Experimental Testing and Validation of the Mathematical Model for a Self-Humidifying PEM Fuel Cell

This paper presents an experimental testing and validation results for a zero-dimensional self-humidifying PEM (Proton Exchange Membrane) fuel cell stack. The model incorporates major electric and thermodynamic variables and parameters involved in the operation of the PEM fuel cell under different operational conditions. The mathematical equations are modelled by using Matlab-Simulink tools in order to simulate the operation of the developed model with a commercially available 1 kW Horizon (H-1000) PEM fuel cell stack, which is used for the purposes of model validation and tuning of the developed model. The model is mathematically modelled and presented in the recent published work of authors. The observations from model simulations provide sufficient evidence and support to the results and observations obtained from testing 1 kW Horizon (H-1000) PEM fuel cell stack used in this research. The developed model can be used as a generic model and simulation platform for a self-humidifying PEM fuel cell with an output power varying from 50 W to 1 kW, with extrapolation to higher powers is also possible.

PEM fuel cells have several features comparing to other types of fuel cells, such as: low corrosion, low weight and compact size, which make them suitable for mobile and stationary applications. The operational temperatures of the PEM fuel cell range between 30˚C -100˚C, with a dynamical response faster than solid oxide fuel cell which operates at temperatures over 700˚C [4] [5] [6].
A one dimensional isothermal steady-state model for a PEM fuel cell with Nafion117 membrane has been developed [7] to determine the impact of water transport mechanisms on the performance of the fuel cell. [8] Investigated the conductivity of Nafion117 membrane as a function of drawn current densities.
While, [1] adopted the model developed by [9] in order to consider the impact of heat transfer between the fuel cell body, gas channels, and cooling water.
A non-linear dynamic model of the PEM fuel cells using electrochemical-thermodynamic and zero-dimensional fluid mechanics principles has been developed [10]. While, [11] developed a non-isothermal one dimensional model of a PEM fuel cell is in order to investigate and examine the impact of the design and operating conditions on the performance of the PEM fuel cell.
A simple dynamic electrical model of a PEM fuel cell has been developed by [12] via extending the static current-voltage behavior of the model to implicit the impact of the temperature on the performance of the fuel cell. [13] Developed a dynamic model of 1.2 kW PEM fuel cells that is used for optimal operational strategies development and to control design of the fuel cell based power systems.
A new dynamic model of 20 cells stack has been proposed [14] to investigate starting up and transient behavior of the model under different conditions of load current, temperature, and coolant flow rate. The impact of temperature and the two phases of water (gas and liquid) in the gas diffusion layer need to be taken into consideration. While, [15] a lumped model of the PEM fuel cells is developed to determine the impact of various operating and design parameters such as: input temperature, pressure, stoichiometric ratio, thickness of membrane and gas diffusion layer on the performance of the fuel cell.
A three-dimensional multi-phase fuel cell model has been developed [16] to predict the impact of operating parameters such as operating pressure and temperature of the fuel cell, relative humidity of reactant gases, and air stoichiometric ratio on the performance of the PEM fuel cells operates under steady-state conditions. While, [17] a mathematical model of a 750 W PEM fuel cell is developed to predict the behavior of the fuel cells under steady and transient states.
Although many of the fuel cell models are available in literatures, but most of

Modelling of the PEM Fuel Cell
A simplified mathematical model of the self-humidifying PEM fuel cell is developed by modelling the major electric and thermodynamic variables and parameters, as it was mathematically modelled and presented in the recent published work of the authors in [18]. Consideration is given to the changes in the where, E oc represents open circuit voltage of the PEM fuel cell as it has been derived previously for a liquid state of water produced by the fuel cell and given by [19]. V act , V ohm , and V con , represent the activation overvoltage, ohmic overvoltage, and concentration overvoltage of the PEM fuel cell, respectively. n is the number of cells connected in series in the stack. T is stack temperature in Kelvin which is nearly equal to cell temperature. I is the drawn current in Ampere, and ζ n represents the empirical parametric coefficient based on the experimental data, which may vary from one stack to another or cell to another depends on the geometrical design and the materials used in the construction of the PEM fuel cell. A fc is the membrane active area (cm 2 ), and l is the thickness of membrane (cm). R is the universal gas constant, and F is Faraday's constant.
The mass flow rate of air flows between the exit of supply manifold W sm,out,ca and the cathode is determined as given in the equation below [18], where, P ca,in is the pressure of air enter the cathode, and W sm,out,ca is assumed to be equal to W sm,in,ca under condition of steady flow. k sm,out,ca is the nozzle constant of supply manifold outlet (kg/s·kPa) which represents the ratio of mass flow rate of air to the pressure. While, the pressure of air enter and exit the cathode can be determined as given in equation below [18], where, m w,gen , m w,mbr , and m O2,rct represent mass (kg) of produced water as a result of electrochemical reaction, the mass of water vapour across the electrolyte membrane, and the mass of reacted oxygen in the cathode, respectively, V ca is the volume of cathode (m 3 ), and T st is the stack temperature. M w and M O2 represents the molar mass of water and oxygen (kg/mol), respectively. The mass flow rate of hydrogen at the exit of the supply manifold of anode W sm,out,an is determined by the equation below [18],

( )
, , , sm,out an sm,out an sm,out an an,in where, P an,in is the pressure of hydrogen enter the anode, and W sm,out,an is assumed to be equal to W sm,in,an under condition of steady flow. k sm,out,an represents the nozzle constant of supply manifold outlet of anode (kg/s·kPa), which represents the ratio of mass flow rate of hydrogen to the pressure. While, the pressure of where, V an is the volume of anode (m 3 ), m H2,rct represents mass of the reacted hydrogen (kg), and M H2 is the molar mass of pure hydrogen (kg/mol), and W H2,rct is the mass flow rate of the reacted hydrogen as a result of electrochemical reaction.
In this research, Horizon (H-1000) fuel cell stack system is adopted as an experimental prototype, which is designed by the manufacturer to be self-humidified fuel cell stack [20]. Figure 1 shows the mechanical components and flow variables associated with the Horizon (H-1000) fuel cells stack system. It has been assumed that all the gases inside the stack of the fuel cells will behave as an ideal gas; also the properties of gases leaving the specific volume are the same as those inside that volume. The dimensions of the Horizon (H-1000) fuel cell stack are relatively small, hence the distances between the supply-return manifolds and anodes-cathodes of the fuel cell are small, therefore it is assumed the impact of heat radiation or conduction between anodes-cathodes and supply-return manifolds are very small and can be ignored. Hence, the temperature of gases in the anodes-cathodes and also along the supply-return manifolds will be uniform and equal to the stack temperature. Moreover, because of the small size of the stack, it is assumed that the flow of gases within any cross sections in the stack has approximately zero flow fractions. Also, it has been assumed that the average stack temperature and relative humidity inside the cathode and anode are well regulated and maintained for all the stages of modelling, analysis, and control design [18]. to the supply voltage is 360/V. Al's Hobbies Professional analogue-digital servo tester is used to adjust the rotational speed of the BLDC motor and its propeller via generating a PWM signal to the electronic speed controller (ESC) in order to increase-decrease the current drawn from the fuel cell stack. A pressure reduce valve (Swagelok) is used to maintain the supply pressure of hydrogen to the stack at 55 kPa. A temperature and humidity data-logger (KTH-300 Kistock), integrated with thermo-hygrometry (TH) probe sensor, is used to measure the temperature of the exit air from the stack. TH sensor is mounted at each fan outlet in an attempt to obtain an accurate estimate of temperature. The stack temperature is determined by taking the average of the sums of temperature readings for these four TH sensors. Figure 2 shows the block diagram configuration and bench layout of the Horizon (H-1000) fuel cell stack configured with measuring and controlling devices and the BLDC motor load  Table A1 in the Appendix.

First Test
Horizon

Second Test
Horizon

Third Test
Horizon    temperature measurements. Figure 7 shows the output voltages and drawn currents for the tested Horizon (H-1000) fuel cell stack, while Figure 8 shows the average of voltages for each level of current.
Different values of efficiency (83%, 84%, 85%, and 86%) for developed PEM fuel cell are adopted in order to find the best tuning value between the tested fuel cell stack and the developed model. It is noticed that the best value of efficiency for the developed model that enables the model to perform and produce output        stack's temperature will be adopted for any further simulations for the developed mathematical model of PEM fuel cell in this research.

Fourth Test
Horizon (H-1000) PEM fuel cell stack is tested under atmospheric pressure and 21.5˚C room temperature. Test is started after leaving the fuel cell stack for about one hour from the last running test in order to refresh and rest the stack.   Figure 13. Output voltage of Horizon fuel cell stack under the impact of constant drawn current is almost stable around 51.6 V as shown in Figure 14.
Where, the fluctuations in the output voltages as a result of the drop in the pressure of hydrogen in the anode chambers of Horizon PEM fuel cell stack due to frequent breathing process triggered by hydrogen purging valve are eliminated from the captured results. It is clear from the results presented for the tested Horizon (H-1000) fuel cell stack that the stack's temperature has intendancy to increase with operating time and drawn current. The temperature of the stack is maintained around the level of (30˚C) even under further extend in operating time or further increase in the drawn current. This is returned to the potential role of stack's controller which works to suppress any further increase in the stack's temperature above (30˚C) by pumping more air to the cathode in order to maintain the operating temperature of the stack around certain level of operating temperature.
[21] Adopted a 100 W Horizon PEM fuel cell stack as prime source of power for small unmanned aircraft. The test results and the performance evaluation obtained from continuously operating the stack for about 5 hours under 50 W of constant load have shown that the temperature of the stack is increased from 22˚C to 35˚C for the first 30 minutes of stack's operation, while the stack's temperature is maintained below 35˚C for the rest hours of the test.   Furthermore, the observations from model simulations provide sufficient evidence and support to the results and observations obtained from testing 1 kW Horizon (H-1000) PEM fuel cell stack used in this research. The developed model can be used as a generic model and simulation platform for a self-humidifying PEM fuel cell with an output power varying from 50 W to 1 kW, with extrapolation to higher powers is also possible.