<figure><img src="image_1.png" /></figure>

# PEMFC cathode humidification: Can direct water injection compete with membrane humifiers? A direct comparison study

Flavien Marteau<sup>a, D,*</sup>, Pedro Affonso Nóbrega<sup>a, D</sup>, Cédric Sernissi<sup>a, D</sup>, Pascal Biwole<sup>a, b, D</sup>, Iona De Bievre<sup>c</sup>, Christophe Vacquier<sup>c, D</sup>, Christian Beauger<sup>a, D</sup>

## ARTICLE INFO

### Keywords:

Proton-exchange membrane fuel cell

Cathode humidification

Direct water injection

Membrane humidifier

## ABSTRACT

Proton exchange membrane fuel cells (PEMFCs) require effective water management for optimal performance. To achieve this, the majority of current PEMFC systems for mobility applications employ a membrane humidifier. Membrane humidifiers are effective but costly, cumbersome, and fragile. Direct water injection in the airflow feeding the cathode represents a promising alternative. However, it remains relatively under-explored in the literature, as flooding issues encountered in early studies were considered a drawback compared to membrane humidifiers. To our knowledge, no previous study directly compared the performance of both direct water injection and membrane humidifiers for the same fuel cell stack and operating conditions. The present study addresses this gap. We present experimental results obtained with a recent 2 kW short-stack that confirm the effectiveness of direct water injection, but show a 5% decrease in cell voltage compared to the membrane humidifier method under nominal operating conditions. We argue that this voltage decrease is due to poorer membrane hydration, despite a sufficient amount of water entering the cathode, and identify opportunities for optimization of direct water injection performance.

## 1. Introduction

Proton exchange membrane fuel cells (PEMFCs) convert hydrogen and oxygen into electricity, heat and water. They can be used to power electric vehicles without emitting atmospheric pollutants. Hydrogen is therefore considered a promising alternative to fossil fuels in the transportation sector. This technology is particularly adapted to heavy-duty applications such as trucks, buses and trains, offering the potential for electrification when weight limitations prevent the use of battery storage alone [1–3]. However, further advancements are still needed to facilitate widespread adoption, including cost reduction, increased durability, and improved system integration.

In this context, effective water management is critical for the optimal performance of PEMFCs. In such cells, the two electrodes are separated by a perfluorosulfonic acid membrane, which must be correctly hydrated to achieve good proton conduction [4]. However, the accumulation of liquid water in the cell’s porous media or channels can obstruct the delivery of reactants to the catalytic sites, a phenomenon known as “flooding”. Therefore, the water content in the stack must

be properly controlled to prevent membrane dehydration or water flooding, which both reduce performance and degrade the stack [5]. Several parameters impact membrane hydration, including material characteristics and operating conditions (temperature, pressure, relative humidity), but such parameters cannot be freely adjusted due to other constraints. An effective method to achieve sufficient membrane hydration is humidifying the air entering the cathode [6]. The optimal cathode inlet relative humidity (RH) depends on various factors, including stack design and operating conditions such as temperature, current density and pressure [7–10]. In general, relative humidities above 30% are required to ensure convincing performance.

+One way to humidify the air entering the cathode is using a membrane humidifier. In fuel cell vehicle systems, a compressor circulates air within the cathode and increases the operating cathode pressure. Compression raises the air temperature to around 100 °C under nominal conditions, and up to 200 °C under high-pressure conditions. The hot air exiting the compressor is cooled in an intercooler, usually a gas-liquid heat exchanger, before being humidified by a membrane

<footnote><sup>a</sup> Mines Paris, PSL University, Centre for processes, renewable energy and energy systems (PERSEE), 1 rue Claude Daunesse, Sophia Antipolis, 06904, France</footnote>

<footnote><sup>b</sup> California State Polytechnic University, School of Engineering, Arcata, CA 95521, USA</footnote>

<footnote><sup>c</sup> Symbio, 10 Rue Spécia, Saint-Fons, 69190, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: flavien.marteau@minesparis.psl.eu (F. Marteau), pedro.affonso_nobrega@minesparis.psl.eu (P. Affonso Nóbrega), cedric.sernissi@minesparis.psl.eu (C. Sernissi), pascal.biwole@humboldt.edu (P. Biwole), iona.de-bievre@symbio.one (I. De Bievre), christophe.vacquier@symbio.one (C. Vacquier), christian.beauger@minesparis.psl.eu (C. Beauger).</footnote>
humidifier. The membrane humidifier is a passive device that transfers water vapour from the wet gases exiting the cathode to the dry air coming from the compressor. A water-permeable membrane separates the two air flows. Hollow-fibre humidifiers are mostly used, where a bundle of membrane tubes is packed to form a shell-and-tube humidifier [11]. The RH at the exit of the humidifier depends on the operating conditions. Such a system architecture supplies the cathode with a mixture of air and water vapour and ensures good performance under normal operating conditions. Membrane humidifiers currently account for the majority of the systems installed in hydrogen vehicles. Nevertheless, they are expensive, fragile, bulky, and cumbersome. Moreover, humidity cannot be optimally adjusted according to actual requirements.

Other humidification systems exist, such as bubbling humidifiers and enthalpy wheel humidifiers, but these are less adapted to fuel cell electric vehicles (FCEVs), mainly due to their bulkiness and thermal inertia [6]. Dry inlet gas can also be humidified by mixing it with moist exhaust gas, a method commonly referred to as recirculation. This technique is not appropriate for the cathode side because of the low oxygen content in the exhaust, but it is effective for the anode. In addition to providing humidification, it improves anode stoichiometry without increasing hydrogen consumption. Efficient anode humidification, combined with internal strategies such as thin membranes and counter-flow, could enable operation without cathode-side humidification. Striednig et al. [12] investigates liquid water evaporation within the fuel cell as a way to provide both humidification and cooling. However, introducing liquid water into the stack remains a significant technical challenge.

Direct air injection consists of injecting liquid water into the dry heated air exiting the compressor. This method is considered a promising alternative to membrane humidifiers. Injection devices are compact and robust, although other components might be required, such as a water tank, a water pump, and a condenser for water recovery. The amount of water entering the stack can be precisely regulated. Unlike membrane humidifiers, this humidification method relies on the direct introduction of a gas/liquid water mixture into the stack. Liquid water enables the membrane to achieve a higher water content compared to water vapour and could be an effective method for humidification [13]. However, early publications reported flooding problems preventing the adoption of this architecture [6,13]. Wood et al. mitigated flooding by using an interdigitated flow field [13]. More recent works reported fewer flooding issues, which could be explained by improvements in stack technology, independently of direct water injection. Membranes materials and structures have improved, with modern membranes being much thinner, around 6 µm to 15 µm. The gas diffusion layers and their structure have been optimized to be hydrophobic and microporous layers have been added between the catalyst layer and the gas diffusion layer. The design of the flow channels has also been optimized. Those advancements reported in [14] have contributed to improved water management with limited flooding issues. For instance, Hwang and Kim [15] used direct water injection without reporting flooding issues. They humidified a 250 cm² five-cell stack with a two-fluid nozzle at the cathode inlet. The nozzle produced fine droplets with a Sauter mean diameter in the range of 20 µm to 25 µm. The humidification apparatus was compact, robust and controllable. Their results showed that direct water injection is quite effective in cathode humidification. The cell voltage and the dew point at the cathode outlet increased after water injection. They encountered flooding issues only when too much water (5 mL/min at 1 A/cm² and 60 °C) was injected. Finally, evaporative cooling could evacuate up to 10% of the thermal power generated by the fuel cell. The same research group later conducted a parametric study that confirmed the effective humidification of direct water injection, showing a maximum performance increase of about 17% [16] after adding a spray to the 20% RHᵢₜₜₐₗ provided by a bubbler. However, no performance comparison was made with membrane humidifiers. Further, the tests were

conducted under operating conditions different from common practice for mobility applications. The tests were conducted at atmospheric pressure, whereas fuel cells typically operate at higher pressures [17]. Also, the fuel cell temperature was set to 60 °C and 70 °C, whereas current operating temperatures are generally around 80 °C [18]. The fuel cell temperature plays a crucial role in water management, with small variations having significant impacts. For instance, a relative humidity of 100% at 60 °C corresponds to only 42% relative humidity at 80 °C if the water vapour pressure remains constant. No flooding issues were reported by Snyder et al. [19,20] either, who used an ultrasonic atomizer to inject 2.8 µm water droplets into the anode inlet stream. The results showed an increase in the average cell voltage of approximately 30 mV to 50 mV (or 7% to 16%), that demonstrates that water injection at the anode also improves the humidification of fuel cells. Here again, no direct comparison was made with membrane humidifiers.

To prevent flooding issues due to direct water injection, a heater and/or a phase separator can be used to increase the evaporation rate and avoid the introduction of liquid water into the stack. The heater can harness the heat generated by the fuel cell to avoid additional energy consumption. The heater temperature is then limited by that of the stack, which restricts the evaporation rate. The fluids' temperature being limited, thermal transfer is however limited. Zhang et al. [21] designed a humidifier for a 5 kW fuel cell operating at high temperatures (90 °C to 95 °C). Air flowed through a cavity containing heat exchange tubes, while a nozzle at the top of the humidifier injected a water spray into the heated airflow. Excess water was then drained from the bottom of the humidifier. Jung et al. [22] designed a humidifier for a 5 kW fuel cell operating at lower temperatures (65 °C to 75 °C). A spray was injected into a chamber heated by an annular coolant jacket, with excess water being collected by a phase separator. Both humidifiers demonstrated efficient humidification, achieving RH levels over 40% across a wide range of operating conditions [21,22]. However, including heat exchangers increases the overall size of the system. Jung et al. estimated that a spray humidifier for a 80 kW fuel cell would require a volume of approximately 30 L.

Sung et al. [23] developed a humidifier in which the air is heated to 90 °C using an electrically heated pipe. An ultrasonic atomizer generated very fine droplets with a mean diameter around 2 µm. The RH at the humidifier's outlet reached up to 90% at the stack temperature of 40 °C and was easily controllable. But here too, the low operating temperature was not representative of current practice, and the resulting dew point was too low to effectively humidify a fuel cell operating at 80 °C.

These previous works demonstrate that a PEM fuel cell could be operated with direct water injection. However, most reported tests were conducted on fuel cell or under operating conditions that significantly diverge from current practice for mobility applications, which have a considerable impact on water management and fuel cell performance. Moreover, these studies do not offer any direct comparison with membrane humidifiers, which are widely adopted for fuel cell systems. Such a comparison under relevant operating conditions is necessary to draw meaningful conclusions about the relative value of direct water injection. The present work aims to fill this gap by experimentally comparing the performance of these two humidification methods under similar operating conditions. A state-of-the-art fuel cell short stack is operated with each humidification method, and the results are compared. A parametric study is conducted to evaluate the impact of liquid water on the performance of the fuel cell.

## 2. Materials and methods

### 2.1. Experimental setup

The experimental study is conducted with a 2 kW short stack from Symbio with wavy parallel channels and a cell active area of 150 cm².
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Simplified P&ID of the experimental setup for the two system architectures considered: reference and DWI and flows diagram.</figcaption></figure>

Two system architectures are considered, corresponding to two humidification methods. The first architecture, hereafter referred to as *reference architecture*, replicates a typical fuel cell system architecture for mobility applications, including a compressor, an intercooler, and a membrane humidifier. The second architecture, hereafter called direct water injection (*DWI* architecture, replaces the intercooler and the membrane humidifier with a single water injector. Both architectures are detailed in the following sections.

### 2.1.1. Reference architecture

In the reference architecture, a membrane humidifier is used for cathode humidification. A simplified P&ID for this architecture is presented in Fig. 1(a). The stack is supplied with compressed air. A mass flow controller (Brooks SLA5853S 12Nm³/h) and a heating resistor (Omega AHP-7562 750W) simulate the behaviour of a car air compressor. An intercooler is used to keep the air temperature close to the fuel cell operating temperature (temperature of the coolant exiting the stack). The intercooler is positioned before the dry side inlet of the membrane humidifier. A shell-and-tube Fumatech H02 membrane humidifier is used. The intercooler and humidifier are oversized for this short stack, allowing good performance with minimum pressure drop. The humidified air stream from the humidifier is supplied to the fuel cell cathode manifold. The flow of air out of the cathode

flows through the wet side of the humidifier. A dome-loaded pressure regulator controls the cathode inlet pressure. To prevent liquid water from affecting the operation of the dome-loaded regulator, the water exiting the humidifier is collected through a condenser and a water trap.

Although most fuel cell systems operate with an anode recirculation loop, the present experimental setup uses a flow-through anode because of its simplicity. The hydrogen flow is controlled by a mass flow regulator (Brooks SLA5851S 5Nm³/h). A counterflow configuration with respect to the cathode stream is adopted as shown in Fig. 1(c). To approximate operation with recirculation, the hydrogen is humidified by an active evaporator (Bronkhorst CEM system 1000 g/h 6Nm³/h), which also regulates the hydrogen temperature. Similar to the cathode, the water leaving the anode is collected by a condenser and a water trap, allowing water mass measurements and water balance analysis. This provides information on the water transport between the two compartments through the membrane. The hydrogen inlet pressure is also regulated by a dome-loaded regulator.

The thermal power generated by the stack is dissipated through the cooling circuit. A pump circulates deionized water through the stack. The water then passes through a water-to-water heat exchanger connected to a chiller unit. Controlling the cold water flow rate through the heat exchanger regulates the temperature of the coolant leaving the
<table><caption>**Table 1**
Measurement accuracy of different sensors used in this work.</caption><thead><tr><td>Sensors</td><td>Model</td><td>Manufacturer</td><td>Measurement accuracy</td></tr></thead><tbody><tr><td>Electronic load</td><td>DS15624</td><td>H&amp;H</td><td>±0.2% of setting, ±0.1% of full scale</td></tr><tr><td>Data acquisition system</td><td>34980A</td><td>Keysight</td><td>±0.0035% of reading, ±0.0005% of full scale</td></tr><tr><td>Thermocouple</td><td>J-type</td><td>–</td><td>±0.5°C</td></tr><tr><td>RH probe</td><td>HMP7</td><td>Vaisala</td><td>±2%</td></tr><tr><td>Temperature probe</td><td>TMP1</td><td>Vaisala</td><td>±0.1°C</td></tr><tr><td>Pressure transmitter</td><td>23SX</td><td>Keller</td><td>±0.1% of full scale</td></tr><tr><td>MFC air</td><td>SLA5853S (12 Nm³/h)</td><td>Brooks</td><td>±max (0.02 Nm³/h, 0.9% of reading)</td></tr><tr><td>MFC H2</td><td>SLA5851S (5 Nm³/h)</td><td>Brooks</td><td>±max (0.009 Nm³/h, 0.9% of reading)</td></tr><tr><td>MFC nozzle</td><td>F-203AV (40 Nm³/h)</td><td>Bronkhorst</td><td>±0.5% of reading, ±0.1% of full scale</td></tr><tr><td>MFC water (CEM)</td><td>Liqui-Flow L2</td><td>Bronkhorst</td><td>±0.1% of full scale</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Assembly of the pneumatic nozzle and injection zone at the cathode inlet.</figcaption></figure>

stack. A co-flow configuration with respect to the cathode stream is adopted as shown in Fig. 1(c). The temperature difference between the inlet and the outlet of the cooling circuit is approximately 3 °C under nominal conditions (1 A/cm²).

The electrical energy produced by the stack is dissipated by a current-controlled electrical load (H&H, DS15624, 600 A, accuracy ±0.2% of setting and ±0.1% of full scale) regulating the current.

### 2.1.2. DWI architecture

In the direct water injection (DWI) architecture, a water injection system replaces the intercooler and the membrane humidifier. The rest of the experimental setup is identical to the reference system. No heating system or water trap is added, so liquid water can enter the stack. This choice is motivated by two reasons: to keep the architecture simple and compact and to study the impact of liquid water at the cathode inlet. The simplified P&ID for the DWI architecture is shown in Fig. 1(b).

An important aspect of the DWI architecture is the choice of the water injection device. The spray flow rate must be precisely controlled within a range of 3 g/min to 20 g/min under various experimental conditions. The droplet diameter must be as small as possible to ensure their fast evaporation and that they follow the gas trajectory, entering the channels without obstructing them. This work uses a pneumatic nozzle XAPR 050 from BETE®, which is a pressure-fed system with an internal mix. The spray has a Sauter mean diameter of around 20 µm. The injection flow rate is controlled by a solenoid-driven metering pump from ProMinent® (series gamma/ X, reference GMXa 1602). The nozzle has a narrow spray angle of 12°.

Fig. 2 presents the nozzle assembly at the cathode entry. An injection chamber was designed for the experiment. The design was chosen after several iterations to minimize the coalescence of water droplets on the walls. To achieve this, the nozzle faces the manifold as closely as possible to the inlet. Part of the air flow feeding the stack is used to supply the pneumatic nozzle at 1.5 Nm³/h (secondary airflow). The

remaining air (primary air flow) is mixed with the spray in the injection zone. The airflow enters through a set of holes to prevent the spray from impinging the wall.

## 2.2. Instrumentation

Table 1 presents the sensors used and their accuracy. A data acquisition unit (Keysight technologies, 34980 A, accuracy ± 0.0035% of reading and ± 0.0005% of full scale) collects the experimental data, including single-cell voltage measurements. The sampling frequency is 2 Hz.

Several thermocouples (type J, ±0.5 °C) and pressure sensors (Keller, 23SX, ±0.004 bar) are located at the inlet and outlet of the stack as shown in the P&IDs. For the reference architecture, three RH probes (Vaisala, HMP7, ±2% of measured RH) are placed at the cathode inlet and outlet, and at the wet outlet of the humidifier, respectively. Under certain conditions, the air is saturated at these measurement points and liquid water may be present. RH measurements are still possible thanks to the warming characteristic of the probe which minimizes condensation, and because the liquid water flows along the walls without coming into contact with the sensor. The sensor measures the air humidity (100%) without accounting for the water at the bottom of the pipe. For the DWI architecture, some of the injected water remains in liquid form at the cathode inlet. A large amount of droplets would be projected on the probe, preventing RH measurements. For this reason, in the DWI configuration only one RH probe is used at the cathode outlet. There is no humidity measurement at the anode outlet, as most of the water there is in liquid form. The water collected by the water traps at the outlets of the anode and cathode is weighed.

## 2.3. Experimental procedure and conditions

The stack was first tested with the reference architecture, to evaluate the performance of the membrane humidifier for cathode humidification and get reference data for comparison. Afterwards, the system architecture was changed and the stack was tested with the DWI architecture. The architectures and corresponding humidification methods were compared based on a series of results obtained under similar operating conditions, with the only difference being the humidification method. The discussion is based on polarization curves and stabilized current steps, obtained under various operating conditions as described in Section 2.3.1. The discussion variables are the injected water flow rate, air temperature, and cooling temperature, as these parameters significantly influence water evaporation and overall water management. Except for the polarization curves, for which the procedure is described in Section 2.3.2 the measurements were averaged over 30 min following a 30 min stabilization period. Each curve was repeated twice with a deviation of less than 5 mV.
<table><caption>**Table 2**
Nominal operating conditions adopted in this work.</caption><thead><tr><td>Parameter</td><td>Nominal</td></tr></thead><tbody><tr><td>Current density</td><td>1 A/cm²</td></tr><tr><td>Cooling outlet temperature</td><td>80 °C</td></tr><tr><td>ΔT<sub>cooling</sub></td><td>3 °C</td></tr><tr><td>Cathode inlet pressure</td><td>1.8 bar</td></tr><tr><td>Cathode stoichiometry</td><td>2</td></tr><tr><td>Anode inlet pressure</td><td>1.9 bar</td></tr><tr><td>Anode stoichiometry</td><td>1.5</td></tr><tr><td>Anode inlet RH</td><td>30%</td></tr><tr><td>Air inlet temperature (DWI)</td><td>80 °C</td></tr><tr><td>Air flow rate nozzle (DWI)</td><td>1.5 Nm³/h</td></tr><tr><td>Water flow rate (DWI)</td><td>15 g/min</td></tr></tbody></table>

### 2.3.1. Operating conditions

The performance is first evaluated under the nominal conditions presented in Table 2. The outlet temperature of the cooling water is set at 80°C. Hydrogen enters the anode at a pressure of 1.9 bar absolute, at the outlet cooling temperature (80°C), with an RH of 30%, and a stoichiometric ratio of 1.5. Air enters the cathode at an absolute pressure of 1.8 bar and with a stoichiometric ratio of 2. With the membrane humidifier, the RH at the cathode inlet is not regulated and depends on the operating conditions. Under the nominal conditions, the RH calculated at the cooling inlet temperature of 78°C (cooling outlet temperature set to 80°C) is 67%.

In the DWI architecture, a volumetric pump controls the injected water flow rate, adjusted to match the amount of water entering the stack with the reference architecture. A heating resistor controls the air temperature entering the injection zone, which is set to 80°C. Higher temperatures would better simulate the operation of an air compressor without intercooler.<fnref n="1" /> However, we adopt 80°C as a nominal value to limit the risk of damaging the fuel cell stack in case of a failure of the water injection system and the associated evaporative cooling. The nominal value for the airflow through the nozzle is set according to supplier data, at 1.5 Nm³/h.

The impact of current density, injected water quantity, and outlet cooling temperature was evaluated with sensitivity analyses, by varying one parameter while keeping the others fixed. These parameters were within the following ranges: current density from 0 A/cm² to 1.5 A/cm², injected water flow rate from 0 g/min to 25 g/min, and temperature from 70°C to 85°C.

### 2.3.2. Polarization curves

The steady-state fuel cell performance is evaluated across the entire current range using polarization curves. The cell voltage is evaluated as a function of current density under specific operating conditions. The protocol used to obtain these polarization curves is inspired by that presented by the Joint Research Centre (JRC) of the European Commission in [24]. The current setpoint is increased in steps, starting from 0 A/cm² up to 1.5 A/cm², and then decreased back to 0 A/cm². The duration of the steps should be sufficient to achieve voltage stabilization, with the criterion proposed in [24] being ±5 mV. A stabilization duration of 5 min per step is retained to meet this criterion. The duration of current steps below 0.1 A/cm² is reduced to 1 min to limit cell degradation most likely to occur at high voltage. The polarization curve is plotted by averaging the voltage over the last 2 min of each step, and the last 30 s for points with a current density below 0.1 A/cm². The average voltage is calculated considering only cells 3 to 18 to exclude edge effects. The stoichiometric ratio is 1.5 for the anode and 2 for the cathode under nominal conditions, as described in Section 2.3.1. At low current density, the gas flow rates must be sufficient to ensure an appropriate

feed of all cells. Below 0.3 A/cm² the hydrogen flow is maintained at 0.5 Nm³/h (corresponding to a stoichiometric ratio of 1.5 at 0.3 A/cm²). Below 0.5 A/cm² the air flow is set at 3 Nm³/h (corresponding to a stoichiometric ratio of 2 at 0.5 A/cm²).

### 2.3.3. Water balance measurements and RH values

Water distribution between the anode and the cathode can provide information on water transport across the membrane and its hydration. The water balance can be evaluated by comparing the amount of water injected in the stack and produced at the cathode during operation (proportional to the current) to that exiting the stack, both at the anode and the cathode. For both architectures, at the anode side, the amount of water injected is measured by the mass flow controller of the active evaporator. Preliminary tests confirmed that all the injected water is evaporated. The amount of water exiting the anode is collected by a water trap and weighed. For the reference architecture, water entering and exiting the cathode is measured by an RH probe. For the DWI architecture, water entering the cathode is measured by the volumetric pump and that exiting the cathode is collected by a water trap and weighed. These measurements are taken over 30 min after a 30 min stabilization period. In steady-state conditions, all the water entering the stack and that generated is assumed to exit the stack.

Note that in the case of DWI, the presence of liquid water in the airflow prevents total water measurements with the RH probe since the amount of liquid water present would not be accounted for. The data given by the probe is nevertheless used to determine the water exiting as vapour. The RH measurements presented at the cathode outlet come from the RH probe. In the case of the reference architecture, the water exiting the cathode cannot be collected as it supplies the membrane humidifier.

To facilitate the comparison with the reference architecture, a theoretical RH is calculated under the assumption that all the injected water is evaporated. It is hereafter referred to as “theoretical RH at the cathode inlet” (or simply “theoretical RH”) and noted RH<sub>th</sub>. This theoretical RH does not necessarily correspond to the actual RH in the stack at the cathode inlet. Indeed, as liquid water is evaporated in the injection zone, air is cooled, thus limiting the evaporation process. Assuming thermodynamic equilibrium is reached, saturated air enters the cathode at the wet-bulb temperature (which equals the dew point temperature at saturated conditions). The “cathode inlet RH at thermodynamic equilibrium” is also calculated as the portion of the spray that can evaporate before the saturation vapour pressure and the wet-bulb temperature are reached in an adiabatic evaporative cooling process.

All RH values are calculated based on the temperature of the cooling circuit at the corresponding point (inlet or outlet), as shown in Fig. 1(c). The underlying hypothesis is that due to the low thermal inertia of the gas flow, the local gas temperature can be approximated by the local cooling circuit temperature. Since the cathode and cooling circuit flows have the same direction (co-flow), the RH measurements at the cathode inlet and outlet are presented at the temperature of the cooling circuit inlet and outlet, respectively. The anode and cooling circuit flow in the opposite direction (counter-flow). Therefore, the RH value at the anode inlet is calculated at the temperature of the cooling circuit outlet.

## 3. Results and discussion

### 3.1. Comparison of the two architectures under nominal conditions

The performance of the two architectures was evaluated under the nominal conditions, first using polarization curves. Fig. 3 compares a polarization curve obtained with the reference architecture with that obtained with the DWI architecture. For the sake of clarity, only polarization curves obtained while decreasing current density are shown. Except for the cathode humidification method, these two curves are obtained under the same operating conditions, as detailed in the

<footnote n="1">¹ The calculated temperature at the outlet of a compressor with an isentropic efficiency of 70% and at a pressure ratio of 1.8 is 96°C.</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 3.** (a) Decreasing polarization curves for the two architectures. (b) Relative humidity (RH) at the cathode inlet (solid lines) and outlet (dashed lines). Measurements were conducted under nominal operating conditions: operating temperature of 80 °C, anode/cathode pressure of 1.9/1.8 bar, anode/cathode stoichiometry ratio of 1.5/2, anode inlet RH of 30% and cathode inlet RH in DWI equivalent to that measured with the reference architecture.</figcaption></figure>

Nominal column of Table 2. As the reference architecture uses a passive membrane humidifier, the RH at the cathode inlet depends on the fuel cell operating conditions and is presented in Fig. 3(b) (dashed line). It varies between 30% at 0 A/cm<fnref n="2" /> and 76% at 1.5 A/cm<fnref n="2" />. The discontinuity of the RH curve is due to the increase in stoichiometry below 0.5 A/cm<fnref n="2" /> to ensure an appropriate feed of all cells, as previously mentioned. These RH values were then used as targets to control the water flow to be injected with the DWI architecture considering complete spray evaporation. In the case of DWI, the theoretical RH at the cathode inlet is thus equal to the RHᵢₙ reported for the reference in Fig. 3(b). As mentioned before, the shown RHs do not correspond to the actual RHs in the stack at the cathode inlet. Dry air enters the injection zone at 80 °C but cools down due to evaporation, thus limiting the process. The cathode inlet RH, assuming thermodynamic equilibrium is reached, is also presented in Fig. 3(b) (solid line). Under the chosen nominal conditions, the wet-bulb temperature, and therefore the dew point, is close to 33 °C, which results in a corresponding RH at the cathode inlet temperature of only 12%. The remaining water is assumed to enter the stack in liquid form.

The two polarization curves in Fig. 3(a) show that the voltage obtained with the DWI architecture is lower than that obtained with

the reference architecture, for the entire range of current densities. The drop in voltage observed at 1 A/cm<fnref n="2" /> between the DWI architecture and the reference architecture is of 40 mV per cell (6%). The humidification method has a significant impact on the performance.

The difference in performance is most probably due to the supply of a liquid-vapour mixture to the stack in the case of DWI whereas, for the same water flow rate supplied, only vapour enters the stack with the membrane humidifier.

Fig. 3(b) also presents the relative humidity measured at the cathode outlet during the polarization curves (dashed lines). With the humidifier, the RH at the cathode outlet progressively increases up to 100% from 0 A/cm<fnref n="2" /> to 0.25 A/cm<fnref n="2" />. Between 0.25 A/cm<fnref n="2" /> and 1 A/cm<fnref n="2" /> the air at the outlet is saturated. Above 1 A/cm<fnref n="2" /> the RHₐ₉₉ slightly decreases, which is explained by a small reduction in absolute humidity at the cathode inlet.<fnref n="2" /> The stack seems well humidified, thus exhibiting good performances with 0.7 V at 1.0 A/cm<fnref n="2" />.

With the DWI architecture, the RH at the cathode outlet shows a plateau at 85% RHₐ₉₉. Note that the plateau is reached at a current density significantly higher than for the reference architecture (0.6 A/cm<fnref n="2" /> vs 0.25 A/cm<fnref n="2" />). The measured RH at the cathode outlet is lower with DWI than with the humidifier even though the same amount of water enters the stack. In steady-state conditions, there are two possibilities: either this water is transferred across the membrane and exits at the anode outlet, or it remains at the cathode but in liquid form. It can be expected that the injected liquid water is not fully evaporated. The analysis of the water balance presented hereafter confirms this hypothesis.

Fig. 4 presents water balances conducted for both architectures at 1 A/cm<fnref n="2" /> under nominal operating conditions, with a cathode inlet water flow rate of 15 g/min (67% RHᵢₙ). Although in both architectures the same amount of water enters the stack (2 g/min at the anode and 15 g/min at the cathode), the water distribution between the outlet of the two compartments is significantly different. More water comes out from the anode with the reference architecture (7 g/min) than with the direct water injection (2 g/min). Water transfer from the cathode to the anode is much more important in the case of the reference architecture. Moreover, with the DWI architecture, 30 g/min is collected at the cathode outlet after condensation while the RH measured by the probe corresponds to only 20 g/min. The difference between the probe measurement which accounts only for the vapour phase, and the collected water measurement, which accounts for both the liquid and vapour phases, confirms that a portion of the water exits the cathode in liquid form (around 10 g/min out of 15 g/min).

One hypothesis to explain the liquid water at the cathode outlet is that a significant number of spray droplets are accumulated within the channels. This accumulation reduces the available exchange surface area, thus limiting liquid water evaporation. For this reason, some water remains in liquid form even if the saturated vapour pressure is not reached in the stack. Partial evaporation of the spray injected in a stack was already observed by Hwang and Kim [15]. They estimated the evaporation rate from the difference in the cathode outlet RH, measured before and after water injection begins. They do not consider the crossover through the membrane. They calculated the evaporation efficiency, defined as the mass ratio of evaporated water to injected water. They showed that the evaporation efficiency depends on the operating conditions but never exceeds 20%. This suggests that only a small fraction of the liquid water entering the stack is eventually evaporated.

Several factors may explain the poorer performance observed when a liquid-vapour mixture is injected into the stack (DWI case). First,

<footnote n="2">² The cathode inlet RH is calculated at the cooling inlet temperature, which varies depending on the heat to be dissipated, to maintain a constant cooling outlet temperature of 80 °C. Since the temperature changes, an increase in RH does not necessarily indicate an increase in absolute humidity.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 4. Water balance with reference and DWI architectures, under nominal conditions and a current density of 1.0 A/cm².</figcaption></figure>

since not all the water evaporates, the relative humidity in the fuel cell is lower, and part or all of the membrane may be drier, increasing its protonic resistivity. The limited cathode humidification with DWI affects water transport across the membrane, resulting in reduced hydration on both the cathode and anode sides, as suggested by the water balance measurement (the amount of water collected at the anode outlet with DWI corresponds to a RH of only 30%). Additionally, liquid water injection increases the risk of flooding. Accumulation of liquid water in channels or porous media can obstruct the delivery of reactants to the catalyst sites. Finally, introducing liquid water into the fuel cell may influence its temperature due to evaporative cooling. Different experiments were carried out to further identify the reasons for the voltage drop observed and discuss to which extent the presence of liquid water can impact the performance. The following sections discuss the effects of varying the amount of water injected and varying the cell temperature.

## 3.2. Effect of the injected water flow rate

In Fig. 3 discussed in the previous section, the injected water flow rate with DWI was set to correspond to the measured RH at the cathode inlet with the reference architecture. Here, to better understand the impact of the amount of water injected in the stack and that of the RH, the flow rate is successively set to correspond to two constant theoretical RH values<fnref n="3" /> at the cathode inlet (considering full spray evaporation), specifically 30% and 70% RH<sub>th</sub>. The other parameters are kept at nominal conditions. Fig. 5 presents the two respective polarization curves obtained, as well as the one obtained with the reference architecture under nominal conditions. Although the injected water flow rate is significantly different, the voltage measured for 30% and 70% RH<sub>th</sub> is almost identical. Additional water injected to reach a theoretical RH of 70% does not seem to contribute significantly to the fuel cell humidification.

The relative humidity measured at the cathode outlet during the three polarization curves is also presented in Fig. 5. The RH at the cathode outlet is similar for both water injection flow rates in DWI. Both show a plateau at 82% and 85% RH<sub>out</sub> respectively for 30% and 70% RH<sub>th</sub> targeted at the cathode inlet. Despite the significant difference in injected flow rates, the increase in evaporated water is minimal. Moreover, the measured RH at the cathode outlet is lower with DWI than with the humidifier, even under conditions where more water is injected. Increasing the theoretical RH from 30% to 70% has little effect on the RH within the fuel cell, mainly increasing the amount

<figure><img src="image_6.png" /><figcaption>Fig. 5. Decreasing current density polarization curves (solid lines) and cathode outlet relative humidity (dashed lines) for reference architecture and DWI. RH<sub>th</sub> stands for theoretical RH at the cathode inlet calculated from liquid water injected considering full spray evaporation.</figcaption></figure>

of liquid water passing through the stack. This has a negligible impact on membrane humidification, and consequently, performance remains similar. Besides, no significant changes in transport losses is observed in the polarization curves for 30% and 70% RH<sub>th</sub>, indicating that the additional liquid water does not impact reactant transport, at least for the moderate current densities considered here.

To better understand the behaviour of the water injected with the DWI, the water flow rate was varied on a larger range while keeping the current density fixed at 1 A/cm². Two different air supply temperatures were tested, 30 °C and 100 °C, to vary the amount of water that could evaporate in the injection zone before reaching the saturation vapour pressure. For comparison, we also performed tests using an active evaporator (Bronkhorst CEM-system 1000 g/h 6 Nm<fnref n="3" />/h) to introduce only water vapour in the stack while controlling the water flow rate. The resulting mean cell voltages and the RH measured at the cathode outlet as a function of the cathode inlet water flow rates are shown in Fig. 6(a).

With the active evaporator, the cell voltage increases with the cathode inlet water vapour flow rate up to about 10 g/min (50% RH), before reaching a plateau at 0.68 V. Meanwhile, the RH at the cathode outlet continues to rise beyond 10 g/min, reaching 95% at 17 g/min. This suggests that the membrane is sufficiently hydrated from 10 g/min onward, explaining why the voltage no longer increases despite the further rise in RH. With DWI, the cell voltage also increases with the cathode inlet water flow rate, up to about 10 g/min. Beyond this point, the increase in voltage is marginal, with a change of less than 5 mV over the 10 g/min to 25 g/min range. The performance and RH<sub>out</sub> obtained with the DWI are always lower than with the active evaporator. For low water inlet flow rates, the difference in voltage and RH<sub>out</sub> between DWI and active evaporator is limited. Indeed, at low flow rates, one can expect a high fraction of the injected water to be evaporated with the DWI. The voltage difference increases with the flow rate until the plateaus are reached. This may be ascribed to the limitation in water evaporation in the case of DWI, with the fraction of injected water that evaporates depending on the injected flow rate. Beyond 10 g/min the increase in evaporation is marginal with a change of less than 3% RH<sub>out</sub> in the range 10 g/min to 25 g/min. For DWI, the plateau is likely reached because the amount of water evaporated stops increasing, rather than due to the membrane being sufficiently hydrated, which accounts for the voltage difference compared to the evaporator consistent with the difference in RH<sub>out</sub>. The increase in air supply temperature allows for a higher evaporation rate, resulting in a slightly better RH<sub>out</sub> and voltage at 100°C compared to 30°C. Finally, despite the significant amount of liquid water, no voltage drop is observed, indicating that the additional liquid water injection does

<footnote n="3">³ It should be noted that to ensure a constant theoretical RH, the amount of water injected varies with the air flow rate and therefore with the current density.</footnote>
<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Effect of the cathode inlet water flow rate at 1 A/cm² for active evaporator (purple) and DWI with two different air temperatures at the injection zone inlet: 30°C and 100°C (green and orange) (a) Mean cell voltage and RH measured at the cathode outlet (b) Water vapour flow rate in the cathode inlet based on thermodynamic equilibrium (solid lines) and mean cell voltage comparison between DWI and active evaporator.</figcaption></figure>

not hinder reactant transport, as already evidenced by the polarization curves in Fig. 5.

Fig. 6(b) presents the thermodynamic equilibrium (solid lines) reached in the case of the active evaporator (purple) and the DWI (orange and green). For the active evaporator, the liquid water injected is completely evaporated whatever the inlet water flow rate, and no liquid water enters the stack. As mentioned before, in the case of the DWI, the evaporation of liquid water results in a decrease in the air temperature since there is no additional heat provided as in the case of the active evaporator. Hence, the portion of the spray that can evaporate before the saturation vapour pressure is reached, considering an adiabatic evaporative cooling process, is limited by the air inlet temperature, respectively 1.0 g/min at 30°C and 3.2 g/min at 100°C. This corresponds to RH of 5% at 30°C and 16% at 100°C. Hence above 1.0 g/min at 30°C and 3.2 g/min at 100°C some liquid water enters the stack, part of which can evaporate along its way to the outlet. One way to estimate the amount of water that evaporates in the stack is to consider the results obtained with the active evaporator, assuming a same amount of evaporated water results in similar voltage in both configurations (active evaporator and DWI). It should be noted, however, that water evaporated at the end of the channel does not have the same effect on hydration as water vapour from the entrance of the channel. It is possible to estimate from Fig. 6(a) the amount of water vapour necessary to reach a given voltage in DWI and thus the amount of liquid water that evaporates. These values have been added as single points in Fig. 6(b). The measured points are somewhere in between: although full spray evaporation is not achieved (except for very small flow rates), the effect of DWI on the cell voltage corresponds to a vapour flow rate higher than the one that would be obtained considering the wet bulb temperature as the dew point at the inlet of the stack. Those results support the hypothesis that some of the liquid water, even though limited, evaporates inside the stack, as observed by Hwang and Kim [15]. A plateau in water evaporation is still reached after about 10 g/min. It is noteworthy that this also corresponds to the plateau reached for the mean cell voltage in DWI (Fig. 6(a)). To sum up, the lower voltage reached with DWI clearly results from a lower water evaporation, 4.5 g/min (20% RH) and 5 g/min (28% RH) at maximum, respectively at 30°C and 100°C injection temperature, corresponding to 0.65 V and 0.66 V. For comparison, the highest voltage at 1 A/cm² (0.68 V) was reached with the active evaporator for about 50%RH (11 g/min). Even though the difference in voltage is limited considering the large difference in RH, there is still room for improvement. Eventually, a significant amount of liquid water enters the stack for DWI. The question is can it contribute to humidifying the ionomer in the catalyst layer and the membrane? Given the hydrophobic nature of the gas diffusion layer, it can be assumed that the liquid water

accumulated in the channel is carried along by the airflow down to the cathode outlet without penetrating the gas diffusion layer and reaching the catalyst layer and the membrane, which might remain insufficiently hydrated. The increased ohmic losses would explain the lower voltage obtained with the DWI. The reduced water transfer from the cathode to the anode observed in the case of DWI (Fig. 4) supports the hypothesis of lower water content on the cathode side of the membrane.

### 3.3. Effect of the cell temperature

Cell temperature significantly influences water management. Higher temperatures increase humidification requirements to maintain membrane hydration. Investigating the effect of cell temperature contributes to evaluating humidification methods. Fig. 7(a) presents the variation of the mean cell voltage at 1.0 A/cm² versus the cooling circuit temperature measured at the stack outlet under nominal operating conditions. The amount of water injected with the DWI architecture is calculated to be identical to that entering the cathode side with the humidifier, which is in the range 10 g/min to 20 g/min corresponding to 66% to 68% RH<sub>th</sub>. For temperatures up to 75°C, the voltage difference between the reference and the DWI cases is less than 10 mV. This observation is readily explained by the fact that at low temperatures, the need for air humidification is rather low. Therefore, the amount of water injected and the membrane is well hydrated whatever the humidification method. The RH measured at the cathode outlet is the same for both architectures. At higher temperatures, the difference in voltage increases, reaching almost 50 mV at 85°C. With the membrane humidifier, the fuel cell is well humidified since the RH is above 90%. The cell voltage keeps increasing with the cell temperature. However, the water injected in DWI does not provide sufficient membrane hydration compared to that achieved with the humidifier, and the RH<sub>out</sub> drops below 80% at 85°C. The amount of water needed to humidify the stack, and reach the necessary RH, increases with the stack temperature since the water saturation pressure increases. Moreover, while the amount of water produced by the reaction remains constant, its contribution to maintaining a high RH within the stack decreases, as shown in Fig. 7(b) (grey line). From 102% at a cell temperature of 70°C it drops down to 57% at 85°C. The behaviour observed in Fig. 7, indicates that even if the evaporation inside the stack increases, it is not enough to compensate for the higher humidification needs at higher temperatures. Note that the outlet coolant temperature is regulated, while the inlet temperature is approximately 3°C lower. Small variations in coolant the temperature difference (ΔT<sub>cooling</sub>) less than 0.5°C, are observed, mainly due to evaporative cooling from water injection. These minor ΔT<sub>cooling</sub> fluctuations have a marginal effect on the cell voltage, as a sensitivity analysis on ΔT<sub>cooling</sub> showed that a variation from 3°C to 12°C results in a voltage change of less than 10 mV.
<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Mean cell voltage (a) and cathode inlet and outlet RH (b) at different stack (cooling outlet) temperatures with reference and DWI architectures, under nominal conditions.</figcaption></figure>

## 4. Conclusions

This work compared the performance of direct water injection and membrane humidifiers for humidifying the cathode air supply in PEM fuel cells. To our knowledge, such a direct comparison has not been previously reported in the literature. The results confirmed the feasibility of humidifying the stack through direct water injection at the cathode, as already shown by [15,16]. However, the performance obtained with DWI was not as good as for the reference system architecture based on a membrane humidifier. A 40 mV decrease in cell voltage was observed with DWI, at 1 A/m² under the nominal operating conditions of this study. As the heat generated by compression was insufficient to completely evaporate the spray, some liquid water entered the stack. Nevertheless, the recorded voltage difference is limited and could be offset by the gains in durability, compactness, and cost of the humidification method.

Even with a high amount of liquid water injected, theoretically corresponding to an inlet RH of 100%, the fuel cell is not sufficiently hydrated with DWI architecture. A significant portion of the injected liquid water appears to flow through the channels without evaporating and does not contribute to the humidification process. An assumption is that liquid water accumulates in the channels and can neither evaporate due to low liquid-gas interface surface area, nor penetrate the gas diffusion layers because of their hydrophobic nature. Therefore, a

portion of the injected water does not reach the membrane and the cathode catalyst layer ionomer, thus limiting the effectiveness of the DWI method. However, an increase in the amount of injected water does not lead to a voltage drop, which would result from increased reactant transport limitations. That indicates that additional liquid water flowing through the channels does not cause flooding issues. As future work, fuel cell modelling might be used to provide new insights into DWI performance and help with the interpretation of the experimental results obtained here.

Since the limitations of DWI seem to stem from the accumulation of the spray droplets, reducing this accumulation could enhance the DWI humidification efficiency. Potential improvement for DWI could involve developing a specific manifold, improving the injection area, or reducing the droplet size so that they enter the channels without coalescing. Indeed, the fuel cell stack used for the tests was not designed for direct water injection. Adding an evaporator at the cathode inlet could help evaporating all the water before it enters the stack, allowing for a performance gain but at the expense of an additional component and increased system complexity compared to DWI without an evaporator. The design of membrane electrode assembly materials better suited to DWI humidification is another very interesting perspective. System-level analysis could help determining the optimal operating conditions and system design that could further improve DWI performance. The nominal operating conditions (Table 2) considered in this work correspond to the optimal conditions specified by the manufacturer for operation with a membrane humidifier. For operation with direct water injection, the optimal conditions might differ (temperature, pressure, stoichiometry). For instance, when possible, the stack temperature should be limited to 75°C to increase the DWI humidification performance. The optimal operating conditions with DWI still require further investigation and must consider the whole fuel cell system design and constraints related to vehicle integration in mobility applications. Another aspect that requires investigation is how liquid water injection into the stack could impact its durability, a topic that has not been treated yet in the literature.

Finally, while DWI results in a performance decrease of a few percent, this architecture does not require a membrane humidifier and an intercooler in the air loop. Replacing these components with an injection system and a condenser is expected to provide significant benefits in terms of durability, space and cost savings. In the end, a techno-economic study would be necessary to confirm whether these advantages are sufficient to offset the efficiency losses.

### CRediT authorship contribution statement

**Flavien Marteau:** Writing – original draft, Visualization, Validation, Methodology, Investigation, Data curation, Conceptualization. **Pedro Affonso Nóbrega:** Writing – review & editing, Visualization, Supervision, Methodology, Conceptualization. **Cédric Sernissi:** Resources, Investigation. **Pascal Biwole:** Writing – review & editing, Supervision, Methodology. **Iona De Bievre:** Methodology, Conceptualization. **Christophe Vacquier:** Writing – review & editing, Supervision, Resources. **Christian Beauger:** Writing – review & editing, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: MARTEAU Flavien reports financial support and equipment, drugs, or supplies were provided by Symbio. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments

This work has been supported by the European Union (Next Generation EU) and the French State (France 2030, France Relance).

References

[1] Cullen DA, Neyerlin KC, Ahluwalia RK, Mukundan R, More KL, Borup RL, et al. New roads and challenges for fuel cells in heavy-duty transportation. Nat Energy 2021;6(5):462-74.

[2] Gray N, McDonagh S, O'Shea R, Smyth B, Murphy JD. Decarbonising ships, planes and trucks: An analysis of suitable low-carbon fuels for the maritime, aviation and haulage sectors. Adv Appl Energy 2021;1:100008.

[3] Aryanpur V, Rogan F. Decarbonising road freight transport: The role of zero-emission trucks and intangible costs. Sci Rep 2024;14(1):1-11.

[4] Kusoglu A, Weber AZ. New insights into perfluorinated sulfonic-acid ionomers. Chem Rev 2017;117(3):987-1104.

[5] Jiao K, Li X. Water transport in polymer electrolyte membrane fuel cells. Prog Energy Combust Sci 2011;37(3):221-91.

[6] Chang Y, Qin Y, Yin Y, Zhang J, Li X. Humidification strategy for polymer electrolyte membrane fuel cells - A review. Appl Energy 2018;230:643-62.

[7] Janicka E, Mielniczek M, Gawel L, Darowicki K. Optimization of the relative humidity of reactant gases in hydrogen fuel cells using dynamic impedance measurements. Energies 2021;14(11).

[8] Jeon DH, Kim KN, Baek SM, Nam JH. The effect of relative humidity of the cathode on the performance and the uniformity of PEM fuel cells. Int J Hydrog Energy 2011;36(19):12499-511.

[9] Sanchez DG, Ruiu T, Biswas I, Friedrich KA, Sanchez-Monreal J, Vera M. Effect of the inlet gas humidification on PEMFC behavior and current density distribution. ECS Meet Abstr 2014;MA2014-02(21). 1223-1223.

[10] Xu Y, Chang G, Zhang J, Li Y, Xu S. Investigation of inlet gas relative humidity on performance characteristics of PEMFC operating at elevated temperature. World Electr Veh J 2021;12(3):1-11.

[11] Linh Nguyen X, Khoi Phan V, Choi Y, Choi S, Yu S. Empirical correlation of water diffusivity in hollow fiber membrane humidifier by measuring latent effectiveness. Appl Therm Eng 2024;236:121846.

[12] Striednig M, Cochet M, Boillat P, Schmidt TJ, Büchi FN. A model based investigation of evaporative cooling for polymer electrolyte fuel cells - stack level analysis. J Power Sources 2022;517:230706.

[13] Wood DL, Yi JS, Nguyen TV. Effect of direct liquid water injection and interdigitated flow field on the performance of proton exchange membrane fuel cells. Electrochim Acta 1998;43(24):3795-809.

[14] Cai F, Cai S, Tu Z. Proton exchange membrane fuel cell (PEMFC) operation in high current density (HCD): Problem, progress and perspective. Energy Convers Manage 2024;307(January):118348.

[15] Hwang SH, Kim MS. An experimental study on the cathode humidification and evaporative cooling of polymer electrolyte membrane fuel cells using direct water injection method at high current densities. Appl Therm Eng 2016;99:635-44.

[16] Choi EJ, Hwang SH, Park J, Kim MS. Parametric analysis of simultaneous humidification and cooling for PEMFCs using direct water injection method. Int J Hydrog Energy 2017;42(17).

[17] Radica G, Tolj I, Lototskyy MV, Pasupathi S. Air mass flow and pressure optimization of a PEM fuel cell hybrid system for a forklift application. Energies 2024;17(1).

[18] Chen Q, Zhang G, Zhang X, Sun C, Jiao K, Wang Y. Thermal management of polymer electrolyte membrane fuel cells: A review of cooling methods, material properties, and durability. Appl Energy 2021;286(September 2020):116496.

[19] Snyder LE. A feasibility study of internal evaporative cooling for proton exchange membrane fuel cells a feasibility study of internal evaporative cooling for proton exchange membrane fuel cells. (December). 2004.

[20] Snyder E, Lalk TR, Appleby AJ. Performance enhancement of PEM fuel cells by use of anode gas ultrahumidification via ultrasonic nebulization. In: Proceedings of 4th international ASME conference on fuel cell science, engineering and technology, FUELCELL2006, vol. 2006, 2006.

[21] Zhang H, Qian Z, Yang D, Ma J. Design of an air humidifier for a 5 kW proton exchange membrane fuel cell stack operated at elevated temperatures. Int J Hydrog Energy 2013;38(28):12353-62.

[22] Jung SH, Kim SL, Kim MS, Park Y, Lim TW. Experimental study of gas humidification with injectors for automotive PEM fuel cell systems. J Power Sources 2007;170(2):324-33.

[23] Sung CC, Bai CY, Chen JH, Chang SJ. Controllable fuel cell humidification by ultrasonic atomization. J Power Sources 2013;239.

[24] Tsotridis G, Pilenga A, Marco G, Malkow T. EU harmonised test protocols for PEMFC MEA testing in single cell configuration for automotive applications. In: EUR, scientific and technical research series, vol. 27632, 2015.