Practical Approach to Fuel Cell Modelling – Extending ... · Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 7 PEM-Modelling (1)

Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 1

Practical Approach to Fuel Cell Modelling –Extending the Capabilities of SimulationTools in an Integrated Development Process

M. Schuessler, G. Rabenstein, P. Prenninger,G. G. Scherer, I. Mantzaras, W. Brandstätter


Contents

Brief look at ICE-Engine Development Process(Simulation and Experiment)

PEM technology

0D-PEM Model for System Applications

3D-PEM Modeling: Domain Splitting and AVL-Focus

GDL-Submodel for Parameter-Evaluation

Measuring GDL-Parameters

Conclusions and Outlook


Company Profile

Turnover:1984: 40 Mio €

2002: >400 Mio €

Employeesmployees:1984: 5602002: 2850

Average R&D spending:10 % of turnover

AVL Advanced Simulation Technology

AVLInstrumentationand Test Systems

AVLPowertrain Engineering

Engineering

Simulation

Testing


00 1818 303066 1212 2424 3636 4242

Concept StudyPrototypeDevelopment

Pre-ProductionDevelopment

SOP

Months

ProductionChecks

Reduction ofReduction ofDevelopment TimeDevelopment Time

Concept Study

SOP

Pre-ProductionDevelopment

ProductionChecks

AVL Engine Development Process


Example: Thermomechanical Fatigue

αgas(x)

Nfail(x)

αcool(x)

pint(t), Tint(t) λdmfuel/dt

Twall(x)

pexh(t), Texh(t)

T(x,t)σ(x,t)u(x,t)

Fbolt, PFP, VS

n, P

dm/dt

1D thermodyna-mics (rated power)

Coolant-side heattransfer(rated power)

Gas-side heattransfer(rated power)

Heat transferanalysis(rated power)

Transient heattransfer analysis(TS cycle)

Stress &deformation FEA(assy.)

Stress &deformation FEA(submodel)

Transient stress &deformation FEA(assy.)1D thermodyna-

mics (severaloperating points)

T(x)

Damage post-processing

ZMAT

material model(visco-plastic,damage)

n, P

αgas

Tgas(x)

Tgas

Fbolt, PFP, VS

Coolant-side heattransfer (severaloperating points)

αcool(x)

dm/dt

σ(x,t) εP(x,t)ε(x,t) D(x,t)


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)exp()ln(0 inmibiREV cellcell ⋅⋅−⋅−⋅−=

FastFast Matlab Matlab-Codes for-Codes foroff-line system analysis and on-line application (off-line system analysis and on-line application (HiLHiL))

0D semi-empirical model by Kim*

Model fit to measured data by the parameters E0, R, b, m, n All five parameters are turned into f(p,T)

Calibration by automated parameter fit (non-linear least square)

*Kim, J., Lee, S.-M., Srinivasan, S., Modelling of proton exchange membrane fuel cell performance withan empirical equation, Journal of Electrochemical Society, 142, 8, 1995, p. 2670-2674


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Necessary data input: 3 polarization curve measurements

Performance check of the approach using data from literature

Wang, L. et al., A parametric study ofPEM fuel cell performances,Int. Journal of Hydrogen Energy, 28,2003, p. 1263-1272

Kocha, S.S., Principles of MEApreparation, In: Handbook of Fuel Cells,Volume 3, John Wiley & Sons, 2003

Bevers, D. et al., Simulation of a polymerelectrolyte fuel cell electrode, J. Appl.Electrochemistry, 27, 1997, p. 1254-1264

data from:


Precise “tuning“ in a limited parameter space

drawbacks:

Original component must exist to feed the model

No tool for optimisation of component design

High effort for limited performance prediction

Linkage to deeper level models

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but:

Tendency of shifting the problem to another model level

Submodel has to supply:

additional equations that connect the parameters

parameters that can be determined before componentexists

Develop helpful experimental techniques


PEM-Modelling (2)

Domain Splitting

Separating membrane andcatalyst layer from flow fieldand GDL

Support an interface to aMECA-model outside

H+

Diffusion of protons + liquid Water

Diffusion of gas + liquid water

Fluid Flow

• Species mass fractions• Temperature• Pressure

• Species fluxes• Heat fluxes

1DMECA – Modell

Detailed3D-CFD Model

CFD-codes for transport of reactants in flow field and GDL

Heat transport in solid phase can be solved in Co-Simulation withFEM


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In MECA domain:

Data often proprietary

Important parameters can be derived from laboratory set-ups, ifmaterial is available

Focus on transport of heat, gases, liquid and currentin bipolar plate and GDL


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Membrane - local water transport combined with localelectrical conductivity acc. Springer model*

Catalyst-Layer- Butler-Volmer-Equation for activationpolarisation

Model fits measured polarisation curvefor low current densities.

* Springer T.E., Zawodinski T.A., Gottesfeld S.;”PolymerElectrolyte Fuel Cell Model”; Journal of the ElectrochemicalSociety, 138(1991), 2334-2342

0

200

400

600

800

1000

1200

0 0.2 0.4 0.6 0.8 1

Current Density [A/cm2]

Cel

l Vol

tage

[mV]

Experimental dataCFD-Model Data

Simple 1D-MECA Model

Single cell measurements (no radial gradients),source: PSI


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Assumptions

Stationary conditions

Laminar flow

Isotropic porous zones

Calculation with in house CFD-code FIRE

3D CFD-calculation


O2 molar fraction in themiddle of the gas-diffusionlayer

O2 molar fraction in themiddle of the gas-channel height

Current density overthe membrane

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Relative pressure inthe gas diffusion layer

Convective flow in thegas diffusion layer

Water molar fraction in gasdiffusion layer

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PEM-Modelling (3)

Major challenges:

Accurate description for transport of gases and liquid water inpore structure

Standard CFD-treatment for gas-diffusion layer

detailed description of flow paths in porous media via CFD is unrealistic

volume-averaging method introduces new parameters like permeability

dealing with liquid phase via two-phase flow in porous medium with adjustable interaction

Wanted: Microscopic description of fluid behaviour in gas-diffusion layerin order to deduce effective parameters for the CFD-simulation


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Promising modeling approach to derive CFD-coefficients :

Lattice Boltzmann Method (LBM)

Simulate fluid flow behaviour not by the numerical solution of differentialequation systems but rather by the dynamic interaction of particlesystems

Solid microscopic structure of GDL is used as boundary, no assumptionof isotropy

Cartesian grid with high resolution and simple boundary conditions

Appropriate for microscopic modeling of liquid water


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Ensemble of molecules in a small volume has a Maxwell-Boltzmanndistribution in phase space.

Ensemble is represented by a dramatically reduced phase space: only afew directions i and one velocity is used, with “probabilities densities” orweigthing factors fi

These discrete “particles” i move in discrete time steps to theirneighbour nodes and collide

Propagation according to the LB-Equation:

( ) ( )τ

),(),(),(1, tftftftefeqii

iiixxxxrr

rrr −−=++

BGK-collision operator


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The equilibrium density distribution used in the BGK-collisionoperator

is chosen in such a way, that the solution of the LB-equation isequivalent to the solution of the Navier-Stokes equations.

( ) ( )

( ) 3/5,08,6,4,236/17,5,3,19/1

23

2931

231

94

22

20

−τ=ν====

−++ρ=

−ρ=

iQiQ

uueueQf

uf

ii

iiieqi

eq

rrrrr

r

( )τ

),(),( tftf eqii xx rr

−−


PEM-Modelling (3)

∑

∑

=

=

iii

ii

efu

f

rr

ρ

ρ

1

Approach is mathematically valid for:

Knudsen numbers 0.1 -10

low velocities (Mach number < 0.3)

Macroscopic quantities at therespective node


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calculation in porousdomain efficient due to

explicit algorithm / noiteration

simple boundaryconditions

parallel computingpossible (only localinformation needed)

Propagation

local:

Collision

Boundary Condition(Bounce Back)

vρρ,

( )L,,,, vtxf eqi ρρ

Time step


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Two phase phenomena can be implemented in LBM by amodification of the collision operator:

Adding interaction terms with nearest-neighbour nodesin the calculation of equilibrium velocity distribution feq

i

Leads to phase separation and interface dynamics likewettability or contact angles


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LB- Simulationof a simple threephase domain


Using the correlationfunction a 3D-model isreconstructed

LBM was introduced to model with resolved micro pore structure.

Method needed to generate geometrical model of GDL

Morphologicalinformation is gainedfrom measurement

Tw o-Point Corre lation

0.5

0.55

0.6

0.65

0.7

0.75

0 10 20 30r

The geometricalinformation is condensedto a few statisticalcorrelation functions

Parameter Measurement


2D- Cut through pore structure

Computer Tomograph – recording

GDL can be rather anisotropic

Activelayer

E-TEK electrode

Carbonfibres


Micro-Comp. Tomography (PSI) of ETEKelectrode (left) and torray paper (right)



First results of thecombination LBMwith reconstructedporous structure

input: 2D-pictures

0

50

100

150

200

250

300

350

0 20 40 60 80 100 120 140Mass flow [kg/h]

Pres

sure

dro

p [P

a

Validation of LBM-predictedpressure drop


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LB submodel operating in the GDL generates theparameter input to the CFD model

Coupling to CFD-code via source terms in Navier-Stokes-Equation

vK

SPrr

−=µ

( ) ( ) PSvpvvtv rrrrr

+∇∇+−∇=∇∂+∂∂ µρρ


Conclusions

For PEM development the described concept ofdifferent level models up to LBM defines a good steptowards an efficient development process:

optimisation can be carried out largely by simulation and fewmeasurements

dedicated development of new materials is enabled

fast control models are supported

Interface concept allows customer to couple his ownMECA-model

With a validated transport model correct boundaryconditions for MECA-model can be supplied


Outlook

Extract parameters for CFD by LBM-submodel

Extension of LB-code to 2-phase flow (spatial resolution ofliquid water in GDL)

Strengthen experimental techniques in parallel

Work in continued cooperation with Paul Scherrer Instituteand Christian-Doppler Laboratory, Leoben


Thank you for your attention

Practical Approach to Fuel Cell Modelling – Extending ... · Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 7 PEM-Modelling (1)

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