AN INTEGRATED APPROACH TO MODELING AND MITIGATING SOFC FAILURE

Andrei Fedorov, Comas Haynes, Jianmin QuGeorgia Institute of Technology

DE-AC26-02NT41571Program Manager: Donald Collins, National Energy Technology Laboratory

Project Overview

Electrochemical Reaction

Thermal Transport

Failure

Fracture

CellPerformance

Thermomechanical Damage

Phase I is a one-year effort to investigate and evaluate the feasibility of the solution proposed and/or the merits of the scientific path of inquiry.

Phase II will seek to mature the science and technology developed to a sufficient level that it can be utilized by the SECA Industry Teams.

Technical Issues to be Addressed

Thermomechanical Damage and FailureThermal stresses due to thermal mismatchDelamination and fracture due to thermal mismatch and thermal shockWarpage due to thermal mismatchSeal reliability

Thermal Transport Flow, heat and reagent species transport in porous mediaThermal radiation heat transfer in porous mediaCoupling between radiation heat transfer and other modes of heat transferSource/sink terms for transport equations due to electrochemical reactions

ElectrochemistryCell and stack level engineering modelsInterdependency between electrochemistry and thermal/mass transport Transient processes and failure modes

Electrochemistry

Model Objectives Achieved

Ø Engineering Code§ Accurate and viable

§ Customized structural-language algorithms that are portable to software

§ Enhanced designer insight via graphically intuitive trends

ØComplement to SECA DOE National Labs’ Efforts§ Resolution of reformate stream analysis (NETL)

§ Automated convergence upon set fuel utilization (PNNL)

• Anode-supported cell• Designs capable of 2 W/cm2

• P-E-N dimensions from Kim, J., Virkar, A. V., Fung, K., Mehta, K., and Singhal, S., 1999

Interconnect (~1500 micron LaCrO3)

Anode (-) (~750 micron porous Ni-YSZ)

Electrolyte (~10 micron YSZ)

Cathode (+) (~50 micron LaMnO3)

Interconnect (~1500 micron LaCrO3)Not to scale

Planar SOFC Co-flow Diagram

Planar SOFC Co-flow Model

Pressure(n)=f(xi, Po)PH2 PH2O PCO PCO2 PCH4

Pressure(n)=f(xi, Po)PO2 PN2

Pressure(n+1)=f(xi, Po)PH2 PH2O PCO PCO2 PCH4

Pressure(n+1)=f(xi, Po)PO2 PN2

Flow rates(n)=f(Pi, Qfuel, i(n))NH2 NH2O NCO NCO2 NCH4 Ntotal

Flow rates(n)=f(NOS, Ntotal)NO2 NN2

Flow rates(n+1)=f(P i, Qfuel , i(n))NH2 NH2O NCO NCO2NCH4 Ntotal

Flow rates(n+1)=f(NOS, Ntotal)NO2 NN2

Temperature(n)=f(Q(i)) Temperature(n+1)=f(Q(i))

i(n)

i(n)

nO2

Ano

dech

anne

lC

atho

dech

anne

l

1 2 3 n

Air

Fuel

L

( )

+−

−+−−−=

asOH

Ho ip

ip

FRTi

FRT

iiEiVo

o

2

21ln2

1ln2

lnas

ii

baR

Electrochemical model is a combination of the polarization model of Kim et al. (1999) and Haynes’ slice technique (Haynes and Wepfer, 1999)

Planar SOFC Co-flow Model Validation• Model agrees with experimental data• Discrepancies, primarily differences in fuel

utilization, caused by comparing a button cell to a much larger channel model

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

Current Density [A/cm2]

Vol

tage

[V]

Model Experimental

• Assumptions– Isothermal channels as a design goal– Convection to air stream is the dominant form of cell

thermal management– Laminar, hydrodynamically fully developed flow at the

leading edge due to extensive manifolding • Methodology

– Use well-regarded laminar flow Nusselt correlations for airflow within rectangular ducts, to determine appropriate inlet air temperatures and resulting cell temperature profile

– Vary parameters as required to determine impact• Voltage• Fuel utilization• Fuel-based inverse equivalence ratio / “number of

stoichs” (NOS)

Thermal Model for Cells

Promoting Isothermal Cells

100010501100115012001250130013501400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cell Distance [dimensionless]

Tem

pera

ture

[K]

Base Best

∆Τ = 39

∆Τ = 270

FU=0.3, Vop=0.9, and NOS=81000

1100

1200

1300

1400

1500

1600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cell Distance [dimensionless]

Tem

pera

ture

[K]

Base FU = 0.3 FU = 0.9

∆Τ = 270∆Τ = 391

∆Τ = 142

1000

1100

1200

1300

1400

1500

1600

1700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cell Distance [dimensionless]

Tem

pera

ture

[K]

Base NOS = 2 NOS = 8

∆Τ = 270∆Τ = 135

∆Τ = 527

↑ Vop ↑ NOS

↓ Fuel UtilizationBest Case

1000

1100

1200

1300

1400

1500

1600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cell Distance [dimensionless]

Tem

pera

ture

[K]

Base Volt = 0.3 Volt = 0.9

∆Τ = 270

∆Τ = 157

∆Τ = 378

Graphically Intuitive Design Aids Development

Fuel Cell M&S UpdatesP

ower

(W

)

328

98.4

267.1739

Eta

(%

)

52.1

19.3

33.1078

EA

PD

(mW

/cm

^2) 393

118

320.4608

CV

DP

(kW

/I)

1.64

0.492

1.337379

TA

IR(K

)

1140

46.8

928.7051

sfc

0.691

0.256

0.403396

Voltage(0.5,0.75)

0.5

0.750.61979

NOS(1.5,4.5)

1.5

4.53.0625

Press(2,5)

2 53.5625

Fuel Util(0.5,0.9)

0.5

0.90.69167

Horiz VertVoltage(0.5,0.75)NOS(1.5,4.5)Press(2,5)Fuel Util(0.5,0.9)

Factor0.6197917

3.0625 3.5625

0.6916667

Current X

Power (W)Eta (%)EAPD(mW/cm^2)CVDP(kW/I)TAIR(K)sfc

Response 213

. . .

593.40.4736189

Contour267.1739133.107801320.460831.3373789928.705150.4033964

Current Y 213

. . . . .

Lo Limit . . . . .

0.48

Hi Limit

0.75

Vol

tage

(0.5

,0.7

5)0.

5

Power (W)

sfc

0.5 Fuel Util(0.5,0.9) 0.9

Real-Time Visualization of Constraint Space

Real-Time Visualization of Constraint Space

SFC

Latter Phase I/ Phase II Developments

ØGreater collaboration with SECA-affiliated national labs

ØMitigation of transient mode failure§ Process optimization of transitional phase

of SOFC start-up via modifications to fuel utilization, load allowance, etc.§ Resolving mini thermal cycles due to load

fluctuation

Latter Phase I/ Phase II Developments

ØEnhanced integration with colleagues for multi-physics simulation and mitigation of thermomechanical failure modes. Examples:

§Strength requirements for designated operating conditions

§Gleaming effective mass transport diffusivities for better characterizing concentration polarization

ØViable performance/reliability tools and training for industry

Thermal-Fluid Modeling of SOFC

Thermal-Fluid Modeling of SOFC

Focus of Thermal – Fluid Modeling Efforts

Porous Media Modeling Radiation Modeling• Knudsen, dispersion, diffusion-thermo (Soret) and thermo-diffusion (Dufour) mass and heat transfer effects

• Non-equilibrium heat transfer in porous electrodes to account for unequal gas and solid matrix temperatures

• Effective thermal conductivity of solid matrix of porous electrodes

• SOFC’s are high temperature systems – radiation modeling important

• Coupling between radiation and other modes of heat transfer affects reaction rates and cell output voltage

• Discrete Ordinate Method is computationally intensive –need for alternate modeling schemes

Radiation Modeling – Optical Properties

1 3 5 7 9 110

10

20

30

40

50

60

70

80

90

100

Reflectance

Transmittance

Wavelength (µm)

Per

cent

age

rati

o (%

)

1 32 4 5 6 7 8 9 100

1

2

3

4

5

Wavelength µm

Ebλ

W/m

2µ

m (1

05 )

λ ~ 1.86 µmWien’s law: (n λ T)max = 2898 µm.n ~ 1.6; T = 700 oC = 973 K; λmax = 1.86 µm

80% of fractional emissive power is contained within 1.4µm < λ < 6.1µm

Electrodes: Optically thick/opaque

Electrolyte: Weakly absorbing (κ=496.2 m-1) and optically thin (κL<0.003)

0 1 2 3 4 5 6 72

4

6

8

10

12

14

Wavelength (µm)

ε”

Radiation Modeling – Discrete Ordinate Method

0 0.005 0.01 0.015 0.02 0.025 0.03850

900

950

1000

1050

1100

1150

Distance along cathode-electrolyte wall (m)

Tem

pera

ture

(0 K )

No RadiationDO Model

• Inclusion of radiation results in ~150 oK drop in the overall temperature level of the monolith type SOFC

• Coupled radiation effects result in increase of cell voltage from 0.65 V 0.74V

0 0.005 0.01 0.015 0.02 0.025 0.03850

900

950

1000

1050

1100

1150

Distance along anode-electrolyte wall (m)

Tem

pera

ture

(0 K )

No RadiationDO Model

0 0.001 0.002 0.003 0.004 0.005 0.006850

900

950

1000

1050

1100

1150

0 0.005 0.01 0.015 0.02 0.025 0.03850

900

950

1000

1050

1100

1150

Radiation Modeling – Two-flux ApproximationT

empe

ratu

re (0 K

)

Distance along monolith cell width (m)

Tem

pera

ture

(0 K )

Methodology Cell Voltage (V) CPU time* (min)

Discrete Ordinate Method

Two-Flux Approximation

0.734

0.731

658

76

* Based on time to convergence of Fluent simulations carried out on a 2.8 GHz pentium 4 personal computer

Distance along anode-electrolyte wall (m)

Cell Length X=0.025 m

No RadiationDO Model2-Flux Approx.

No RadiationDO Model2-Flux Approx.

Cell Width Y=0.0035 m

Porous Media – Reagent Transport Modeling

Species Conservation – Reagent and Intermediate Mole Fraction:

( ) , i i ii i TT

V Y Y ST

D Dρ ρ∇ ∇⋅ = ∇⋅ ∇ − ±

r Di - effective diffusion coefficient Di,T - thermal diffusion coefficientSi - species production / depletion rate

, , ,

11 1 1

i

i k

ii

m i i dD D Dx

Dετ

α−

−= + +

Di,m - molecular diffusion ε - porosityDi,k - Knudsen diffusion τ - tortuosityDi,d - dispersion

( ) ( )2

1 ( ) - - - e

V VVV V p V g T T

Kf

Kµ

ρ ρµ ρ βε ∞∇ ⋅ = − ∇ + ∇ ⋅ ∇ +

r rrr r r r

Momentum Conservation - Forchheimer and Brinkman Model:

µe - effective viscosity ε - porosityK - permeabilityf - inertia coefficient

Porous Media – Diffusion Modeling

, , ,

11 1 1

i

i k

ii

m i i dD D Dx

Dετ

α−

−= + +

Diffusion Coefficient for Species Conservation :

∑

−=

≠ik ik

k

imi

Dxx

D1

,

21

1

−=

m

ii M

Mαwhere

Mi - molecular weight of component i Mm – average molecular weight

Molecular Diffusion Coefficient:

xi - molar fractionDik - binary diffusion

coefficient

Knudsen Diffusion Coefficient:

rMRT

Di

ki2

1

,8

32

=

π

R - gas constantT - fluid temperature r - pore radius

Dispersion Coefficient:

( )ε,, PefD di =

Pe = uR/Di,m (Peclet #)Yi - mass fraction of i

Thermal Diffusion Coefficient:

∑

∑•

−∑

×−=

=

=

=

−N

iii

N

iii

iN

iii

iiTi

xM

xMY

xM

xMTD

1

489.0

1

511.0

1

511.0

511.0659.07

, 1059.2

Porous Media – Energy Conservation Modeling

( ) ( ) ( )( ) ( ) phase) (Solid - 0

phase) (Gas - -

,

,

sgvseffs

iisgvgeffggp

TThTk

HSTThTkTcV

+∇⋅∇=

∆∑+∇⋅∇=⋅∇r

ρ

Energy Conservation: Non-Equilibrium Thermal Model:

Non-equilibrium thermal model necessary when:

a) Difference in solid and fluid thermal properties is non-negligibleb) Significant generation in porous media – existence of hot spotsc) Low Reynolds number or flow velocities through porous media

kg,eff - gas phase thermal conductivity ks,eff - solid phase thermal conductivityhv - volumetric heat transfer coefficient ∆Hi - enthalpy of reaction species

Research Tasks – Accomplishments & Future Work

• Thermal radiation effects were investigated by coupling of radiative heat transfer and other modes of heat transfer à significant effects on the temperature and cell voltage were found warranting more detailed analysis, including experiments.

• Accurate models of species transport physics and the effective properties for reagent transport in the porous electrodes are currently being developed.

March ‘03 May ‘03 July ‘03 Sept. ‘03

Develop and validate radiation models for different fuel cell configurations

Linking of Fluent, ANSYS & Electrochemical models

Implement porous media modeling schemes

Develop porous media transport models

Thermomechanical Failure Analysis

Major Thermomechanical Failure Modes and Mechanism

• Warpage• Cracks in seal• Cracks in electrodes• Cracks in electrolyte• Delamination of interfaces• Creep/fatigue of interconnects• ?? (industry inputs)

• Thermal mismatch• Thermal gradient (spatial)• Thermal shock (temporal)• Thermal diffusion• Mass diffusion

Modeling Methodologies

Cell Structure(L > 10-3 m)

PEN Structure(10-5 m < L < 10-3 m)

Material StructureL < 10-5 m

x

za a

• Warpage• Seal failure• Seal design• Residual stresses

• Plate and laminate theories

5 µm

anod

eca

thod

eel

ectr

olyt

e

5 µm

anod

eca

thod

eel

ectr

olyt

eelectrolyte

cathode

anode

A CB

F

D

GEelectrolyte

cathode

anode

A CB

F

D

GE

• Cracks growth• Delamination• Spalling

• Fracture mechanics• Finite element method

• Crack initiation• Plasticity• Creep

• Micromechanics• Damage mechanics

x

za a

Warpage and Stress Analysis

2 211 0 11 00 2 2

11 11 11

( )( ) ( )

2[ ( )( )]s

s s

A E h M B Nw x a x

B D aE h A E h+ −

= −− + +

Deflection due to temperature change

0 50 100 150 200 250 300-0.2

0.0

0.2

0.4

0.6

0.8CathodeElectrolyteAnode

sE

(GPa)

(GPa)

xσ

Max. cell stress vs. seal stiffness

0 50 100 150 200 250 300100

101

102

103

104

Max

. Def

lect

ion

(µm

)

Es (MPa)(GPa)

Max. deflection vs. seal stiffness

cathode

anode

electrolyte

cathode

anode

electrolyte

( )x zσ (MPa)

0500T C∆ = −LSM + YSZ

Ni + YSZ

YSZ

0 50 100 150 200 250 300

0.0

0.2

0.4

0.6

0.8

uniform anodegraded anode

sE

(GPa)

(GPa)

xσ

Max. stress in anode

0 50 100 150 200 250 300-0.2

0.0

0.2

0.4

0.6

0.8

uniform anodegraded anode

sE

(GPa)

(GPa)

xσ

Max. stress in cathode

0 50 100 150 200 250 300100

101

102

103

104

uniform anodegraded anode

Max

. Def

lect

ion

(µm

)

Es (GPa)

Effect of Graded Anode

anode

cathode

electrolyte

Porosity in anode

10%

50%

Max. cell stress vs. seal stiffness

Max. deflection vs. seal stiffness

0 50 100 150 200 250 300-0.2

0.0

0.2

0.4

0.6

0.8uniform anodegraded anode

sE

(GPa)

(GPa)

xσ

Max. stress in electrolyte

Finite Element Analysis

Deformed shape

In-plane normal stress (σx)

Shear stress (σxy)

Out-of-plane normal stress (σy)Finite element mesh

anode

cathode

electrolyte

Single cell

2a

h

2

21.2235

1c

E ha

συ

= −

222( ) 1.22351

(1 )[1 0.9021(1 )] (1 )T Eh h

GT a

αυ υ α υ

∆ ∆ = − − + − ∆ ∆ +

0 200 400 600 800 1000 1200 1400 1600 18000.0

0.5

1.0

1.5

2.0

2.5

3.00 100 200 300 400 500 600 700 800

h = 5 µm

h = 10 µm

h = 20 µm

h = 30 µm

h = 40 µm

h = 50 µm

Temperature Change (oC)

Compressive Stress in the Electrolyte Layer (MPa)

Crit

ical

Fla

w S

ize

(mm

)Blister vs. Edge Delamination

Relationships between processing temperature, electrolyte layer thickness and critical flaw size

anode

electrolyte h

21.028 ( )1Eh

G T αυ

= ∆ ∆−

0 1 2 3 40

5

10

15

20

25

30

35

Flaw Size (mm)

Ene

rgy

Rel

ease

Rat

e (J

/m^2

)h = 5 µm

h = 20 µm

h = 10 µm

Comparison of energy release rate between edge and blister delamination

Effective Properties of Porous Electrodes0 0

20 0 0

2(1 )(5 7)2(5 7) (13 2 15 )

c EE

cν

ν ν ν− −

=− + − −

5 µm

anod

eca

thod

eel

ectro

lyte

5 µm

anod

eca

thod

eel

ectro

lyte

2 20 0 0 0

20 0 0

2(10 9 7) (25 6 19)2(5 7) (15 2 13)

cc

ν ν ν νν

ν ν ν− − + + −

=− + + −

00

0 0

91 3

KE

K µ=

+

0 00

0 0

1 2 32 2 3

KK

µν

µ−

=+

Input:Properties and volume fractions of Ni, LSM and YSZ and porosity

Output:Effective properties of Ni/YSZ and LSM/YSZ

0.00 0.05 0.10 0.15 0.20 0.25 0.300

40

80

120

160

200

240

Pore Volume Fraction

Effe

ctiv

e M

odul

us (G

Pa)

Young's modulus

Shear modulus

Experimental data (E. Lara-Curzio from ORNL) Model prediction

0 5 10 15 20 25 300

100

200

300

400

500

5%20%30%

Fracture Toughness 2(J/m )cG

(J sec)

q

Thermal Shock Induced Microcrack Initiation

22sU Nbπ γ=

Temp Distribution

Surface Energy

Strain Energy

( )0s bd U U

da+

=Griffith Fracture Criterion

q = rate of heat generation (J/sec)

Gc = Fracture toughness of the material

b = crack size

N = number of cracks per unit volume

k = Thermal conductivity

α = Coefficient of linear thermal expansion

r0 = A length parameter characterizes the

spatial non-uniformity of the heat source.

2 2 30

0

3 (1 )16(1 )1

2 9(1 2 ) (1 )ckr GNb

qE b

π π ννα ν ν

−−= + − +

2 2

2 2 3 20

(1 2 )6 (1 )b

q EU

k rα ν

ν π−

=−

020 0

( , ) erf erf4 4

q r rT r t T

rk r r tπ κ

= − + +

( )2

3 20

0

( ) expq r

frc rρ π

= −

rHeating Source

( )2

3 2 23 2 200

( , )exp

44

T t q rT

t r tc r t κρ π κ

• ∂ −= = ∂ ++

x

Failure Analysis Activities for the Next 6 Months

1.1 Obtain fracture mechanics parameters for cohesive, interfacial and impinging cracks.

1.2 Model spalling phenomenon and thermal expansion induced stress during thermal transients and shock.

1.3 Identify and quantify crack path selection and crack propagation.

1.4 Implement temperature gradient as driving force for cracking. Investigate the individual and combined influences of electrochemical and mechanical load stress, as well as temperature gradients on crack initiation and propagation. Review and utilize/adapt, where appropriate, existing, available fracture mechanics models in order to advance the state-of-the-art.

1.5 Evaluate and validate the accuracy of developed fracture mechanics models using either experimental data or modeling results from PNNL/NETL/ORNL or other SECA members.

GT Project Summary

Major Accomplishments of the First 4 months• “Slice technique” model/code to simulate the polarization

curve, and reformate stream analysis model.• Radiation models and porous models for thermal/fluid analysis.• Models for cell deflection, thermal stresses, buckling induced

delamination and thermal shock induced microcracking.

Focus for the Next 6 Months• Enhance, improve, test and validate the models developed

during the first 4 months. • Integrate these models into a common computational testbed

vehicle (a model cell) for validation.• Transfer GT’s modeling modules to the PNNL/NETL

simulation platform.