Numerically Modeling of Anode Supported Tubular SOFC

Numerical models of Solid Oxide Fuel Cells (SOFCs) are important tools in understanding and investigate the effect of design and operation parameters of the SOFC performance and SOFC development works. In this study, one of the clean and highly efficient energy production systems, single tubular anode-supported SOFC is modeled numerically. Mathematical model of the single tubular SOFC is given in terms of the incompressible NavierStokes, Knudsen diffusion models, Butler–Volmer kinetic equations and Brinkman equations. For two-dimensional axisymmetric geometry, operating conditions, parameters of fuel cell and governing equations are solved by finite element method software ComsolMultiphysics. Pure H2 89% and H2O 11% are used at anode and air is used at the cathode side as reactant gasses. Temperature, pressure, porosity, permeability and especially distance of current collectors to the cell reactant gas inlet are studied. Optimal cell parameters for this model are determined and reasons of cell performance effects are explained. ji Flow depends on Mass velocity ratio (kg/m 2s) ε Porosity -Mi, Mj Molar mass (kg/mol) Si Species -μ Dynamic viscosity (Pa.s) K Permeability (m2/sn) rp Diameter of the porous space (m2) DK Knudsen Diffusion (m 2/sn) Di,eff Effective diffusion (m 2/sn) β Charge transfer coefficient -Σ Conductivity (S/m) T Temperature (°C) n Perpendicular vector to the boundary -Introduction Generating energy from clean, renewable and environmentalfriendly sources are one of the most important engineering problems. Hydrogen is one of the most abundant and the simplest energy carrier element. Using the energy of hydrogen effectively is a vital factor to prevent destructive effect of global warming. Since 80% efficient values, fuel cells which are converts chemical energy of fuels directly electrical energy, will have a major role next years. Easy to use on mobile Journal of Applied Mechanical Engineering J o u r n al o f A pp lied ical Eninee r i n g


Abstract
Numerical models of Solid Oxide Fuel Cells (SOFCs) are important tools in understanding and investigate the effect of design and operation parameters of the SOFC performance and SOFC development works. In this study, one of the clean and highly efficient energy production systems, single tubular anode-supported SOFC is modeled numerically. Mathematical model of the single tubular SOFC is given in terms of the incompressible Navier-Stokes, Knudsen diffusion models, Butler-Volmer kinetic equations and Brinkman equations. For two-dimensional axisymmetric geometry, operating conditions, parameters of fuel cell and governing equations are solved by finite element method software ComsolMultiphysics. Pure H 2 89% and H 2 O 11% are used at anode and air is used at the cathode side as reactant gasses. Temperature, pressure, porosity, permeability and especially distance of current collectors to the cell reactant gas inlet are studied. Optimal cell parameters for this model are determined and reasons of cell performance effects are explained.

Introduction
Generating energy from clean, renewable and environmentalfriendly sources are one of the most important engineering problems. Hydrogen is one of the most abundant and the simplest energy carrier element. Using the energy of hydrogen effectively is a vital factor to prevent destructive effect of global warming. Since 80% efficient values, fuel cells which are converts chemical energy of fuels directly electrical energy, will have a major role next years. Easy to use on mobile applications and obtain higher power density via power stations make fuel cells applicable and commonly used. Compared with another energy conversion device, high efficiencies of fuel cells can be reached, also for rather small units make fuel cells attractive energy conversion systems [1]. Fuel cells work on lower temperature also may work higher temperature depend on electrolyte material. There are several number of group for fuel cells. Higher efficiency value, SOFCs which are operating higher temperature 600-1000°C have many advantages.
In case of their higher operating temperatures, SOFCs, can convert chemical energy via different kinds of fuels without combustion, such as hydrogen, natural gas, and ethanol [2][3][4][5]. They can be produce planar and tubular geometry. Advantages of tubular SOFC versus planar geometry mainly consist of higher power density and no need for sealing materials. The layers of fuel cell specially triple phase boundaries are responsible for converting chemical energy to electrical energy, for this reason thickness, density and characteristic and the numerical modeling of the reaction which occur on these layers are important parameters to increase the performance of fuel cell [6].
In recent years there are lots of works to developing design and performance criteria of SOFCs [7]. These works are generally modeling to predict experimental works. Fuel cells are electrochemical devices, for that there are lots of factor effecting their working performance. Models which are developed for this aspect decreasing performance losses and optimization of some parameters are done. In literature modeling works are generally aimed to decrease costs [8] and investigating the cell working parameters before the experiments [9]. Modelling works done for not only all components of fuel cell but also every single components of SOFCs [10][11][12][13].
In this study temperature, pressure, porosity, permeability and distance of current collectors to the cell reactant gas inlet area are studied using COMSOL finite elements method software, Battery and Fuel Cell Module.

Mathematical modeling of tubular SOFC
In Figure 1 axis symmetrical tubular SOFC is demonstrated. In this work, NiO-YSZ is used at the anode side, YSZ is used at the electrolyte and at the cathode side LSM was. Axisymmetric geometric problem is chosen to better and easy solutions for numerical calculations.
In this work: • Model is in steady state situations and H 0 -H 2 O mixture is used at the anode side and air is used at the cathode site.
• Flow in channels are laminar, reactant gasses are ideal and non-compressible.
• Model is under isothermal condition and cell working temperature is 800°C

Conservation of species
Flow on the porous media generally described with molecular diffusion or Knudsen diffusions [19].
Non-reacting sides in the SOFC steady state diffusion and conduction equations are used.
At the outside of the anode steady state equations are used. , In the reacting side in fuel cell conservation of species estimated with these equations.  = iA Ri nF (2.10) At the cathode-electrolyte interface equations below applied to investigate concentration ratio of oxygen. Boundary conditions for conservation of species at the inlet of anode side take into account the concentration of reacting gasses.

Conservation of charge
If current production is only electrode-electrolyte interface and ohmic losses are just in electrolyte, electrode and current collectors, charge conservation at anode side can be described with equation below.
, , Boundary condition of current collector,

Model validation
In order to observe validation of model the same geometry and cell working conditions are applied than compared with Cheng et al. [19]. As seen in Figure 2

Effect of cell temperature
For this model in Figure 3 shows the effect of cell temperature, increasing temperature from 700 to 800°C the performance of the cell rises. In case of that increasing temperature to 1000°C cell performance decreasing the cause of entropy, decreasing the viscosity of gas reactants and change of effective diffusivity with temperature. In addition increasing temperature reduces the mobility of SOFCs.

Effect of cell reactant pressure
In Figure 4 increasing the cell working pressure, cell performance increases. Higher pressure values increase the Nerst voltage; this is the most important reason of increasing cell performance. At the same time, diffusion of species and concentration are increasing.

Effect of cathode electrode porosity
Another important factor of cell performance is porosity value of electrodes. In this work, anode porosity is constant and this value is 0.3, cathode porosity is changed between 0.2-0.5. Electrode porosity has lower effect for performance than other cell working factors. As seen in Figure 5 for 0.4 and 0.5 porosity value, result of the big gaps between particles which conduct electricity, cell performance reduces whereas between 0.2-0.3 value cell performance not increases significantly.

Effect of permeability
Effect of permeability is more important than porosity values. Permeability is the function of the thickness of electrode layer and the pressure drops. In Figure 6 changing permeability between 10-15-10-12 cell performance increases the result of the decreasing flow resistances in porous media (Tables 1-3). Decreasing flow resistance causes the more reactant transfer to the reaction site. Figure 7 depicts the effect of current collector distance to inlet area, increasing step by 0.5 mm between 1.5-3.5 mm. As a result, it can be seen from the figure, current density changes with opposite direction with length of current collectors. It is the reason of the ohmic losses, causing the bigger contact resistance of current collector surface.

Conclusions
SOFCs generally work between 600-1000°C cell temperatures. In this work we observed maximum performance value is between 800-900°C.
Higher temperature values caused decreasing of cell performance as a result of changing the diffusion, viscosity, concentration, density and conductivity values. However, higher the cell pressure, cell performance is increased due to the bigger value of Nerst voltages. As well as higher pressure value increase the concentration value of ideal gasses. For this reason exchange current density is increased. In addition porosity values are another factor of performance of fuel cell, but porosity value is not effective like other parameters. 0.2-0.3 values have better results for cell working conditions. Permeability is more important parameter, increasing this parameter in experimental procedures, performance will increase slightly. Distance of current collector surface to r axis is another vital factor for causing ohmic losses. Lower surface areas of current collection implement higher power density for fuel cells.