Hybrid CFD and equivalent-circuit impedance modeling of solid oxide

electrochemical cells

11/12/2013 Valerio Novaresio

Valerio Novaresio, Christopher Graves, Henrik Lund Frandsen, Massimo Santarelli

Risø campus

Attention curve (…a joke…)

Time

Attention level

Lunch End day

Attention threshold

level

We are here…

Outline

Chapter 1

SOC: relevance of geometry

Nernstian effects vs. Butler- Volmer effects

Chapter 2

EIS & FV: state of the art

Hybrid model (focus on LF)

Some results

Future works

500

600

700

800

900

1000

1100

1200

-30 -20 -10 0 10 20 30

Vo

ltag

e [

mV

]

Current [A]

Experimental Simulation

SOC modeling at high current density

Modeling “mantra”: good agreement with experimental data!

SOC modeling at high current density

500

600

700

800

900

1000

1100

1200

-30 -20 -10 0 10 20 30

Vo

ltag

e [

mV

]

Current [A]

Experimental Simulation

At high current density sometimes (usually…) something’s wrong…

Assume a spherical cow…

U∞

U∞

U∞

U∞

With far field approximation we can

usually obtain good results

…or neglect the real SOC geometry

500

600

700

800

900

1000

1100

1200

0 5 10 15 20 25 30 35

Vo

ltag

e [

mV

]

Current [A]

H2 50%, H2O 50% H2 30%, H2O 70%

Experimental vs. Simulations

These effects are mainly Nernstian effects!

Nernstian vs. Butler-Volmer

Two way to “capture” high current density behavior:

Artificial “denaturation” of Butler-Volmer equation (extreme modification

of symmetry factor and exponents in exchange current density)

Simulation of right 3D geometry in order to feed the cell with the right local gas composition (tacking into

account shadow effects)

75%

25% 3D Nernstian effects

Non linearity Butler-Volmer effects

Ratio between Butler-Volmer non linearity effects and 3D Nernstian effects

in complete SRU simulation

EIS in SOC simulation

• Impedance spectroscopy is widely used to study the electrochemical performance of the individual components (electrodes, electrolytes, gas transport) of solid oxide cells and how the components degrade over time.

• Impedance spectra contain much more information than DC polarization curves.

• Nearly all SOC impedance studies are conducted at open circuit and use 0D impedance model. It would however be very valuable to be able to properly study impedance measured during cell operation (DC polarization).

FV in SOC simulation

• Complex geometry • Huge number of elements • Good approximation of mass transport phenomena • Poor (less good…) approximation of electrochemical phenomena

• Simple geometry • Huge number of elements • Good approximation of mass transport phenomena • Good approximation of electrochemical phenomena

• Very simple geometry • Huge (very…) number of elements (high parallelization) • Excellent approximation of mass transport phenomena • Excellent approximation of electrochemical phenomena

CFD

fo

r st

acks

C

FD

for

elec

tro

des

MD

&

LBM

How can couple them?

1D EIS models: good results for electrochemical processes,

not trivial mass transport process evaluations

CFD models both at cell and stack level: accounting for cells

performances (degradation, conversion rate, etc…) at stack

level requires a huge amount of computational elements (~109)

Series of 1D EIS model overlapping a

fully 3D CFD mass transport model (also in porous supporting

electrode)

Frequency domain

Time domain

Hybrid model: the idea

State of the art

1D EIS models: good results for electrochemical processes,

not trivial mass transport process evaluations

CFD models both at cell and stack level: taking into account cells performances (degradation,

conversion rate, etc…) at stack level requires a huge amount of

computational elements (~1015)

Series of 1D EIS models overlapping a

fully 3D CFD mass transport model (also in porous supporting

electrode)

Improving step

Frequency domain

Time domain

Input: geometry and

parameters

Output: Variables

distributions and spectrum

impedance

Hybrid model approach

Coupled code increases performance far from

OCV and doesn’t requires parameters

tuning

Hybrid model: LF description

Typical EIS models accounts mass transport only with an equivalent

impedance through a fictitious equivalent circuit

Warburg Element

Transient PDE for species mass transport (+ compressible Navier Stokes)

Hybrid model: paradigm

Emulation (reproduction of the effects)

vs.

Simulation (reproduction of the causes)

Focus on LF processes: mass transport

“Extreme” assumption in order to emphasize (and isolate) mass transfer LF

effects:

ηact + ηOhm = const

Hybrid model: algorithm

Navier Stokes and species equations

are solved

Local Nernst potential value is

calculated

Electrolyte function provides

impedance only due to processes

computed in frequency domain

Total impedance value is calculated from voltage and

current peaks (magnitude and

delay)

Impedance due to mass transfer is

obtained

For all ω…

…do these steps in OpenFOAM®

EIS SOFC: typical experimental data

Impedance decreases as the

frequency increases

Picks move on the right as the

frequency increases

EIS SOFC: simulation results (hybrid code)

H2=97%, ohmic resistance + mass transport impedance

3D geometry aspects

Inlet

Outlet

Electrode

Gas channel

Interconnector

Inlet

3D geometry results

Small inductive effects

Fu = 75%

0

0,05

0,1

0,15

0,2

0,25

0,045 0,095 0,145 0,195 0,245

-Zim

ag [

Ω c

m2 ]

Zreal [Ω cm2]

OCV

FU = 13%

It seams ohmic resistance reduction…

10% difference (isothermal case)

…but it could be a cathode Nernstian effect

xO2 = 21.00 % xO2 = 21.00 % xO2 = 21.00 %

xH2 = 90.00 % xH2 = 89.99 % xH2 = 89.98 %

xH2O = 10.00 % xH2O = 10.01 % xH2O = 10.02 %

η1 = 0.51 mV η 2 = 0,45 mV η 3 = 0.40 mV

η 1

i1

η 2

i2

η 3

i3 VOCV 𝑅𝑂𝐶𝑉

𝑔=

∆𝑉

∆ 𝑖𝑘𝑘

xO2 = 21.00 % xO2 = 20.95 % xO2 = 21.90 %

xH2 = 90.00 % xH2 = 84.30 % xH2 = 79.15 %

xH2O = 10.00 % xH2O = 15.70 % xH2O = 20.85 %

η1 = 245.51 mV η 2 = 221,56 mV η 3 = 205.49 mV

η 1

i1

η 2

i2

η 3

i3 V0.9 𝑅0,9

𝑔=

∆𝑉

∆ 𝑖𝑘𝑘

𝑹𝟐𝜴< 𝑹𝟏

𝜴

0

0,1

0,2

0,3

0 0,05 0,1 0,15 0,2 0,25

-Zim

ag [

Ω c

m2]

Zreal [Ω cm2]

OCV - With pin

OCV - Without pin

OCV

0,1

0,15

0,2

-0,05 0,15 0,35 0,55 0,75

-Zim

ag [

Ω c

m2 ]

Log(f)

OCV - With pin

OCV - Without pin

Differences (little 5%) are present at OCV

0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,045 0,055 0,065 0,075 0,085

-Zim

ag [

Ω c

m2 ]

Zreal [Ω cm2]

FU 13% - With pin FU 13% - Without pin

13% FU

Pins play the role of occlusions: the impedance is about 10% greater (FU 13%)

0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0 0,5 1 1,5

-Zim

ag [

Ω c

m2 ]

Log(f)

FU 13% - With pin FU 13% - Without pin

13% FU

Pins play the role of occlusions: the impedance is about 10% greater (FU 13%)

Some comments…

• Fuel utilization effects can be taken into account

• Incipient occlusion effects can be analyzed

• Geometry can be further optimized

• High computational time required

• Coupling with reliable HF equivalent circuit is only in working progress (“definitive” validation with experimental data still is a “to do” activity)

Outlook

• Start from experimental data

• Set up a fully 3D FV simulation

• Tune the FV parameters in order to fit experimental data

• Start transient simulation for different frequencies ω

Many (many…) computational elements

Different parameters set can fit the same experimental data

…that means a lot of computational time

Conclusions

• FV algorithm for impedance spectra analysis was built.

• LF spectrum (mass transfer) can be described starting from physical PDE. Does it make sense? Yes!

• Incipient occlusion or degradation (pore occlusion) problems can be showed and studied (with proper code addition).

• Good approximation of species concentration fields can provide a more realistic bulk values also for HF models.

• The model can be improved by adding other phenomena directly described by PDE.

People

Valerio Novaresio (PhD student, Polytechnic of Turin)

– CFD simulations with open source tool (OpenFOAM®)

– Mass transport modeling in SOFC/SOEC

Christopher Graves (Scientist, DTU)

– Impedance modeling

– Materials and microstructure development

Henrik Lund Frandsen (Senior Scientist, DTU)

– Physical and mathematical modeling

– Mechanical testing and modeling

Massimo Santarelli (Associated Professor, Polytechnic of Turin)

– Experimental analysis of SOFC/SOEC at cell and short-stack level

– Design, development and testing of FC-based complete systems

– System analysis of electro-chemical and thermo-chemical plants

The Occam razor

“...the simplest hypothesis proposed as an explanation of phenomena is more likely to be the true one than is any other available hypothesis, that its predictions are more likely to be true than those of any other available hypothesis, and that it is an ultimate a priori epistemic principle that simplicity is evidence for truth..”

Swinburne - 1997

Thank you for your attention!

Annex - Bibliography • [1] J.I. Gazzarri, O. Kesler, Electrochemical AC impedance model of a solid oxide fuel cell and its

application to diagnosis of multiple degradation modes, Journal of Power Sources. 167 (2007) 100–110.

• [2] J.I. Gazzarri, O. Kesler, Non-destructive delamination detection in solid oxide fuel cells, Journal of Power Sources. 167 (2007) 430–441.

• [3] J.I. Gazzarri, O. Kesler, Short-stack modeling of degradation in solid oxide fuel cells: Part I. Contact degradation, Journal of Power Sources. 176 (2008) 138–154.

• [4] J.I. Gazzarri, O. Kesler, Short stack modeling of degradation in solid oxide fuel cells: Part II. Sensitivity and interaction analysis, Journal of Power Sources. 176 (2008) 155–166.

• [5] S. Gewies, W.G. Bessler, Physically Based Impedance Modeling of Ni/YSZ Cermet Anodes, J. Electrochem. Soc. 155 (2008) B937–B952.

• [6] W.G. Bessler, A new computational approach for SOFC impedance from detailed electrochemical reaction–diffusion models, Solid State Ionics. 176 (2005) 997–1011.

• [7] W.G. Bessler, Rapid Impedance Modeling via Potential Step and Current Relaxation Simulations, Journal of The Electrochemical Society. 154 (2007) B1186–B1191.

• [8] R. Barfod, M. Mogensen, T. Klemensø, A. Hagen, Y. Liu, P. V. Hendriksen, "Detailed Characterization of Anode-Supported SOFCs by Impedance Spectroscopy" J. Electrochem. Soc. 154 (4), B371-B378 (2007).

• [9] R. Mohammadi, M. Ghassemi, Y. Mollayi Barzi, M. H. Hamedi, “Impedance simulation of a solid oxide fuel cell anode in time domain” Journal of Solid State Electrochemistry volume 16, issue 10, pp 3275-3288 (2012)

• [10] V. Novaresio, M. G. Camprubí, S. Izquierdo, P. Asinari, N. Fueyo, “An open-source library for the numerical modeling of mass-transfer in solid oxide fuel cells”, Computer Physics Communications, Volume 183, Issue 1, January 2012, Pages 125-146.

Annex – OpenFOAM® code

• The code used in present work was developed using the open source tool OpenFOAM®

• The mass transport library (that is part of the code) was release as an open source code in 2012

• The first release of the code was presented at Piero Lunghi EFC 2009

• The complete SOC code will be release soon as a open source code

Annex - Photos