:1-dimentional (1D) modeling methods of fuel cell stack are investigated. To ensure numerical simulation of life-long system operation in permissible calculation time and accuracy, physical/empirical models of mass transfer, heat transfer, and electrochemistry in fuel cell stack with proper resolution are developed. These models are validated and verified by the actual fuel cell system data collected in a variety of operating conditions, such as low to high loads, operating temperatures, and total pressures. Modeling and implementation: For a high-speed computation, 2D (along-the-channel + across-the-channel distribution) model was reduced to 1D (across-the-channel distribution) model by introducing weighting function for state variables at inlet and outlet of the fuel cell stack (flowrate, pressure, temperature, and molar fractions of gaseous species), as shown in Fig.1.The physics implemented in the fuel cell stack model are listed in Table 1. Of the models listed in the table, the short-circuit current model, effective enthalpy voltage model, and direct-combustion reaction model were newly developed and implemented. The other models were employed from the representative literature [1][2][3][4]. The model parameters were calibrated by the microscopic measurement results of geometrical structures as well as electrochemical test results measured at a variation of current, gas composition, humidity, and temperature using small cells [5][6].For reducing the computational load, the models were integrated based on a discrete-time explicit numerical solver without any iterative calculations for numerical convergence. To achieve high accuracy even in such a simple framework of the numerical solving methods, the features of mass transport dynamics were expressed by discrete first-order lag model with the unique time-constants, which were determined empirically. All the models were implemented on MATLAB/SIMULINK platform and the interface of the fuel cell stack model was designed so that it could be easily integrated with the balance-of-plants models (air-supply, hydrogen-supply, and cooling subsystems) and the existing libraries of the fuel cell system controllers. Results and discussion Extensive testing was conducted and a lot of validation data were collected in the variety of operating conditions such as low to high loads, operating temperatures, and total pressures. The validation data were utilized for the validation of the fuel cell stack model accuracy and modeling strategies.An example of the validation results is shown in Fig.2. Time-series data of the interfacial conditions of the fuel cell stack (current, temperature, flowrate, pressure, and gas composition) are inputted to the fuel cell stack model, and voltage and resistance are calculated by the model. Then, calculated and measured values are compared. Newly developed models (the short-circuit current model, effective enthalpy voltage model, and direct-combustion reaction model) were found to be beneficial to close a gap of the acceleration / deceleration transient features between dynamic fuel stack responses in the validation data and the calculation results.The computational time of the numerical simulation is listed in Tables 2 and 3. A considerable reduction in computation time (more than 50-times faster than real time) was confirmed even under the standard-performance computational resources. References R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Revised Second Edition, John Wiley & Sons, New York (2006).S.V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw–Hill, New York (1980).T.E. Springer, T.A. Zawodzinski, and S. Gottesfeld, “Polymer electrolyte fuel cell model”, J. Electrochem. Soc., 138(8), 2334–2342 (1991).D.M. Bernardi and M.W. Verbrugge, “A mathematical model of the solid-polymer-electrolyte fuel cell,” J. Electrochem. Soc., 139(9), 2477–2491 (1992).T. Tsukamoto et al., “Three-dimensional numerical simulation of full-scale proton exchange membrane fuel cells at high current densities,” J. Pow. Sour., 588, 229412 (2021).N. Nonoyama et al., “Analysis of oxygen-transport diffusion resistance in proton-exchange-membrane fuel cells,” J. Electrochem. Soc., 158(4), B416–B423 (2011). Figure 1
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Jan 19, 2024
Basem E Elnagi + 3
Open Access
