소 흡middot탈장 모델
수소 흡middot탈장 모델 해석 결과
수소
저장용기
Large scale PEFC simulation High-Temperature PEMFC model
GDL deformation IV curve validation
Current density water contents distribution
Fuel cell model development amp structural analysis rArr FSI(fluid-structure interaction) approach
High performance computing cluster
Master PC
266GHz x
4core cpu x 2
Sub node
266GHz x
4core cpu
Introduction of Eco Smart Power Lab (ESPL)
3
HCM DMFC simulation
Performance curve and methanol crossover validation Johan Ko et al JPS 2011 3D DMFC simulation result
Polymer Electrolyte Fuel Cell
고분자전해질연료전지 (PEFC)
2 2 2H H e Anode
2 2
12 2
2O H e H O Cathode
Hydrogen oxidation reaction (HOR)
Oxygen reduction reaction (ORR)
4
관련 모델
bull 2-phase steady state non-isothermal model
(Large scale simulation gt 135M cells)
bull PEFC cold start(CS-PEFC) model (with HMC)
bull Single phase transient model
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 2009191259-68
외 SCI급 11편
( ) mu S
uu p
Ku p
( ) g g eff g g l l
i i i i i i im u D m m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
5
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 2009191259-68
mem mem
m i w w
i
S S M D EW
i i d iS M n F I s j nF
i i iS M s j nF
S j
질량 보존식
화학종 보존식
전하 보존식
운동량 보존식 Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
Fuel cell modeling 3-D two phase PEFC
For water in the CLs
For other species in the CLs
In the CLs
bull Total number of cells ndash 13538070 (~ 135 million)
bull Number of iterations required for convergence 5000
bull CPU time iteration 781 minutes
bull Intel core i7 with 253 GHz
bull Each processor memory 2 GB
Active Area (cm2) 200
Operating cell voltage 0713 V
H2 Concentration () 30
Anode Stoichiometry 133
Cathode Stoichiometry 20
AnodeCathodeCoolant Outlet Pressure
Atmospheric
Cell operating temperature 60 oC
PEFC large-scale simulations
Mesh configuration
Channel [EA] 24 24
Channel width [mm] 1 1
Channel Depth [mm] 06 08
Rib width [mm] 1 1
Thickness of GDLCLMEM [mm]
025001003 025001003
Total channel area [m2] 144E-5 192E-5
Reaction area [cm2] 200 200
Cell dimensions
Operating conditions
Anode
Inlet
Cathode Inlet
Cathode
outlet
Anode
outlet
6
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Large scale PEFC simulation High-Temperature PEMFC model
GDL deformation IV curve validation
Current density water contents distribution
Fuel cell model development amp structural analysis rArr FSI(fluid-structure interaction) approach
High performance computing cluster
Master PC
266GHz x
4core cpu x 2
Sub node
266GHz x
4core cpu
Introduction of Eco Smart Power Lab (ESPL)
3
HCM DMFC simulation
Performance curve and methanol crossover validation Johan Ko et al JPS 2011 3D DMFC simulation result
Polymer Electrolyte Fuel Cell
고분자전해질연료전지 (PEFC)
2 2 2H H e Anode
2 2
12 2
2O H e H O Cathode
Hydrogen oxidation reaction (HOR)
Oxygen reduction reaction (ORR)
4
관련 모델
bull 2-phase steady state non-isothermal model
(Large scale simulation gt 135M cells)
bull PEFC cold start(CS-PEFC) model (with HMC)
bull Single phase transient model
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 2009191259-68
외 SCI급 11편
( ) mu S
uu p
Ku p
( ) g g eff g g l l
i i i i i i im u D m m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
5
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 2009191259-68
mem mem
m i w w
i
S S M D EW
i i d iS M n F I s j nF
i i iS M s j nF
S j
질량 보존식
화학종 보존식
전하 보존식
운동량 보존식 Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
Fuel cell modeling 3-D two phase PEFC
For water in the CLs
For other species in the CLs
In the CLs
bull Total number of cells ndash 13538070 (~ 135 million)
bull Number of iterations required for convergence 5000
bull CPU time iteration 781 minutes
bull Intel core i7 with 253 GHz
bull Each processor memory 2 GB
Active Area (cm2) 200
Operating cell voltage 0713 V
H2 Concentration () 30
Anode Stoichiometry 133
Cathode Stoichiometry 20
AnodeCathodeCoolant Outlet Pressure
Atmospheric
Cell operating temperature 60 oC
PEFC large-scale simulations
Mesh configuration
Channel [EA] 24 24
Channel width [mm] 1 1
Channel Depth [mm] 06 08
Rib width [mm] 1 1
Thickness of GDLCLMEM [mm]
025001003 025001003
Total channel area [m2] 144E-5 192E-5
Reaction area [cm2] 200 200
Cell dimensions
Operating conditions
Anode
Inlet
Cathode Inlet
Cathode
outlet
Anode
outlet
6
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Polymer Electrolyte Fuel Cell
고분자전해질연료전지 (PEFC)
2 2 2H H e Anode
2 2
12 2
2O H e H O Cathode
Hydrogen oxidation reaction (HOR)
Oxygen reduction reaction (ORR)
4
관련 모델
bull 2-phase steady state non-isothermal model
(Large scale simulation gt 135M cells)
bull PEFC cold start(CS-PEFC) model (with HMC)
bull Single phase transient model
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 2009191259-68
외 SCI급 11편
( ) mu S
uu p
Ku p
( ) g g eff g g l l
i i i i i i im u D m m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
5
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 2009191259-68
mem mem
m i w w
i
S S M D EW
i i d iS M n F I s j nF
i i iS M s j nF
S j
질량 보존식
화학종 보존식
전하 보존식
운동량 보존식 Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
Fuel cell modeling 3-D two phase PEFC
For water in the CLs
For other species in the CLs
In the CLs
bull Total number of cells ndash 13538070 (~ 135 million)
bull Number of iterations required for convergence 5000
bull CPU time iteration 781 minutes
bull Intel core i7 with 253 GHz
bull Each processor memory 2 GB
Active Area (cm2) 200
Operating cell voltage 0713 V
H2 Concentration () 30
Anode Stoichiometry 133
Cathode Stoichiometry 20
AnodeCathodeCoolant Outlet Pressure
Atmospheric
Cell operating temperature 60 oC
PEFC large-scale simulations
Mesh configuration
Channel [EA] 24 24
Channel width [mm] 1 1
Channel Depth [mm] 06 08
Rib width [mm] 1 1
Thickness of GDLCLMEM [mm]
025001003 025001003
Total channel area [m2] 144E-5 192E-5
Reaction area [cm2] 200 200
Cell dimensions
Operating conditions
Anode
Inlet
Cathode Inlet
Cathode
outlet
Anode
outlet
6
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
( ) mu S
uu p
Ku p
( ) g g eff g g l l
i i i i i i im u D m m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
5
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 2009191259-68
mem mem
m i w w
i
S S M D EW
i i d iS M n F I s j nF
i i iS M s j nF
S j
질량 보존식
화학종 보존식
전하 보존식
운동량 보존식 Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
Fuel cell modeling 3-D two phase PEFC
For water in the CLs
For other species in the CLs
In the CLs
bull Total number of cells ndash 13538070 (~ 135 million)
bull Number of iterations required for convergence 5000
bull CPU time iteration 781 minutes
bull Intel core i7 with 253 GHz
bull Each processor memory 2 GB
Active Area (cm2) 200
Operating cell voltage 0713 V
H2 Concentration () 30
Anode Stoichiometry 133
Cathode Stoichiometry 20
AnodeCathodeCoolant Outlet Pressure
Atmospheric
Cell operating temperature 60 oC
PEFC large-scale simulations
Mesh configuration
Channel [EA] 24 24
Channel width [mm] 1 1
Channel Depth [mm] 06 08
Rib width [mm] 1 1
Thickness of GDLCLMEM [mm]
025001003 025001003
Total channel area [m2] 144E-5 192E-5
Reaction area [cm2] 200 200
Cell dimensions
Operating conditions
Anode
Inlet
Cathode Inlet
Cathode
outlet
Anode
outlet
6
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
bull Total number of cells ndash 13538070 (~ 135 million)
bull Number of iterations required for convergence 5000
bull CPU time iteration 781 minutes
bull Intel core i7 with 253 GHz
bull Each processor memory 2 GB
Active Area (cm2) 200
Operating cell voltage 0713 V
H2 Concentration () 30
Anode Stoichiometry 133
Cathode Stoichiometry 20
AnodeCathodeCoolant Outlet Pressure
Atmospheric
Cell operating temperature 60 oC
PEFC large-scale simulations
Mesh configuration
Channel [EA] 24 24
Channel width [mm] 1 1
Channel Depth [mm] 06 08
Rib width [mm] 1 1
Thickness of GDLCLMEM [mm]
025001003 025001003
Total channel area [m2] 144E-5 192E-5
Reaction area [cm2] 200 200
Cell dimensions
Operating conditions
Anode
Inlet
Cathode Inlet
Cathode
outlet
Anode
outlet
6
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
PEFC large-scale simulations
Pressure distribution (Pa)
Anode Gas Channel
Cathode Gas Channel
Hydrogen concentration distribution In the anode (molm3)
Oxygen concentration distribution In the cathode (molm3)
7
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Liquid saturation contours
PEFC large-scale simulations
Current distribution in the membrane (Am2)
Cathode
inlet
Water content distribution in the membrane
8
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Two-dimensional cross-sectional view
PEFC large-scale simulations
9
Overall polarization curves for Cases 1-3
Liquid saturation curves in different regions of the cathode GDL at 15 Amiddotcm-2
Mesh configuration
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
PEFC large-scale simulations
10
Case 1 Case 2 Case 3
Current density contours at 15 Amiddotcm-2 Liquid saturation contours at 15 Amiddotcm-2
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
11
sgsgeff
e
eo
T hSi
T
UTjS
2
Proton
Electron jS
jS
nF
jsS
i
i
c
Water
Other species
2 2 2H O H O H Oec d sg
IjS s n q
nF F
2 ( ) ( )2
em a H w w m w d
ijS M M D C n
F F
2 2 ( ) ( )4 2
em c O H O w w m w d
ij jS M M M D C n
F F F
Anode
Cathode
Fuel cell modeling 3-D transient CS-PEFC
Reference J Ko Comparison of numerical simulation results and experimental data during cold-start of PEFCs
Applied Energy 2012 94 364-374
질량 보존식
화학종 보존식
전하 보존식
에너지 보존식
u
dt
du
Kgpuuu
t
u s
seff
11
i
c
ii
eff
ii
SCDCut
C
0 Se
eff
e
0 Ss
eff
s
T
OH
effp
gpcellp
STkTuCt
TC
t
TC
2
energy
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Ice evolution contours in the cathode catalyst layer
CS-PEFC simulations
Current density evolution contours in the membrane (Am2)
Cell voltage evolution curve
12
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
13
직접메탄올연료전지 (DMFC)
Anode
Cathode
Methanol oxidation reaction (MOR)
Oxygen reduction reaction (ORR)
2 2
12 2
2O H e H O
3 2 26 6CH OH H O H e CO
Fuel cell modeling 3-D two phase DMFC
관련 모델
bull 2-phase steady state non-
isothermal model
(Large scale simulation gt 12M cells)
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 205 2012 32-47
외 SCI급 4편
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
( ) mu S
uu p
Ku p
( ) g g eff g l l eff l
i i i i i i
g l l
i i i
m u D m D m
m m j S
0mem mem
mem l
w w d w l
I KD M n M P
EW F
0eff
e S
0eff
s S
14
Fuel cell modeling 3-D two phase DMFC
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 205 2012 32-47
질량 보존식
화학종 보존식
전하 보존식
Flow channels (Navier-Stokes equation) Porous media (Darcyrsquos equations)
Flow channels and porous media Water transport in the membrane
Proton transport Electron transport
6
6
lCMeOHj i mema e cataS S M n Dm k MeOH MeOHd MeOHF F mem
k
memj imema eM D nw w dF EW F
Anode CL Cathode CL 2 4 2
c cm k O w
kxovermem
mem e MeOH MeOHw w d
CL
j jS S M M
F F
i M nM D n
EW F
l
MeOHmema e cata
MeOH MeOH d MeOH MeOH
mem
Cj iS M n D
6F F
2 2
xover
c MeOH
O O
CL
j n3S M
4F 2
MeOH O2
jS xover
cS j j
Anode CL Cathode CL
운동량 보존식
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Flow channel geometry and numerical procedures
15
bull Total number of cells 12 million
bull CPU time iteration 16 sec
bull Intel core i7 with 253 GHz
Description Value
Channel rib width 1005 mm
Thickness of anode GDL 190 times10-6 m
Thickness of anode CL 30 times10-6 m
Thickness of cathode GDL 235 times10-6 m
Thickness of cathode CL 30 times10-6 m
Thickness of membrane 127 times10-6 m
Thickness of bipolar plate 2 times10-3 m
Porosity of GDLs 07
Porosity of CLs 07
Volume fraction of ionomer in CLs 023
Permeability of GDLs 10times10-12 m2
Permeability of GDLs 10times10-12 m2
Hydraulic permeability of MEM 50times10-19 m2
Contact angle of GDLs and CLs 92deg
Anode cathode stoichiometry 25 30
Cell operating temperature 60 oC
Anodecathode inlet pressure Atmospheric
Inlet methanol concentration 1000 mol m-3
Cell properties and operating conditions
3-D two-phase DMFC simulations
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Methanol concentration contours (molm3)
3-D two-phase DMFC simulations
16
Anode flow channel Anode CL
Anode GDL [molm3] [molm3] [molm3]
Oxygen concentration contours (molm3) at 400 mAcm2
Cathode flow channel Cathode GDL Cathode CL [molm3] [molm3] [molm3]
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Liquid saturation contours at 400 mAcm2
Cathode GDL
Anode GDL
17
Cathode CL
Anode CL
3-D two-phase DMFC simulations
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
18
3-D two-phase DMFC simulations
Flow field design and optimization
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
질량 보존식
Fuel Cell modeling HT-PEMFC
19
mu S
2
1( )
( )
uu p for flow channels Navier Stokes equations
Ku p for porous media Darcy s equations
eff
i i i iuC D C S
0
0
eff
e
eff
s
S for proton transport
S for electron transport
eff
p TC uT k T S
2
2 2
2
4 2
am H
c cm k O H O
k
jS M for anode catalyst layer
F
j jS S M M for cathode catalyst layer
F F
2
2 2
2
4 2
aH
c cO H
jS for anode catalyst layer
F
j jS S for cathode catalyst layer
F F
a
c
S j for anode catalyst layer
S j for cathode catalyst layer
2
2
2
eT a eff
eT eff
e OT c ceff
IS j for anode catalyst layer
IS for membrane
I dUS j j T for cathode catalyst layer
dT
운동량 보존식
화학종 보존식
전하 보존식
에너지 보존식
전기화학 반응 z
i iks M ne i
i
M chemical formula of species i
s stoichiometry coefficient
n number of electrons transferred
2
2 2
2 2
2 4 4
H H e Hydrogen oxidation reaction at the anode side
H O O H e Oxygen reduction reaction at the cathode side
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Cell dimensions and base operating conditions
Description Value
Cell length 08 m
Anodecathode channelrib width 1 times 10-3 m
Anodecathode channel height 07 times 10-3 m
Coolant channel width 05 times 10-3 m
Coolant channel height 05 times 10-3 m
Thickness of the anodecathode GDLs 350 times 10-6 m
Thickness of the anodecathode CLs 15 times 10-6 m
Thickness of the membrane 70 times 10-6 m
Anodecathode inlet pressure 10 atm
Anode stoichiometry 125 (70 H2)
Cathode stoichiometry 20 (Air)
Anodecathode inlet temperature 383K
RH of the anodecathode inlet 00
Phosphoric acid doping level 62
Description Value
Porosity of GDL CL 06 04
Volume fraction of ionomers in CL 03
Permeability of GDL CL 1 times 10-12 10 times 10-13 m2
Electronic conductivity in the GDL CL BP 1250 300 14000 S m-1
Specific heat capacities of GDL CL
membrane and BP respectively 568 3300 1650 2930 J kg-1K-1
Specific heat capacities of species (H2 O2
N2 H2O) 14430 929 1042 1968 J kg-1K-1
Thermal conductivities of GDL CL
membrane BP 12 15 095 20 W m-1K-1
Thermal conductivities of species (H2 O2
N2 H2O)
02040 00296 00293 002378 W m-
1K-1
Volumetric reference exchange current
density in anode 10 times109 A m-3
Volumetric reference exchange current
density in cathode 10 times 104 A m-3
Anode transfer coefficient 05
Cathode transfer coefficient 065
Reference H2O2 molar concentration 4088 mol m-3
Physiochemical and transport properties
20
HT-PEFC simulations
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
21
Model validation Gas crossover effects
HT-PEFC simulations
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
22
1
gg
m
s
m
u S for hydrogent
S for metalt
C Rate constant
E Activation energy
R Gas constant
eq
s
emp
P Equlibrium pressure
Saturated metal density
Empty metal density
s
sat
0
1 0
H 1 1exp
M
nn
eq n
g
HP a a
R T T
p g g effp T
cc uT k T S
t
1 1
gg
u u
uuu P S where S u
t K
Dynamic viscosity
Permeability
1
1
s s g gp p p
eff s g
o g sT m p p
where c c c
k k k
S S H T c c
exp ln
exp
g s sam a sat
eq a
g eq d s sdm d emp
eq d
where
PES C for absorption
RT P
P PES C for desorption
RT P
Modeling of the hydrogen absorption desorption
질량 보존식 평형 압력
에너지 보존식
운동량 보존식
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Metal hydride LaNi5 Hydrogen absorption
LaNi5 + 3H2 rarr LaNi5H6
Reference J Nam Three-dimensional modeling and simulation of
hydrogen absorption in metal hydride hydrogen storage
vessels Applied energy 89 2012 164-175
외 SCI 1편 23
Model validation
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
24
Metal hydride LaNi5 Hydrogen desorption
LaNi5H6 rarr LaNi5 + 3H2
Model validation
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
25
Metal hydride simulations
outer diameter
inner diameter
Layer thickness
inlet
Model assumption
수소는 이상기체
베드는 동종 다공성 미디어
금속과 수소 사이에는 국부적 온도평형
부피팽창 비열의 변화는 무시
2 x
xZrCo H ZrCoH (0 x 3 )
2
Absorption desorption formula
Absorption exothermic reaction
Desorption endothermic reaction
Computational domain mesh and dimensions of numerical geometry
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
26
2 0 32
x
xZrCo H ZrCoH x
0
1 0
0
0
H 1 1exp
M
T =433K (absorption)
T =523K (desorption)
nn
eq n
g
HP a a
R T T
where
Curve fitting for equilibrium pressure
최소자승법을 이용하여 실험적으로 측정한 평형압력을 온도와 HM atomic ratio의 다항식으로 근사
bull 흡장 ndash 9차 다항식 탈장 ndash 7차 다항식
S Konishi Journal of Nuclear Materials 223 294p 1995
absorption desorption
a0 -2420956395 -6471388017
a1 3728572074 2970420677
a2 `-1667306731 -8930753043
a3 4186656358 1852136064
a4 -6500433016 -2526795731
a5 6586728692 2098084651
a6 -4452244562 -9333352094
a7 1970334294 1689306846
a8 -5217131085
a9 6276235435
3D hydrogen absorptiondesorption simulations in the ZrCo bed
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
27
Reaction kinetics thermal physical properties and operating conditions
3D hydrogen absorptiondesorption simulations in the ZrCo bed
( )( )
s MH MM
sat
k kk H M k
H M
kM
kMH
(HM)sat
Thermal conductivity
Description absorption desorption
Initial inlet temperature T0 Tin 2525 ordmC 350 350
Initial pressure Pi 71 kPa 3 kPa
Pre-exponential factor Ca 02 s-1 0043 s-1
Activation energy Ea 130 kJmol-1 132 kJmol-1
Specific heat of hydrogen gas Cgp 14890 kJ(molK)-1
Specific heat of the metal Csp 0508 kJ(molK)-1 0630 kJ(molK)-1
Thermal conductivity of hydrogen gas kg 0167 W(mK)-1 0351 W(mK)-1
Thermal conductivity of ZrCo kZrCo 3013 W(mK)-1
Thermal conductivity of ZrCo hydride kZrCoH3 0524 W(mK)-1
Thermal conductivity of the SUS 162 W(mK)-1
Porosity of the metal ε 0629
Permeability of the metal K 10-8 m2
Heat transfer coefficient h 1652 W(m2K)-1
Hydrogen-free metal density ρsemp 7620 kgm-3
Saturated metal density ρssat 77479 kgm-3
Reference pressure Pref 1 bar
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
28
2
22
H i M M
g i Hi M
R T V HP P MW
V MW M
2 2 2H H initial H abskg kg kg
금속수소화물에 수소가 저장됨에 따른 수소공급탱크의 압
력변화를 적용
실험적으로 측정한 온도 profile과 모델을 이용하여 계산한
온도 profile을 비교함으로써 모델의 정확성을 검증
수소 흡장반응은 발열반응으로 반응초기 급격히 온도가 상
승하지만 시간이 지남에 따라 용기외부에서의 냉각으로 인
하여 온도가 감소
계산결과 HM atomic ratio 18 기준 90 흡장되는 시간이
약 37분 99 흡장되는 시간은 약 135분으로 나타남
(실험결과 90 - 4분 99 - 14분)
90 desorbed 37min 99 desorbed 135min
3D hydrogen absorptiondesorption simulations in the ZrCo bed
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
29
temperature HM ratio
반응 초기 활발한 흡장반응으로 인하여 온도가 급격히 상승 (5325K 까지 상승함)
시간이 지남에 따라 용기 외부에서의 냉각으로 인하여 외벽의 온도가 감소하여 용기 벽면 부근에서 우선적으로 흡장반응이 일어남
ZrCo 층이 얇게 설계되어 radial 방향으로 큰 편차를 보이지 않음
3D hydrogen absorptiondesorption simulations in the ZrCo bed
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
30
temperature
HM atomic ratio
실험에서 측정한 용기 온도 profile과 계산한 결과를
비교함으로써 모델을 검증
탈장반응은 흡열반응으로 반응 초기 온도가 급격히 감
소하나 시간이 지남에 따라 용기 외벽에서의 가열로
인하여 온도가 상승
계산결과 HM atomic ratio 18기준 90 탈장도달시
간이 196분으로 실험에서 측정한 18분과 근사한 결과
를 나타냄
3D hydrogen absorptiondesorption simulations in the ZrCo bed
Page 31 31
Page 31 31