Modeling Fuelcells
with ANSYS Fluent
Shaoping Li, PhD
Principal Software Developer
Manager, Fluent Reacting Flow Dev.
ANSYS, Inc. USA
1
Outline
• Model Framework
• Fuel Cell Models
❑ Resolved Membrane Approach
o PEMFC (质子交换膜燃料电池 – 低温）
o SOFC (固体氧化剂燃料电池 – 高温）
o Electrolysis (电解 – 高温）
❑ Unresolved Membrane Approach
o SOFC
o Electrolysis
❑ New PEMFC Module – 重点！
• Some Examples
Model Framework
• All fuelcell modeling capabilities are provided as add-on modules with the standard FLUENT
(with no additional charges)
• Users can write their own customized functions and link to the add-on module (usually for
the purpose of using their own properties and in-house model parameters or coorelations)
• GUI and TUI for easy model setup and input.
Fluent Addon Modules:
0. None
1. MHD Model
2. Fiber Model
3. Fuel Cell and Electrolysis Model
4. SOFC Model with Unresolved Electrolyte
5. Population Balance Model
6. Adjoint Solver
7. Single-Potential Battery Model
8. Dual-Potential MSMD Battery Model
9. PEM Fuel Cell Model
10. Macroscopic Particle Model
Enter Module Number: [ ]
Fuel Cell Principles (e.g. PEMFC)
• 氢离子 and 电子 are produced in anode catalyst
layer:
H 2  2H + + 2e −
•氢离子 and 电子 travel via the membrane and
external circuit, respectively, to the cathode
where they combine with oxygen to produce
water:


1
O 2 + 2e − + 2H +  H 2 O
2
Cooling
water
passage
Cooling
water
passage
2e-
Current collector
Cathode
Flow channel
Gas diffusion layer
O2
H2O
Pt catalyst layer
Membrane
Anode
Pt Catalyst layer
Gas diffusion layer
Flow channel
H+
H2
Current collector
Cooling water passage
2e-
Fuel Cell and Electrolysis Model
1. FuelCell and Electrolysis Module 简介
Integrated model framework for PEMFC, SOFC & Electrolysis
with MEA being included in the computational domains
Domains Modeled
(Resolved MEA e.g. PEMFC)
Cooling Channel(s)
Anode Collector
Gas Channel
Anode GDL
Anode Catalyst Layer
MEA
Membrane
Cathode Catalyst Layer
Cathode GDL
Fuelcells Modeled
➢ PEMFC
➢ SOFC
➢ Electrolysis
Gas Channel
Cathode Collector
Cooling Channel(s)
PEMFC, SOFC, Electrolysis
Proton Exchange Membrane
Fuel Cell (PEMFC)
--- low temperature
Solid Oxide Fuel Cell (SOFC)
--- high temperature
Electrolysis
--- high temperature
H2
 H + + e−
2
1
O2 + H + + e −  H 2 O
4
H 2 + O 2−  H 2O + 2e −
1
O2 + 2e −  O 2−
2
H 2O + 2e −  H 2 + O 2−
O 2− 
1
O2 + 2e −
2
(Anode)
(Cathode)
(Anode)
(Cathode)
(“Anode”)
(“Cathode”)
Highlights of Key Model Capabilities
• Integrated model framework for PEMFC, SOFC & Electrolysis
• Multi-component diffusion for gas species transport
• Liquid water transport in porous media, clogging to gas diffusion and
reaction sites (PEMFC)
• Non-isotropic electric conductivity in porous GDL (PEMFC)
• Compatibility with non-conformal interface meshing
• User-Modifiable Properties/Correlations
• Automated udf library path, independent of FLUENT version numbers
Mathematical Model Description (dual potentials)*
• Electro potentials:
−
‐ solid phase potential: ( e transport in conducting solid)
‐ membrane phase:
( H + transport in MEA )
  ( ee ) + S e = 0.0
  ( mm ) + S m = 0.0
•Surface over-potential (activation loss):
• Advantages:  = e − m − Voc
‐ Account for current transport in all regions
‐ Facilitate modeling of contact resistance at material interface
ref
* All Math Descriptions are valid for the new PEMFC module too !
Mathematical Model Description (transfer currents)
Butler Volmer
S a = ja ,ref (
S c = jc ,ref (
jref
ci
ci ,ref

ch 2
ch 2,ref
co 2
co 2,ref
a
) (e
c
a F
RT
) ( −e
volumetric reference exchange
current density
local species molar concentration
and its reference value, respectively.
concentration dependence,
a
a F
RT
c
−e
−
+e
c F
RT
−
a
c F
RT
)
c
)
 the transfer coefficient,
subscripts a and c indicate the
anode and the cathode side,
respectively
Boundary Conditions for  e
inside catalyst layers
Se = −Sa  0
(anode)
Se = + Sc  0
(cathode)
anode
cathode
Boundary Conditions for m
inside catalyst layers
Sm = +Sa  0
(anode)
S m = −Sc  0
(cathode)
anod
catalyst
emembrane
MEA
catalyst
m
=0
n
Use  S a dV =  S c dV to obtain a unique solution
Van
Vca
Local Sources Due to Electrochemistry (e.g. PEMFC)
−
‐ H2-equation:
M o2
−
S c dV
4F
‐ O2-equation:
‐ H2O-equation:
M h2
S a dV
2F
+
M h 2o
S c dV − rw dV
2F
‐ Conservation of current and mass requires
 S dV =  S dV
a
Van
c
Vca
物性参数 (User-Customizable)- e.g. PEMFC
• Most commonly used correlations are coded as default options
• Users can overwrite with their own formulation/data
Default membrane phase electric conductivity (Springer et al)
1268 (
 m =  (0.514 − 0.326) e
Default osmotic drag coefficient
1
1
− )
303 T
(Springer et al)
Default membrane water diffusivity (Dutta et al)
Gas diffusivity (Wang, Bird, Kaviany)
nd = 2.5

22
Dw = D exp{2416(
Di =   (1 − s)b D o i (
p0  T 1.5
) ( )
p T0
1
1
− )}
303 T
Solution Procedure
• Specify solid phase potential BCs at cathode current collectors (cell
voltage or average current density),
Vcell or I ave
• Solve the system of equations for
u, v, w, p, yi , T , e , m , s, 
S

=
a
dVa
• If run-to-voltage, average current is:
I ave
• If run-to-current,
Vcell = e |cathode wall
cell voltage is:
• Polarization curve
( I ave, Vcell )
Amem
Some Examples
Tubular Cell SOFC
cathode
193,475 computing cells
electrolyte
air pipe
anode
O2
current
Stack Simulation - SOFC
10-cell stack, concentration limited,
matches theoretical limiting current
I = m O2
F
M O2
O2 mass fractions at x-plane
O2
Stack Simulation - SOFC
4-Cell Stack: 2.25 million computing cells.
H2
O2
Non-Conformal Interface
Straight-Serpentine Channels:
607,097 cells
anode interface
cathode interface
SOFC with Internal Reforming (tubular cell)
steam reforming: CH4 + H2O --- 3H2 + CO
water-shift:
CO + H2O →H2 + CO2
I=5.458 A
CH4
H2
CO2
High-Temperature Electrolysis
h2o
h2
• Split Water vapor into Hydrogen and Oxygen
• cell voltage is higher than open-circuit voltage
• endothermic process
o2
T
1e-5
SOFC with unresolved Electrolyte
SOFC with unresolved electrolyte
Domains Modeled
SOFC Module GUI Panel
(Unresolved MEA)
Anode Collector
Gas Channel
Anode GDL
Anode Catalyst Layer
MEA
Membrane
Cathode Catalyst Layer
Cathode GDL
Gas Channel
Cathode Collector
• MEA is not included in the computing mesh
• MEA is modeled as wall-wall interface
• Advantage:
less costly
• Disadvantage: no inormation about MEA; not
compatabile with non-conforming mesh
• Capabilities: very similar to its resolved counterpart
No more discussions here
For details, see theory
manual & user-guide
New PEMFC Module
New PEMFC Module (since FLUENT 17.0)
New
New
•
•
•
•
•
Developed under externally funded projects
New
Several significant improvements over the old PEMFC module
Much improved numerical robustness
New water management concept that guarantees mass conservation
Recommended for pmefc applications !
Model Options
New Concept for Water Management
➢ Water can exist in 3 forms
• Dissolved in the ionomer
• Water vapor in the porous
media and gas channels
• Liquid water in the porous
media and gas channels
➢ Water is generated in the
dissolved phase !
➢ Deviation from equilibrium as
driving force for phase changes
Liquid Water Transport in Porous Media
▪
Implemented new liquid water equation in Porous Media
--- solve capillary pressure equation in MEM, CAT, MPL, GDL
--- determine saturation from pc-s relations.
 KK rl


( i  l s) =   
( pc + p g )  + S gl − Sld
t
 l

Gas-to-Liquid
New
from GDL to channel
New
Dissolved Phase Water Transport in MEA
▪ Transport equation for dissolved (3rd phase) water in MEA
(catalyst-membrane-catalyst assembly) (Wu 2009)
New
i 
nd  





  +    M w im  =    M w l Dw   + S  + S gd + S ld
  i M w,H 2o
t 
EW 
F 
EW



Reaction
Old:
M W , H 2O
S =
Rcat
2F



   M w l Dw  = 0
EW


---------
Gas-to-Dissolved
Liquid-to-Dissolved
solved only in membrane
new osmotic drag treatment through the entire MEA
water is produced in dissolved phase (rather than vapor phase)
mass transfer with other two phases: vapor and liquid (absorption/desorption)
mass conservation is always observed
Liquid Water Transport in Gas Channels (optional)
▪
Solve liquid saturation in gas channels to obtain meaningful values to model pressure
drop through viscous momentum resistance, using a user-modifiable function in
pemfc_user.c
New


vl =  v g


(  l s ) +   ( l vl s ) =   ( Dliqs )
t
default resistance:
R momentum = f ( s ) =  s 
liquid saturation in cathode channel
static pressure
with liquid
w/o liquid
Addition of Micro Porous Layer (MPL)
➢ Include MPL as separate layers with different properties
from GDLs
Polarization
1.00
w/o MPL
0.90
with MPL
0.80
0.70
V (v)
New
0.60
0.50
0.40
0.00
0.20
0.40
0.60
I (A/cm2)
0.80
1.00
1.20
The Two Potentials
− I leak
New
Leakage Current
Temperature-Dependent
New
Overpotentials
New
Nernst half cell potentials
Cathode Particle Model
New
➢ considers mass transfer resistance in microstructure
Case
I (A/cm2)
Cathode Particle Model On
0.886205
rp=0, Rion=0
0.924535 (+4%)
Cathode Particle Model Off
0.924535
Other Improvements
1. Calculation of thermal conductivity for multiphase fluid
2. Use Entropy to compute reaction heat
3. Variable phase change rates
4. Thermal contact resistance
What is solved ? and Where?
Anode to
cathode
e- Pot.
uds-0
H+ Pot.
uds-1
Pc
uds-2
Cur. Coll.
Solid
Channel
Fluid
GDL
Fluid
y
y
MPL
Fluid
y
y
Cat. Layer
Fluid
y
Membrane
Solid
Cat. Layer
Fluid
y
MPL
Fluid
y
y
GDL
Fluid
y
y
Channel
Fluid
Cur. Coll.
Solid

uds-3
s
uds-4
y
y
y
y
y
y
y
y
y
y
y
y
y
PEMFC: O2 Mass Fraction and Temperature
T
yO 2
anode
cathode
cathode: mass fraction of O2 reduces along the channel due to reaction
anode: no O2 crossover due to presence of membrane
PEMFC: Liquid Distribution and its Effect on Performance
Liquid saturation at the cathode catalyst layer
Cell Performance
s
Polarization
1
without liquid
water
with liquid
water
0.9
anod
e
flow
V_cell (V)
0.8
cathod
e flow
0.7
0.6
0.5
0.4
0.3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
I (A/cm^2)
• global & local polarizations
• current density distribution
Model Validation
50 cm2 MEA of Mench et al (2004)
Inlet
Channel depth: 3.18; width: 2.16
➢ 48 gold-plated steel current collecting
ribs embedded into an insulating slab
o
o
o
➢ Tcell = 80 C ; P = 1.5atm; Ta = 90 C ; Tc = 80 C
71.12
➢  an = 1.875;  ca = 1.5, 2.25
Outlet
2.54
➢ mass flow rate was kept constant in
each cathode stoichiometry run
70.99
Figure 1. Schematic diagram of the test cell of Mench et al
[1]: all numbers in mm
Current Density Measurement Locations
Segmented current collector right under the cathode ribs
(Segmented areas are actually continuous)
Species Mass Fractions in Gas Channels
H
O2
2
 ca = 1.5
Vcell = 0.45
Liquid Saturation at Different Cell Voltage
location: mid-plane of cathode gas diffusion layer
Vcell = 0.4 V
Vcell = 0.6 V
 ca = 1.5
Vcell = 0.8 V
Global Polarization
Polarization
1.00
Experiment: 2.25 equiv.
Experiment: 1.50 equiv.
0.90
FLuent: 1.50 equiv.
Fluent: 2.25 equiv.
0.80
V (v)
0.70
0.60
0.50
0.40
0.30
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
I (A/cm2)
Computed (lines) and measured (symbols) global polarization
curves for cathode stoichiometry of 1.5 and 2.25 equiv.
Local Polarization
1.5
Local Polarization
2.25
x/L=0.109
x/L=0.109
Local Polarization
x/L=0.283
1.0
x/L=0.717
0.9
x/L=0.891
0.8
0.7
V (v)
0.6
1.0
x/L=0.283
x/L=0.717
0.9
x/L=0.891
data: x/L=0.891
0.8
data: x/L=0.891
data: x/L = 0.717
0.7
data: x/L = 0.717
data: x/L=0.283
V (v)0.6
data: x/L=0.109
0.5
data: x/L=0.283
data: x/L=0.109
0.5
0.4
0.4
0.3
0.3
0.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
0.2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
I (A/cm2)
I (A/cm2)
Computed (lines) and measured
(symbols) local polarization curves for
cathode stoichiometry of 1.5 equiv.
Computed (lines) and measured
(symbols) local polarization curves for
cathode stoichiometry of 2.25 equiv.
Local Current Density
1.5
I (A/cm2)
2.25
0.85 V
0.80 V
0.70 V
0.85 V
0.80 V
0.70 V
0.65 V
0.55 V
0.45 V
0.65 V
0.55 V
0.45 V
0.40 V
0.35 V
data- 0.85 V
0.40 V
0.35 V
data- 0.85 V
data- 0.80 V
data- 0.70 V
data- 0.65 V
data- 0.80 V
data- 0.70 V
data- 0.65 V
data- 0.55 V
data- 0.45 V
data- 0.40 V
data- 0.55 V
data- 0.45 V
data- 0.40 V
I (A/cm2)
data- 0.35 V
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
x/L
Computed (lines) , measured (symbols):
cathode stoichiometry of 1.5 equiv.
data- 0.35 V
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
fractional distance from cathode inlet
Computed (lines), measured (symbols):
cathode stoichiometry of 2.25 equiv.
Guidelines for solution control
1. Under-Relaxation Factors (URF’s) for Transport Equations
a. Pressure: 0.3 ~ 0.5
b. Momentum: 0.3
c. All other equations: 1.0 (do not use anything less than 1.0)
2. Under-Relaxation Factors (URF’s) for Source Terms (in PEM Fuel Cell Model panel)
a. Liq.-Vap. Source: reduce to as low as 0.02 (often required)
b. Dis’d-Vap./Liq. Source: reduce to as low as 0.02 (often required)
c. Osmotic Drag Source: 0.5~1.0
d. GDL Liquid Removal: 0.2~0.5
3. AMG Solver In Solve→Controls→Advanced→Multigrid… panel
Choose F-Cycle as Cycle Type for all variables.
- can be done by clicking “F-Cycle for All Equations” in the PEMFC GUI panel.
4. Parallel Partition
Use Laplace Smoothing for better mesh quality
5. …. see “Best Practices for PEMFC Simulation”
Useful Documents for Fuel Cell Modeling
➢ ANSYS Advanced Fluent Add-On Modules
➢ Tutorial Package
➢ Best Practices for PEM Fuel Cell Simulations
Areas for Future Improvement
o material data for porous GDL/MPL in actual PEM operation for accuracy
o more accurate characterization of membrane and catalysts --quantitative relationship of microstructure and compositions with cell
performance
o reliable experimental data under well-defined operating conditions for
systematic model validations (global, local, transient)
Looking forward to working with industrial/academic leaders
Membrane Water Transport
Current modeling of osmotic drag and back diffusion is
mostly based upon Springer et al’s paper of (1991)
Jw
Jw
diff
osm
nd M h 2o 
=
i
F
=−
m
Mm
M h 2 o D w 
nd = 2.5

22
Dw = D exp{2416(
1
1
− )}
303 T
Questions:
• Validity of measured correlations for today’s membranes ?
Liquid Water Transport in Porous Media
Liquid water flux is mostly modeled using Darcy’s law

K K rl dpl
 lVl s =  l
s
l ds
 cos 
pc =
J ( s,  )
0.5
(K /  )
1.417 (1 − s ) − 2.12 (1 − s ) 2 + 1.263 (1 − s ) 3 (  90 0 )
J ( s,  ) = 
2
3
(  90 0 )
1.417 s − 2.12 s + 1.263 s
hydrophilic
hydrophobic
Questions:
• pc-s relation was obtained in the study of geosciences such as soil
or sand, not valid for GDL used in PEMFC
• Lack of sensitivity to wetting property
Liquid Water Transport in Gas Channel
In practice, flow in gas channel is two-phase and strongly
affected by channel surface wettability.
However, a programmatic approach is adopted, mainly to
model the effect of increased pressure drop due to the
presence of liquid water.
谢谢！