## 4 Results and Discussion
### Polarization Curves with 10 Single Cells
However, there existed obvious voltage differences and power density differences between the experiment data and the simulation results for different relative humidities. The C10 polarization curves and power density curves are shown in Figure 6a under a relative humidity of 40%. It can be observed that the voltage was in the range of 0.5\(\sim\)1.0 V when the current density varied from 0 to 400 mA\(\cdot\)cm\({}^{-2}\). There was a maximum voltage for the experiment data and the simulation model results when the current density was around 0, because the electrochemical reaction rate was low, due to a lower gas inlet flow rate. The voltage differences between the experimental data and the simulation model data increased first, and then they gradually decreased as the current density increased. The maximum voltage difference appeared at around the current density of 50 mA\(\cdot\)cm\({}^{-2}\). This is because the activation loss enhancement is related to the proton transfer rate and voltage reduction. The current density and reaction rate improvement causes an activation loss enhancement [17]. More specifically, the ARH model results were more reliable because they were always closer to the experimental results than the Fluent model results. The error between the ARH model (0.534 V) and the experiment data (0.499 V) was almost 7% at around a current density of 400 mA\(\cdot\)cm\({}^{-2}\). This is because the ARH model not only takes into account the pressure drop between the flow channels of the single cells, but it also considers the pressure drop among the single cells in the stack. Also, water saturation improved with the increase of current density, resulting in the adsorption rate and throughput rate of the H\({}^{+}\) rise on the proton exchange membrane. Compared with the research of [PERSON] [34], we concluded that there are almost no concentration regions from the presented power density curves, so that there is no flooding phenomenon. In Figure 6b, the polarization curves and power density curves for a relative humidity of 55% are shown. Compared against the polarization curves in Figure 6a, the minimum voltage was from 0.499 V up to 0.599 V. This was relevant to the higher ionic conductivity and lower resistance, and this could be attributed to the higher proton exchange membrane water content and the relative humidity [35]. The Fluent model results, ARH model results, and experiment results had a similar tendency to those in Figure 6a, and the curves changed more gently as the current density increased. When the current density was 0, the Fluent model, ARH model, and experiment voltages respectively were 0.972 V, 0.97 V, and 0.969 V and there was no difference, as the gas had not yet begun to react. It can be seen that there was a sharp drop in voltage when the current density was in the range of 0-50 mA\(\cdot\)cm\({}^{-2}\). During this stage, the proton exchange membrane water content depended largely on the gas humidification, due to the lower electrochemical reaction. Similarly, the maximum differences of voltage and power density occurred near the current density of 50 mA\(\cdot\)cm\({}^{-2}\), and the differences of the voltage and power density between the Fluent model (0.873 V, 43.65 mW\(\cdot\)cm\({}^{-2}\)) and the experiment (0.78 V, 39 mW\(\cdot\)cm\({}^{-2}\)) were 0.093 V and 4.65 mW\(\cdot\)cm\({}^{-2}\), which were bigger than those (0.047 V, 2.35 mW\(\cdot\)cm\({}^{-2}\)) between the ARH model (0.827 V, 41.35 mW\(\cdot\)cm\({}^{-2}\)) and the experiment. It could easily be observed that the ARH model values were closer to the experiment values, to better predict the cell performance. There was a softer drop in voltage when the current density was in the range of 50-400 mA\(\cdot\)cm\({}^{-2}\). The water content mainly came from the electrochemical reaction, and it was almost not affected by gas humidification with the increase of the current density.