NUMERICAL INVESTIGATION OF EFFECTS OF WORKING CONDITIONS ON PERFORMANCE OF PEM FUEL CELL

In this study, the effects of the working pressure and temperature on the performance of the PEM fuel cell were investigated numerically. Non-isothermal, steady-state and single-phase model was used to examine the behaviour of the proton exchange membrane (PEM) fuel cells in the three-dimensional condition. The threedimensional single-cell model has been developed within FLUENT 6.3 software by utilizing the PEMFC module. The results of polarization (voltage) variation curves and current density distribution were given and compared with each other. According to the results obtained, by keeping humidification and cell temperatures in equilibrium, the performance of the cell improves with the increasing cell temperature. In addition, the current density of the cell increases with the increasing operating pressure.

increasing temperature and pressure. They found out that saturation level the most effective parameter on cell performance and the increasing saturation reduced the cell performance.
The present study, the effects of the working pressure and temperature on the performance of the PEM fuel cell were investigated numerically. To investigate the effects of the working condition on the performance of the PEM fuel cell, a three-dimensional model was developed. Three-dimensional single-cell was modelled with FLUENT 6.3 software by utilizing a PEMFC module. After creating a model, the convergence curves were checked to examine the accuracy of the model. Also, the independence of the solution from the number of mesh elements was examined by using five different mesh structures. The model was confirmed with the experimental data that the Wang et al. [13] had published. After verifying the model, analyses were performed for the various temperature and operating pressure values. Consequently, to assess the effects of the working pressure and temperature on the performance of the PEM fuel cell, the polarization (voltage) and power curves, the distribution of the current density that is in the form of the counter line graphics, the current density curves according to pressure and temperature were given and evaluated systematically.

NUMERICAL MODEL
To investigate the working conditions on the performance of PEMFC, three-dimensional single-cells were modelled. A cross-sectional view of the PEMFC is shown in Figure 1 and dimensions of the cell are given Water is only in the vapour phase. The governing equations of mass conservation, momentum conservation, energy conservation, species concentration, proton transport and electron transport are as follows: In the momentum conservation equation, u S are external body forces and presented in Table 2.
 Energy conservation equation Where, h is the enthalpy, k is the thermal conductivity and h S is the energy source term and is defined in Table 2.
In Equation 4, k S is the source term and is given Table 2, eff k D is the effective gas species diffusivity and can be expressed as:  Proton transport and electron transport equation .( ) In the proton transport and electron transport equation,  m is the ionic conductivity,  m is the membrane potential,  s is the electrical conductivity,  s is the solid phase potential. i S and e S are the source terms of these equations and are given Table 2. Electrochemical and transport properties are listed in Table 3.

Boundary and Operating Condition
Boundary conditions have to be defined to solve the discretized equation. At the inlet of the gas flow channels, the mass flow inlet boundary conditions are defined as a boundary condition. Flow rate, temperature, and spices concentrations are described as the inlet values at the flow channels. Well-humidified hydrogen enters the anode side flow channel and well-humidified air enters the cathode side flow channel. The values of mass flow rates of air and hydrogen are 4.68x10 -5 kg.s -1 and 1.762x10 -6 kg.s -1 , respectively. At the outlet of the gas flow channels, pressure outlet boundary conditions are used. Solution zone, except the current collector plates areas, are defined as fluid, the current collector plates are defined as a solid. Top and bottom surfaces of the cell are assumed as walls which have a constant temperature.

Solution Method
The equations were solved in the FLUENT 6.3 software which uses finite volume method to discretize equations. The solution zones were created and meshed in the GAMBIT software as shown in Figure 2. To investigate independent of grid size and balancing solution time, the solution zones were meshed in five different mesh sizes. In all calculations, the SIMPLE algorithm was used to solve the discretized equations of pressurevelocity coupling. To discretize pressure, the standard scheme was used and the first-order upwind scheme was used to discretize other equations. For all characteristics, iterations were continued until solutions converge up to 10 -6 .

Model Validation
In order to validate the model, the results obtained from the computations were compared with the experimental data which was taken from the study of Wang et al. [13]. Geometrical parameters of the reference study were given Table 4. To compare the model predictions and experimental results, the polarization curves were shown in Figure 3. As can be seen in Figure 3, the model results are overwhelmingly in good agreement with the experimental data from the literature [13] except for the values of current density greater than about 1.1 A/cm 2 . The difference in this interval is probably due to the poor performance of the PEM fuel cell because of the adverse effects of water flooding which was ignored at the model.

RESULTS AND DISCUSSION
In order to investigate the effect of operating conditions on cell performance, the analyses were performed for three different temperature and pressure values. After the analyses, the polarization (voltage) and power variations with respect to the current density are given in Figures 4-6 according to the various values of the temperature and pressure. The current density distributions were given in Figures 7 and 8 for various temperatures (313 K, 333 K and 353 K) and pressures (100 kPa, 200 kPa and 300 kPa) in the form of contour line graphics. In addition, the current density variations with respect to temperature and pressure were given in Figures 9 and 10. Figure 4, Figure 5 and Figure 6 demonstrate the variations of the polarization (voltage) and power curves in the conditions of three different temperatures and operating pressures. As it can be seen in Figures 4-6, the effect of temperature is extremely clear at the values of the high current densities and it can be said that the increase of temperature increases cell voltage and cell power. Especially after the 1.1 A/cm 2 of the current density, these differences have become more obvious for both the polarization (voltage) and power. The results are similar for Journal of Thermal Engineering, Research Article, Vol. 5, No. 1, pp. 14-24, January, 2019 19 the three operating pressures but the effect of temperature is more pronounced at high pressures. The cell voltage and cell power increase with increasing operating pressure. At all conditions, the cell potential decreases with increasing current density; also with increasing current density, firstly, power reaches its maximum value and then decreases.  For different temperatures, the current density distribution is given as counter graphic in Figure 7. The comparison was carried out at 300 kPa pressure and 0.5 V cell potential. It is seen that increasing the temperature increases the amount of maximum current density and the nonhomogeneous distribution of the current density. The maximum current densities occur near the flow channel and the amount of current density decreases towards the outlet cross-section. Figure 8 shows the current density distribution in the form of counter line graphics for three different operating pressures. The graphics were drawn by using data obtained for a temperature of 353 K and a cell potential of 0.5 V. Referring to Figure 7 and Figure 8, it can be said that the effect of pressure on current density is less than the effect of temperature. For 0.5 V, 0.6 V and 0.7 V cell voltages and 300 kPa operating pressure, the current density variation with respect to the temperature were given in Figure 9. As seen in Figure 9, it can be said that the current density value increases with increasing temperature and the effect of temperature variation at low temperatures and low voltages on the current density is much more apparent. Figure 10 shows the current density change curves with respect to the pressure of 0.5, 0.6 and 0.7 V cell voltages for the temperature of 333K. As shown in Figure 10, the current density magnitude increases with increasing pressure and the effect of pressure variation at low pressure on current density is much more apparent. Referring to Figure 9 and Figure 10, it can be said that the effect of the temperature variation on the current density is greater than the variation of the pressure. Compared with similar studies in the literature, it can be concluded that the results are compatible with the literature. Yuan et al. [14], studied the effect of operating parameters on the cell performance for the PEM fuel cell with parallel flow channel structure. Their results show that, as in the current study, the increase in working pressure and working temperature increase cell performance. Besides, while increasing the current density, the effects of heat and pressure increase. With the increasing current density, the cell potential decreases and the power values increase after reaching the maximum value power values decrease. Additionally, their results showed that the effect of temperature on cell performance is more pronounced than the effect of pressure. In this study, the current density is about 2.5 A/cm 2 at 0.4V cell potential. Yuan et al. [14], found the current density about 1.1 A/cm 2 at 0.4V cell potential. On the other hand, Obayopo et al. [15] who have modelled the single PEM fuel cell, found the current density about 3 A/cm 2 at 0.4V cell potential. The main reason for the different results is that the reactant flow rates were different. Also, it can be said that the design parameters are effective in different results. In general, it can be said that the results obtained in the current study and in the literature show a similar tendency.

CONCLUSIONS
In this study, a three-dimensional model was used to investigate the effects of temperature and pressure on the performance of the single PEM fuel cells. The polarization (voltage) and power variations with respect to current density, current density distributions in the form of the contour line plots and the current density variations with respect to temperature and pressure are given graphically. According to the obtained result, the cell voltage and cell power have increased with increasing temperature and the cell has shown similar performance for three different pressure values. Nevertheless, the effect of temperature on PEM fuel performance is much more pronounced at the high pressures. Consequently, by keeping humidification and cell temperatures in equilibrium, the performance of the cell improves with the increasing cell temperature and the cell voltage and cell power increase with the increasing operating pressure.