INTRODUCTION
Last few decades have observed an exponential growth in world population that puts extra burden on the energy supply chain. Present day energy demand is met mostly through the conventional sources like fossil based fuels that produce undesired by-products causing air pollution and greenhouse gas (GHG) emissions. Fossil-fuel-based environmental pollution is the major cause of smog formation and global warming [1]. Human interventions caused by the abundant and unprotected use of fossil-based fuels are the major factors upsetting the global ecosystem and energy balance of the Planet. In addition to the above factors, fluctuations in global oil market and depletion of oil reserves are the other vulnerabilities associated with the use of fossil fuels. These issues paved the way for the scientists and researchers to explore alternative sources of energy that are clean and sustainable [2]. These alternate sources of energy include fuel cells (FCs) and electrolyzers that are electrochemical energy conversion devices used to convert chemical energy of gaseous fuels e.g., hydrogen into electrical energy [3]. FCs are classified based on the operating temperature (high, medium, and low), operating mode (active and passive), and electrolyte membrane type and concentration. Platinum (Pt) and Pt-alloy catalysts used in low-temperature FCs (e.g., Proton exchange membrane FC or PEMFC) are not only expensive but also susceptible to contaminants like CO. Solid Oxide Fuel Cells (SOFCs) fall under the high-temperature category. Transition metals are used in both the electrodes (i.e., cathode and anode) enabling the SOFCs to handle a variety of different fuels such as biogas and syngas [4,5]. SOFCs are cost-effective, exhibit high productivity, and appear to have no adverse environmental impact. A number of advantages are associated with the high temperature operability (700°C–1000°C) of SOFCs. For example, gas leaving the anode (anode-off-gas or AOG) still contain significant amount of thermal energy due to high temperature operation of SOFCs. This could be used to feed endothermic reforming reactions in a cogeneration or CRP (combustion-reforming-power) system. Hence, efficiency of the SOFC-based CRP systems could go as high as 90% [6]. Numerous design configurations of SOFC have been reported in literature. Anode-supported SOFC (AS-SOFC) design is popular amongst the other designs. In AS-SOFC, anode acts as the support-structure for cell components. This allows a thinner electrolyte layer (EL) giving rise to lower ohmic resistance across the electrodes [7]. Four major components or layers constituting AS-SOFC are cathode functional layer (CFL), electrolyte layer (EL), anode functional layer (AFL), and anode support layer (ASL). Ni/Yttria-stabilized zirconia (YSZ), Strontium-doped lanthanum manganite (LSM) with YSZ, and YSZ are the most popular materials serving as the anode, cathode, and electrolyte respectively of AS-SOFC. Fuel cell efficiency has direct impact on the energy production cost of the cell. Fuel cell efficiency can be improved through optimization of design and operating parameters [8]. Design parameters are associated with the geometry and dimensions of the fuel and oxidizer flow channels. In addition, structural parameters like thickness, porosity, and permeability of the CFL, EL, and ASL have substantial impact on the performance and efficiency the fuel cell. Operating parameters impacting the cell performance include operating temperature and pressure (fuel and oxidizer) [9].
Experimental characterization and parameter optimization of SOFCs is laborious, expensive, and time-consuming. Besides, high operating temperature in SOFCs further limits the experimental measurement and evaluation of these parameters [10–12]. Mathematical modeling, on the other hand, has shown promise in characterizing fuel cells and components in a time-efficient and cost-effective manner. Different modeling approaches have been used to improve fuel cell performance through parameter optimization [13]. Tubular and planar design configurations have been the focus of modeling and simulation oriented research of SOFCs [14]. Nonetheless, planar architecture offers numerous advantages like simple construction, easy to fabricate, and higher power density [7,15]. Numerous studies corresponding to SOFC parameter optimization using different numerical approaches are reported in literature. Effect of design and structural parameters on the performance of different SOFC configurations has assiduously been studied and reported in literature [10,16–23]. Similarly numerous studies corresponding to the effect of operational parameters on SOFC performance have also been reported [8,9,24–27]. In addition to the design and operating parameters, SOFC performance is directly linked to the rate of electrochemical reactions taking place within the electrodes and voltage drop across the electrodes. Voltage drop is caused mainly by the polarization (activation and concentration) and ohmic resistances. SOFC power is a function of current density (a measure of electrochemical reaction rate) and cell potential. Hence reduction in either of the two parameters i.e., current density and potential negatively impacts the power deliverance capabilities of the fuel cell. Rate of electrochemical reaction and cell potential are regulated by the kinetic and thermodynamic parameters respectively. Hence, in addition to the operational and design parameters, optimization of kinetic and thermodynamic parameters could significantly improve performance and maximize efficiency of the SOFCs. Contrary to the widely reported numerical studies regarding structural and operational parameters of SOFCs, research articles corresponding to the SOFC reaction kinetics and thermodynamics are seldom found in the published literature. Thence, some of the recently published research articles devoted exclusively to the numerical studies focusing SOFC reaction kinetics and thermodynamics are presented.
Electrochemical kinetics and polarization related losses in SOFCs are generally studied using semi-empirical models. Semi-empirical models require expensive experimental data for building the correlations and validation of simulation results. Physics-based models involving mass, momentum, and energy balances show promise in this regard. Such models are computationally intensive but more accurate [28]. Model dimensionality is another important aspect impacting accuracy and computational burden. In 0D models the cell domain is represented by a single point in space used to evaluate global performance of the cell. 3D models predict the cell local responses and give a clear picture of spatial gradients occur within the cell domain. 1D and 2D models represent trade-offs between computational speed of 0D models and prediction accuracy of 3D models [29]. Bruno Conti et al. [30] proposed a simplified semi-empirical kinetic model for an intermediate-temperature SOFC. Model assumed linear dependence of parameters on ohmic and activation overpotentials while neglecting concentration variations. Detailed experiments were carried out to measure temperature and gas composition for model validation. Simulation results were found in good agreement with the measured data. F. R. Bianchi et al. [31] extended the model proposed in [29] for a button AS-SOFC into a more generic formulation. 0D and 1D steady-state mass balance equations were used simulate the cell global responses and optimize concentration overpotential respectively. Optimized concentration overpotential was subsequently used to evaluate the effect of diffusion across the cell thickness on cell voltage. Y. Sahli et al. [32] proposed a thermodynamic model to optimize SOFC performance. Effect of losses due to ohmic and polarization resistances and species concentrations were investigated. SOFC power output was found to be directly proportional to oxidizer O2 concentration and operating temperature while inversely proportional to the thickness of AFL, EL, and CFL. It was found that temperature has more pronounced effect on SOFC power density than the thickness of functional layers. Min, Park and Hong [33] proposed a 1D thermodynamic model for SOFC stack to optimize operating conditions. Simulations supplant tedious, costly, and time-consuming experiments required to find optimum operating conditions for SOFC stack. Due to the involvement of Multiphysics phenomena and complex dynamics of SOFC systems, lower model dimensionalities often prove insufficient in adequately capturing the local responses and spatial gradients within the cell. 3D CFD models involving coupled physics on a 3D level have shown promise in resolving these shortcomings. Fewer research articles are found in literature focusing on the comprehensive evaluation of electrochemical kinetic and thermodynamic parameters using CFD simulations with higher model dimensionality. Li et al. [34] developed a 3D non-isothermal model to optimize the performance of a planer AS-SOFC as a function of interconnect land-width and thickness of cathode. Transport equations were solved using volumetric reaction and kinetic source terms. They concluded that reduction in local temperature as well as thermal gradient is crucial for a highly uniform distribution of current density indicating a strong link between current density and temperature variation within the cell. A. N. Celik [35] implemented a 3D Multiphysics model into COMSOL Multiphysics software package coupling electrochemical model equations with computational fluid dynamics (CFD). This coupled approach gives a comprehensive understanding of the system behavior through different operating and boundary conditions. Tabish et al. [36] developed a 2D CFD model of anode supported SOFC using triple-phase boundary (TPB) based kinetics. Effect of operating temperature and TPB density on the cell performance was investigated.
Reference exchange current density, transfer coefficients, reaction enthalpy, and entropy are the major kinetic and thermodynamic parameters having pronounced impact on the performance and efficiency of SOFCs. Due to the inter-dependence of Multiphysics phenomena, 3D simulations using Multiphysics CFD software are required to optimize these parameters. In view of the above cited literature, such studies have not been reported that justifies the efforts behind present study. Present work addresses this gap by optimizing the above-mentioned kinetic and thermodynamic parameters using a Multiphysics CFD simulation software ANSYS Fluent. The aim is to contribute to the ongoing efforts in SOFC research supporting the goal for clean and sustainable energy future.
MODEL DEVELOPMENT
A 3D model of a planer AS-SOFC was developed accounting for electrochemical and thermodynamic properties of the system. The model was implemented into a CFD simulation software package ANSYS Fluent. ANSYS Fluent is a Multiphysics CFD software capable of simultaneously solving transport equations (mass, momentum, heat, and species) coupled with electrochemical reaction kinetics using computational algorithms. A built in SOFC Add-on module of ANSYS Fluent was used to compute the electric parameters across 3D cell domain.
Model Geometry
A 13-channel planar AS-SOFC designed at the Chinese academy of science Ningbo Institute of Material Technology and Engineering (NIMTE) has been selected for this study. Owing to the symmetric construction of the squared-shaped cell, simulation domain was reduced to a single channel to reduce computational cost. The actual domain consisted of 13 rectangular-shaped air (oxidizer) and fuel (hydrogen) channels. Reduced single channel geometry model shown in Fig. 1b was developed using ANSYS Design Modeler. Geometrical design parameters derived from [37] are presented in Table 1.
Schematic diagram of a planar AS-SOFC cross-section is shown in Fig. 1b. The model consisted of anode support (diffusion layer), anode catalyst (functional layer), electrolyte layer, cathode support (diffusion layer), cathode catalyst (functional layer), flow channels, and interconnects. Diffusion and catalyst layers are also referred to as the gas-diffusion-layer or GDL and triple-phase-boundary or TPB.
Mesh Independence
Accuracy of the simulation results have strong dependence on quality of the mesh generated as a result of discretization of the domain. Hence, a highquality rectangular or mapped mesh (with hexahedral elements) instead free mesh (with tetrahedral elements) was used across the whole domain. Prior to conducting numerical simulations, mesh quality check was performed using mesh quality indices e.g., element aspect ratio, orthogonal quality etc. to ensure the accuracy of model predictions. Mesh size and density significantly impacts simulation results; hence mesh size independency study was conducted to further ensure accuracy. The analysis revealed that increasing mesh density above 93000 elements, simulations exhibited negligible variations in H2 mass fraction illustrated in Fig. 2. Hence, a mesh density of 93000 elements was used for model validation and subsequent simulation experiments. Simulation domain with different mesh densities is shown in Fig. 3. Optimum mesh resolution ensures reliability of the simulation outcomes of the present study.
Governing Equations
During operation, multiple physical and chemical processes occur simultaneously within different components of SOFC. These processes include transport of species, momentum, mass, and heat, fluid flow, and charge transport (ions and electrons). Hence a fully coupled Multiphysics model is developed and implemented into ANSYS Fluent. The transfer processes mentioned above along with the electrochemical reaction were incorporated in the model. These processes occur simultaneously and are mutually influential influencing impact each other [39]. Electrochemical reactions taking place at the anode and cathode sides are given as:
Anode: 2H2 + 2O2– ↔ 2H2O + 4e–
Cathode: O2 + 4e– ↔ 2O2–
The cell potential is given as a function of open circuit potential and overpotentials due to activation, concentration, and ohmic losses [40].
Momentum Conservation
In SOFC, gases flow through channels and diffuse through the porous electrodes. The fluid flow is governed by Navier Stokes equation. This equation describes the flow in the channels; however, friction is created when the gases pass through the porous electrode structures. The additional pressure loss induced by the movement of gas through the porous media can be described by Darcy’s law. The momentum loss of a fluid moving through a porous media is represented by the Eq. 2. Incompressible flow is assumed in both the channels and within the porous electrodes while neglecting the effect of gravity.
The Brinkman equation describes the fluid flow through the porous media by introducing Darcy’s law into Navier Stokes equation.
Where μ is the dynamic viscosity of gaseous mixture; P is the total gas pressure in the mixture; V →
Species Transport
Transport of gas components in the porous electrodes and gas channels is affected by diffusion and convection respectively. A modified Fick’s law is used to better describe the diffusion behavior of gases in flow channels and porous media. incorporation of Knudsen diffusion. For each chemical species ι the conservation equation is given as:
Where F is Faraday’s constant; M is the molar mass; J is the exchange current density and subscript c and a represent cathode and anode respectively. Exchange current density can be expressed as:
ke is pre-exponential factor and Eact is the activation energy.
Charge Conservation
The ions and electron are in motion during an electrochemical reaction and their mobility with ionic and electronic potentials follows Ohm’s law. Ohm’s law can be used to formulate the equation of charge conservation.
Where specific surface area is represented by Sa; in addition, itrans,an and itrans,ca represent the transfer current density produced by electrochemical process at anode and cathode respectively. ϕion and ϕelec are ionic and electronic potentials respectively. The following expression can be used to compute effective ionic and electronic conductivities in Eq. 9 and 10 [41].
In the porous electrode, the relative volume fraction of electron carrier particles is denoted by θ. Whereas σion for anode and cathode (σion,an, σion,ca) and σelec are given by [42]:
Mass Conservation
Despite the fact that species generate and degenerate during the ongoing reaction within the SOFC anode and cathode, the total mass of materials remains conserved. The following is the mass conservation equations [36].
Where V → W ·
Energy Conservation
The temperature field across the entire domain described by the energy conservation equation. In porous electrodes, the local thermal equilibrium concept indicates that the fluid and solid phases are at the same temperature. In SOFC convection, gas and solid phase heat conduction, heat transport by the gas species, and heat source term are incorporated in the thermal energy equation [43].
Where cP and keff are specific heat capacity and effective thermal conductivity terms given by:
cg and cs represent the specific heat capacity of gas and solid while kg and ks denotes the thermal conductivity of gas and solid respectively. ST is the heat source term which is equal to the sum of heat generated due to polarization overpotential, joule heating, and heat due to electrochemical reaction [34].
Where Jη represents polarization overpotential, i e 2 / K e f f i s 2 / σ e f f
Boundary Conditions
ANSYS Fluent was used to solve the model equations. User-defined scalars (UDS) were used for the implantation of charge transport equations and the source terms. At the anode and cathode flow channel inlets, mass flow rate, species mass fractions, and temperature were applied as inlet boundary conditions. Pressure-outlet type boundary condition is used at the outlet of flow channel. SOFC anode was used as grounded and hence an electric potential of 0 volt was applied. Whereas, the electric potential at the cathode was used as Vcell. Adiabatic boundary conditions were used at the cell walls to simulate thermal insulation. Detailed description of the boundary and operating conditions is presented in Table 2. User Defined Function (UDF) was used for the implementation of momentum and energy source terms.
RESULTS AND DISCUSSION
SOFC simulation domain was discretized using finite volume method (FVM). ANSYS Fluent Add-on Fuel Cell Module was used for the model implementation. Convection and diffusion coupling was implemented using the second order upwind differencing scheme (UDS). To implement source terms in the governing equations, user-defined functions (UDF) were used. UDS was written using a C-based code which was compiled using Visual Studio 17.0 compiler. Prior to carrying out the detailed simulation study and parameter optimization, it is important to validate the model for authenticity of the predictions. Hence, the following section includes the validation results and description.
Model Validation
Model validation is an essential step in proving the authenticity of the subsequent predictions resulting from detailed simulations. To validate the model, polarization curve resulting from numerical simulation was compared to the experimental data derived from [37]. The Chinese Academy of Sciences, Ningbo Institute of Material Technology and Engineering (NIMTE). NIMTE produced Ni-YSZ anode-supported SOFCs, which were used for both modeling and testing. The data presented in [37] used for model validation was the outcome of experiments carried out at NIMTE. Details of the experimental setup and procedure have not been provided in reference [37]. Nevertheless, details regarding operating conditions e.g., flow rates, temperature etc. were provided. Anode and cathode were supplied with humidified hydrogen and air respectively. The operating temperature used in the experiments was 800°C (1073 K). Fuel intake mass flow rate per duct was 2×10−8 kg/s, whereas air inlet mass flow rate per duct was 0.8×10−6 kg/s. Operating voltage of 0.7 V was used applied at the cathode keeping the anode grounded (0 V). Simulations were carried out using the same operating conditions used in the experiments. A previous research article [38] from the same institute i.e., NIMTE, Chinese Academy of Sciences presents a similar study with details of the experimental setup procedure included. Component dimensions of the AS-SOFC used in the study were quite the same with minor differences. Hence reference [38] could be referred for details of the experimental procedure adopted in [37].
Experimental and simulated polarization curves are shown in Fig. 4. A reasonably good agreement is found between the simulated and measured polarization curves. Validation results prove authenticity of the model for subsequent investigations based on detailed simulation experiments. Slight deviation at the middle and towards the end of the polarization curve could be attributed to the assumptions and simplifications made in an attempt to reduce the model complexity and computational load of the simulations. Nonetheless, deviation is well within the allowable range for most of the model predictions. Furthermore, constant exchange current density and entropy values were used in the model, but in reality, they vary as a function of other parameters. This could also be the contributing factor to the deviation.
Effect of Reference Exchange Current Density
Different values of reference exchange current densities (J0) have been adopted from previous studies. Simulations were carried out at different applied voltage using different values of reference exchange current densities. In Fig. 5, V–I curves with different values of reference exchange current density are plotted along with the experimental curve. Exchange current density has pronounced effect on the local current density as can be seen in Fig. 5. V–I curve corresponding to the anodic and cathodic reference exchange current densities of 3500 A/m2 and 2013 A/m2 respectively fall within the closest vicinity of experimental V–I curve. Reference exchange current densities is an important kinetic parameter that significantly impacts local current density and hance the power output of SOFC.
Effect of reference exchange current density on the local current density of SOFC is shown in Fig. 5. It can be seen that the maximum current density is delivered with anodic and cathodic reference exchange current densities corresponding to 7460 A/m2 and 10090 A/m2 respectively. Power output of SOFC as a function of applied current density is shown in Fig. 6. Maximum power is delivered at the anodic and cathodic reference exchange current densities corresponding to 7460 A/m2 and 10090 A/m2 respectively. So, the optimized values of reference exchange current density correspond the maximum power output of SOFC. Hence in this case, 7460 A/m2 and 10090 A/m2 are the optimized reference exchange current densities for anode and cathode respectively.
In SOFC during operation, hydrogen enters the anode side, diffuses through porous electrode i.e., GDL and reacts with oxygen to form water. So, major part of hydrogen entering the anode gets consumed with some left unreacted and leaves at the channel outlet. Fig. 7 shows contour plots of hydrogen mass fraction at different exchange current densities of the anode and cathode with 0.7 V applied voltage. It can clearly be seen in Fig. 7 that more of the hydrogen gets consumed as we move from top to bottom. Maximum hydrogen consumption is achieved at J0,a = 7460 A/m2 and J0,c = 10090 A/m2 while fraction of H2 leaving the anode is as little as 0.0006. This indicates an increases reaction rate and favorable kinetics. The lowest consumption of hydrogen is observed at J0,a = 2100 A/m2 and J0,c = 700 A/m2 with unreacted mass fraction of 0.18. In this case the amount of current obtained is also minimum as compared to the other cases. This suggests slow reaction rate and unfavorable kinetics.
As reaction proceeds, hydrogen react with oxygen and the water formed at anode side. Fig. 8 Shows contours of water mass fraction corresponding to different exchange current densities at 0.7 V applied voltage. Higher water formation indicates higher reaction rate and favorable reaction kinetics. Maximum rate of reaction indicated by higher water formation is observed at J0,a = 7460 A/m2 and J0,c = 10090 A/m2. Water formation starts very close to the inlet implying that reaction starts immediately as the gas (hydrogen) enters the channel again indicating the faster kinetics. The lowest water formation is observed at J0,a = 2100 A/m2 and J0,c = 700 A/m2. It can be seen that water starts forming far from the inlet indicating slower kinetics.
Oxygen or air is used as oxidizer in SOFCs that enters the inlet of cathode channel and leaves at the outlet. In the simulations used in this study air was used as the oxidizer but only oxygen considered while analyzing the results since only oxygen in the air reacts with hydrogen during the reaction. Fig. 9 shows that O2 follows the same pattern as that of the hydrogen. Again, different reference exchange current densities were used in the simulation experiments applying 0.7 V as the operating voltage. Minimum reaction rate was observed at J0,a = 2100 A/m2 and J0,c = 700 A/m2 that corresponds to oxygen fraction of 0.182 at the cathode outlet. On the contrary maximum reaction rate was observed at J0,a = 7460 A/m2 and J0,c = 10090 A/m2 indicated by the immediate consumption of oxygen as it enters the cathode. Maximum reaction rate is also indicated by the lower fraction of oxygen at the cathode outlet i.e., 0.056.
Effect of Transfer Coefficient
In addition to exchange current density, transfer coefficient (α) is another important kinetic parameter that influence the reaction kinetics and hence the power deliverance capabilities of SOFC. Hence, optimization of this important kinetic parameter is also worthwhile and opted in this study. From Fig. 10, it can be seen that changing α, significantly effects the characteristics of V–I curve which is the indicator of SOFC output power. Maximum power is achieved at α=0.5 (anodic), 0.5 (cathodic) as indicated by the graph in Fig. 11.
Effect of Entropy
Entropy (∆S) is an important thermodynamic parameter influencing the reaction rate and hence the performance of SOFC. In this case, entropy of the reaction is varied to see its impact on the V–I curve and power output of the SOFC. Heat source term in energy conservation equation contain entropy change (a thermodynamic term), which represents heat production due to reaction. A user define function (UDF) was used to define energy source term by compiled in Visual Studio. For each of the simulation experiments, a new value of ∆S was used in the UDF. Fig. 12 shows V–I curves with different reaction entropies. It can be seen that at higher current densities and lower applied voltages effect of entropy becomes more dominant. It can be explained by the increase reaction rate at higher currents that gives rise to higher polarization and ohmic resistances. Fig. 13 shows the power curve under different values of entropy change. At peak power i.e., higher current, effect of entropy becomes more dominant. At peak power maximum current density corresponds to maximum reaction rate, since, current density is the direct measure of the rate of electrochemical reaction. Hence, the effect of entropy is dominant and visible more clearly.
Water formation occur at anode side due to the reaction between hydrogen and oxygen. The higher water formation implies reaction rate between the reacting species is higher. Water formation at the anode side during reaction between hydrogen and oxygen is elucidated by the contours of water mass fraction shown in Fig. 14. As mentioned above and illustrated in Fig. 12 and Fig. 13 that entropy has little impact on the cell power and hence performance except for the sufficiently higher currents or reaction rates. The same is supported by the contours of water fraction shown in Fig. 14. There is negligibly small variation in contours of water fraction produced at different entropy values. This can be explained by the fact that at low to moderate power of SOFC i.e., < 0.5 W/cm2 entropy has negligibly small impact on its performance. But at higher power output entropy starts impacting the SOFC power performance. Results presented in Fig. 12–14 show that maximum power is delivered by the cell at ∆S = –0.056 J/(mol∙K) whereas minimum power output corresponds to ∆S = –54.9 J/(mol∙K). Mass fraction of water at the outlet corresponding to maximum and minimum power output of the cell is 0.93 and 0.90 again indicating little impact of entropy.
Another important parameter that determines the performance of SOFC is the overpotential. After identifying the impact of entropy change on the power output of the cell, it is important to study how does entropy change influence the cell overpotential. In anode supported SOFC, the overpotential has largest contribution to overall losses of cell voltage and hence the efficiency. The overall overpotential comprised by the activation, ohmic and concentration overpotentials. These individual overpotentials correspond to the resistances due to activation, electronic and ionic flow, and concentration changes. Fig. 15 shows the effect of entropy on overpotential in terms of V–I curve. During operation in SOFC, overpotential increases with an increase in current density due to increased reaction rate. In other words, higher power output of SOFC is associated with increased losses due to an increase in overpotential at higher reaction rate as indicated in Fig. 15. It can be inferred that effect of entropy change on the power output of the cell is negligible (Fig. 13) but this effect is quite marked in case of overpotential (Fig. 15). Despite a significant difference in the magnitude of impact in both the cases, trend is the same. That means ∆S = –0.056 J/(mol∙K) is favorable in both the cases i.e., it is associated with higher power (Fig. 13) and low overpotential (Fig. 15).
Effect of Operating Pressure
Pressure is an important operating parameter that has pronounced impact of SOFC performance. After the optimization of kinetic and thermodynamic parameters, operating parameters like pressure and fuel utilization were also investigated. Fig. 16 shows the effect of operating pressure on the power output and V–I characteristics of the cell. As mentioned before that V–I curve is a useful way to calibrate operating voltage and current to optimize the cell power output.
Operating pressure is varied between 1 bar and 4 bar. It is clear from Fig. 17 that as operating pressure increases; current and power density increases. Current and power densities increase as the operating pressure increases. As pressure increases, activation and concentration overpotentials drop causing an increase in the power output. At higher pressures, the activation overpotential drops due to increase in fuel concentration in the porous electrode. The gas diffusion rate increases at the same time, resulting in a drop in the concentration overpotential, which consequently raises the power performance of the cell.
Effect of Fuel Utilization
As mentioned above that fuel utilization is an important operating parameter. In Fig. 17, the effect of fuel utilization (UF) on current and power curve can be seen. At higher fuel utilization, both current and power density decreases. This is due to the fuel depletion near the exit of anode assembly. Although high FU is advantageous in order to attain high electrical efficiency, the main disadvantage is its lower power density. This implies that a larger cell surface area is required for optimum cell operation. As a result, FU should be carefully chosen in order to achieve high electrical efficiency at a tolerable power density.
CONCLUSIONS
Kinetic parameters i.e., reference exchange current density and transfer coefficient and thermodynamic parameter i.e., entropy are studied simultaneously to optimize SOFC performance. First the model is validated with the experimental voltage–current (V–I) plot. Simulations were carried out using the same parameters and conditions used in the experiments. The model was found in a reasonably good agreement with the experimental data. Subsequently SOFC performance optimization study was conducted by carrying out simulation experiments. The main optimization parameters selected included kinetic and thermodynamic parameters i.e., reference exchange current density (anodic and cathodic), transfer coefficients, and reaction entropy. In addition, SOFC operational parameters including operating pressure and fuel utilization were also studied. Optimized kinetic parameters including J0,a, J0,c, αa, and αc (anodic and cathodic reference exchange current densities and transfer coefficients) correspond to 7460 A/m2, 10090 A/m2, 0.5 and 0.5 respectively. Optimized entropy (∆S) corresponds to –0.056 J/(mol∙K). Following the kinetic and thermodynamic parameter optimization, SOFC operating pressure was optimized ranging between 1 bar and 4 bar. It was found that increasing operating pressure decreases cell overpotential thereby improving the cell performance. Furthermore, cell current and power densities increase at higher pressures giving rise to an improved cell performance. Finally, the effect of fuel utilization on current and power density was investigated. Simulation results indicate that higher fuel utilization lowers the power density of the cell. Although different important parameters have been identified and optimized to improve the overall cell performance. Nonetheless, further research on the optimization of other physical and chemical parameters like diffusivity, enthalpy, specific heat, and thermal conductivity is required.
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