Open Source Modelling of Fuel Cells - EERA · Open Source Modelling of Fuel Cells ... Computational...

Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering

Mitg

lied

der H

elm

holtz

-Gem

eins

chaf

t

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


Forschungszentrum Jülich GmbH – Location

Jülich


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


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


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


Single cell with 3-fold serpentine CFD model of gas channels 16 cm2 active area

Jülich HT-PEFC cells


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.


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


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


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


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::


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


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


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


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


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.


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 !!!


lCell web site


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’


Cell

Parent mesh

Fuel Child mesh

Air Child mesh Interconnect/BPP

Child mesh

PEN/MEA Child mesh


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 !


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


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

=

∏

∏


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

∆ ′′′ ′′′= − −


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


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 = ∑


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


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.


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.


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:


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


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)

Institute of Energy and Climate Research IEK-3: Electrochemical Process Engineering 36 36

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


Fuel mesh

quickTestStack case

37


Air and fuel

quickTestStack case

38


Electrolyte mesh

quickTestStack case

39


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


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


Nernst potential


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.


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


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


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?


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


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.


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.

Open Source Modelling of Fuel Cells - EERA · Open Source Modelling of Fuel Cells ... Computational...

Documents

Transcript of Open Source Modelling of Fuel Cells - EERA · Open Source Modelling of Fuel Cells ... Computational...