Modelling of miniature PEM fuel cells
Modelling of miniature proton exchange membrane
fuel cells for portable applications
J.O. Schumacher1, E. Fontes3, D. Gerteisen1, F.
Goldsmith1, R. Klöfkorn2, A. Hakenjos1, K. Kühn1,
M. Ohlberger2, A.Schmitz1, K. Tüber1, C. Ziegler1
1. Fraunhofer Institute for Solar Energy Systems,
Heidenhofstr. 2, 79110 Freiburg, schum@ise.fhg.de,
Germany
2. Institute of Applied Mathematics, University of Freiburg,
Herrmann-Herder-Str. 10, 79104 Freiburg, Germany
3. COMSOL AB, Tegnergatan 23, SE-111 40 Stockholm,
Sweden
Modelling of miniature PEM fuel cells
Overview
 Examples of portable fuel cell systems
 Model based analysis of impedance spectra
 Modelling of self-breathing fuel cells
 Characterisation of an along-the-channel fuel cell
 Dynamic simulation of two-phase flow
 Conclusion and outlook
Modelling of miniature PEM fuel cells
Fuel cell system for a 50 Wmax laptop
Modelling of miniature PEM fuel cells
Fuel cell system for a professional broadcast camera
• Completely integrated
system with 4 fuel cell stacks
• 40 W average system power
• 2 Metal Hydride Storages
(100 Nl H2 or 150 Whel)
•Integrated DC/DC- Converter
• Miniature fans for air supply
Modelling of miniature PEM fuel cells
Mobile power box
• Portable power supply
• Power: max. 100 W
average 50 W
• Metal Hydride Storage
• Control based on micro
processor
• 12 V voltage supply with
DC/DC- Converter
Modelling of miniature PEM fuel cells
Electrode agglomerate model

Electrode is assumed to be made
of porous spherical catalyst
grains

Oxygen is dissolved at the outer
surface of the agglomerate

Diffusion of dissolved oxygen in
the grain and the film in radial
direction

Local current density is given by
the Tafel-equation
Graph: Jaouen et al., 2002
Modelling of miniature PEM fuel cells
Cathode agglomerate model
Mass balance
Charge balance
Oxygen flux in agglomerate
Modelling of miniature PEM fuel cells
Cathode agglomerate model
Charge balance
Ohm`s law
Modelling of miniature PEM fuel cells
Comparision of measured and simulated polarisation curves
Small current density: change
Influence of surface-to-volume
of Tafel-slope
ratio L of agglomerates
cell potential / [V]
cell potential / [V]
L = 6 105 m-1
current density / [A/m2]
L = 9 104 m-1
current density / [A/m2]
Modelling of miniature PEM fuel cells
Simulation of impedance spectra

Perturbation of solution variables of PDEs

Small perturbations: linearise and Laplace-transform PDEs

Calculate impedance:
Resistance [Wm2]
Resistance [Wm2]
Modelling of miniature PEM fuel cells
Comparision of measured and simulated impedance spectra
• Minimum value of
the radius of the
impedance arc is
reached at a current
density of
260mA/cm2.
current
density [A/m2]
meas
• Mass transport
limitation is observed
for higher current
density: increase of
radius of impedance
arc.
sim
Modelling of miniature PEM fuel cells
Influence of double layer capacitance on impedance spectra
Double layer capacitance
Small double layer capacitance:
CDL = 3 107 F m-3
Two seperate semicircles
appear
GDL
current
density [A/m2]
current
density [A/m2]
Influence
of electrode
Modelling of miniature PEM fuel cells
Planar and self-breathing fuel cells based on printed circuit board
technology
Benefits of technology:
• Small cell thickness
• High mechanical strength
• Low cost components
• Well known printed circuit board production technology
• Integration of electronic circuits
Modelling of miniature PEM fuel cells
Modelling domain and assumptions
• Two dimensional model
• Plug flow conditions in
anodic gas channel
• Convective flux of
species through
membrane and on
cathode side neglected
• No phase transition
accounted for
Modelling of miniature PEM fuel cells
Discretisation mesh and governing equations
• Multicomponent
diffusion of gas species:
Stefan-Maxwell equation
• Electronic and protonic
potential: Poisson
equation
• Transport of water
across membrane:
modified Stefan-Maxwell
equation
• Temperature
distribution: heat
equation
l
Modelling of miniature PEM fuel cells
Hydrogen and oxygen distribution
H2 molar fraction
O2 molar fraction
anode
Arrows: total
flux of hydrogen
and oxygen.
Vcell = 0.4 V
cathode
Modelling of miniature PEM fuel cells
Water distribution and flux
H2O molar fraction x 10-3
H2O molar fraction
anode
Arrows: total
flux of water.
Vcell = 0.4 V
cathode
Modelling of miniature PEM fuel cells
Heat flux and temperature
T [K]
anode
• Arrows: total flux of heat.
• Cooling effect of ribs.
Vcell = 0.4 V
cathode
Modelling of miniature PEM fuel cells
Electronic and protonic potential, current direction
Electronic potential
fe [V]
Arrows indicate the technical current direction.
Protonic potential
fp [V]
Modelling of miniature PEM fuel cells
Comparison of Experiment and Simulation
Experiment
Simulation
• Opening ratio = cathode opening width / current collector rib width.
• Limiting current is determined by oxygen supply through cathode opening.
Modelling of miniature PEM fuel cells
Current distribution in cathode gas diffusion layer
cathode
electrode
cut line (e)
GDL
(e)
membrane
Normalised x-coordinate
(e)
Normalised y-coordinate
Modelling of miniature PEM fuel cells
PEM fuel cell model based on FLUENT CFD-software
Submodels:
• The electrochemical
submodel predicts the
local current-tovoltage relation in the
MEA.
• The electrical
submodel accounts for
electron flow and
ohmic heat
generation.
• The MEA submodel
describes transport of
water and ions
through a Nafion
membrane.
Modelling of miniature PEM fuel cells
‚Along - the - Channel‘
• Flow-field geometry:
Parallel channels
• Determination of
spatially resolved
current density
• Measured values:
temperature,
gas flow-rates,
relative humidity
current per segment [A]
Segmented fuel cell
0,16
row 1
row 2
row 3
0,14
0,12
0,10
0,08
0,06
0,04
0,02
0
1
2
3
4
5
6
7
8
9
position
10 11 12 13 14 15 16
Modelling of miniature PEM fuel cells
• Comparison of
measurement (dots)
and simulation (lines)
• Variation of air flow
rate on the cathode
side
• All model parameters
are kept constant
except air flow and
average current
Current Density [A/cm²]
Current distribution along the channel
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
600sccm
300sccm
50sccm
1 2 3 4 5 6 7 8 9 101112131415
Segment Position
gas flow direction:
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
600sccm
300sccm
50sccm
Temperature
of air in the
channel
1 2 3 4 5 6 7 8 9 101112131415
Segment Position
600sccm
300sccm
50sccm
1 2 3 4 5 6 7 8 9 101112131415
Segment Position
Membrane
protonic
resistivity
335
330
325
320
315
310
305
300
295
290
Protonic Resistivity [Wm]
Relative
humidity of
air at MEA
Relative Humidity
Relative
humidity of
air in the
channel
Relative Humidity
Analysis
Temperature [K]
Modelling of miniature PEM fuel cells
600sccm
300sccm
50sccm
1 2 3 4 5 6 7 8 9 101112131415
Segment Position
600sccm
300sccm
50sccm
1
0.1
1 2 3 4 5 6 7 8 9 101112131415
Segment Position
Modelling of miniature PEM fuel cells
Profiles of flow velocity and temperature including inlet region
velocity profile
temperature profile
Modelling of miniature PEM fuel cells
Dynamic simulation of two phase flow
Modelling concept by
Mario Ohlberger
(Institute for Applied
Mathematics,
Freiburg).
Solution of the PDEs for:

Two phase flow in porous media

Species transport in the gas phase

Energy balance in the porous media

Potential flow of electrons and protons
Adaptive grid generation in space / time
Colours: pressure
distribution for
counter-flow case.
Problem: Determination of material parameters
Modelling of miniature PEM fuel cells
Two-phase flow in porous gas diffusion layer and electrodes
phase-transition
Mass balance
Darcy-law
Water and gas saturation
Capillary pressure
Modelling of miniature PEM fuel cells
Model geometry and discretization mesh
Modelling of miniature PEM fuel cells
Simulation examples
H2
Mass fraction of gas
components and
saturation of liquid
water
Colors:
Red: 1, Blue: 0
O2
Wasserdampf
flüssiges
Wasser
Modelling of miniature PEM fuel cells
Conclusion
Agglomerate model
• The agglomerate model reproduces both,
measured polarisation curves and impedance
spectra.
• Change of active agglomerate surface-to-volume
ratio depending on the operation point?
Planar fuel cells
• Our two-dimensional one-phase model includes
all relevant processes of planar fuel cells: gas
transport, heat transport, electrochemical reaction.
• The model serves as a design tool for selfbreathing planar fuel cells.
Modelling of miniature PEM fuel cells
Conclusion
Current distribution
• We validated the CDF model with locally
distributed current measurements.
• The CFD model agrees to measurement results if
the cell is operated in the one-phase regime.
Two-phase flow
• We are working on a dynamic two-phase flow
model taking into account liquid water transport in
porous media.
• The model is extended to 3D. Parallel computing
and adaptive grid generation is utilised.