## 4 Results and Discussion
### Polarization Curves with 10 Single Cells
The calculation precision improved for the ARH model, because it considers the saturation pressure based on the pressure drop of the real PEMFC structure, and not the conventional equation. A proper relative humidity is responsible for improved membrane water content and ion conductivity [36]. As shown in Figure 6c, several representative data for a relative humidity 70% are expressed in the polarization curves and power density curves. It could be found that simulation data and experiment data matched well. The voltage and power density differences gradually decreased when the current density was bigger than 50 mA\(\cdot\)cm\({}^{-2}\). Especially, the Fluent model data (0.643 V) was the closest to the experiment data (0.598 V) at the current density of 360 mA\(\cdot\)cm\({}^{-2}\), and even the voltage error was reduced to 8%, the same as [PERSON] [37] explained. As we expected, the ARH model data (0.619 V) was closer to experiment data compared to the Fluent model data at 360 mA\(\cdot\)cm\({}^{-2}\). The water contents of the proton exchange membrane were produced by the electrochemical reaction and gas humidification. Additionally, it was obvious that the voltage and power density differences were smaller than that in Figure 6a,b. This is because the current density and relative humidity improvement caused the saturation of proton exchange membrane improvement, thus facilitating ion conductivity and reducing the resistance. As shown in Figure 6d, the polarization curves and power density curves under the relative humidity 85% are displayed. The simulation data and experiment data showed no significant difference at around the current density of 0. The voltage differences between the simulation data and experiment data gradually increased from 0 to 50 mA\(\cdot\)cm\({}^{-2}\), due to the increase of gas humidification and pressure drop. During the low current density region, gas humidification plays a vital role in the water content of the proton exchange membrane. The simulation data were consistent with the experiment data, and their differences were gradually ignored with the increase of the current density (50-400 mA\(\cdot\)cm\({}^{-2}\)). It can be observed that ARH model result (0.645 V) was closer to experiment data (0.636 V) at around the current density of 360 mA\(\cdot\)cm\({}^{-2}\), and even the relative accuracy was increased by 72% compared with the Fluent model result (0.669 V). Since PEMFC operation temperature was relatively high, the ionic conductivity influenced by the high relative humidity was considered. In addition to the operating temperature, saturation pressure in ARH model takes into account the pressure drop, hydrogen inlet pressure, and the structural parameters of the cell. Thus, the ARH model results are more reliable than the Fluent model. [PERSON] et al. [19] also confirmed that cell system efficiency improvement depends on the relative humidity rather than the operation temperature. Additionally, the fuel cell is likely to be prone to flooding, due to the high operation temperature and the relative humidity [38]. There are, respectively, three polarization curves and power density curves with a relative humidity of 100% in Figure 6e. The simulation results and experiment results in Figure 6e were similar to the Figure 6a-d results. There existed a sharp drop in voltage at a current density of 0\(\cdot\)50 mA\(\cdot\)cm\({}^{-2}\). As a result of a low electrochemical reaction, gas humidification was necessary to ensure water content on the membrane. When the current density was about 360 mA\(\cdot\)cm\({}^{-2}\), the Fluent model voltage (0.692 V) increases by 9% more than the experimental voltage (0.635 V), and the ARH model voltage (0.649 V) was closer to the experiment value, and it almost increased by 3% compared to the experiment voltage. The voltage differences decreased as predicted in Figure 6a-c. However, the voltage differences in Figure 6e rose again compared to that in Figure 6d.