INTRODUCTION
As interest in sustainable energy technologies grows, fuel cells have emerged as a promising alternative to conventional fossil-fuel-based systems owing to their high efficiency and environmental benefits [1–3]. By directly converting chemical energy into electrical energy, fuel cells minimize energy losses while generating negligible carbon dioxide and other harmful emissions, which helps reduce the environmental impact [4–6]. Furthermore, fuel cells are gaining attention as a key technology for sustainable energy transitions owing to their fuel flexibility and compatibility with energy storage technologies. In addition to power generation, fuel cells can be used in combined heat and power systems and electricity-to-hydrogen conversion technologies [7–9]. The transportation sector, in particular, offers significant avenues for fuel cell applications, aimed at leveraging their efficiency and environmental advantages [10–12]. Hydrogen fuel cell vehicles have already been commercialized, with gradually increasing market coverage, and are being actively considered for use in various transportation modes, including commercial heavy-duty trucks, buses, railway vehicles, and maritime vessels [13–16].
In the railway sector, hydrogen-fuel-cell-powered trains are being explored as an alternative to conventional diesel trains to reduce carbon emissions [17, 18] and maintenance costs. Unlike diesel engines, fuel cells have fewer moving parts, resulting in lower operational costs and enhanced system durability [19]. Additionally, with the strengthening of global carbon-neutrality targets, the large-scale commercialization of hydrogen fuel cell trains is becoming increasingly feasible. Notably, Germany has deployed the world’s first commercial hydrogen fuel cell train, equipped with a 100-kW-class polymer electrolyte membrane fuel cell (PEMFC) [20]. Similarly, Japan has developed a test railway vehicle equipped with a 100-kW-class fuel cell, achieving a 70% reduction in CO₂ emissions compared with conventional diesel trains [21]. In China, a prototype train with a 250-kW-class PEMFC has been developed to evaluate the feasibility of hydrogen fuel cell technology in railway applications [22].
Despite these advancements, the successful integration of hydrogen fuel cells into railway systems requires the identification of optimal operating conditions tailored to railway environments. Fuel cell performance is influenced by various operational parameters, including temperature, pressure, and humidity, which can vary significantly with season, route, and regional climate [23–26]. For instance, extreme temperatures can lead to performance degradation and stability issues. Furthermore, pressure and humidity considerably influence the electrochemical reaction efficiency and water management within the fuel cell. For example, in high-altitude areas or arid regions, moisture loss within the fuel cell membrane can reduce protonic conductivity, leading to a decline in power output. To address these challenges, the variations in fuel cell performance under different operational environments must be assessed to establish optimal operational strategies.
In this context, numerous researchers have attempted to examine how operating parameters influence the performance of PEMFCs. Wu et al. [27] simplified the system design of a single air-cooled PEMFC by combining the air and coolant flows. The authors investigated the effects of various operating conditions (e.g., cell temperature and air flow rate) on the cell voltage and total ohmic resistance, highlighted the significant role of cell temperature and humidity in reducing ohmic resistance. Lee et al. [28] analyzed the effects of the operating temperature and relative humidity (RH) on PEMFC performance degradation and attempted to clarify the degradation mechanisms in various environments. Results of long-term operation tests indicated that increased temperatures resulted in damage to the Nafion structure, carbon corrosion, and catalyst agglomeration, which contributed to performance degradation. Moreover, as the RH decreased, the ion conductivity of the membrane decreased rapidly, accelerating degradation. Jiang et al. [29] attempted to optimize PEMFC operating parameters to enhance performance. The authors identified cell temperature, gas supply pressure, and gas humidification degree as the key operating parameters. Experiments were conducted to acquire performance data under various conditions, and the optimal operating conditions were determined to be 80oC, 3 atm, RH 100% at both the anode and cathode. Ogungbemi et al. [30] provided a comprehensively review of the operating conditions, design parameters, and material properties that affect PEMFC performance, focusing on moisture management. Given that moisture levels considerably influence the efficiency and durability of the PEMFC, various factors were analyzed to optimize this parameter. Their analysis highlighted the critical roles of temperature, pressure, and humidity on the PEMFC performance. Specifically, temperature affects the hydration state and conductivity of the membrane. Pressure directly influences the performance by varying the moisture distribution within the cell and membrane hydration. Humidity determines the hydration state of the membrane, thereby affecting the conductivity and cell efficiency.
Considering these aspects, this study was aimed at analyzing the influence of key operational variables— temperature, pressure, and humidity—on the output performance of fuel cells in railway applications. The objective was to optimize operating conditions suitable for railway environments to facilitate the practical implementation of fuel-cell-based railway systems. Additionally, fuel-cell load fluctuations were simulated based on railway driving cycles to quantitatively assess performance degradation and provide insights for ensuring long-term performance stability in future railway operations.
NUMERICAL MODELING
Unit cell model design and simulation parameters
Designing and analyzing fuel-cell models are complex tasks that require precise and accurate computational calculations. In this study, numerical analysis were performed using Ansys Fluent, a commercial computational fluid dynamics (CFD) software [31]. The geometric configuration and structural components of the large-area PEMFC single-cell model used for numerical simulations are illustrated in Fig. 1.
This model is based on a previous project supervised by the Ministry of Land, Infrastructure, and Transport, titled “Optimization of railway vehicle propulsion system using hydrogen fuel cell hybrid power system (1.2 MW or more) and development of operation technology” [32]. Hydrogen and air, from external sources, are delivered to the gas diffusion layer (GDL) through flow channels. Subsequently, these gases diffuse through the catalyst layer (CL) into the electrolyte. In a PEMFC, a thin polymer membrane serves as the electrolyte, with the anode and cathode CLs positioned on either side of the membrane. The combination of the electrolyte membrane and CL is referred to as the membrane electrode assemble (MEA) [33]. Equation 1 describes the electrochemical reactions occurring at the triple-phase boundary of the anode and cathode. Table 1 summarizes the numerical parameters used in fuel cell modeling, while Table 2 presents the material properties under various operating and boundary conditions.
The flow channel geometry in PEMFCs can be categorized into three main types: parallel, interdigitated, and serpentine. In this study, the serpentine configuration was selected owing to its superior cell performance, durability, and reliability [34,35]. Although the PEMFC bipolar plate typically consists of multiple flow channels, it was excluded from the model owing to computational domain-size limitations and simulation time constraints. Instead, only the lower flow channels were considered. To enhance accuracy in mesh generation, the edge sizing function was used to progressively refine the mesh density, and a quadrilateral hexahedral structure was applied. The final model consisted of 4,783,980 nodes and 4,064,550 elements.
For CFD analysis, the following assumptions were defined:
(1) Gravity was neglected.
(2) The fuel cell operates under steady-state conditions.
(3) The channel temperature of the fuel cell is constant.
(4) The reaction gases are considered laminar and incompressible.
(5) Hydrogen and oxygen are treated as ideal gases, with no phase change.
(6) The gas diffusion layer, catalyst layer, and electrolyte membrane are assumed isotropic and homogeneous.
(7) The electrolyte membrane is fully hydrated.
(8) The membrane is impermeable to the reactant gases.
(9) The activation overvoltage is assumed constant within both the anode and cathode compartments.
Governing equations
Various equations were used to describe the electrochemical reactions occurring within the PEMFC: The continuous, kinetic, and energy equations were adopted to explore thermofluidic phenomena within the flow channel in the cathode and anode. Specifically, the mass conservation equation (Eq. 2) represents the balance between the mass influx and efflux of reactant gases (hydrogen and oxygen) and generated products within the fuel cell. The fluid flow within the PEMFC flow channels and GDL, including the transport of hydrogen, oxygen, and water is described by the Navier–Stokes equation (Eq. 3), which enables the assessment of fluid dynamics and pressure drop inside the PEMFC. These equations are also used to examine the channel structure design and uniformity of fluid distribution. Equation 4 describes the temperature distribution within the fuel cell, accounting for heat transfer induced by electrochemical reactions, enabling the assessment of the impact of temperature control on fuel-cell performance and lifespan.
where ρ denotes the density [kg/m3], u denotes the velocity vector [m/s], p is the pressure [Pa], μ represents the viscosity coefficient [Pa·s], F denotes the body force [N/m3], CP represents the specific heat capacity [J/kg·K], T is the temperature [K], κ represents the thermal conductivity [W/m·K], and Q denotes the heat source term [W/m3] [36].
In addition to the basic governing equations for fluid dynamics (e.g., mass, momentum, and energy conservation), the model considers mass transfer in the GDL and electrochemical reactions in the CLs. The distribution of reactant gas ions and current density is calculated using Eq. 5. This equation also describes the charge transport phenomena occurring at the electrodes (where electrochemical reactions take place), enabling the analysis of current density distribution and fuel cell performance. The concentration distributions of hydrogen, oxygen, and water, considering both diffusion and convection phenomena, are modeled using Eq. 6. This equation describes the diffusion and consumption processes of reactant gases within the fuel cell and models mass transport in the GDL and CLs. The electrochemical reaction rate at the electrodes, modeling the activation process in electrochemical reactions, is determined using Eq. 7. This equation also enables the computation of voltage losses, facilitating the analysis of PEMFC performance degradation and output characteristics. Equation 8 calculates the voltage drop due to membrane resistance (ohmic loss), based on membrane thickness and proton conductivity. This allows a straightforward evaluation of the effects of membrane moisture and temperature variations on PEMFC output.
where σ denotes ion conductivity [S/m]; ϕ represents the potential [V]; S denotes the reaction source term [A/m3]; Ci denotes the concentration of i [mol/m3]; Di denotes the diffusion coefficient [m2/s]; Ri represents the reaction term [mol/m3·s]; i0 is the exchange current density [A/m2]; α is the charge transfer coefficients of the anode and cathode, respectively; n denotes the number of electrons transferred in the electrochemical reaction; η denotes the overpotential [V]; F represents Faraday’s constant [C/mol]; i 0 ref C R ∗ C R 0 ∗ C p ∗ C p 0 ∗
RESULTS AND DISCUSSION
Validation of numerical analysis results
As this study builds upon an existing PEMFC model, a verification process was performed. The validation was conducted over a voltage range of 0.45–0.8 V, using the initial cycle (0 cycle) as the reference. Notably, the previous study used COMSOL Multiphysics as the CFD software and included experimental validation [32]. Fig. 2 presents the voltage and power as functions of the current density (I–V–P curve), enabling a comparative analysis of the experimental data and results obtained from two CFD simulations. In the COMSOL- based analysis [32], the current density ranged from 0.045 to 1.740 A/cm2 while the power output was 8.013–176.124 W. The experiments yielded a current density of 0.048–1.416 A/cm2 and power output of 8.704–143.370 W. In the present study, using Ansys Fluent, the simulated current density was 0.056–1.089 A/cm2, and the power output ranged from 10.044 to 110.542 W. In comparing the accuracy of the two CFD simulations relative to the experimental results, COMSOL Multiphysics exhibited error ranges of 6.25– 44.35% and 6.54–44.49% for current density and power output, respectively. In comparison, Ansys Fluent displayed an error range of 16.25–36.40% for current density and 15.40–29.02% for power output. Notably, COMSOL Multiphysics exhibited significant variations between the minimum and maximum errors, whereas Ansys Fluent demonstrated a narrower error range. This indicates that, compared with COMSOL Multiphysics, Ansys Fluent yielded a smaller discrepancy between the minimum and maximum errors in current density and power output relative to the experimental values. These results suggest that Ansys Fluent maintains a more consistent trend with experimental data, thereby offering greater reliability and stability in numerical analysis.
Fig. 3 presents the I–V–P curves obtained using Ansys Fluent after the validation process, illustrating the results at 0, 1,000, 2,000 cycles. At the initial cycle (0 cycle), the fuel cell exhibited high voltage and current density, with a maximum power output of 110.542 W. However, as the cycle count increased, both current density and power output exhibited a gradual decline. Specifically, after 1,000 cycles, the maximum power output decreased to 101.535 W, a reduction of 8.15% compared with the initial cycle. At 2,000 cycles, the maximum power output further reduced to 88.067 W, corresponding to a 20.33% decrease. This trend indicates reduced efficiency within the active area owing to structural changes or performance degradation in the fuel cell. Notably, the decline in current density was more pronounced in the low-voltage region. Fig. 4 illustrates the variation in water content distribution at the cathode catalyst layer–membrane interface during cycling. At the initial stage (0 cycle), the distribution was relatively uniform across the entire region, whereas at 1,000 and 2,000 cycles, nonuniformity became more evident. This effect was more pronounced near the cathode outlet, suggesting that local membrane dehydration or excessive accumulation adversely affected both the electrochemical reaction rate and mass transport processes.
Evaluation of cell performance under various environmental and operating conditions
Fig. 5 presents the numerical analysis results of the PEMFC under different operating voltages. Simulations were conducted over a voltage range of 0.45–0.8 V, considering 2,000 cycles as the reference condition [32], to analyze the correlation between the current density and power output. As the operating voltage decreased, the current density increased, a trend consistent with the Butler–Volmer equation (Eq. 7). Specifically, as the voltage decreased, the overpotential increased, prompting the fuel cell system to extract more energy. Consequently, the forced electrochemical reactions at the anode and cathode increased the reaction rate, resulting in enhanced current density. At 0.8 V, the current density was 0.017 A/ cm2, whereas at 0.45 V, it reached 0.870 A/cm2, representing an increase of approximately 50.52-fold. The power output increased from 3.099 W at 0.8 V to 88.067 W at 0.45 V, corresponding to an increase of approximately 28.42 times.
Fig. 6 shows the simulation results under different anode RH values. The RH was varied from 10% to 100%, while the cathode humidity was fixed at 0%. In addition, the operating voltage was set at 0.7 V with 2,000 cycles, reflecting typical conditions for railway vehicle operation [20,37,38]. As the RH increased, both the current density and output increased, reaching maximum values at 90% RH. On the other hand, at 100% RH, the values were lower than those recorded at 90% RH. This is because, at 100% RH, water accumulates in the gas paths and GDL capillaries, obstructing the diffusion of reactants and reducing the active area and local current density [39,40]. Xu et al. demonstrated that approximately 90% RH represents the balance point between membrane hydration and gas diffusion resistance [41]. As the RH increased from 10% to 90%, the current density increased from 0.150 A/cm2 to 0.197 A/cm2, while the output increased from 23.695 W to 30.959 W, representing a 30.66% improvement. In general, as the humidity decreases, the internal resistance increases owing to the dryness of the electrolyte membrane and CL. In addition, the proton conductivity of the electrolyte membrane decreases. These synergistic effects lower the cell voltage, which adversely affects the cell performance. However, excessive moisture in the electrode may hinder gas transport or cause water flooding. Therefore, an appropriate moisture level must be maintained to ensure stable cell performance [42–45].
Fig. 7 shows the simulation results under different operating temperatures. The operating temperature was varied from 50oC to 90oC, with a voltage of 0.7 V and 2,000 cycles. As the operating temperature increased from 50oC to 90oC, the current density decreased from 0.190 A/cm2 to 0.013 A/cm2, while the output decreased from 29.868 W to 2.001 W, representing a 93.30% reduction. In general, an appropriate increase in the operating temperature can promote the electrochemical reaction rate of the fuel cell and improve its performance by removing moisture that otherwise hinders gas diffusion. Thus, the fuel cell must be maintained at an optimal temperature to ensure appropriate moisture and permeability levels of the electrolyte membrane. However, indiscriminately high moisture evaporation rates driven by excessive temperatures can reduce the moisture content of the electrolyte membrane, resulting in membrane dehydration and reduced ionic conductivity, ultimately degrading the fuel cell performance [46–48]. In addition, as the operating temperature increases, resistance and concentration losses occur. In particular, as the temperature increases, the electrolyte membrane undergoes rapid dehydration, which hinders photon transmission, thereby increasing resistance loss [49–52]. These phenomena increase the voltage loss, lower the cell voltage, and reduce the efficiency and performance of the fuel cell.
Fig. 8 shows the simulation results under different pressure conditions applied to the inlet of the PEMFC flow channel. The operating pressure was varied from 1 atm to 3 atm, with a voltage of 0.7 V and 2,000 cycles. As the operating pressure increased from 1 atm to 3 atm, the current density increased from 0.072 A/cm2 to 0.116 A/cm2, and the output increased from 11.344 W to 18.22 W, representing a 60.62% increase. The output at higher operating pressures (2 or 3 atm) was considerably higher than that at 1 atm. This is because the mass transfer ability of the reactants improves as the pressure increases, which increases the concentration, reaction rate, and efficiency. In addition, water evaporation in the flow channel is suppressed as the pressure increases [46,53,54]. In summary, with increasing pressure, the concentration and diffusion rates of the reactants increase, ion conductivity is enhanced through superior moisture retention within the electrolyte membrane, and gas permeability of the reactants increases. These effects reduce losses and enhance the performance of the fuel cell [47,55].
Lifetime prediction based on train performance simulation (TPS) cycles
In addition to the numerical analyses described above, a simulation was conducted based on the actual driving cycle of a hydrogen-electric locomotive using train performance simulation (TPS). The driving cycle conditions are outlined in Fig. 9. One cycle was defined as 280 s of operation followed by 20 s of stopping, and this pattern was repeated for approximately 34,000 s (100 cycles). To prevent cell instability caused by rapid voltage changes, a 20 s stabilization step was added between the operation and the stopping phases, during which the voltage was held constant before being gradually increased or decreased. During operation, the PEMFC installed in the hydrogen-electric locomotive supplied power under minimal load, while it charged the propulsion battery at maximum load during stops. The driving cycle was implemented using the Expression Editor function in Ansys Fluent.
By applying this driving cycle to the simulation, variations in the current density and power output at the start and end points of the first and last cycles were examined. Table 3 summarizes these differences. Compared with the first cycle, the last cycle exhibited differences of approximately 0.003 A/cm2 and 0.002 A/cm2 in the current density during the operation and stop phases, respectively. Moreover, compared with the first cycle, the last cycle presented differences of approximately 0.457 W and 0.293 W in the power output during the operation and stop phases, respectively. In conclusion, compared with the first cycle, the current density and power output in the operational phase of the last cycle decreased by 1.11%, while those in the stationary phase decreased by 0.24%. These findings suggest that power consumption increases in the high-voltage operating range when a railway vehicle operates under the abovementioned conditions. Figure 10 shows the water content distribution at the cathode CL–membrane interface after 100 TPS cycles. The repeated humidification and drying during the driving cycle resulted in a nonuniform distribution near the interface, where localized water accumulation and dry regions may accelerate performance degradation in both the CL and membrane.
CONCLUSIONS
This study was aimed at evaluating the performance of a large-area PEMFC using a commercial CFD simulation program. The numerical model was simplified by excluding the bipolar plates, and a serpentine flow-channel structure was adopted. Through a comprehensive numerical analysis, the effects of various degradation factors were investigated, and their importances and interrelationships were derived. Under lower voltage conditions, the power output was approximately 28.42 times higher than that in high-voltage conditions. In terms of the RH, the output improved as the humidity increased, increasing by approximately 30.66% when the RH was 90% relative to that at 10%. However, an increase in the operating temperature reduced the power output by approximately 93.30%. In contrast, increasing the operating pressure from 1 atm to 3 atm enhanced the output by approximately 60.62%. Ultimately, among the examined degradation factors, elevated operating temperature had the most detrimental effect on fuel cell performance, whereas increased anode RH had the least impact. To enhance the reliability of the numerical analysis, the implementation of more precise degradation modeling techniques or real-world operational data from railway vehicles is recommended. Overall, identifying and analyzing degradation factors through numerical simulations is a crucial step in improving both the performance and longevity of PEMFCs. This process can help validate the simulation model and facilitate the development of effective performance-improvement strategies tailored to actual operating environments.
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