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.
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
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
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
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
Electrodes ◦ Use of effective thermal conductivity and effective heat capacity to account for porosity Electrolyte and Interconnects ◦ Conduction only
Physical Properties and Parameters AnodeCathode Permeability (m 2 )2.42 x x Porosity Pore Diameter (µm) Electronic/Ionic/Pore Tortuosity7.53, 8.48, , 3.4, 1.80 Electronic/Ionic Volume Fraction0.257, , 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) Solid Density (kg/m 3 ) ElectrolyteInterconnect Thermal Conductivity (W/m-K)2.720 Specific Heat Capacity (J/kg-K) Solid Density (kg/m 3 )
5 Separate Fuel Inlet Cases Examined ◦ Fuel concentrations chosen to represent typical syngas composition ranges. Simulated Fuel Feed Mole Fractions Case H2H H2OH2O CO CO CH N2N 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
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
Typical Inlet velocity profile ( m) Inlet effects occurring in initial 0.2% of length
Typical Inlet pressure profile ( m) Inlet effects occurring in initial 0.2% of length
Case 1 Anode: No reactions, κ=2.42x Case 1 Anode: No reactions, κ=2.42x10 -5 H2H2 CO 2
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)
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
Comparison of Maximum Temperatures for each Case at E cell =0.7 Case Max Temperature (K) Example Temperature Profile Case 1, 0.4V
Example Polarization Curve with OCV Case 1 OCV values for all cases ranged between ~0.95 to 1.0V
Case 1 Max Power Density: 720 W/m 2
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
Example Case 1, 0.7V ERL-Electrolyte Interface Current Density Inlet effects observed in initial 0.2% of total cell length
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.
S.A. Hajimolana et al., “Mathematical Modeling of Solid Oxide Fuel Cells: A Review,” Renewable and Sustainable Energy Reviews, vol 15, pp , M. Tweedie Thesis. CFD Modeling and Analysis of a Planar Anode Supported Intermediate Temperature Solid Oxide Fuel Cell. May, 2014.