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Melissa Tweedie May 1, 2014

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http://www.ztekcorporation.com/ http://fuelcellsworks.com/ CHP Propane Fueled SOFC Power Plant for large automotive applications

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Reference 2 http://www.ceramatec.com

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Anode Electrode ERL Cathode Electrode BL Electrolyte Cathode ERL Anode Interconnect Cathode Interconnect Anode FF Cathode FF Anode Electrode BL Fuel Air Electrochemistry

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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.

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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

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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

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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

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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

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Electrodes ◦ Use of effective thermal conductivity and effective heat capacity to account for porosity Electrolyte and Interconnects ◦ Conduction only

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Heat Generation Source Terms Chemical Reaction Electrochemical Reaction Activation Polarization Types of SOFC Heat Sources Fuel CellTypeRelative % Contribution MSR ReactionConsumption27 WGS ReactionGeneration6 Electrochemical ReactionsGeneration47 Concentration PolarizationGeneration< 1 Activation PolarizationGeneration16 Ohmic PolarizationGeneration3

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Heat Generation Source Terms Summary of Heat Source Equations used in Model Anode Flow Field Anode Backing Layer Anode ERL ElectrolyteQ = 0 Cathode ERL Cathode BL, FFQ = 0 InterconnectsQ = 0

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Water Gas Shift Reaction Species Balance Equations ◦ Implemented as source term in mass transfer equation Kinetics

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Probability of Carbon Formation ◦ Boudouard Reaction ◦ CO/H 2 Reaction ◦ If carbon activity is greater than 1 then carbon will form in the cell

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Electrochemistry ◦ Anode Oxidation of CO and H 2 Fuels ◦ Cathode Reduction of O 2 ◦ Species Balance Equations

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Ion and Charge Transfer Summary of Charge Transfer Equations used in Model Electrode Backing Layers Anode ERL Cathode ERL Electrolyte

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Cell Potential (Voltage) Relationship between potential and current density determined by Butler-Volmer kinetic equation General Equation for activation polarization BC=0V Varied BC

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H 2 kinetics CO Kinetics

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O 2 Kinetics Current Density Relationships

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Electronic and Ionic Conductivities Summary of Effective Conductivity Equations used in Model Electrode Backing Layers Anode ERL Cathode ERL Electrolyte

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Cell Dimensions (mm) Cell length100Air channel height1.0 Cell height3.31Cathode Backing Layer Height0.05 Interconnect Height0.5Cathode ERL Layer Height0.01 Fuel channel height0.6Electrolyte Height0.02 Anode Backing Layer Height0.6 Anode ERL Layer Height0.03 Cell Materials Anode and Cathode InterconnectStainless Steel Anode Electrode and Anode ERL LayerNi-YSZ (Nickel - Yttria Stabilized Zirconia) ElectrolyteYSZ (Yttria Stabilized Zirconia) Cathode Electrode and Cathode ERL Layer LSM-YSZ (Strontium doped Lanthanum Manganite – Yttria Stabilized Zirconia)

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Physical Properties and Parameters AnodeCathode Permeability (m 2 )2.42 x 10 -14 2.54 x 10 -14 Porosity0.4890.515 Pore Diameter (µm)0.9711 Electronic/Ionic/Pore Tortuosity7.53, 8.48, 1.807.53, 3.4, 1.80 Electronic/Ionic Volume Fraction0.257, 0.2540.232, 0.253 Electronic/Ionic Reactive Surface Area per Unit Volume (m 2 /m 3 ) 3.97x10 6, 7.93x10 6 Solid Thermal Conductivity (W/m-K)116 Solid Specific Heat Capacity (J/kg-K)450430 Solid Density (kg/m 3 )33103030 ElectrolyteInterconnect Thermal Conductivity (W/m-K)2.720 Specific Heat Capacity (J/kg-K)470550 Solid Density (kg/m 3 )51603030

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5 Separate Fuel Inlet Cases Examined ◦ Fuel concentrations chosen to represent typical syngas composition ranges. Simulated Fuel Feed Mole Fractions Case123 45 H2H2 0.30 0.200.30 H2OH2O 0.07 0.170.270.07 CO 0.50 0.40 CO 2 0.10 0.20 CH 4 0.01 N2N2 0.02 0.120.02 Operating Conditions Inlet Temperature (K)1023Anode Fuel Feed x i Varies Cathode Inlet Velocity (m/s)6.5Cathode Air Feed x i.21 O 2.79 N 2 Anode Inlet Velocity (m/s)0.5Operating Voltage (V)0.6 to 1.0 Outlet Pressure (atm)1.0

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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

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

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

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Case 1 Anode: No reactions, κ=2.42x10 -14 Case 1 Anode: No reactions, κ=2.42x10 -5 H2H2 CO 2

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Highest WGS rate observed with greatest amount of H 2 O in fuel (3) Increased CO 2 in fuel results in negative reaction rate in FF (5) Increased CO in fuel increases WGS rate (1)

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All carbon activities in this study below 1, case 1 with highest observed activities Increasing H 2 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-H 2 reaction (0.766) Higher carbon activity at electrode inlets

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Comparison of Maximum Temperatures for each Case at E cell =0.7 Case123 45 Max Temperature (K) 1036.11033.5103410351033.3 Example Temperature Profile Case 1, 0.4V

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Example Polarization Curve with OCV Case 1 OCV values for all cases ranged between ~0.95 to 1.0V

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Case 1 Max Power Density: 720 W/m 2

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Example Case 1, 0.7V ERL ranges from 1.58mm to 1.61mm Most of the current generated in initial 1.7% to 3.3% of total ERL thickness

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Example Case 1, 0.7V ERL-Electrolyte Interface Current Density Inlet effects observed in initial 0.2% of total cell length

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Model agrees reasonably well with experimental data, data at slightly different conditions. Case 1 best performance with max power density 720W/m 2, Case 4 2 nd 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.

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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.

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