## 5 Results and Discussion
In this study, the membrane is assumed impermeable to gas based on the simulation for the open-cathode PEM fuel cell. Open-cathode PEM fuel cells are common in low-power stacks and operate at a low pressure. The membrane is assumed impermeable to gas to reduce the complexity of the calculation. Even if infiltration occurs at all, the amount of gas seepage through the membrane is negligible. Thus, hydrogen is only present at the anode, whereas oxygen is only at the cathode side, as shown in Figure 8a,b, respectively. The molecular number of hydrogen and oxygen on the side near the CL is relatively low, which is due to the constant consumption of fuel on each side of the CLs. As cell voltage decreases, the diffusion capacity of hydrogen and oxygen in the anode and cathode decreases. The corresponding change of gas flux also verifies this phenomenon, as shown in Figure 8c,d. The mechanism of water transport is complicated because it involves phase transition. The distribution of water vapor and the transport of water in the ionomer are discussed in the simulation. As mentioned above, the fuel cell stabilization after a period of time, and the anode water molecules are almost in a saturated state. The purge valve of the gas supply system will regularly trigger to update the internal gas and remove excess water, and water in liquid form is observed. Therefore, the gas inside the anode is basically saturated. However, the cathode side is affected by the fan, which can be taken away by the flowing air in a time when the fuel cell produces water, failing to gather liquid water. For these reasons, the water vapor in the cathode runner cannot reach the saturation state, which causes the rapid diffusion of water molecules. The diffusion of water is more active on the cathode side, as shown in Figure 9a,b. The content of dissolved water in the membrane is not high, but it has a remarkable influence on proton conductivity, and its related activity subdomain is mainly on the cathode side. In this simulation, the distribution and diffusion of dissolved water are shown in Figure 10a,b, respectively. When the relative humidity of the gas in the channel is saturated, the water generated by the fuel cell reaction will be directly precipitated out in the form of liquid. In case water cannot be purged out in time, the porous media will be blocked by water, thus reducing the contact area between the catalyst and the reaction gas, resulting in a decrease in reaction rate. The transport state of liquid water is described in Figure 11a,b. The theory of describing the transport of liquid water is based on [PERSON]'s law. The activity of liquid water is mainly affected by pressure difference and gas saturation. At the same time, \(\mathrm{RH_{ca}}\) = 20% at a given humidity on one side of the cathode, the voltage at the maximum output power is 0.6 V, and the water distribution on the fuel cell proton exchange membrane is observed at a different anode humidity, as shown in the results Figure 12. The water content of the membrane on the anode side is affected by the water content on the cathode side. This phenomenon is mainly caused by osmotic pressure  
Figure 7: Thermal profiles along through-plane (**a**) temperature distribution; (**b**) heat flux profile. difference and electric traction. In the case of fixed cathode humidity, the influence of different anode humidity on fuel cell output performance is presented in Figure 13. The results show that the output performance is more superior when the anode membrane is adequately humidified. Figure 8: Evolution of the gas profiles on through-plane (**a**) hydrogen diffusion profile; (**b**) oxygen diffusion profile; (**c**) hydrogen flux profile; (**d**) oxygen flux profile. Figure 9: Evolution of the water vapor profiles on through-plane (**a**) water vapor diffusion profile; (**b**) water vapor flux profile. Figure 11: Evolution of the liquid water profiles on through-plane: (**a**) liquid water diffusion profile; (**b**) liquid water flux profile.