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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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 2
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 3
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 4
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 5
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)
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 6
PEM-Modelling (1)
)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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 7
PEM-Modelling (1)
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:
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 8
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
PEM-Modelling (1)
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 9
PEM-Modelling (1)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 10
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 11
PEM-Modelling (2)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 12
PEM-Modelling (2)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 13
PEM-Modelling (2)
Assumptions
Stationary conditions
Laminar flow
Isotropic porous zones
Calculation with in house CFD-code FIRE
3D CFD-calculation
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 14
O2 molar fraction in themiddle of the gas-diffusionlayer
O2 molar fraction in themiddle of the gas-channel height
Current density overthe membrane
PEM-Modelling (2)
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 15
Relative pressure inthe gas diffusion layer
Convective flow in thegas diffusion layer
Water molar fraction in gasdiffusion layer
PEM-Modelling (2)
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 16
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 17
PEM-Modelling (3)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 18
PEM-Modelling (3)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 19
PEM-Modelling (3)
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
−−
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 20
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 21
PEM-Modelling (3)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 22
PEM-Modelling (3)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 23
PEM-Modelling (3)
LB- Simulationof a simple threephase domain
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 24
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 25
2D- Cut through pore structure
Computer Tomograph – recording
GDL can be rather anisotropic
Activelayer
E-TEK electrode
Carbonfibres
Parameter Measurement
Micro-Comp. Tomography (PSI) of ETEKelectrode (left) and torray paper (right)
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 26
Parameter Measurement
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 27
PEM-Modelling (3)
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 28
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 29
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
Fuel Cell Research Symposium - Modelling and Experimental Validation, ETH Zurich 17.04.04 | Page 30
Thank you for your attention