**A Thermodynamic Analysis of an Air-Cooled Proton Exchange Membrane Fuel Cell Operated in Di**ff**erent Climate Regions**

## **Torsten Berning \* and Søren Knudsen Kær**

Department of Energy Technology, Aalborg University, 9100 Aalborg, Denmark; skk@et.aau.dk **\*** Correspondence: tbe@et.aau.dk

Received: 23 April 2020; Accepted: 18 May 2020; Published: 20 May 2020

**Abstract:** A fundamental thermodynamic analysis of an air-cooled fuel cell, where the reactant air stream is also the coolant stream, is presented. The adiabatic cell temperature of such a fuel cell is calculated in a similar way as the adiabatic flame temperature in a combustion process. Diagrams that show the dependency of the cathode outlet temperature, the stoichiometric flow ratio and the operating cell voltage are developed. These diagrams can help fuel cell manufacturers to identify a suitable blower and a suitable operating regime for their fuel cell stacks. It is found that for standard conditions, reasonable cell temperatures are obtained for cathode stoichiometric flow ratios of ξ = 50 and higher, which is in very good agreement with manufacturer's recommendations. Under very cold ambient conditions, the suggested stoichiometric flow ratio is only in the range of ξ = 20 in order to obtain a useful fuel cell operating temperature. The outside relative humidity only plays a role at ambient temperatures above 40 ◦C, and the predicted stoichiometric flow ratios should be above ξ = 70 in this region. From a thermodynamic perspective, it is suggested that the adiabatic outlet temperature is a suitable definition of the fuel cell operating temperature.

**Keywords:** air-cooled proton exchange membrane fuel cells; adiabatic fuel cell temperature; thermodynamic analysis of proton exchange membrane fuel cells

#### **1. Introduction**

Air-cooled, low-temperature proton exchange membrane fuel cells (PEMFCs) are attractive for applications in the range of up to a few kW. Among the salient features is their simplicity of operation because they do not need a secondary coolant loop. The major disadvantage is the relatively low observed maximum current density of around 0.3–0.4 A/cm<sup>2</sup> , which severely limits the power density [1]. Moreover, it is often difficult to operate these fuel cells in extreme climate conditions.

The principle of air-cooled fuel cells is the same as of liquid-cooled fuel cells: oxygen from air is combined with hydrogen to produce water and electricity. A certain amount of waste heat is produced due to overpotentials that predominantly occur at the fuel cell catalysts and inside the proton conductive membrane. The half-cell reactions are:

$$\begin{array}{cccc} Anode: & H\_2 & \Rightarrow 2H^+ + 2e^-\\ \text{Cathode:} & \frac{1}{2}O\_2 + 2H^+ + 2e^- & \Rightarrow H\_2O\\ \text{Combined:} & H\_2 + \frac{1}{2}O\_2 & \Rightarrow H\_2O \end{array}$$

The electrons produced by the anode half-cell reaction are driven through an external circuit to the cathode by the electro-motive force, and the protons migrate through the polymer electrolyte membrane, which is proton conductive and electron repellant. In order to have the reactions occurring at an appreciable rate, overpotentials have to be applied, and these are the sources of waste heat. While the theoretical cell potential between anode and cathode based on thermodynamics should be 1.23 V, practical operating voltages are 0.5–0.8 V. In order to obtain an appreciable voltage, numerous single fuel cells are combined in a fuel cell stack, where the stack voltage is the sum of the individual cell voltages and the current that is drawn through all cells in series. A simple schematic of a fuel cell is shown in Figure 1.

**Figure 1.** Proton exchange membrane fuel cell (PEMFC) schematic [2].

The thermo-neutral potential of the fuel cell reaction is 1.482 V, assuming that the product water is in the liquid phase [3]. The corresponding potential based on the lower heating values is 1.254 V [3]. The difference between the thermo-neutral potential and the fuel cell operating voltage multiplied with the fuel cell current density is the amount of waste heat that is produced inside the fuel cell, and the fuel cell efficiency is directly proportional to the fuel cell voltage.

x In air-cooled, low-temperature PEMFCs, the waste heat is removed by excessive air that is being fed to the fuel cell. Therefore, the reactant air is, at the same time, the coolant air, and the stoichiometric flow ratio, ξ, must be high. Such units are already widely commercially available, a leading manufacturer being Ballard Power Systems [4].

One of the disadvantages of air-cooled PEMFCs is their low maximum current density of only around 0.4 A/cm<sup>2</sup> (e.g., References [5,6]), which severely limits the power density. By comparison, liquid-cooled PEMFCs that are being developed for automotive applications have a maximum current density of up to 2.0 A/cm<sup>2</sup> , which lead to power densities in the range of 1.0 W/cm<sup>2</sup> . It should be a goal to increase the maximum current density that can be drawn from an air-cooled fuel cell because this will lead to a substantial increase in their power density. It is clear that such an increase in power density also leads to a cost reduction.

Since the reactant air is directly taken from the environment, the performance and thermal management of these fuel cells is very sensitive to the ambient conditions. While it is no problem to operate such a fuel cell stack at an ambient temperature of 25 ◦C and typical relative humidity levels for temperate climate regions, the air-cooled fuel cell operation becomes less stable in regions with extreme temperatures. These systems are also placed in remote regions with extreme climates, and stable operation must be ensured. Thus, there is a need to fundamentally understand the impact of the ambient temperature on the expected performance or even the possibility to operate such a stack at extreme conditions.

Figure 2 summarizes suitable operating ranges as identified experimentally by Ballard Power Systems [4]. The nominal power density at standard conditions is around 0.225 W/cm<sup>2</sup> and the maximum current density is around 0.4 A/cm<sup>2</sup> [4]. Depending on the outside conditions, the cathode stoichiometric flow ratio is typically in the region ξ*ca* = 50–120, and the stack performance was observed to become unstable below a cathode side stoichiometric flow ratio of ξ*ca* = 20. The ambient relative humidity has a stronger effect at temperatures higher than 40 ◦C, and the effect on the performance is stronger in very dry regions. On the anode side, the stoichiometric flow ratio must be as low as possible in order to preserve the hydrogen, and in practice, stacks are operated below an anode side stoichiometry of ξ*an* = 1.1 [4].

**Figure 2.** Effect of (**a**) the stoichiometric flow ratio and (**b**) of the ambient relative humidity and temperature on the performance of an air-cooled fuel cell stack. Adapted from Reference [4] with permission from Ballard Power Systems, January 2019.

Over the past decade, air-cooled fuel cells have been studied by several research groups. An important distinction to make is between (i) air-breathing fuel cells that rely on natural convection to provide the reactant air and which can be used for power ranges up to 100 W, and (ii) air-cooled fuel cells, where the reactant air is provided by a fan or compressor which necessitates work and increases the system complexity [7]. The latter are being considered for remote power supply, such as telecom back-up, and they operate in power ranges of up to a few kW. Because the reactant air is directly taken from and removed to the environment, this type of fuel cell is also termed an open cathode fuel cell.

Jeong et al. [8] conducted experiments on air-breathing fuel cells in a climate chamber where the operating conditions were varied. The recorded maximum current density was 0.4 A/cm<sup>2</sup> , and the power density was below 0.2 W/cm<sup>2</sup> . The anode was operated on dry hydrogen, and the water balance of the cell was measured by placing a water-absorbing material in the anode outlet and weighing the amount of water that has accumulated over a certain amount of time. The recorded water balance results were in very good agreement with our own experiments [9].

Publications of experimental studies on an existing commercial stack included Zhu et al. [5], Del Real et al. [6] and Adzakpa et al. [10]. All these groups reported current densities below 0.4 A/cm<sup>2</sup> .

The publication by Wu et al. [11] included a detailed literature study, and this group conducted experiments on a single cell and a stack that consisted of 5 cells. The cells were operated on humidified hydrogen at 55 ◦C at the anode and dry, ambient air at the cathode. The observed maximum current density for the single fuel cell experiments was around 0.3 A/cm<sup>2</sup> , and in case of the stack, it was below 0.25 A/cm<sup>2</sup> . There was no additional heating or cooling in the end plates and the results showed that the center temperature was 8 ◦C higher than the outer cells near the end plates.

Beside these experimental research efforts, several groups have conducted modeling studies to better understand heat and mass transfer in air-cooled PEMFCs. Sasmito et al. [12–15] published several computational fluid dynamics studies that included the predicted cell performance using the commercial software ANSYS Fluent. In Reference [12], this group investigated the placement of the fan and the effect of the channel height on the predicted performance and pressure drop. One finding was that the height of the cathode channels had a strong impact on the maximum current density, which was slightly above 0.3 A/cm<sup>2</sup> . In Reference [13], this group compared the performance of the cell for a natural convection stack and a forced convection stack, where the fan was placed before the stack and the fan power was varied. For forced convection, the maximum current density was 0.35 A/cm<sup>2</sup> before the stack was overheated, while it was below 0.2 A/cm<sup>2</sup> for natural convection. A novel flow reversal concept was then proposed by the same group in Reference [14], where a fan was placed before

and behind the stack and flow shifting was introduced with the goal of preventing stack overheating. While the model predicted a temperature reversal according to the periodicity of the flow shifting, no performance improvement was indicated. However, this concept helped to reduce the temperature gradients and better understand the frequency of the flow reversal. Finally, the selection of the fan based on different fan types with different performance curves was studied in Reference [15].

Shahsavari et al. [16] and Akbari et al. [17] developed a single-phase computational model of an air-cooled fuel cell using COMSOL Multiphysics®. The focus was put on a better understanding of the thermal management and the prediction of the maximum stack temperature as well as the main temperature gradient, which occurs in the flow direction. They simulated a commercial fuel cell stack by Ballard Power Systems and obtained very good agreement between their modeling predictions and the measured maximum temperature. Unfortunately, performance data or maximum current densities obtainable from that fuel cell stack were not released.

Other, very interesting work on air-cooled fuel cells was published by Meyer et al. [18,19]. Their studies focused on a commercial fuel cell design by Intelligent Energy, and the fuel cells differ from the above-listed stacks in that air is used as a coolant in separate cooling channels. The reactant air is fed in flow channels at a low stoichiometry. These air-cooled fuel cells are consequently more similar to liquid-cooled fuel cells, which was also pointed out by Sasmito et al. [13].

More work on air-cooled fuel cell stacks that have separate cooling channels include the study by Chen et al. [20], who developed a high-power air-cooled fuel cell stack with a current density above 0.8 A/cm<sup>2</sup> . The resulting power density was an impressive 0.6 W/cm<sup>2</sup> , and the stoichiometric flow ratio of the reactant air was only 1.5–2.0 and below. However, the cooling channels accounted for 55% of the bipolar plates' frontal area, which also means that the membrane-electrode-assembly had to be larger compared to, e.g., a Ballard stack. The active area of that stack was roughly 113 cm<sup>2</sup> and the maximum current was 100 A. The resulting power output was 2.55 kW.

Finally, a very good overview of the different cooling strategies in PEMFC stacks was given by Zhang and Kandlikar [21], while Flückiger et al. [22] conducted a thermal modeling analysis of an air-cooled fuel cell stack with edge cooling.

Air-cooled fuel cells are often used as telecom back-up applications in regions with extreme climates. In order to understand, under which conditions such fuel cells may operate, a thermodynamic analysis based on the first law of thermodynamics is conducted in this work. The calculations presented here are inspired by the calculation of the adiabatic flame temperature in a combustion process, and it will be shown that the outlet temperature of the reactant gases depend only on the ambient conditions, the stoichiometric flow ratio of the cathode air (the anode side stoichiometry is fixed to a low value) and the operating cell voltage. The latter determines the amount of waste heat that has to be removed predominantly by the excess air. In doing so, feasible operating regimes for these air-cooled fuel cells are identified and compared to the empirically determined regimes by Ballard Power Systems.

The main motivation for the current study is therefore:


#### **2. Formulation of the Molar Flow Rates and the Energy Balance**

#### *2.1. Assumptions*

The analysis carried out below is conducted in a similar way as the calculation of the adiabatic flame temperature in a combustion process by applying the first law of thermodynamics. It is based on assuming ideal gas behavior, and changes in potential and kinetic energy are neglected. Moreover, the calculations assume steady-state operation.

#### *2.2. Thermodynamic System Considered*

The system under consideration is shown in Figure 3. It is the goal to determine the adiabatic outlet temperature of the reactant gases, so all the waste heat is carried out of the cell in the form of internal heat and the temperature of the product gases is increased. In contrast to the calculation of the adiabatic flame temperature in a combustion process, the electrical work performed by the fuel cell has to be accounted for because it is clear that the adiabatic outlet temperature of a fuel cell depends strongly on the cell performance. For simplicity, it is assumed that anode and cathode gas streams enter and leave the cell at the same temperature. Under such conditions, the exact water balance of the fuel cell plays no role, i.e., it does not matter whether the product water leaves from the cathode side or anode side because the water vapor leaves the cell at the same temperature.

**Figure 3.** System boundary for the first-law analysis.

#### *2.3. Molar Inlet Streams*

In order to conduct a first-law analysis of an air-cooled system, the molar flow rates have to be formulated before the enthalpy streams are calculated. This has already been done in numerous previous articles in PEMFC (e.g., Reference [23]). The incoming molar stream of oxygen depends on the cathode stoichiometric flow ratio, ξ*ca*, and the total current that is drawn from the fuel cell stack, *I*:

$$
\dot{m}\_{O\_2, \text{in}} = \xi\_{ca} \frac{I}{4F} \tag{1}
$$

4*F* , 2 where *F* is Faraday's constant (96,485 C/mole). Note that the total current is not the physical current drawn from the fuel cell stack in experiments, but the physical current drawn from each cell multiplied with the number of cells in the stack.

On a molar basis, the incoming amount of nitrogen is:

$$
\dot{m}\_{\text{N}\_2,in} = \frac{79}{21} \dot{m}\_{\text{O}\_2,in} = \frac{79}{21} \times \xi\_{ca} \times \frac{I}{I} \frac{1}{4F} \tag{2}
$$

2 2 , , 21 21 4 There is a certain amount of water vapor entering the cell that depends on the relative humidity of the ambient air, *RHin*, which is introduced as a free parameter:

$$RH\_{\rm ini} = \frac{p\_{\rm H\_2O}}{p\_{\rm sat}(T)} = \mathbf{x}\_{\rm H\_2O} \frac{p\_{\rm amb}}{p\_{\rm sat}(T)} = \frac{\dot{n}\_{\rm H\_2O,in}}{\dot{n}\_{\rm tot,in}} \frac{p\_{\rm amb}}{p\_{\rm sat}(T)} \tag{3}$$

,

*Energies* **2020**, *13*, 2611

From this, it follows that:

$$\dot{m}\_{\rm H\_2O,in} = \rm RH\_{\rm in} \times \frac{p\_{\rm sat}(T)}{p\_{\rm amb}} \times \dot{n}\_{\rm lot,in} = \rm RH\_{\rm in} \times \frac{p\_{\rm sat}(T)}{p\_{\rm amb}} \times \left(\dot{n}\_{\rm H\_2O,in} + \dot{n}\_{\rm O\_2,in} + \dot{n}\_{\rm N\_2,in}\right) \tag{4}$$

which results in:

$$\dot{m}\_{\rm H\_2O,in} = \mathcal{R}H\_{\rm ini} \times \left(\frac{p\_{\rm amb}}{p\_{\rm sat}(T)} - \mathcal{R}H\_{\rm ini}\right)^{-1} \times \left(\dot{n}\_{\rm O\_2,in} + \dot{n}\_{\rm N\_2,in}\right) \tag{5}$$

It is desirable to express the amount of water entering the cell as a function of the current and the stoichiometry, similar to the oxygen and nitrogen stream. Inserting Equations (1) and (2) and reformulation yields:

$$\dot{m}\_{H\_2O,in} = RH\_{in} \times \left(\frac{p\_{amb}}{p\_{sat}(T)} - RH\_{in}\right)^{-1} \times \frac{1}{0.21} \times \xi\_{ca} \frac{I}{4F} \tag{6}$$

The ratio between the water vapor flux and the incoming amount of oxygen is thus:

$$\frac{\dot{m}\_{H\_2O,in}}{\dot{m}\_{O\_2,in}} = \frac{1}{0.21} \times RH\_{in} \times \left(\frac{p\_{amb}}{p\_{sat}(T)} - RH\_{in}\right)^{-1} \tag{7}$$

The saturation pressure is only a function of the temperature and it can be conveniently expressed by Antoine's equation:

$$p\_{\rm sat}(T) = D \times \exp\{A - \frac{B}{\mathcal{C} + T}\} \tag{8}$$

where *A* = 8.07131, *B* = 1730.63, *C* = 233.426 and *D* is introduced to convert from the unit (mmHg) into (*Pa*), and it is 133.233. *T* is the temperature given in ◦C. For an ambient temperature of 25 ◦C, the saturation pressure is thus 3158 Pa. Assuming an atmospheric total pressure, the molar flow rate of water vapor is, at a maximum (*RHin* = 1), 15.3% that of oxygen.

At the anode side, dry hydrogen is assumed to enter the cell at a specified stoichiometric flow ratio:

$$
\dot{m}\_{\text{H}\_2\text{in}} = \xi\_{\text{an}} \frac{I}{2\text{F}} \tag{9}
$$

#### *2.4. Molar Outlet Streams*

For the molar stream of oxygen leaving the cell, it holds that:

$$
\dot{m}\_{O\_2,out} = (\xi\_{ca} - 1)\frac{I}{4F} \tag{10}
$$

and the stream of the inert nitrogen is:

$$
\dot{m}\_{\text{N}\_2\text{out}} = \dot{m}\_{\text{N}\_2\text{in}} = \frac{79}{21} \times \xi\_{\text{c3}} \times \frac{I}{4F} \tag{11}
$$

The water at the outlet is the amount that has entered the cell plus the product water. In this case, the overall water balance of the fuel cell does not matter as both the anode and outlet stream are assumed to leave the cell at the same temperature. In case of doubt, it may be assumed that all of the product water leaves at the cathode side owing to the very low anode side stoichiometric flow ratio.

$$\dot{m}\_{\text{H}\_2\text{O,out}} = \dot{m}\_{\text{H}\_2\text{O,in}} + \frac{I}{2F} = RH \times \left(\frac{p\_{\text{amb}}}{p\_{\text{sat}}(T)} - RH\right)^{-1} \times \frac{1}{0.21} \times \xi\_{\text{c1}} \frac{I}{4F} + \frac{I}{2F} \tag{12}$$

#### *2.5. Formulation of the Energy Balance*

Applying the first law of thermodynamics to an air-cooled PEMFC according to Figure 3, it holds that:

$$Q - W\_{\rm el} = H\_{\rm prod} - H\_{\rm react} \tag{13}$$

here, *Q* is the heat loss of the cell and *Wel* is the work that is extracted from the cell. In the current case, the system is considered adiabatic, *Q* = 0, and *Wel* is expressed as:

$$\mathcal{W}\_{\rm el} = V\_{\rm cell} \times I\_{\rm cell} \tag{14}$$

Because the system is assumed to be adiabatic, the calculated temperature of the outlet gases is at a maximum. If the amount of heat loss from the stack to the surroundings is known, it may be entered here. The current analysis reveals no information about the temperature distribution inside the fuel cell stack, where the local temperature can be higher than the adiabatic outlet temperature of the reactant gases. Such a temperature distribution may be obtained by a detailed analysis, as carried out by Shahsavari et al. [16].

Assuming ideal gas behavior, the enthalpy streams can be calculated as follows:

$$H = \sum \dot{n}\_i h\_i = \sum \dot{n}\_i \left[ h\_f^0 + \left( h - h^0 \right) \right] = \sum \dot{n}\_i \left[ h\_f^0 + c\_p \left( T - T^0 \right) \right] \tag{15}$$

where *h* indicates molar enthalpies in (J/mol). The molar enthalpy of any species consists of two terms: the enthalpy of formation, *h* 0 *f* , at 25 ◦C and 1 atm and the sensible enthalpy due to a temperature increase. The enthalpy of formation for stable elements like oxygen, nitrogen and hydrogen is zero, whereas the enthalpy of formation, *h* 0 *f* , of liquid water vapor is −285,830 J/mol and of water vapor is −241,820 J/mol [24].

For the calculation of the adiabatic gas outlet temperatures, the first law of thermodynamics thus reduces to:

$$\mathcal{W}\_{el} = \sum \dot{n}\_{prod} h\_{prod} - \sum \dot{n}\_{reac} h\_{reac} \tag{16}$$

The required properties are listed in Table 1.

**Table 1.** Gas properties at 298 K [24].


For demonstration purposes only, we assume the incoming gas stream of the air-cooled system to be at the standard conditions of 25 ◦C and 1 atm, so that the incoming enthalpy streams of oxygen, nitrogen and hydrogen are zero compared to the standard condition. Moreover, it is assumed for simplicity that the incoming air is completely dry so that there is no water vapor entering. Therefore, according to Equation (15), the incoming enthalpy stream is zero relative to the standard conditions. The outlet pressure of the fuel cell shall also be assumed to be 1 atm.

Inserting the above expressions into the energy balance then results in:

$$\dot{V}\_{\text{cell}} \times I\_{\text{cell}} = \dot{n}\_{\text{O}\_{2},\text{out}} \left(\text{h} - \text{h}^{0}\right)\_{\text{O}\_{2}} + \dot{n}\_{\text{N}\_{2},\text{out}} \left(\text{h} - \text{h}^{0}\right) + \dot{n}\_{\text{H}\_{2},\text{out}} \left(\text{h} - \text{h}^{0}\right) + \dot{n}\_{\text{H}\_{2}\text{O},\text{out}} \left(\text{h}^{0}\_{f} + \text{h} - \text{h}^{0}\right) \tag{17}$$

The unit on both sides is in Watts, and it is observed that the enthalpy of formation is only considered for the water. So far, we have not decided whether the product water will be in gas or liquid phase. Obviously, the maximum cell temperature will be lower when the product water is in the gas phase, but it depends on the outlet temperature when the outlet gas phase will become saturated. Given the fact that these fuel cells operate on ambient air which is typically heated up inside the cell by 20–30 ◦C at a high stoichiometric flow ratio, it may be assumed that the product water leaves the cell in the vapor phase.

It is observed that, according to Equations (1), (2) and (5), the molar flow rates depend directly on the cell current, *Icell*, which means that it can be canceled out in Equation (17). Inserting the molar flow rate and canceling yields:

$$\begin{array}{l} V\_{cell} \ = \frac{1}{4F} \times (\xi\_{ca} - 1) \times \left( h\_{O\_2} (T\_{out}) - 8682 \frac{\text{kJ}}{\text{kmolle}} \right) \\ \ + \frac{1}{4F} \times 3.762 \times \xi\_{ca} \times \left( h\_{N\_2} (T\_{out}) - 8669 \frac{\text{kJ}}{\text{kmolle}} \right) \\ \ + \frac{1}{2F} \times (\xi\_{an} - 1) \times \left( h\_{H\_2} (T\_{out}) - 8468 \frac{\text{kJ}}{\text{kmolle}} \right) \\ \ + \left[ RH \times \left( \frac{p\_{amb}}{p\_{ad}(T)} - RH \right)^{-1} \times \frac{1}{0.21} \times \frac{\xi\_{ad}}{4F} + \frac{1}{2F} \right] \\ \ \times \left( -241, 820 \frac{\text{kJ}}{\text{kmolle}} + h\_{H\_2O} (T\_{out}) - 8468 \frac{\text{kJ}}{\text{kmolle}} \right) \end{array} \tag{18}$$

From Equation (18), it follows that there are only four independent parameters in this analysis: the cell voltage, *V*, the stoichiometric flow ratio of the cathode side, ξ*Ca*, the outside relative humidity, *RH*, and the temperature of the outlet gases, *Tout*. This leaves aside the anode stoichiometric flow ratio, which should always be as close to unity as possible, which leads to the fact that the anode enthalpy stream is negligible. In combustion analysis, it is common to apply an iterative method to determine the temperature of the outlet gases. On the other hand, it is just as convenient to construct diagrams where the cell voltage is the *y*-axis and the adiabatic outlet temperature of the gases is the *x*-axis. With the anode stoichiometric flow ratio fixed at a low value of ξ*an* = 1.1, and for a given ambient pressure and relative humidity, the cathode stoichiometric flow ratio is then the only free parameter left and a different value for ξ*ca* will give a different curve in the *V-Tad-*Diagram. Such diagrams can be constructed for different ambient conditions in which the fuel cell is placed, and these are shown and analyzed in the next section.

#### **3. A Thermodynamic Analysis of Air-Cooled PEM Fuel Cells Using** *V-Tad***-Diagrams**

The above equations can now be applied to study the adiabatic cell temperature, i.e., the temperature of the product gases assuming all the waste heat is carried out by the flew gases. To this end, the above equations can be entered into spreadsheet calculation software where the outlet temperature is the adjustable parameter. As can be seen from Equation (18), the relative difference between the inlet and outlet molar enthalpy streams can be given in terms of a voltage. This voltage depends only on the temperature of the outlet gases and the outside conditions. Besides the cell voltage, the cathode stoichiometric flow ratio is the most important parameter. Clearly, the ambient air temperature and the relative humidity have an impact on the adiabatic outlet temperature. In the following, four different cases will be examined in detail. In all cases, the ambient pressure was assumed to be 1 bar, but according to Equation (18), that property only plays a role in the calculation of the amount of water vapor that enters the cell.

#### *3.1. Case 1: Standard Conditions*

Standard operating conditions are that the inlet gas streams enter at 25 ◦C. It is assumed that the relative humidity of the ambient air was 30%. Figure 4 shows the resulting dependency between the gas outlet temperature, the stoichiometric flow ratio and the cell voltage. All the lines have a negative slope because if the cell voltage decreases for a given stoichiometric flow ratio, more waste heat is produced and therefore, the cathode outlet temperature increases. The right-hand side of Figure 4 zooms in on the region of interest. The supplier of our fuel cell stack states that the stack outlet temperature should not exceed 60 ◦C and the stack voltage should be below 0.9 V to avoid irreversible degradation [4]. On the other hand, the voltage should be above 0.6 V, if possible, to ensure satisfactory cell performance. From this diagram, a working point under the given operating conditions may be read, e.g., a stoichiometry of 50 and a cell voltage of 0.7 V. Under these conditions, the adiabatic outlet temperature of the reactants will be 50 ◦C. Thus, the thermodynamic analysis yields a fundamental explanation of the preferred operating conditions, as specified by the manufacturer.

**Figure 4.** Dependency of the adiabatic outlet temperatures of the product stream on the operating cell voltage. The incoming conditions were a temperature of 25 ◦C and a relative humidity of 30%. (**a**) Entire voltage range, (**b**) close-up on the region of interest.

Varying the RH of the inlet air has only a very small impact on the results (not shown), and this is also in good agreement with Figure 2. It is interesting to note that when the cell potential drops from 0.7 V to 0.6 V, the adiabatic outlet temperature increases by only 5 ◦C and it would even stay the same if the stoichiometric flow ratio would be increased from 50 to around 57. In practice, the fuel cell temperature is monitored in a position inside the cathode flow channel and adjusted by the fan drawing the air through the stack [4]. Overall, these diagrams suggest that there is no inherent reason why an air-cooled fuel cell should not be operational at high current densities.

#### *3.2. Case 2: Cold and Dry Conditions*

It is a requirement that fuel cell systems for telecom back-up applications also operate in an environment with a temperature as low as −40 ◦C. For the sake of demonstration, it is assumed that cold air at −20 ◦C is indeed fed to the fuel cell. Obviously, such air cannot contain any water vapor, and the RH is set to zero (even if it would be set to 100%, there would be no water vapor entrained). Figure 5 indicates that the stoichiometric flow ratio is now a much more sensitive parameter compared to the previous case.

Reasonable cell outlet temperatures can be achieved by using a relatively low stoichiometric flow ratio between ξ = 20 and ξ = 30. An obvious problem is that the stoichiometry has to be very accurately controlled, otherwise it is nearly impossible to control the adiabatic outlet temperature. It can be seen from Figure 5 that a change of the stoichiometric flow ratio, from, e.g., ξ = 22 to ξ = 24, leads to a change in the adiabatic outlet temperature by around 5 ◦C. Therefore, it may be required to pre-heat the incoming air in such extreme climates.

**Figure 5.** Dependency of the adiabatic outlet temperatures of the product stream on the operating cell voltage. The incoming conditions are a temperature of −20 ◦C and a relative humidity of 0%. (**a**) Entire voltage range, (**b**) close-up on the region of interest.

#### *3.3. Case 3: Hot and Humid Conditions*

A second extreme climate case is an ambient temperature of 40 ◦C and an RH of 100%. As shown in Figure 6, in such a case, the stoichiometric flow ratio has to be chosen very high. Assuming a cell voltage of 0.7 V, the stoichiometric flow ratio would need to be in the range of ξ = 75 and higher to attain a reasonable adiabatic outlet temperature of 60 ◦C. Especially at elevated current densities, this would require a stronger blower. Thus, the blower specification is very tightly coupled to the fuel cell operating region. These diagrams clearly show that in every different climate zone, there is a different operating regime for the same hardware, which has to be carefully adjusted.

**Figure 6.** Dependency of the adiabatic outlet temperatures of the product stream on the operating cell **Figure 6.** Dependency of the adiabatic outlet temperatures of the product stream on the operating cell voltage. The incoming conditions were a temperature of 40 ◦C and a relative humidity of 100 %. (**a**) Entire voltage range, (**b**) close-up on the region of interest.

#### *3.4. Case 4: Hot and Dry Conditions*

Finally, hot and dry outside conditions shall be investigated. Figure 7 shows the diagrams for an inlet temperature of 40 ◦C and an outside relative humidity of 30%. While the inlet RH at lower temperatures has a weak effect on the ability to operate the cell, at elevated temperatures, this effect becomes larger. This is in very good accord with the operating conditions suggested by Ballard Power Systems [4]. From Figure 7, it is suggested to maybe choose a target cell voltage to 0.75 V in order to obtain the same adiabatic outlet temperature of 60 ◦C for the same stoichiometric flow ratio of ξ = 60.

The question of how well the membrane is hydrated under such conditions is being addressed in a computational fluid dynamics study of the same fuel cell, with surprising results that have been published separately [25]. The current work focuses on thermodynamic aspects, and it can be seen that the adiabatic outlet temperature of the reactant gases can be calculated out of knowledge of the cell voltage and the stoichiometric flow ratio. The operating temperature of these air-cooled fuel cells is

usually adjusted by trial-end-error, and it may be concluded from the current analysis that the adiabatic outlet temperature is a suitable definition for the operating temperature of these fuel cells.

**Figure 7.** Dependency of the adiabatic outlet temperatures of the product stream on the operating cell **Figure 7.** Dependency of the adiabatic outlet temperatures of the product stream on the operating cell voltage. The incoming conditions were a temperature of 40 ◦C and a relative humidity of 30%. (**a**) Entire voltage range, (**b**) close-up on the region of interest.

#### **4. Conclusions**

In this work, the first law of thermodynamics has been applied to an air-cooled fuel cell stack to calculate the adiabatic outlet temperature of the reactant gases in a similar way as is routinely done in combustion analysis. *V-Tad-*Diagrams of the fuel cell voltage versus the adiabatic outlet temperature have been constructed that show the feasibility to operate the fuel cell in extreme climate conditions. For very cold inlet gases, the cathode stoichiometry has to be below ξ = 30 to attain reasonable cell operating temperatures. The diagrams have also shown that it is very important to supply all fuel cell channels with the same amount of air under cold conditions. Even a mal-distribution of less than 10% can lead to a cell-to-cell variation in the adiabatic outlet temperature of 5 ◦C, when generally, the cell-to-cell variation in temperature should be kept below 6 ◦C [4].

The second and third extreme climate cases were an outside temperature of 40 ◦C and either fully humidified or very low outside relative humidity. While the relative humidity generally plays a minor role in the construction of the diagrams, the inlet RH becomes more important at high outside temperatures, and this is in good agreement with the stack manufacturer's observations [4]. Stoichiometric flow ratios should be between ξ = 60 and ξ = 80 to keep the gas outlet temperatures within a reasonable region. Overall, the diagrams have shown that there is no inherent reason why air-cooled fuel cells cannot be operated at elevated current densities.

It is also important to realize that in the current study, it is assumed that all the waste heat is carried out by the reactant gases, i.e., that the stack is perfectly insulated. This was done for simplicity and to examine the extreme case. In real stacks, there is a certain amount of waste heat leaving the stack at the top and bottom, and the maximum temperature is often observed in the center of the stack [4].

While such a thermodynamic analysis gives valuable insight into the general feasibility to operate a fuel cell in extreme climate conditions, it does not allow a glimpse in the interior of the cell, and it did not give an answer to the question of why the limiting current density is only around 0.4 A/cm<sup>2</sup> . From a thermodynamic perspective, a higher current might be attainable just by placing a larger fan behind the stack. Therefore, a computational fluid dynamics study has been conducted in order to shed light into the underlying heat and mass transfer that occurs inside such an air-cooled fuel cell [25].

#### **5. Patent**

Berning, T. Fuel cell assembly with a turbulence-inducing device for reduction of a temperature gradient. Patent No. WO/2019/120415, International Filing Date (17/12/2018).

**Author Contributions:** Conceptualization, T.B. and S.K.K.; methodology, T.B.; formal analysis, T.B.; resources, S.K.K.; writing—original draft preparation, T.B.; writing—review and editing, T.B. and S.K.K.; project administration, T.B. and S.K.K.; funding acquisition, S.K.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EUDP, Journal number 64012-0117, and carried out in collaboration with Dantherm Power A/S and Ballard Power Systems.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Nomenclature**


## **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **Heat Transfer Optimization of NEXA Ballard Low-Temperature PEMFC**

**Artem Chesalkin 1,\* , Petr Kacor <sup>2</sup> and Petr Moldrik <sup>2</sup>**


**Abstract:** Hydrogen is one of the modern energy carriers, but its storage and practical use of the newest hydrogen technologies in real operation conditions still is a task of future investigations. This work describes the experimental hydrogen hybrid energy system (HHS). HHS is part of a laboratory off-grid system that stores electricity gained from photovoltaic panels (PVs). This system includes hydrogen production and storage units and NEXA Ballard low-temperature proton-exchange membrane fuel cell (PEMFC). Fuel cell (FC) loses a significant part of heat during converting chemical energy into electricity. The main purpose of the study was to explore the heat distribution phenomena across the FC NEXA Ballard stack during load with the next heat transfer optimization. The operation of the FC with insufficient cooling can lead to its overheating or even cell destruction. The cause of this undesirable state is studied with the help of infrared thermography and computational fluid dynamics (CFD) modeling with heat transfer simulation across the stack. The distribution of heat in the stack under various loads was studied, and local points of overheating were determined. Based on the obtained data of the cooling air streamlines and velocity profiles, few ways of the heat distribution optimization along the stack were proposed. This optimization was achieved by changing the original shape of the FC cooling duct. The stable condition of the FC stack at constant load was determined.

**Keywords:** hydrogen; fuel cells; hydrogen hybrid energy system; thermography; CFD modeling; heat transfer; optimization

#### **1. Introduction**

Hydrogen technologies find their use in a wide range of mobile and stationary applications. One of the most developing and applied ways for renewable energy storage is a way of electrochemical energy storage [1]. Hydrogen hybrid systems (HHSs) can utilize renewable energy sources (RESs) and eliminate the fluctuations of their power output by energy storage in form of hydrogen. These types of hybrid systems were examined and tested by the authors in different studies [2–4]. Typically, HHSs consist of energy production units from RESs, combined with hydrogen production and storage unit for power-to-gas conversion (PtG), fuel cell (FC) unit, and classical backup energy storage in a battery bank [5].

The proton-exchange membrane fuel cell (PEMFC) is a promising, widely developed type of the FC that could be operated at the relatively wide temperature range and uses "green" hydrogen as an alternative energy carrier for the grid-connected and off-grid installations [6]. Cells are often combined in series—FC stack [7–9]. Figure 1 shows a simplified diagram of the hydrogen PEMFC in terms of its design and principle of operation, where FP—flow plates, GDL—gas diffusion layers, and CL—catalyst layers.

**Citation:** Chesalkin, A.; Kacor, P.; Moldrik, P. Heat Transfer Optimization of NEXA Ballard Low-Temperature PEMFC. *Energies* **2021**, *14*, 2182. https://doi.org/10.3390/en14082182

Academic Editors: Samuel Simon Araya and Jinliang Yuan

Received: 11 February 2021 Accepted: 12 April 2021 Published: 14 April 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** Construction and principle of hydrogen proton-exchange membrane fuel cell (PEMFC) [10,11].

Fuel cells use direct conversion of chemical energy into electric power, and that is the reason for their high efficiency and almost no emissions. The main type of FC emission is a thermal emission that occurs during FCs operation, especially at high loads. The FC voltage as a function of current density can be seen in Figure 2 below, where OCV is the open-circuit voltage. The value of 1.2 V represents a theoretically loss-free voltage. The actual cell voltage, including the off-load voltage, is always lower than this value.

**Figure 2.** Fuel Cell (FC) polarization curve with voltage losses during FC load [12].

Each FC can produce the maximum theoretical voltage of 1.187 V (for 25 ◦C and 101.325 kPa). The FC efficiency is calculated as the ratio of the actually produced and the theoretically achievable cell voltage

$$\eta = \frac{V\_{real}}{E\_{cell}} = \frac{V\_{real}}{1.187} \tag{1}$$

where *Ecell* refers to the voltage in every cell related to the Gibbs free energy. The real voltage in an actual cell is measured at the power load per cell as *Vreal* = 0.5–0.6 V. The offload voltage reaches the value of 1.1 V [13]. The typical service electrochemical efficiency per cell is approximately between 40% and 50% [14].

Studied NEXA Ballard PEMFC uses the air-based heat exchange system for stack cooling. High-temperature PEMFC provides easier heat regulation, in comparison with studied low-temperature PEMFC, due to higher working temperatures and using liquid refrigerants for stack cooling [15–17].

Several studies were focused on hydrogen storage methods development. In some cases, due to space limitation and pressure-based safety restrictions, it is possible to use hydrogen storage in a solid-state way in metal hydrides (MHs) [18–20]. Joint use of fuel cell (FC) technologies with hydrogen storage systems based on metal hydrides (MHs) allows the utilization of FC excess heat energy for the MH hydrogen desorption process and thereby increases the HHS energy efficiency. MHs application for solar energy accumulation is one of the possible ways described by the authors in various papers [21,22]. In addition, using FCs and MHs in one system gives the possibility to provide the required pure hydrogen to the PEMFCs. LaNi—based alloys allow storing hydrogen at ambient temperatures of 25–40 ◦C and low pressures of 1.0–1.5 MPa, which makes the application of these alloys quite attractive in mentioned above specific conditions [23–28].

The complete experimental setup described in the work is an integral hydrogen hybrid system, which serves for the possibility of optimal energy storage from solar panels in various forms—in the form of electrical energy for direct use or storage in storage batteries, or in the form of gaseous hydrogen in classical gas cylinders and/or in a compact "solid" form in the form of metal hydrides.

One of the main components of this system is fuel cells and the associated fuel source, hydrogen, which, as mentioned above, can be stored in various forms. During the operation of the hybrid plant, overheating of the fuel cells was detected at loads close to maximum and automatic shutdown of fuel cells was observed at high loads when the ambient temperature rose above 25 degrees, while the maximum operating ambient temperature for this fuel cell declared in the documentation was 30 degrees. In this regard, the analysis of the fuel cell and the identification of local overheating zones were started, followed by the simulation of heat transfer along the entire stack of the fuel cell and modification of the elements of the cooling channel.

The main motivation of the work is the improvement in the FC cooling and heat transfer along the FC stack, which is an important issue of safe and efficient operation of the FC and hydrogen hybrid system (HHS) [29–31]. Experimental HHS was developed for joint MH and FC testing. This system, shown in Figure 3, basically consists of photovoltaic panels (PVs), a few power inverters batteries bank, hydrogen production, and storage units. Hydrogen could be stored in three different ways—in pressure vessels in a gaseous state, in metal hydrides in solid state, or converted to electricity via FC and directly used or stored in the battery bank. The lead batteries accumulation enables the storage of 550 kWh of power, and an additional 80 kWh can be stored in the lithium iron phosphate (LiFePO) batteries bank, which provides energy accumulation from the PV plant and avoid energy fluctuation for the stable H<sup>2</sup> production via water electrolysis process.

**Figure 3.** The basic scheme of the experimental hybrid energy system (HHS) energetic system.

According to the nameplate, the ambient operating temperature of the cell must be in the range of 3–30 ◦C. At a temperature around 22–25 ◦C, the maximum operating state cannot be reached due to local overheating of the PEMFC in its front part. This was the main reason to make an FC heat transfer optimization for more uniform stack cooling. The FC heat transfer could be studied using infrared (IR) thermography and appropriate PEMFC computational fluid dynamics (CFD) modeling [32]. IR thermography has been widely used in different industrial and research fields including analysis and cracks determine in membrane materials and characterizing of PEMFC parameters [33–36]. Increasing the efficiency of FC cooling is indeed a popular topic in scientific studies and can be found in a number of literature sources [37,38]. Unfortunately, many authors focus their studies on the single cell and rarely assess the behavior of the PEMFC stack as a whole; therefore, the study of more uniform stack cooling was the main goal on the way of the FC heat transfer optimization.

#### **2. Testing and Measurement Methods**

The thermal field distribution over the low-temperature PEMFC was measured by the FLIR E45 thermal camera. The hydrogen produced via the anion-exchange membrane (AEM) electrolyzer with an output pressure of 3.0 MPa before entering the MH storage system or PEMFC passes through the pressure reducer. Heat field distribution across the surface of the PEMFC body was controlled by IR thermo-vision camera. Laboratory measurements of the heating curves of the NEXA module were conducted according to the block diagram shown in Figure 4.

**Figure 4.** Diagram of the PEMFC heating distribution measurement.

The following measurements were conducted on the NEXA power module of PEMFC: Rated DC power output of this system is 1200 W; operating voltage range of the system is from 26 V (at rated power) to 42 V (no-load voltage); the total numbers of 47 cells are connected in series into the stack. The system further comprises ancillary equipment necessary for its operation, i.e., control unit, hydrogen delivery system, oxidant air supply, and cooling air supply (by cooling fan and compressor). The working parameters of the studied NEXA Ballard PEMFC are shown in Table 1.



#### **3. Experimental and Simulation Results**

The measuring procedure consisted of measurements of the load characteristics of the NEXA module, its hydrogen and oxidant air consumption, water production, and the self-power consumption, which shows the relation of the power output drawn by the NEXA module from its own stack to ensure the operation of its own auxiliary devices at the certain power output. Figure 5 shows the load characteristics of the NEXA module. This module has soft source properties; the voltage of 42 V (at no load) drops to 26 V (at a rated power of 1200 W).

**Figure 5.** Load characteristics of NEXA FC stack.

− − The fuel consumption shown in Figure 6 has been determined from the mass flow meter with an integration member after the so-called cells purging. FC was purged with H<sup>2</sup> once the voltage has dropped below a certain level to restore the higher voltage in cells again. The above-mentioned purge deprives cells of impurities and water on a regular basis since those are accumulated on electrode surfaces to intercept the electrochemical reaction. The frequency of purges rises with the increase of FC power output. The fuel used for this cleaning is drained out of the system. This amount of H<sup>2</sup> is included in the overall fuel consumption. The maximum H<sup>2</sup> consumption rate of the NEXA module is 18.5 L min−<sup>1</sup> . This consumption rate is proportional to the net output power of the NEXA module. The maximum air consumption rate is 90 L min−<sup>1</sup> at rated power. The FC consumes O<sup>2</sup> from the ambient air. − −

**Figure 6.** Fuel (hydrogen) and oxidant air consumption of NEXA FC stack.

NEXA FC stack provides power for its own support system, which consists of an oxidant air pump, cooling fan, sensors, and controllers. The required auxiliary power is 39 W (at no load). This self-power consumption increases with increasing load and is shown in Figure 7. The required auxiliary power is 290 W at rated power. The main electrical appliances include an air pump and cooling fan. The gross power of the NEXA module is given by the sum of the net output power at the module terminals and the power consumption of the module itself.

**Figure 7.** Gross power and self-consumption of NEXA FC stack.

In addition, the NEXA power module efficiency is presented in Figure 8. This efficiency is defined by the ratio of the net output power of the NEXA module to the lower heating value (LHV) of H<sup>2</sup> consumed in the reaction. In the production of electricity from H2, the NEXA module achieves the maximum efficiency at partial load (approx. 300 W). The efficiency decreases at higher—but also lower—loads than the stated 300 W. In the second case, in which the decrease is more dramatic, this is due to a larger ratio of the NEXA module's self-consumption to the amount of H<sup>2</sup> consumed. At maximum load (i.e., at rated power of 1200 W), the NEXA module has an efficiency of approx. 38%.

**Figure 8.** The output efficiency of the NEXA FC stack.

NEXA low-temperature (LT) PEMFC thermography measurements were taken at different loads set on the linked electronic DC load of 100 W, 300 W, 500 W, and 1000 W. FC temperature was measured at the cathode air exhaust of the stack.

There is no local overheating at low or middle PEMFC loads (in the range of 100–500 W), and the presented cooling system seems to be sufficient. The obtained IR thermograms show significant temperature differences between parts of the stack at higher loads; see Figure 9. The left side of the stack, located closer to the entry of the cooling air supply channel, heats up significantly more. At maximum PEMFC loads (in range of 1000–1200 W), the operation temperature of the FC reaches its limit, and FC work stops due to the thermal protection of the system. On the front side of the cooling fins, shown in Figure 9b, local

overheating is visible (marked as a rectangle). The maximum value of temperature is approximately *T* = 338 K.

**Figure 9.** NEXA PEMFC stack infrared (IR)-thermography at P = 1000 W: (**a**) top view and (**b**) side view.

#### *FC CFD Heat Transfer Simulation and Cooling Duct Optimization*

Unequal heating of the FC stack module, detected by IR-thermography measurement, was studied by computed fluid dynamics (CFD) modeling and analyzed using the ANSYS software. The simulation determined the temperature distribution within the NEXA Ballard LT PEMFC stack. The cooling airflow velocity inside the cooling channel and cooling fins was studied. The simulation was performed at the higher problematic *Pel* = 1000 W load. The 47 cells connected in series form a system of channels for cooling air circulation and heat dissipation from the stack. The cooling duct for airflow circulation made from a plastic shell is located below the FC module. This plastic frame acts as well as an FC module mounting system. The inlet of the cooling channel has a shape of a rectangle hole with a dimension of *W* × *H* = 120 × 80 mm. A radial fan is mounted near the inlet of the cooling duct. All walls of the cooling duct are smooth and only the bottom side has a glued roughness surface.

Two small plastic attachments are molded on the inlet of the cooling duct and shown in Figure 10. These attachments make high distortion of the cooling streamlines, which lead to a decrease in the cooling efficiency of the system. The low cooling efficiency at the front side of the FC stack increases the temperature of cooling fins. This phenomenon was previously detected by the infrared (IR) measurements and shown in Figure 9b.

**Figure 10.** Interior of the cooling duct close to the fan outlet. (**a**) side view and (**b**) front view.

ε

It is obvious that the presented cooling system needs to be improved to minimize the stack overheating during operation and at higher loads. One way to improve the FC cooling and heat transfer along the stack is to optimize the shape of the cooling duct. Another condition that should be met is using the original design of a radial fan without its replacement.

The model of the FC stack was designed via SolidWorks software. To simulate the performance of the NEXA PEMFC cooling system, fluid dynamics and thermal analysis were performed using the numerical model on the ANSYS CFX software. This model solves discrete Reynolds averaged Navier–Stokes equations to simulate the flow of the air coolant (heat transfer) along the stack. The governing equations are solved with a standard k–ε model for turbulence modeling. Simultaneously, the energy equation is also solved to determine the heat transfer in both solid and fluid regions [40,41]. The basic 3D model of the cooling duct including PEM and cooling fins is depicted in several view sections in Figure 11. ε

**Figure 11.** Geometric model of NEXA PEMFC stack used for computational fluid (CFD) simulation and optimization.

Internal power losses caused by chemical reactions in PEMFC and Joule's losses produced by electric current inside the cooling fins were modeled by heat sources in mentioned solid components. Internal heat generation is set according to the selected load *Pel* = 1000 W. The PEMFC current and output voltage at that load point can be found in Figure 5 (*Pel* = 1000 W; *V*<sup>1</sup> = 28.5 V; *I*<sup>1</sup> = 35 A; *VCELL* = 0.606 V). The generated heat is calculated by the following equation [42,43]:

> ℎ = k L ∙

> > ሺௌ −

 = 

ሻ ଷ

=

$$Q\_{GEN} = (1.254 - V\_{CELL})I\_1 = P\_{EL} \left(\frac{1.254}{V\_{CELL}} - 1\right) \tag{2}$$

$$Q\_{GEN} = 1000 \left( \frac{1.254}{0.606} - 1 \right) = 1063 \text{ W} \tag{3}$$

− −

−

−

All considered values of power losses and material properties that have been used for modeling are listed in Table 2.


**Table 2.** Material properties and power loss values used for CFD modeling [11,16].

The fluid domain was modeled with air as a coolant at atmospheric conditions. Part of the heat is dissipated via external areas (walls) of PEMFC by natural convection. This fact is taken into account and included in the heat transfer coefficient applied to all vertical walls of the PEMFC CFD model. For vertically oriented surfaces with natural convection conditions, the heat transfer coefficient depends on the Nusselt number, that is, properties of the coolant, geometry of the passages, and flow characteristics. The temperature dependence of the heat transfer coefficient can be evaluated by a combination of the Nusselt, Prandtl, and Rayleigh numbers [36] as follows:

$$h = \frac{\mathbf{k}}{\mathbf{L}} \cdot \mathbf{N}u\_L \tag{4}$$

$$Ra\_L = \frac{\text{g}\,\beta (T\_S - T\_0)L^3}{\nu \alpha} \tag{5}$$

$$P\_r = \frac{\nu}{\alpha} \tag{6}$$

$$Nu\_L = \left\{ 0.825 + \frac{0.387 Ra\_L^{1/6}}{\left[ 1 + \left( \frac{0.5}{Pr} \right)^{9/16} \right]^{8/27}} \right\}^2 \tag{7}$$

where *h*—heat transfer coefficient (W m−<sup>2</sup> K −1 ); *g*—gravity (m s−<sup>2</sup> ); *β*—thermal expansion coefficient (K−<sup>1</sup> ); *L*—characteristic length (m); *ν*—kinematic viscosity (m<sup>2</sup> s −1 ), *α*—thermal diffusivity (m<sup>2</sup> s −1 ); *TS*—surface temperature (K); and *T*0—surroundings temperature (K). Figure 12a shows the application of heat transfer coefficient on external areas of the proton-exchange membrane (PEM) and Figure 12b shows its temperature dependence derived from Equations (4)–(7).

The CFD analysis requires high-density mesh, especially inside of all fluid parts. The velocity gradient reaches high values in the solid–fluid layers, and any coarse mesh may cause serious inaccuracy of the calculation and complicate the convergence. In this regard, the inflations of mesh cells at each transition between fluid–solid parts were applied.

Figure 13a shows the distribution of air velocity at the cross section of the front part of the original FC stack cooling duct. The mentioned figure shows a phenomenon of the swirling streamlines behind the plastic attachments. The airflow is interrupted in the front part of the cooling fins. The situation is similar in the top and bottom sides of the cooling duct. A number of the performed simulations showed the reverse airflow from cooling fins because of the low pressure behind the plastic attachments. Both CFD in Figure 13b and IR in Figure 9b temperature analysis of the NEXA PEMFC stack show the local overheating at the front part of cooling fins due to the intensive swirling of the airflow.

=

<sup>−</sup> *ν*

−

⎩ ⎪ ⎨ ⎪ ⎧

0.825 +

0.387

<sup>−</sup> <sup>−</sup> <sup>−</sup> *β*

ቈ1 + ቀ0.5 <sup>ቁ</sup> ଽ/ଵ ଼/ଶ

ଵ/

⎭ ⎪ ⎬ ⎪ ⎫ ଶ

<sup>−</sup> *α*

**Figure 12.** Applying heat transfer coefficient for external surfaces of the stack (**a**) application on external areas, (**b**) temperature dependence of heat transfer coefficient.

**Figure 13.** (**a**) Streamlines of the air coolant and (**b**) temperature distribution at *Pel* = 1000 W of load.

In the simulated model, the temperature differences are somewhat slightly higher. This is mainly due to the applied simplification of the CFD model, which does not take into account the complex construction of a real PEMFC. Additional devices (humidifier, control card, sensors, etc.) are placed on the sidewalls of the PEMFC structure, which generally decrease the heat dissipation to the surroundings and thus increase its overall temperature.

In the CFD model, temperature-dependent heat transfer coefficients have been applied to the entire walls of the PEMFC stack, and the CFD model is generally better cooled. Thus, the simulated temperature distribution and values on our model differ. In the CFD model, we emphasized a precise computing network (mesh) in the air duct and the boundary layer between fluid and solid objects. The model contains more than 15 million elements, and its solution is very time consuming. We believe that even with this simplification in the construction of the model, there can be found a fairly good match with real PEMFC.

The internal plastic attachments are the integrated part of the radial fan assembly and cannot be simply removed. It is possible to slightly modify its height. To increase the airflow rate to the front part of the stack, the shape modification of the airflow streamlines has to be made. The airflow adjustment can be realized without any significant disruption of the original duct design by using appropriately formed inserts (wings) and blades placed into the cooling duct.

Several modifications of the adjustments in the inlet part of the cooling duct and in its interior have been simulated. The basis of all analyzed modifications was the insertion

of variously shaped blades, which direct the flow of cooling air. Each of the mentioned options was also dimensionally modified (length of the blades, their inclination angle, and position in the cooling channel, etc.). Table 3 shows the list of the analyzed modification of the FC cooling duct.


**Table 3.** Analyzed modification of the cooling duct of PEMFC.

The two most appropriate solutions of the cooling duct adjustment (Type A and Type B) are depicted in Figure 14.

**Figure 14.** Streamlines and velocity profile of the modified cooling duct in (**a**) Type A and (**b**) Type B.

Figure 14 shows streamlines and velocity profiles at the input side of the cooling duct cross section. Type A modification, shown in Figure 14a, contains two additional blades. One of the blades is slightly curved and located in the center of the cooling duct. The second one has a straight shape and creates the covering of the top plastic attachment. The bottom plastic attachment is also lowered by cutting. The used system of blades in Type A modification serves especially for suitable airflow direction to the front part of the PEM stack cooling fins. Type B modification, shown in Figure 14b, is created by covering the top and bottom plastic attachment with a round surface. The rounded surface is simply made from the appropriate cut thin PVC tube. These tube pieces are glued to the internal surface of the cooling duct and easily create an effective shape for airflow. To intensify the direction of the streamline, three additional blades in the center of the cooling duct were used. The swirl occurs behind of bottom blade, but it also gradually disappears with increasing the length of the channel.

Figure 15 shows how cooling duct modification changes the temperature distribution. The local overheating at the front side of PEM, shown in Figure 15b, that corresponded to the original design of the cooling duct has been removed. The area with a higher temperature is now closer to the middle of the PEM assembly. The maximal value of temperature is also decreased in the range of 7 K, from *T*<sup>1</sup> = 338 K in the original design to

*T*<sup>2</sup> = 331 K in Type A and Type B modifications. Type B modification also shows the better temperature distribution along the stack, without any significant local temperature rise. Moreover, the round surfaces and straight blades in Type B modification can be simply manufactured in comparison to the complicated shaping of a curved blade used in Type A.

Figure 16 shows the temperature distribution and velocity profile on the section area located near the coolant outlet (approx. *H* = 5 mm). Both Type A and Type B duct modifications improve the airflow in the front part of PEMFC, which is visible mainly on the velocity profile. The temperature here also reaches lower values in comparison to the rest part of the section area. Important values of performed simulations are collected in Table 4.

**Figure 15.** Temperature distribution on the proton-exchange membrane (PEM) stack across (**a**) Type A and (**b**) Type B.

**Figure 16.** Temperature distribution and velocity profile on section area of PEMFC outlet in (**a**) Type A and (**b**) Type B.

The uniformity of the temperature distribution can be assessed using the homogeneity factor (temperature uniformity coefficient). The coefficient can be determined as the ratio of the temperature value to its maximum. Temperature uniformity coefficient represents the balanced distribution of temperature on the outlet surface of the PEMFC as follows:

$$
\varepsilon = \frac{T\_{AVG}}{T\_{MAX}} \cdot 100\tag{8}
$$

− Tெ Based on the performed simulations, the Type B modification (rounded covers and blades) was chosen for the final adjustment of the PEMFC cooling channel. The rounded covers were made of a plastic tube with a diameter of *D* = 25 mm and were fixed to the sides of the cooling channel by gluing. The straight blades were made of thin steel sheets

−

−

−

and were also glued to the sides of the channel. The blades were adjusted to have a slight inclination with respect to the cooling air inlet from the fan; see Figure 17.

After adjusting the cooling channel, the PEMFC stack was reassembled, and its parameters were measured. To validate the results of the cooling duct optimization, a load of *P* = 1000 W was applied, in which the PEMFC showed a local overheating of the plates in the vicinity of the fan inlet.

Figure 18 shows the measurement of the PEMFC temperature using an infrared camera on the surface of the cooling air outlet. Figure 18a shows the original state of PEMFC without performed optimization, and Figure 18b shows the temperature distribution with an optimized cooling channel according to Type B.

Measurement of the PEMFC surface temperature shows that the modification leads to a temperature reduction and a more accurate heat distribution across the stack. The measurements also show that the temperature difference between the original and optimized variant of the cooling duct design is approximately 7 K, which was also shown by the performed CFD simulations; see Figures 13 and 15.

**Table 4.** Output values from analysis of CFD model.


**Figure 17.** Adjustment of cooling duct close to the fan outlet seen in (**a**) side view and (**b**) front view.

**Figure 18.** NEXA PEMFC stack IR-thermography at loads *P* = 1000 W in (**a**) original design and (**b**) modified cooling duct (Type B).

#### **4. Conclusions**

In this work, a concept of the HHS based on low-temperature NEXA Ballard PEMFC is presented. IR measurements and CFD analysis of the FC stack determined problematic overheated zones of the NEXA FC due to unequal heat distribution (air-cooling distribution) across the stack during high loads. Ways of the FC heat transfer optimization were studied. To avoid local overheating of the stack at the air-cooling inlet side, the modification of the original cooling duct was provided. The heat transfer computer simulation of the PEMFC with different cooling duct designs allowed us to determine the optimal conditions for the NEXA stable working and sufficient cooling at high loads around *Pel* = 1–1.2 kW.

In search of a more advantageous shape of the inlet shape of the PEMFC cooling duct, we have performed a number of analyses and simulations of the flow in the cooling duct. We have selected the most interesting results for our publication.

The basic entry condition for these analyses was to preserve the original FC cooling duct design/structure as much as possible. Our solution is therefore a compromise between preserving the original construction and the necessary modification of the inlet shape of the duct, which leads to an improvement in the PEMFC cooling. From this point of view, our solution is also optimal because we have achieved by simple means (glued covers and blades) the improvement of the FC cooling and temperature distribution of the PEMFC stack. The internal protrusions cannot be easily removed due to the stability of the inlet fan mount. The inner protrusions form stabilizing elements that ensure resistance to the deformation of the channel structure. The inlet part of the duct, which is attached to the fan bases of these protrusions, increases the overall stiffness of the plastic structure.

Of course, it is possible to create a new shape of the cooling channel, in which the protrusions in the inlet of the channel will be on its outer part. Such a construction can be realized, for example, by means of 3D printing. However, in the upper part of the duct, this method is impossible for application due to the overlap (dimensions) of the fan. By removing the protrusions in the lower part, the rigidity of the system will be significantly reduced.

Our main goal was the stability of the operation of PEMFC, especially at operating conditions close to the maximum values. Original FC showed instability of operation even before reaching the declared maximum output power (*P* = 1200 W), and the PEMFC was automatically switched off due to an over-temperature state.

The CFD model of the FC was built with significant simplification. The model has been based on the complicated sandwich structure with mutually coupled chemical, electrical, and thermal processes that were assessed rather from a macroscopic point of view of heat dissipation and its effective removal from the FC body.

However, even this applied simplified model shows an unsuitable construction of the cooling channel. Using the CFD model, the influence of several modifications of the inlet part of the duct to achieve higher cooling efficiency was evaluated. On a real PEMFC, this channel modification was performed and a validation measurement of the operating condition and a measurement of the surface temperature of the PEMFC stack were performed. Although the reduction in temperature may not appear significant, the channel treatment performed resulted in more even temperature distribution and generally stabilized the operation of the PEMFC.

The PEMFC is currently operated in our laboratory tends to work with higher currents (*I* > 30 A); thus, we achieve lower efficiency values ( s (*ɳ* < 40%). The main benefit of the performed analysis and modification of the FC cooling channel is therefore the stability of FC operation at its marginal power (*P* > 1000 W). By modifying the cooling duct, we were able to reduce the operating temperature of the PEMFC and minimize local overheating points. Due to more efficient cooling, the permissible ambient temperature can be slightly exceeded while maintaining the stability of PEMFC operation. We have also measured the operation parameters of the FC with an optimized cooling duct. The FC efficiency has occurred in the range shown in Figure 8.

The next possible waste heat utilizing from the stack could be applied for the LT MH H<sup>2</sup> endothermic desorption process. The next steps of the research would correspond to the design of the optimal solution for sufficient heat exchange between NEXA FC and MH storage tank. Most likely, this solution will be based on the direct use of hot exhaust air from the top part of the stack for MH storage heating, without additional heating the liquid heat carrier and using a gas–liquid heat exchanger.

**Author Contributions:** Conceptualization, A.C. and P.K.; methodology, A.C.; software, P.K.; validation, A.C., P.K., and P.M.; formal analysis, A.C. and. P.K.; investigation, A.C., P.K., and P.M.; data curation, P.K.; writing—original draft preparation, A.C.; writing—review and editing, A.C. and P.K.; visualization, P.K. and P.M.; supervision, A.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the internal funding program of the VSB—Technical University of Ostrava, identification no: SP2021/20, and by the project TK03020027: Center of Energy and Environmental Technologies.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations and symbols are used in this manuscript:


#### **References**

