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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 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 Model
Types 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 Terms
Heat 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
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
N20.02 0.02 0.02 0.12 0.02
Operating 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
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
Example Polarization Curve with OCV Case 1
OCV values for all cases ranged between ~0.95 to 1.0V
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
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
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