Hong, Xu, Li, and Ouyang (2017) formulated compact steady one-dimensional and two-zone models of internal water transfer in large-active-area proton exchange membrane (PEM) fuel cells, in which a scalar net water transfer coefficient α\alpha — and, in the downstream-flooded regime, the zone parameters α1\alpha_1, N0N_0, and β\beta — must be supplied by the user because their dependence on operating conditions is not known a priori. The open problem is to determine quantitatively how α\alpha (and α1\alpha_1, N0N_0, β\beta) depends on measurable operating variables (inlet humidities, excess ratios, pressures, temperature, current density, gas-diffusion-layer properties), and to validate the steady model predictions on large-area cells and stacks. Later literature has measured net water drag coefficients empirically on laboratory cells (Ito et al. 2019–2023), developed impedance-based water-content estimation (Hong 2022; Xu et al. 2021), and validated detailed two-phase models against neutron imaging (Tardy et al. 2019), but no validated a priori relation for large-area cells and no experimental validation of the compact model has been established.

Background

A proton exchange membrane (PEM) fuel cell generates electricity from hydrogen and oxygen; the polymer membrane conducts protons only when hydrated, so its internal water balance controls both resistance and durability. Water crosses the membrane by electro-osmotic drag (each proton pulls water molecules toward the cathode) and by back-diffusion along water-content gradients, while vapor moves through the gas diffusion layers (GDLs, the porous carbon layers that distribute reactant gases) and can condense to liquid in the cathode flow field. In compact water-management models all of these mechanisms are lumped into the net water transfer coefficient α\alpha: the net number of water molecules transferred from anode to cathode per proton conducted through the membrane. The classical closures of Springer, Zawodzinski, and Gottesfeld (1991) relate membrane water content to vapor activity and proton conductivity, so once α\alpha and the gas compositions are known, the through-plane water-content profile and the membrane proton resistance follow from a simple steady balance. Because the membrane's alternating-current response at high frequency is dominated by proton conduction, the experimentally accessible high-frequency resistance (HFR) serves as a proxy for membrane hydration. Hong, Xu, Li, and Ouyang (2017) assembled these ingredients into steady models for cells of large active area (automotive scale), where spatial nonuniformity and downstream cathode flooding matter: a one-dimensional model for the regime without cathode liquid water, and two-zone models (counter-flow and co-flow) that split the active area into an upstream electrochemically active zone of fraction β\beta and a downstream flooded zone that is electrochemically suppressed and characterized by a net water flux per area N0N_0 returning water toward the anode, with α1\alpha_1 the upstream transfer coefficient. Their simulations showed that positive α\alpha can dry the anode-side membrane even at high anode inlet humidity and raise proton resistance more than comparable changes in β\beta, that counter-flow operation mitigates drying under flooding, and that the cathode no-flooding operating window is narrow. The models, however, take α\alpha — and in the flooded regime α1\alpha_1, N0N_0, β\beta — as input parameters: the exact relation between α\alpha and the operating conditions is not known a priori, the two-zone parameters cannot all be uniquely determined from the observable variables (specified inlets, measured outlets, and a single measured high-frequency resistance) without additional measurements or constitutive relations, and the downstream flooded zone is treated only through an effective mass balance rather than resolved two-phase physics in the GDL. For vehicular fuel cell systems, where self-humidification and purge strategies require knowing whether net water moves toward or away from the anode, an a priori usable α\alpha relation and an identifiable, experimentally validated model are the prerequisites for predictive water management.

Problem Statement

For PEM fuel cells of large active area, as used in automotive stacks, determine quantitatively how the net water transfer coefficient α\alpha — the net number of water molecules transferred from anode to cathode per proton conducted through the membrane — depends on measurable operating variables: inlet relative humidities, reactant excess (stoichiometric) ratios, inlet pressures, temperature, current density, and gas-diffusion-layer properties, so that α\alpha can be predicted a priori at a given operating point rather than fitted after the fact. Extend this determination to the downstream-flooded regime of the two-zone models, where the upstream transfer coefficient α1\alpha_1, the downstream net water flux N0N_0 (which encodes the unresolved coupling of cathode flooding to GDL two-phase transport and microstructure), and the fraction β\beta of the upstream electrochemically active zone must likewise be determined. Validate the steady one-dimensional and two-zone model predictions (outlet compositions, membrane proton resistance, and the operating window avoiding cathode liquid-water formation) against experiments on large-area cells and stacks, or, where no such experiments are available, by specifying and analyzing the validation protocol they would require. These three deliverables — the a priori relation for α\alpha, the determination of the two-zone parameters α1\alpha_1, N0N_0, and β\beta, and the validation of the model predictions — are jointly required, so that no one of them alone resolves the problem: a proposed relation for α\alpha is a solution only together with the two-zone parameter determination and the validation. The validation deliverable is met by analysis rather than by new experiments: it requires confronting the model predictions for outlet compositions, membrane proton resistance, and the onset of cathode liquid-water formation with the published water-transport and liquid-water measurements that bear on them, and fixing the observables to be compared, the operating envelope, and the acceptance criteria of the coordinated large-area-cell and stack experiments that would complete the validation.

References

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