CFD Modeling and Analysis of a Planar Anode Supported

Intermediate Temperature

Solid Oxide Fuel Cell

Melissa TweedieMay 1, 2014

SOFC Power Plants

http://www.ztekcorporation.com/

http://fuelcellsworks.com/

CHP Propane Fueled SOFCPower Plant for large automotiveapplications

SOFC Stacks

Reference 2

http://www.ceramatec.com

SOFC Unit Cell

Anode Electrode ERL

Cathode Electrode BL

ElectrolyteCathode ERL

Anode Interconnect

Cathode Interconnect

Anode FF

Cathode FF

Anode Electrode BL

Fuel

Air

Electrochemistry

To develop a 2-D model of a single cell solid oxide fuel cell.

To include detailed multi-physics: fluid dynamics, heat transfer, mass transfer, chemical and electrochemical reactions.

To utilize the model in analyzing the performance of varying fuel inlet compositions.

Objective

The 2-D CFD model consisted of five physics sub-models as follows:

◦ Fluid flow and Momentum Model◦ Mass Transfer Model◦ Heat Transfer Model◦ Chemical Model◦ Electrochemical Model

Model Development

Continuity and Navier Stokes Equations◦ Compressible flow, steady state

Fuel and Air Channels:

Porous Electrode Stokes-Brinkman equations:

Wilke and Herning & Zipperer Method to calculate mixture dynamic viscosity

Momentum Model

Maxwell-Stefan Equations

Maxwell-Stefan diffusivity values calculated using Fuller method for flowfields

Effective diffusivity used in porous media combines maxwell stefan binary diffusivity and knudsen diffusivity

Mass Transfer Model

Flowfields◦ Heat capacity and thermal conductivity for individual

species assumes ideal gases and is calculated from temperature dependent polynomials.

◦ Mixture heat capacity

◦ Mixture thermal conductivity calculated using method of Wassiljewa with Mason and Saxena modification

Heat Transfer Model

Electrodes◦ Use of effective thermal conductivity and effective

heat capacity to account for porosity

Electrolyte and Interconnects◦ Conduction only

Heat Transfer Model

Heat Generation Source Terms

Chemical Reaction Electrochemical Reaction Activation Polarization

Heat Transfer ModelTypes of SOFC Heat Sources

Fuel Cell Type Relative % Contribution

MSR Reaction Consumption 27

WGS Reaction Generation 6

Electrochemical Reactions Generation 47

Concentration Polarization Generation < 1

Activation Polarization Generation 16

Ohmic Polarization Generation 3

Heat Generation Source TermsHeat Transfer Model

Summary of Heat Source Equations used in Model

Anode Flow Field

Anode Backing

Layer

Anode ERL

Electrolyte Q = 0

Cathode ERL

Cathode BL, FF Q = 0

Interconnects Q = 0

Water Gas Shift Reaction

Species Balance Equations◦ Implemented as source term in mass transfer

equation

Kinetics

Chemical Model

Probability of Carbon Formation◦ Boudouard Reaction

◦ CO/H2 Reaction

◦ If carbon activity is greater than 1 then carbon will form in the cell

Chemical Model

Electrochemistry◦ Anode Oxidation of CO and H2 Fuels

◦ Cathode Reduction of O2

◦ Species Balance Equations

Electrochemical Model

Ion and Charge Transfer

Electrochemical Model

Summary of Charge Transfer Equations used in Model

Electrode Backing

Layers

Anode ERL

Cathode ERL

Electrolyte

Cell Potential (Voltage)

Relationship between potential and current density determined by Butler-Volmer kinetic equation

General Equation for activation polarization

Electrochemical Model

BC=0V Varied BC

H2 kinetics

CO Kinetics

Electrochemical Model

O2 Kinetics

Current Density Relationships

Electrochemical Model

Electronic and Ionic Conductivities

Electrochemical Model

Summary of Effective Conductivity Equations used in Model

Electrode Backing

Layers

Anode ERL

Cathode ERL

Electrolyte

Cell Dimensions (mm)

Cell length 100 Air channel height 1.0

Cell height 3.31 Cathode Backing Layer Height 0.05

Interconnect Height 0.5 Cathode ERL Layer Height 0.01

Fuel channel height 0.6 Electrolyte Height 0.02

Anode Backing Layer Height 0.6

Anode ERL Layer Height 0.03

Cell Properties and Parameters

Cell Materials

Anode and Cathode Interconnect Stainless Steel  Anode Electrode and Anode ERL Layer Ni-YSZ (Nickel - Yttria Stabilized Zirconia)  Electrolyte YSZ (Yttria Stabilized Zirconia)  

Cathode Electrode and Cathode ERL LayerLSM-YSZ (Strontium doped Lanthanum

Manganite – Yttria Stabilized Zirconia)

Cell Properties and ParametersPhysical Properties and Parameters

Anode Cathode

Permeability (m2) 2.42 x 10 -14 2.54 x 10 -14

Porosity 0.489 0.515

Pore Diameter (µm) 0.971 1

Electronic/Ionic/Pore Tortuosity 7.53, 8.48, 1.80 7.53, 3.4, 1.80

Electronic/Ionic Volume Fraction 0.257, 0.254 0.232, 0.253

Electronic/Ionic Reactive Surface Area

per Unit Volume (m2/m3)3.97x10 6 , 7.93x10 6 3.97x10 6 , 7.93x10 6

Solid Thermal Conductivity (W/m-K) 11 6

Solid Specific Heat Capacity (J/kg-K) 450 430

Solid Density (kg/m3) 3310 3030

Electrolyte Interconnect

Thermal Conductivity (W/m-K) 2.7 20

Specific Heat Capacity (J/kg-K) 470 550

Solid Density (kg/m3) 5160 3030

5 Separate Fuel Inlet Cases Examined◦ Fuel concentrations chosen to represent typical syngas

composition ranges.

Solution Method

Simulated Fuel Feed Mole Fractions

Case 1 2 3 4 5

H2 0.30 0.30 0.20 0.30 0.30

H2O 0.07 0.17 0.27 0.07 0.07

CO 0.50 0.40 0.40 0.40 0.40

CO2 0.10 0.10 0.10 0.10 0.20

CH4 0.01 0.01 0.01 0.01 0.01

N2 0.02 0.02 0.02 0.12 0.02Operating Conditions

Inlet Temperature (K) 1023 Anode Fuel Feed xi Varies

Cathode Inlet Velocity (m/s) 6.5 Cathode Air Feed xi .21 O2 .79 N2

Anode Inlet Velocity (m/s) 0.5 Operating Voltage (V) 0.6 to 1.0

Outlet Pressure (atm) 1.0

COMSOL Multi-physics FEM Modeling Software

Domain◦ 34,400 elements-varied distribution horizontally

Segregated Pardiso Solver with parametric voltage steps

Dampening Factor 0.05% applied to electrochemical species and heat generation source terms

Solution Method

Comparing Dampening Factor

Velocity Profile

Typical Inlet velocity profile (0-0.0065m)

Inlet effects occurring in initial 0.2% of length

Typical Inlet pressure profile (0-0.0065m) Inlet effects occurring in initial 0.2% of length

Pressure Profile

Case 1 Anode: No reactions, κ=2.42x10-14

Case 1 Anode: No reactions, κ=2.42x10-5

Permeability ComparisonH2

CO2

Highest WGS rate observed with greatest amount of H2O in fuel (3)

Increased CO2 in fuel results in negative reaction rate in FF (5)

Increased CO in fuel increases WGS rate (1)

Water Gas Shift Reaction

All carbon activities in this study below 1, case 1 with highest observed activities

Increasing H2 or CO from case 1 or decreasing the current density (incr voltage) will bring the carbon activity closer to or above 1

Carbon activity in Boudouard reaction (0.925) greater than CO-H2 reaction (0.766)

Higher carbon activity at electrode inlets

Carbon Formation

Comparison of Maximum Temperatures for each Case at Ecell=0.7

Case 1 2 3 4 5

Max

Temperature (K)1036.1 1033.5 1034 1035 1033.3

Temperature

Example Temperature Profile Case 1, 0.4V

Characteristic Polarization Curve

Characteristic Polarization Curve

Example Polarization Curve with OCV Case 1

OCV values for all cases ranged between ~0.95 to 1.0V

Characteristic Polarization Curves

Case 1 Max Power Density: 720 W/m2

Example Case 1, 0.7VERL ranges from 1.58mm to 1.61mm

Most of the current generated in initial 1.7% to 3.3% of total ERL thickness

Current Density Profiles

Example Case 1, 0.7VERL-Electrolyte Interface Current Density

Inlet effects observed in initial 0.2% of total cell length

Current Density Profiles

Comparison vs Experiment Data

Model agrees reasonably well with experimental data, data at slightly different conditions.

Case 1 best performance with max power density 720W/m2, Case 4 2nd best performance

WGS rate increases with more reactant species, reverses with more product species in fuel

No carbon formation observed under operating conditions with syngas below 0.95V

Proper selection of microstructural parameters (permeability) important

Complexity of model allows for significant future study of parameters, optimization, etc.

Conclusions

Questions?

1. http://www.fuelcellenergy.com/assets/PID000156_FCE_DFC3000_r3_hires.pdf

2. S.A. Hajimolana et al., “Mathematical Modeling of Solid Oxide Fuel Cells: A Review,” Renewable and Sustainable Energy Reviews, vol 15, pp.1893-1917, 2011.

3. M. Tweedie Thesis. CFD Modeling and Analysis of a Planar Anode Supported Intermediate Temperature Solid Oxide Fuel Cell. May, 2014.

References