Hydrogen fuel cells convert the chemical energy of hydrogen directly into electricity, with the only byproducts being heat and water. The high cost of hydrogen fuel cells due to the expensive platinum catalyst is one of the limiting factors to their global commercialization. Improving fuel-cell performance while reducing the required amount of the catalyst can be achieved by optimizing the water balance in the cell that aims at striking a balance between electrolyte dry-out, which leads to high ohmic resistance, and liquid-water accumulation, which results in reactant starvation. Interpretation of the experimental measurements necessary for making design decisions is, however, often challenging due to the sub-millimeter scale of the fuel-cell components.

Mathematical models have become a valuable instrument for gaining insight into the physical processes taking place in fuel cells. Because of the coupled electrochemical reactions, heat, mass, and charge transport that occur at multiple spatial and temporal scales, fuel-cell modeling is a complex task that is best addressed with the help of numerical simulations. As the common fuel-cell characterization experiments are dynamic in nature, their analysis requires transient models.

In this thesis, an open-source transient numerical model of a hydrogen fuel cell is developed. The model is applied to interpret electrochemical impedance spectra of fuel cells, highlight the shortcomings of the analytical methods previously used for this purpose, and to better understand liquid-water dynamics in fuel cells.

First, the transient model is used to analyze water-management signatures in fuel-cell impedance spectra under dry conditions. This work shows that the low-frequency inductive behavior observed experimentally in hydrogen fuel cells is influenced by the finite-rate water uptake by the electrolyte and water transport within the electrolyte, which impact the frequency and the size of the inductive loops in the spectra. An ohmic-resistance breakdown performed with the model shows that the high-frequency resistance extracted from the impedance spectra does not contain the protonic resistance of the carbon-supported catalyst layers (CLs) and, therefore, is not equivalent to the total ohmic resistance of the cell.

Impedance spectroscopy is commonly used to measure the charge-transport properties of catalyst layers. Some of the analytical impedance expressions in the literature disagree in the equation that relates the conductivity and resistance of the uniform CLs. The numerical model developed in this thesis is used to inspect that disagreement and to examine the impact of the catalyst-layer nonuniformity on its impedance. Practical recommendations for the experimentalists as to which analytical model, and under what conditions, should be used to reliably characterize charge transport in CLs are provided.

Finally, a novel transient two-phase fuel-cell model is developed that incorporates a pore-size-distribution sub-model to establish relationships between the microstructure of the porous fuel-cell components, their liquid- and gas-transport properties, and, ultimately, liquid-water flooding. Those relationships allow for the systematic analysis of the impact of the electrode design on the dynamic fuel-cell performance under the operating conditions that help keep the electrolyte hydrated but favor liquid-water production. For instance, the model captures how the liquid-water accumulation and drainage cycles translate into unstable fuel-cell performance.

The developed transient fuel-cell model will serve as the foundation for more advanced studies in the future, such as the simulations of membrane and catalyst degradation, carbon corrosion, and cold start-up. The open-source design of the developed software makes it an attractive option for the fuel-cell modeling community.