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Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
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Open Source Modelling of Fuel Cells
Steven B. Beale
Institute of Energy and Climate Research, IEK-3,
Forschungszentrum Jülich GmbH, 52425 Jülich
Presentation at 1st EERA Conference,
Birmingham UK, 25 November 2016
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 1
Forschungszentrum Jülich GmbH – Facts and Figures
Founded 11 December 1956 Partners Federal Republic of Germany (90 %) North Rhine-Westphalia (10 %) Revenue € 617 million 2013 (32 % third-party funding) Structure 9 institutes 2 project management organizations (project volume: € 1.8 billion) Employees 5,534 (total) 1,924 scientists, incl. 498 PhD students 335 trainees & students on placement 995 visiting scientists from 39 countries
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 2
Forschungszentrum Jülich GmbH – Location
Jülich
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 3
Institute of Electrochemical Process Engineering (IEK-3)
Employees: 120 Core Competences: Fuel Cells Electrolysers Areas of Expertise • Process & Systems Analysis • Process & Systems Engineering • Fabrication Engineering • Systems Analysis • Electrochemistry • Modelling & Simulation • Catalysis & Reaction Engineering
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 4
What’s a Fuel Cell?
• Convert chemical energy to electricity (and heat)
• Use hydrogen-rich fuels • Commonly found types: polymer electrolyte
(PEFC red) and solid oxide (SOFC black) • Electrolyser is a reverse fuel cell
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 5
Fuel Cells
SOFC PEFC Stationary power applications Mobile applications (transportation)
Fuel: Hydrogen, carbon monoxide, methane, natural gas
Fuel: Hydrogen
Oxidant: air Oxidant: air
Electrolyte – O2- ions transported Membrane (MEA)→Protons + water dragged → water management
Interconnect Bipolar plate (BPP)
High temperature → Thermal radiation + exptl. current density data hard to get
Both low and high temperature. Multi-phase and phase change issues
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
Single cell with 3-fold serpentine CFD model of gas channels 16 cm2 active area
Jülich HT-PEFC cells
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 7
What is CFD?
Computational fluid dynamics - Method of solving problems involving flow of fluids (air, water), heat (in a solid or fluid) or chemical species (in a reaction). Examples; cars, aeroplanes, tunnels, buildings, electronics, food & beverages, fires CFD is a subset of computer aided engineering (CAE) (maybe) 1-5% of CAE. CAE is (maybe) 1-5% of all software today.
Market for commercial CFD software today is around $500M PA. growing at around 5%. This seems small, but commercial sales represent a small fraction of the real market. Since fuel cells companies have limited sales - market for commercial CFD products extremely limited. Good case for open source software.
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Where did CFD come from?
Early beginnings in 1920s with L.F. Richardson - pioneered techniques, based on solution of differential equations for weather prediction. “Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity”
Major breakthroughs came in late 50s and early 60s in T-3 group at LANL (under Francis Harlow). Emphasis on physics not mathematics. MAC method – staggered grid. Poisson eqn. for pressure. Lagrangian/Eulerian approaches. k-ε model for turbulence. Two-phase flow.
Photo by Dr. Harry Edgerton
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 9
Commercial CFD companies/software
Concentration Heat and Momentum (CHAM) formed by Prof. D.B. Spalding Originally located at Imperial College London (1969). First commercial CFD code PHOENICS (Parabolic Hyperbolic or Elliptic Numerical Integration Code Series). Sequential FORTRAN. 1981. Subsequently numerous other codes; Fluent, StarCD, CFX etc. In mid 1990s. H. Weller, H. Jasak and others wrote FOAM while at Imperial College. Object-oriented C++. Became open source with OpenFOAM. Many companies, e.g. car manufacturers use both commercial and OS CFD packages simultaneously
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
Commercial
Hand-written source
OpenFOAM OpenPNM FAST-FC
Fluent StarCD PHOENICS
Applications UDFs Python scripts
Experimental data base
Analytical methods
V&V
Models
Open source software enhances capabilities in a fully-integrated software environment
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
Share the interface - not the application (and then only if you want to)
External repository
Internal protected repository
Researcher B Researcher A
‘git pull’
‘git push’
‘git commit’
Public::
Private::
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openFuelCell
• Project began as a joint German/Canadian research activity
• Multi-physics models within the framework of OpenFOAM (most popular open CFD) suite • Runs with most versions of OpenFOAM
• Approx.10,000 lines of code.
• Initial emphasis was SOFCs. Is now PEFCs.
• Also applied to electrolysers
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 13
openFuelCell cont’d
• As work is published source is checked in to SourceForge repository: http://openfuelcell.sourceforge.net/
• Historical library of research work – definitely not plug and play software
• Web site URL provides reference point in bibliography in journal papers
• Provides scientist mechanism to duplicate published results • Sourceforge site also provides explicit reference to article titles - Increase future
citations • Maintenance presently 100% voluntary
• Original idea - by pooling resources can build better tool(s). Avoid reinventing
the wheel
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 14
Pro and Cons of OpenFOAM (from Wikipedia)
ADVANTAGES Friendly syntax for partial differential equations
Fully documented source code
Unstructured polyhedral grid capabilities
Automatic parallelization of applications written using OpenFOAM high-level syntax
Wide range of applications and models ready to use
Commercial support and training provided by the developers
No license costs
Source: Wikipedia.org
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Pro and Cons of OpenFOAM (from Wikipedia)
DISADVANTAGES Development community suffers from fragmentation, giving rise to numerous
forked projects.
Absence of an integrated graphical user interface (stand-alone Open Source and proprietary options are available)
Programmer's guide does not provide sufficient details, making the learning curve very steep if you need to write new applications or add functionality
Source: Wikipedia.org
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Examples of repositories/working groups
FireFOAM – Open source fire modelling for commercial insurance industry. Must be open source for legal reasons. PorousMultiphaseFoam – Petroleum reservoir engineering. Buckley-Leverett shock, capillary gravity equilibrium, viscous fingering in heavy oil reservoir. Similar setup to openFuelCell. OpenFOAM Turbomachinery working group: ERCOFTAC centrifugal pump study.
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 17
Other open source fuel cell models
DuMuX, DUNE for Multi-{Phase, Component, Scale, Physics, ...}, 2-D multi-phase PEM code (Germany), TRUST -Trio_U Software for Thermohydraulics - Nuclear application. Developed at CEA (France) FAST-FC Queen’s University (Canada)/Ballard/US DOE. Based on OpenFOAM® extend. Performance and degradation modelling. PEFCs openFCST University of Alberta (Canada). FEA based. PEFCs openPNM Pore network modelling. McGill University (Canada) • Little chance fuel cell community will standardise on a single code !!!
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
lCell web site
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
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Code design is important !
Example: domain decomposition
• Solve for temperature on ‘parent mesh’
• All other variables solved on 3-D ‘child meshes’ (volScalarField)
• Electrochemistry solved on a 2-D surface (FvPatchScalarField)
• Main reasons:
(a) Economise on storage – only store/solve variables that actually exist
(b) Minimise on boundary-to-boundary communication between children
(c) Facilitate code parallelisation on large compute clusters
- First divide up parent then child meshes into ‘chunks’
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
Cell
Parent mesh
Fuel Child mesh
Air Child mesh Interconnect/BPP
Child mesh
PEN/MEA Child mesh
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering
Parent mesh
Fuel
Air
Cell
Child mesh
Child mesh
PEN Child mesh
Temperature solved on parent mesh
Velocities and mass fractions solved on gas child meshes
T
ρu
ρu
Mass, species boundary values
Local current density
q
The devil is in the detail !
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 24
Gas transport (typical CFD)
eE V j R′′− η − =
( ) ( )( )0 exp 2 exp 2 1e ej j F RT F RT ′′ ′′= β η − − − β η
,e
a cη = η∑
1. Nernst
2. Kirchhoff-Ohm
3. Butler-Volmer
( ) 0div ρ =u
Electrochemistry
( ) ( )grad div gradD
div pkµ
ρ = − + µ −uu u u
( ) ( )div gradi idiv y yρ = Γu
( ) ( )div gradpdiv c T T Sρ = λ +u
Mass & species sources
Heat transfer Heat sources
0 ln PRTE E KzF
= +
Mass fractions (partial pressures)
Temperatures
Some eqns… Child meshes
Parent mesh
Surface area
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 25
Nernst Equation
Nernst potential Generic form – good idea if change fuel cell type, fuel composition, etc.
0 ln PRTE E KzF
= +
i i j ji j
a R b P=∑ ∑
[ ]
j
i
b
jj
P ai
i
PK
R
=
∏
∏
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 26
When current drawn, Voltage, V, drops
ηa and ηc anode and cathode polarisations/over-potentials, re and ri are Ohmic resistances of electrolyte and interconnect - temperature dependent Total heat source: should be broken up into components (electrochemical, Joule, etc.) and by location.
2. Kirchhoff-Ohm law
Ref: Beale, Ch 2 in; Transport Phenomena in Fuel Cells; Eds. B. Sunden & M. Faghri, 2005 26
e i a cV E j R j R′′ ′′= − − − η − η
Ohm’s law
Cathode
Load Electrolyte
Interconnect
( )1 2
aE − η
( )1 2
cE − η
e eV iR=
Anode
0V =∑
Kirchhoff’s 2nd law
Interconnect
V 2Hq V jF
∆ ′′′ ′′′= − −
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 27
In SOFC, activation overpotentials are small but significant at both electrodes. In PEFC, only cathode is active and η is larger. Tafel equation 1. Solve the Nernst eqn for E 2. Solve Kirchhoff-Ohm for j’’ and 3. Solve Butler-Volmer numerically for η (NB: different approach taken for PEFC) Generic form – would be a good idea for future coding
3. Butler-Volmer Equation
( )02 2exp exp 1F Fj jRT RT
′′ ′′= −β η − − β η
02exp Fj jRT
′′ ′′= −β η
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 28
Variable properties
Density: Viscosity: Specific heat:
ii i
i i i
yp px MRT RT M
ρ = =∑ ∑
( )6
01000 i
i k ki
b T=
µ = ∑
6
0
11
i in
ij ij
jj i
x
x=
=≠
µµ =
+ φ∑
∑( ) ( )
( )( )
1 12 4
12
2
1
8 1
i j j i
ij
i j
M M
M M
+ µ µ φ = +
Thermal Conductivity:
p i pii
c x c= ∑( )
6
,0
1000 ip i k k
ic a T
=
= ∑
1
1 11
n nk
i iki k i
k i
xGx
−
= =≠
λ = λ +
∑ ∑
1 1 12 2 4
2
1.065 1 12 2
i i k iik
k k i k
M M MGM M M
− µ = + + µ
( )6
00.01 1000 i
i k ki
c T=
λ = ∑
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 29
Porous FSG Model for effective diffusivity
Binary FSG coefficients: Porous model: Knudsen model: Wilke model for gas mixture Maxwell-Stefan (generalized Fick’s law) formulation developed by Q. Cao
( )( )
1.75
1 3 1 3
10 1 1i jij
i j
T M MD
p V V
+=
+
ref 1 1ij
ij Kn
DD D
ε= + τ
( )1
1 ji i
j i ij
xD x
D
−
≠
= −
∑
13i Kn p T i
D d= ν8
T ii
RTM
ν =π
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 30
OpenFOAM typical tree structure
‘src’ divided into ‘libsrc’ (pre-compiled libraries) ‘appsrc’ user generated compilable C++ code aka “UDFs” ‘run’ includes ‘0’ (initial & boundary data values) ‘constant’ polymesh files & transport property ‘dictionary’ (input file) system solver ‘dictionaries’ ‘1’, ‘2’, ‘3’ etc. - outputs from solver at time stamps in secs.
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 31
OpenFuelCell Directory structure
Extends standard OpenFOAM structure appSrc contains the ‘main’ program ‘sofc.C’ and a number of ‘header files’ included in ‘sofc.C’ e.g.
‘solveElectrochemistry.H’ More branches in tree due to multiple meshes ‘0/fuel’, ‘0/air’, etc. ‘constant/fuel’, ‘constant/air’ ‘config’ is a new directory where the commands to stitch together blockMesh generated mesh/grid placed
Ref: S.B. Beale et al. Open-source Computational Model of a Solid Oxide Fuel Cell, Comp Phys Com 200 15-26 2016.
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 32
Fuel/air species ‘dictionary’ - easy to change reactants/products
speciesList ( O2 N2 ); O2 O2 31.9988 4 -1 0 205.152; N2 N2 28.0134 0 0 0 191.609; // | | | | | | // | | | | | standardEntropy [J/(mol K)] // | | | | enthalpyOfFormation [J/mol] // | | | produced=1|inert=0|consumed=-1 // | | molecularChargeForFaradaysLaw // | molecularWeight [kg/kmol] // name
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 33
Diffusivity
Multiple models. Defined as instances of an abstract base class, user selects choice at run time with a pointer list by inserting values in a dictionary file. Different regions have different models Diffusivity { Type porousFSG Tname T; pName p; speciesA H2; speciesB H2O; porosity 0.25; tortuosity 3.0; dPore dpore [0 1 0 0 0 0 0] 2.9e-07; // pore size //doBinary false; }
constructs e.g. a porous Fuller-Schettler-Giddings (FSG) model:
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 34
Scalability on RWTH HPC-Cluster
S. Keuler benchmarked openFuelCell with up to 960 cores with near linear performance - 1000 cores typical for CFD cases though max recorded is 100,000 (100 billion mesh points)
Grad students routinely run 25-50 cores
Parallelisation a major advantage of openFuelCell code
All the library cases can be run in parallel
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 35
HT-PEFC cell model
Recent openFuelCell work at Juelich dedicated to HT-PEFC cells and stacks Serpentine channels liquid cooled phosphoric acid-based “liquid” membrane ‘single phase’ problem in channels and GDLs
Grids generated with Salome (open source), ANSYS ICEM-CFD (commercial) Set fuelCellType HTPEFC; in constant/cellProperties Cases quickTest_HTPEFC and quickTestStack_HTPEFC have been prepared but are not on the git repo (pending publications) U. Reimer, B. Schumacher and W. Lehnert, J. Electrochem. Soc. 162 (1) F153-F164 (2015)
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Air mesh ‘Proof of concept’ demonstration for a (very) small 3-cell ‘stack-of-cells’ counterflow model 5 channels per cell. Runs on a single-processor PC.
Library example: quickTestStack case
Courtesy R. Nishida
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 37
Fuel mesh
quickTestStack case
37
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 38
Air and fuel
quickTestStack case
38
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Electrolyte mesh
quickTestStack case
39
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HT-PEFC/SOFC Stack model
Ref: S.B Beale, S.V. Zhubrin. A Distributed Resistance Analogy for Solid Oxide. Fuel Cells, Numer. Heat Transfer, 2005.
Fuel cell operated in stacks to increase voltage Problem: Computational meshes become unmanageable in size Solution: Volume averaging in the ‘core’ of stack. Distributed resistance analogy
(aka porous media analogy). Multiple ‘phases’ occupying same space Full Navier-Stokes system solved in manifolds. Phase drag and inter-phase heat transfer coefficients No parent mesh: ← Parallelisation not an issue
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 41
Fuel stream-lines coloured by hydrogen mass fraction
Ref: R.T. Nishida, S.B Beale, J.G. Pharoah. Computational Fluid Dynamics Modelling of Solid Oxide Fuel Cell Stacks. J. Hydrogen Ener., 2016.
Jülich F-design 10-cell SOFC stack
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 42
Nernst potential
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Current/future research activities
HT-PEFC and LT-PEFC cell and stack models with experimental V&V Complex geometries Both distributed resistance and ‘stack of cells’ approach
Water transport in PEFC assemblies HT vs. LT issues: back-diffusion/drag/evaporation-condensation
phenomena Local impact on membrane performance Non-equilibrium effects
Multi-phase flow in GDL-channel assembles with/without free-surface Drop formation and entrainment Appropriate solvers for porous media; M2, 2-phase Eulerian etc.
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 44
Current/future activities
Two potential (Poisson) models for ion/electron transport as ‘drop in’
replacement for Nernst – losses (Kirchhoff-Ohm eqn.) Important if local membrane conductivity varies Should be run time selectable
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 45
Positive aspects of open source modelling
Open source paradigm has allowed for significant progress in terms of User 100% in control. WYSWYG Code ownership. Can change literally anything. Few disadvantages of commercial licensed software with most of
benefits More science content possible (not a ‘black’ box) Opportunities for sharing functions and data externally with
partners/clients – no limitations ‘Honest’ level playing field for benchmarking (V&V) Parallel performance – very important for large-scale models
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 46
Some reservations too…
Lack of coordinated support/documentation User must know how to do everything themselves. Fuel cell expert
needs to understand maths and physics - not necessarily bad thing OS paradigm runs contrary to traditional corporate structure
– ‘Not invented here’ syndrome encountered – Little uptake by fuel cell manufacturers to-date (typically SMEs)
Professional (sophisticated) computer science support required in addition to relatively sophisticated programming skills
– PhD students not always good at software best practices – Resistance to pay for professional support for open source software
Code forking leads to dilution of effort. Need for coordination. Role for EERA IEA?
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 47
Acknowledgements (in alphabetical order)
Martin Andersson, Lund University/Forschungszentrum Jülich zzz Qing Cao, Forschungszentrum Jülich Hae-Won Choi, Queen’s University Dieter Froning, Forschungszentrum Jülich Duncan Gawel, Queen’s/RMC Fuel Cell Research Centre Hrvoje Jasak, University of Zagreb Ron Jerome, Shared Services Canada Stefanie Keuler, Forschungszentrum Jülich Sohyeon Lee, Forschungszentrum Jülich Werner Lehnert, Forschungszentrum Jülich Robert Nishida, Queen’s University Jon Pharoah, Queen’s University Uwe Reimer, Forschungszentrum Jülich Helmut Roth, National Research Council Canada Detlef Stolten, Forschungszentrum Jülich Shidong Zhang, Forschungszentrum Jülich
Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 48
Recent publications
A Review of Cell-scale Multi-phase Flow Modelling, including Water Management, in Polymer Electrolyte Fuel Cells. M. Andersson, S.B. Beale, M. Espinoza, Z. Wu, W. Lehnert, Appl. Ener., 180, 757-778. 2016. Comprehensive Computational Fluid Dynamics Model of Solid Oxide Fuel Cell Stacks. R.T. Nishida, S.B. Beale, J.G. Pharoah. Int. J. Hydrogen Ener., 2016. Open-source Computational Model of a Solid Oxide Fuel Cell. S.B. Beale, H.-W. Choi, J.G. Pharoah, H.K. Roth, H. Jasak, D.H. Jeon. Comput. Phys.Comm., 200, 15-26. 2016. Mass Transfer Formulation for Polymer Electrolyte Membrane Fuel Cell Cathode. S.B. Beale. Int. J. Hydrogen Ener., 40, 35, 11641 -11650, 2015.
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Recent publications
U.Reimer, B. Schumacher, W. Lehnert. Accelerated Degradation of High-Temperature Polymer Electrolyte Fuel Cells: Discussion and Empirical Modeling. J. Electrochem Soc. 162, 1, F153-F164. 2015 Validation of a Solid Oxide Fuel Cell Model on the International Energy Agency Benchmark Case with Hydrogen Fuel. A.D. Le, S.B. Beale, J.G. Pharoah. Fuel Cells, 15, 1, 27-41, 2015.