Modelling of miniature PEM fuel cells Modelling of miniature proton exchange membrane fuel cells for portable applications J.O. Schumacher 1, E. Fontes

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, [email protected], 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


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


Fuel cell system for a 50 Wmax laptop


• 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

Fuel cell system for a professional broadcast camera


• 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

Mobile power box


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


Cathode agglomerate model

Mass balance

Charge balance

Oxygen flux in agglomerate


Cathode agglomerate model

Charge balance

Ohm`s law


cell

pote

nti

al /

[V]

cell

pote

nti

al /

[V]

current density / [A/m2]current density / [A/m2]

Comparision of measured and simulated polarisation curves

Small current density:

change of Tafel-slope

Influence of surface-to-volume

ratio of agglomerates

= 6 105 m-1

= 9 104

m-1


Resistance [m2]

Resistance [m2]

Simulation of impedance spectra Perturbation of solution variables of PDEs

Small perturbations: linearise and Laplace-transform PDEs

Calculate impedance:


currentdensity [A/m2]

meas sim

• Minimum value of the radius of the impedance arc is reached at a current density of 260mA/cm2.

• Mass transport limitation is observed for higher current density: increase of radius of impedance arc.

Comparision of measured and simulated impedance spectra


Influence of double layer capacitance on impedance spectra

GDL

Influenceof electrode



Double layer capacitance

CDL = 3 107 F m-3

Small double layer capacitance:

Two seperate semicircles appear


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 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


• 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

Discretisation mesh and governing equations


Hydrogen and oxygen distribution

H2 molar fraction O2 molar fraction

Arrows: total

flux of

hydrogen and

oxygen.

Vcell = 0.4 V

anode cathode


Water distribution and flux

H2O molar fraction x 10-3 H2O molar fraction

Arrows:

total flux

of water.

Vcell = 0.4

V

anode cathode


Heat flux and temperature

anode cathode

T [K]

• Arrows: total flux of heat.

• Cooling effect of ribs.

Vcell = 0.4 V


Electronic and protonic potential, current direction

Electronic potential Protonic potential

e [V] p [V]

Arrows indicate the technical current direction.


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.


membrane

GDL

cathodeelectrode

Normalised y-coordinate Normalised x-coordinate

Current distribution in cathode gas diffusion layer

(e)

cut line (e)

(e)


PEM fuel cell model based on FLUENT CFD-software

Submodels:

• The electrochemical submodel predicts the local current-to-voltage 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.


Segmented fuel cell

‚Along - the - Channel‘

• Flow-field geometry: Parallel channels • Determination of spatially resolved current density

• Measured values: temperature, gas flow-rates, relative humidity

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 160,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

row 1 row 2 row 3

curr

ent pe

r se

gmen

t [A

]

position


1 2 3 4 5 6 7 8 9 101112131415

0.060.080.100.120.140.160.180.200.220.24

600sccm 300sccm 50sccmC

urre

nt D

ensi

ty [A

/cm

²]

Segment Position

Current distribution along the channel

• 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

gas flow direction:


1 2 3 4 5 6 7 8 9 1011121314150.00.10.20.30.40.50.60.70.80.91.0

600sccm 300sccm 50sccm

Rel

ativ

e H

umid

ity

Segment Position1 2 3 4 5 6 7 8 9 101112131415

290295300305310315320325330335


Tem

pera

ture

[K]

Segment Position

1 2 3 4 5 6 7 8 9 1011121314150.00.10.20.30.40.50.60.70.80.91.0


Rel

ativ

e H

umid

ity

Segment Position1 2 3 4 5 6 7 8 9 101112131415

0.1

1


Pro

toni

c R

esis

tivity

[m

]

Segment Position

Analysis

Relative humidity of air in the channel

Temperature of air in the channel

Relative humidity of air at MEA

Membrane protonic resistivity


Profiles of flow velocity and temperature including inlet region

velocity profile temperature profile


Dynamic simulation of two phase flow

Solution of the PDEs for:

Adaptive grid generation in space / time

Problem: Determination of material parameters

Two phase flow in porous media

Species transport in the gas phase

Energy balance in the porous media

Potential flow of electrons and protons

Colours: pressure distribution for counter-flow case.

Modelling concept by Mario Ohlberger (Institute for Applied Mathematics, Freiburg).


Two-phase flow in porous gas diffusion layer and electrodes

Mass balance

Darcy-law

Water and gas saturation

Capillary pressure

phase-transition


Model geometry and discretization mesh


Simulation examplesO2H2

Wasser-dampf

Mass fraction of gas components and saturation of liquid water

Colors:

Red: 1, Blue: 0

flüssigesWasser


Conclusion

• The agglomerate model reproduces both, measured polarisation curves and impedance spectra.

• Change of active agglomerate surface-to-volume ratio depending on the operation point?

Agglomerate model

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 self-breathing planar fuel cells.


ConclusionCurrent 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.

• 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.

Two-phase flow

Documents

Modelling of miniature PEM fuel cells Modelling of miniature proton exchange membrane fuel cells for portable applications J.O. Schumacher 1, E. Fontes