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COMPREHENSIVE DEPICTION OF A SUCCESSFUL CFD MODELING COMPREHENSIVE DEPICTION OF A SUCCESSFUL CFD MODELING FOR A REAL GEOMETRY SOLID OXIDE FUEL CELLS FOR A REAL GEOMETRY SOLID OXIDE FUEL CELLS

P M V Subbarao P M V Subbarao Indian Indian Institute of Institute of Technology Technology – – New Delhi New Delhi Mechanical Engineering Department

Associate Professor

More You Can See Through ….. More Confidence…

Research Interests Research Interests

• Use of high end experimental and computational fluid

flow and heat transfer methods for solving Real Time Problems.

• CFD simulation of In-cylinder flow in I.C. Engine to

predict mixture preparation in advanced engines.

• Experimental mapping of temperature and heat

transfer coefficient in advanced fin and tube heat exchangers.

• Experimental and Computational analysis of fluid flow

with shocks in Super Sonic Ejectors.

• CFD analysis of SOFC Stacks for Distributed Power

Generation.

Reference SOFC Reference SOFC-

• GT system

GT system – – Regenerative Brayton cycle Regenerative Brayton cycle

SOFC Generator DC AC Power conditioning system Combustor Recuperator

Air Filter

Compressor

G

Natural Gas Air in

Compressor

Air Fuel Exhaust

Gas Turbine

Excess air

Motivation for hybridization Motivation for hybridization

• Due to the polarization losses

Due to the polarization losses,100% utilization of hydrocarbon fuel is not 100% utilization of hydrocarbon fuel is not possible in the fuel cell stack possible in the fuel cell stack

• Hydrocarbon fuels used in SOFC that produce power also produce

Hydrocarbon fuels used in SOFC that produce power also produce rejected heat. rejected heat. (Reversible reaction, Process irreversibility). (Reversible reaction, Process irreversibility).

• The heat must be rejected in order to maintain its temperature a

The heat must be rejected in order to maintain its temperature at a t a desired level. desired level.

US energy studies

CFD Modeling of SOFC Stacks CFD Modeling of SOFC Stacks

• Solid Electrolyte.
• High temperature and high pressure fluid flow with

heat generation.

• Complex flow geometry: Flow through a system of

micro channels.

• Stack of such geometries.
• Many fuel options.
• Huge scope for optimization and improvements.

Overall Research Objective Overall Research Objective

• To Investigate / develop SOFC based power generation processes

To Investigate / develop SOFC based power generation processes

• Achieve high electricity generation efficiencies

Achieve high electricity generation efficiencies

• Key Issues to be Investigated:

Key Issues to be Investigated:

• fuel composition (Especially H2 and CO mixtures),

fuel composition (Especially H2 and CO mixtures),

• utilization factor,

utilization factor,

• Temperature & pressure,

Temperature & pressure,

• perating cell voltage or current density,
• perating cell voltage or current density,
• efficiency (stack and hybrid cycle) and

efficiency (stack and hybrid cycle) and

• cost (if possible)

cost (if possible)

V

AFC

PEMFC PAFC MCFC SOFC

H2

OH -

Fuel

H2O H2

H +

DMFC

H + H + O 2- CO3

2-

600C 100 kW 600C 250 kW 1900C 11 MW 6500C 2 MW 10000C 1 MW 800C 2 MW

O2 O2 H2O O2 H2O O2 H2O O2 CO2 O2 CH3OH CO2 H2 H2 H2O H2O H2

Anode Electrolyte Cathode Oxygen

e

Max attained production

Classification based on electrolyte used Classification based on electrolyte used

Solid Oxide Fuel Cells Solid Oxide Fuel Cells

Chemical Reactions Chemical Reactions Electrochemical Reactions Electrochemical Reactions

CH CH4

4 + H

+ H2

2O

O 3H 3H2

2 + CO

+ CO Reformation Reaction Reformation Reaction (Endothermic) (Endothermic) Shift Gas Reaction Shift Gas Reaction CO + H CO + H2

2O

O CO CO2

2 + H

+ H2

2

H H2

2 + O

+ O2

2-

• H

H2

2O + 2e

O + 2e-

• CO

CO2

2 + 2e

+ 2e-

• CO + O

CO + O2

2-

• At anode

At anode Exothermic Exothermic At cathode At cathode ½ ½ O O2

2 + 2e

+ 2e-

• O

O2

2-

• Electrolyte is solid and conducts oxygen ion at 650

Electrolyte is solid and conducts oxygen ion at 650 o

• C

C

• High operating temperature and solid electrolyte permits flexibi

High operating temperature and solid electrolyte permits flexibility in choosing the fuel lity in choosing the fuel

• Ideal fuel is hydrogen but any hydrocarbon fuel can be used afte

Ideal fuel is hydrogen but any hydrocarbon fuel can be used after reformation r reformation

• Fuel reformation can be done internally or externally

Fuel reformation can be done internally or externally

Single cell Single cell -

• dismantle view

dismantle view

Anode ( Ni-YSZ ) Cathode ( LSM –YSZ ) Electrolyte ( YSZ ) Interconnects ( Electro ceramic family ) Seals

Stack assemble Stack assemble

Individual fuel cells must be combined to produce appreciable vo Individual fuel cells must be combined to produce appreciable voltage levels ltage levels Stack assemble Array of cells with insulation plate Array of cells Single cell assemble

Stack modeling Stack modeling

Intermediate cell Intermediate cell Top most cell Top most cell Bottom cell Bottom cell

• Stack Power

Stack Power

• Effluent heat Q = Q

Effluent heat Q = Qelect

elect + Q

+ Qs

s -

• Q

Qr

r -

• Q

Qsurr

surr

Electrochemical process Electrochemical process Heat consumed by reforming Heat consumed by reforming Q Qr

r

Heat associated with shift gas reaction Q Heat associated with shift gas reaction Qs

s

cell

P N IV =

∑

elect

Q i T S η = + ∆

∑

• Single cell geometry is analyzed for the

Single cell geometry is analyzed for the given inlet fuel given inlet fuel

• Stack effect is evaluated by multiplying

Stack effect is evaluated by multiplying the number of cells with single cell’s the number of cells with single cell’s result result

System Modeling System Modeling -

• Macroscopic approach

Macroscopic approach

• Thermodynamic modeling of a single cell and a stack
• Polarization modeling for a fuel cell
• Performance analysis of SOFC-GT hybrid power generation

cycle

Cell Potential Calculation Cell Potential Calculation

[ ] [ ] [ ] [ ] ln

δ α β

∆ =∆ +

c

C D G G RT A B

General form of Nernst Expression

[ ] [ ]

ln reactant activity RT E E nF product activity = +

∏ ∏

( . .) i e G nFE ∆ = −

Ideal cell potential

1 2 2 2 298

1/ 2 241 H O H O H kJ mol− + → ∆ = −

2 2 2

1/ 2

ln 2

H O

• H O

P P RT E E F P ⎛ ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

Solid oxide fuel cell

1 2 2 298

1/ 2 283 CO O CO H kJ mol− + → ∆ = −

1 2 2 2 298

1/ 2 241 H O H O H kJ mol− + → ∆ = −

2 2 2 2

1/ 2

ln 2

H O

• H

H O

P P RT E E F P ⎛ ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

2 2 2

1/ 2

ln 2

CO O

• CO

CO

P P RT E E F P ⎛ ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

Actual cell potential ( Actual cell potential (V Vactual

actual ) = Ideal cell potential (E)

) = Ideal cell potential (E) – – losses or polarization losses or polarization

Fuel Cell Efficiency Fuel Cell Efficiency

At STP At STP H H2

2+ ½ O

+ ½ O2

2

H H2

2O

O,

, 237.1 0.83 285.8 η = =

ideal

useful energy H η = ∆ / 0.83 useful power G = ∆ ( ) 0.83 ( ) / 0.83

actual actual ideal ideal

volts current V volts current V × = = ×

Polarization Distinctiveness Polarization Distinctiveness

Actual potential of the cell is less than the equilibrium potential due to irreversible losses or polarization.

Losses or polarizations in Actual Performance Losses or polarizations in Actual Performance

• Activation over potential

Activation over potential – – Flow of ions Flow of ions should overcome the electronic barrier. should overcome the electronic barrier.

• Ohmic over potential

Ohmic over potential – – Resistance Resistance

• ffered by the total cell components to the
• ffered by the total cell components to the

flow. flow.

• Concentration over potential

Concentration over potential

• Gas

Gas transport losses, dilution of fuel as the transport losses, dilution of fuel as the reactions progress. reactions progress.

V V-

• I Characteristics of the Fuel cell

I Characteristics of the Fuel cell

( )

act

η

( )

• hm

η

( )

con

η

Summation of electrode polarization Summation of electrode polarization

Activation and concentration polarizations Activation and concentration polarizations – – both Anode and Cathode both Anode and Cathode

, ,

η η η = +

cathode act c con c

, ,

η η η = +

anode act a con a

Polarizations increase Anode potential and decrease Cathode pote Polarizations increase Anode potential and decrease Cathode potential ntial

η = −

cathode cathode cathode

V E η = +

anode anode anode

V E

Cell potential Cell potential

( ) ( )

actual cathode anode actual cathode cathode anode anode

V V V iR V E E iR η η = − − = − − + −

Fuel flow rate calculation Fuel flow rate calculation

For every molecule of hydrogen (H2), two electrons are Liberated For every molecule of methane (CH4), eight electrons are liberated mH mH2

2 = (

= (½ ½) * (1/96487) * (2.0158) = 1.04445 * 10 ) * (1/96487) * (2.0158) = 1.04445 * 10 -

• 5

5 kg H

kg H2

2 / s

/ s -

• kA

kA mCH mCH4

4 = (1/8) * (1/96487) * (16) = 2.0728 * 10

= (1/8) * (1/96487) * (16) = 2.0728 * 10-

• 5

5 kg CH

kg CH4

4 / s

/ s -

• kA

kA For 1 MW plant I = Power / Voltage = 1000000 / 0.7 = 1429 kA For 1 MW plant I = Power / Voltage = 1000000 / 0.7 = 1429 kA mCH mCH4

4 = 1429 * 2.0728 * 10

= 1429 * 2.0728 * 10 -

• 5

5 (or) mH

(or) mH2

2 = 1429 * 1.04445 * 10

= 1429 * 1.04445 * 10-

• 5

5

Therefore, for 1 MW, Therefore, for 1 MW, Total current = 1000000 / 0.7 = 1429000 amps Total current = 1000000 / 0.7 = 1429000 amps Required area of the cell = Total current / Current density Required area of the cell = Total current / Current density

• No. of cells = required area / area of the individual cell
• No. of cells = required area / area of the individual cell

Number of cells in a stack Number of cells in a stack

Performance characteristics of a single Cell Performance characteristics of a single Cell

Maximum power density is obtained at lower cell voltage which results in lower cell efficiency. To operate on the left side of the power density peak at a point that yields a compromise between low operating cost ( high cell efficiency that occurs at high voltage and low current density ) and low capital cost (less cell area that occurs at low cell voltage and high current density) Also, compromise should be made between cell voltage and current density.

0.0E+00 2.0E-01 4.0E-01 6.0E-01 8.0E-01 1.0E+00 2000 4000 6000 8000 Current density (A m-2) Cell potential (volts) 0.0E+00 5.0E+02 1.0E+03 1.5E+03 2.0E+03 2.5E+03 3.0E+03 3.5E+03 Power density (W m -2)

0.4 0.6 0.8 1 1.2 1.4 800 1000 1200 1400 500 1000 1500 2000 2500 3000

Cell voltage (volt) Operating temperature (K) Power density (W m-2)

Downside of the system modeling Downside of the system modeling

Macroscopic approach is used to understand and study the system’s performance but examining/development of the system is not possible. Only mass and energy balancing of all the components are considered. The individual component’s characteristics depends on internal behavior of the process which is totally neglected in system modeling. Small losses and variation in the single cell is neglected which will give significant amount when it comes to stack. Local variation of operating parameters are neglected which influences the chemical reactions, electrochemical reactions, material morphology and intensity of losses. All the reactions are considered as a single stage reactions.

Mechanistic Model Mechanistic Model – – Microscopic approach Microscopic approach

Computational fluid dynamic modeling to predict steady-state cell performance and gas compositions. Investigate the influence of cell design, microstructure and

• perating variables on steady-state cell performance.

Develop the cell performance map based on operation of H2 and CO mixtures.

Modeling Tool Requirements Modeling Tool Requirements

Versatile multi Versatile multi-

• physics analysis methods

physics analysis methods I. I. Fuel flows with or without steam Fuel flows with or without steam II. II. Diffusion through the porous medium Diffusion through the porous medium III. III. Ionic transport Ionic transport IV. IV. Diffusion of oxygen molecule Diffusion of oxygen molecule V. V. Air flow Air flow Chemical Reactions Chemical Reactions

CH CH4

4 + H

+ H2

2O

O 3H 3H2

2 + CO

+ CO Endothermic Endothermic Reformation reaction Reformation reaction CO CO2

2 + H

+ H2

2

Exothermic or Endothermic Exothermic or Endothermic CO + H CO + H2

2O

O Shift gas reaction Shift gas reaction

Electrochemical Reactions Electrochemical Reactions

H H2

2 + O

+ O2

2-

• H

H2

2O + 2e

O + 2e-

• At anode

At anode Exothermic Exothermic CO CO2

2 + 2e

+ 2e-

• CO + O

CO + O2

2-

• Cell potential should be calculated from

Cell potential should be calculated from these reactions these reactions At cathode At cathode ½ ½ O O2

2 + 2e

+ 2e-

• O

O2

2-

PROPOSED METHODOLOGY PROPOSED METHODOLOGY

Results of representative cell BC Local Species Concentration and temperature Local Species Concentration and temperature

FLUENT Species, Momentum, Energy, Electric potential field FLUENT FLUENT Species, Species, Momentum, Momentum, Energy, Energy, Electric Electric potential field potential field ADD ON Nernst Voltage Current Distribution and Over potentials Electric potential field BC ADD ON ADD ON Nernst Voltage Nernst Voltage Current Current Distribution Distribution and Over and Over potentials potentials Electric Electric potential field potential field BC BC Calculation

• f step

function

• Templates

Stack power, Stack effluent Calculation Calculation

• f step
• f step

function function

• Templates

Templates Stack Stack power, power, Stack Stack effluent effluent Heat loss to the surroundings Heat loss Heat loss to the to the surroundings surroundings

C Programming C Programming Bottoming cycle simulation Bottoming Bottoming cycle cycle simulation simulation

GAMBIT GAMBIT Cell & stack Cell & stack geometry geometry Flow Flow directions directions

Reformation Reformation

Fuel Fuel Species and heat flux at the boundaries Species and heat flux at the boundaries Separate Packag Internal reforming Modified parameters using step function

Governing Equations Governing Equations

• Specifics of the gas and temperature flow are very much dependen

Specifics of the gas and temperature flow are very much dependent on geometry t on geometry

• Regardless of the geometry, governing equations are same

Regardless of the geometry, governing equations are same

Species Balance Equation Species Balance Equation

( )

.

i i i i

Y v Y j r t ρ ρ

→ →

∂ ⎛ ⎞ +∇ =−∇ + ⎜ ⎟ ∂ ⎝ ⎠

Full species field is obtained by solving species balance equati Full species field is obtained by solving species balance equation

• n

CV

(Reaction)

/ E RT i i i i

r AT e

β −

=

Chemical reactions Chemical reactions (Arrhenius expression) (Arrhenius expression)

2

2 2

CO CO O

i r r F = =

Electrochemical reactions Electrochemical reactions

2 2 2

2 2

H H O

i r r F = =

(Faraday’s Law) (Faraday’s Law)

Conversation of Momentum Conversation of Momentum

Essential to model the fluid velocity and species partial pressu Essential to model the fluid velocity and species partial pressure re

• Gravitational body force is neglected ( gases, forced convection

Gravitational body force is neglected ( gases, forced convection, small dimension ) , small dimension )

• Net work includes additional sink along with pressure and stress

Net work includes additional sink along with pressure and stress tensors tensors Newton’s Second law Newton’s Second law

( ) ( ) ( )

→ → → →

∂ + ∇ = −∇ + ∇ + ∂ ρ ρ τ v v v p F t

Net rate of momentum flow = Net rate of momentum flow = ( viscous, Pressure and Body forces ) ( viscous, Pressure and Body forces )

3 3 2 1 1

1 2

i ij i ij mag i j j

F D v C v v µ ρ

= =

⎡ ⎤ =− + ⎢ ⎥ ⎣ ⎦

∑ ∑

i i ij

F v µ α =

Momentum sink term Momentum sink term – – Darcy’s law Darcy’s law For Laminar flows For Laminar flows

( ignoring convective acceleration and diffusion ) ( ignoring convective acceleration and diffusion )

2 3

T

v v vI τ µ ⎡ ⎤ = ∇ + ∇ − ∇ ⎣ ⎦ r r r

Stress tensor Stress tensor

Energy Equation Energy Equation

h f

S

h f

S

Advection Advection conduction conduction diffusion diffusion

net

W

Porosity weighted composite of solid and fluid phase Porosity weighted composite of solid and fluid phase

( )

( )

(1 ) ( ) ( )

h j f f s s f f eff j f j

E E v E P k T h J S t ερ ε ρ ρ ⎛ ⎞ ∂ + − +∇ + =∇ ∆ − + ⎜ ⎟ ∂ ⎝ ⎠

∑

⎡ ⎤ ∇ ⎢ ⎥ ⎣ ⎦

∑

n j j j

h J

h f

S (1 )

eff f s

k k k ε ε = + −

• Conduction flux uses effective conductivity

Conduction flux uses effective conductivity

• Transient term includes the thermal inertia of the solid region

Transient term includes the thermal inertia of the solid region

• Inclusion of species transport in energy equation

Inclusion of species transport in energy equation (enthalpy due to species diffusion, not neglected in case of Lew (enthalpy due to species diffusion, not neglected in case of Lewis Number <<1) is Number <<1)

• Source term contributions ( )

Source term contributions ( ) -

• Heat of chemical reactions and other volumetric sources

Heat of chemical reactions and other volumetric sources

Modeling of Electrochemistry Modeling of Electrochemistry

Conventional approach

Gibbs free energy that results from the overall reaction is arbitrarily assigned to the E/A interface only The oxide ion concentration at either of the interfaces is not accounted At anode:

2 2 2

2 H O H O e

− −

+ → +

2 2

ln 2

H O A H O

P RT E E F P ⎛ ⎞ =− − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ At cathode:

2 2

1/ 2 2 O e O

− −

+ →

( )

2

1/ 2

ln 2

C O

RT E P F =

Overall reaction:

2 2 2

1 2 H O H O + →

2 2 2

1/ 2

ln 2

H O

• H O

P P RT E E F P ⎛ ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

( ) ( )

actual C cathode A anode

E E E iR η η = − − + −

Actual cell voltage:

Multistage Mechanism Multistage Mechanism

• Split the Gibbs free energy into two parts one for the overall r

Split the Gibbs free energy into two parts one for the overall reaction eaction

• ccurring at the C/E interface, and one for those occurring at t
• ccurring at the C/E interface, and one for those occurring at the E/A

he E/A interface. interface.

• Ionic concentration also measured experimentally using electroni

Ionic concentration also measured experimentally using electronics cs impedance spectroscopy impedance spectroscopy

• Losses are accounted locally i.e. post subtraction is avoided

Losses are accounted locally i.e. post subtraction is avoided

( )

/

ln

• C E

G RT K ∆ = −

f b

k Where K k ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

/ /

• A E

C E

E E E = −

• G

nFE −∆ =

Beberle Beberle reaction kinetics reaction kinetics

Local Cell Potential Local Cell Potential

Variation of electric Potential across PEN Variation of electric Potential across PEN

Cathode - Electrolyte interface

2

1/ 2 2 O e O

− =

+ → Anode - Electrolyte interface

2 2

2 H O H O e

= −

+ → +

2

1/ 2 , / /

ln 2

O

• PT C E

C E C C O

P RT E E IR F P η

=

⎛ ⎞ ∆ = + − − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

2 2

, / /

ln 2

H

• O

NT A E A E A A H O

P P RT E E IR F P η

=

⎛ ⎞ ∆ = + − − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

.

Cell potential across PEN

Fuel Air

• EC

EEe EEw EA ENT ∆Ecell

+

i

V

EPT

Negative Negative electrode electrode Electrolyte Electrolyte Positive Positive electrode electrode i i

2 2 2

1/ 2 / /

ln ln 2 2

O H

• O

cell C E C C A E A A ele H O O

P P P RT RT E E IR E IR IR F P F P η η

= =

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ∆ = + − − + + − − − ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

Potential Across PEN Structure Potential Across PEN Structure

0.2 0.4 0.6 0.8 1 1.2 0.002 0.004 0.006 0.008 0.01 Distance across PEN Drop in potential

750 A m-2 1500 A m-2 No load

Ideal drop across PEN Cathode Anode Electrolyte

Conservation of charge:

( )

E s σ ∇ ∇ =

• 1D result for local potential

1D result for local potential across PEN structure across PEN structure

• Reaction rates are adapted

Reaction rates are adapted from surface science literature from surface science literature

• Distance in10

Distance in10-

• 1

1meters and

meters and potential in volts potential in volts

• Potential difference is plotted

Potential difference is plotted for no load, 750 Am for no load, 750 Am-

• 2

2 and 1500

and 1500 Am Am-

• 2

2

• Losses are accounted locally

Losses are accounted locally

16 mm SOFC with 5 air and 5 fuel channels of 2 mm X 2 mm cross section

Air flow f u e l f l

• w
• Cross flow

configuration,

• Electrolyte supported

cell,

• Externally reformed

fuel (H2O,CO&H2)

• Operated at 1273 K,

1 atm

• 0.512 amps cell load

for examination

Cell material (LSM-YSZ / YSZ / Ni-YSZ)

Current Density at wall electrolyte - cathode side ( Neglecting CO electrochemical reaction as in the literatures)

Air flow

Anode side – 2.4358e-06 kg/s, 0.51/0.31/0.17 (H2/ H2O/CO) cathode side – 2.653207e-05 kg/s, 0.78/0.22 (O2/ H2O) Porous media : Permeability – 5.6818e-10 Porosity – 0.5

fuel flow

Hydrogen Concentration Steam Concentration Oxygen Concentration

Species Concentrations along the channels

Actual Cell Potential Actual Cell Potential Actual cell potential ( Actual cell potential (V Vactual

actual ) = Ideal cell potential (E)

) = Ideal cell potential (E) – – { Activation polarization + { Activation polarization + Ohmi Ohmic polarization + c polarization + Conc Concentration polarization } entration polarization } Ideal cell potential - ( Nernst Expression ) Activation over potential Activation over potential – – Flow of ions should overcome the Flow of ions should overcome the electronic barrier. electronic barrier. Ohmic over potential Ohmic over potential – – Resistance offered by the total Resistance offered by the total cell components to the flow. cell components to the flow. Concentration over potential Concentration over potential

• Gas transport losses,

Gas transport losses, dilution of fuel as the reactions progress. dilution of fuel as the reactions progress.

Ideal cell potential Ideal cell potential

Ideal cell voltage at wall electrolyte anode – 0.512 amps load

[ ] [ ]

ln reactant activity RT E E nF product activity = +

∏ ∏

( Neglecting CO electrochemical reaction )

Air flow fuel flow

Activation over potential Activation over potential

{ }

(1 ) / /

act act

nF RT nF RT

i i e e

β η β η − −

= −

Buttlet Volmer Equation Buttlet Volmer Equation

Air flow fuel flow

Ohmic over potential Ohmic over potential

Resistance to the flow of ions in the electrolyte material Resistance to the flow of ions in the electrolyte material

eff Ohmic

iR η =

R Reff

eff-

• effective ionic resistance

effective ionic resistance Electrolyte resistivity in (ohm Electrolyte resistivity in (ohm-

• m)

m)

• Fig. shows that the
• Fig. shows that the

resistivity of resistivity of electrolyte only. electrolyte only.

• As the temperature

As the temperature increases resistivity increases resistivity

• f the electrolyte
• f the electrolyte

decreases hence hot decreases hence hot spots are visible with spots are visible with less resistivity and less resistivity and relatively cold spots relatively cold spots are little more. are little more.

• Effective resistance

Effective resistance for calculating for calculating ohmic

• hmic

polarization will be polarization will be the summation of all the summation of all material resistances material resistances

Concentration over potential Concentration over potential Gas transport losses, dilution of fuel as the reactions progres Gas transport losses, dilution of fuel as the reactions progress. s. Not considered separately It is accounted by considering local species concentration while calculating Nernst potential instead of considering species concentration at the inlet

Actual cell potential Actual cell potential

[ ]

cell cathode cathode anode anode Ohmic

V E E η η η = − − + −

Actual cell potential at anode Actual cell potential at anode Actual cell potential at cathode Actual cell potential at cathode

Few outcomes from the model Few outcomes from the model

Findings Findings

Cell is examined with two different permeability a) 5.68184e+10 (Viscous resistance) from the literatures: b) 1e+13 (Viscous resistivity) material manufacturers

Inference Inference a) cell operation is not limited by mass transfer at any location of the cell. However, at lower cell voltages, it is seen that the current density is decreasing in the flow direction. b) Cell operation is limited by the low diffusivity of species at the inlet conditions Result: Result: Interestingly both the cases will give the same over all output Interestingly both the cases will give the same over all output Air flow Air flow fuel flow fuel flow

Findings… Findings…

• 1. Overall reaction:

2 2 2

1 2 H O H O + →

2 2 2

1/ 2

ln 2

H O

• H O

P P RT E E F P ⎛ ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

Neglecting CO Neglecting CO electrochemical electrochemical reaction reaction H H2

2 + O

+ O2

2-

• H

H2

2O + 2e

O + 2e-

• 2. Both electrochemical Reactions are considered

CO CO2

2 + 2e

+ 2e-

• CO + O

CO + O2

2-

• 1

2

Findings Findings

• Hydrogen diffuses more faster than oxygen in the porous electrodes, so

the rate limiting issue for the whole processes will be the diffusivity of

• xygen in the porous cathode.
• If the porosity of the cathode is much higher than the anode then the

process is governed by the ionic conductivity of the electrolyte.

• High current density increases ohmic losses leading to higher thermal
• gradients. This may In turn lead to mismatching of the assembly because
• f various coefficients of thermal expansion

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