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Article

A Computationally Efficient Pseudo-2D PEM Fuel Cell Model for Studying Humidity Distribution Without External Humidification: The Role of Anode Recirculation

1
Laboratoire de Recherche en Hydrodynamique, Énergétique et Environnement Atmosphérique (LHEEA), Centre National de la Recherche Scientifique (CNRS), Ecole Centrale Nantes, Nantes Université, UMR 6598, F-44000 Nantes, France
2
Laboratoire d’Ingénierie des Fluides et des Systèmes Energétiques (LIFSE), Arts et Metiers Institute of Technology, Conservatoire National des Arts et Métiers (CNAM), F-75013 Paris, France
*
Author to whom correspondence should be addressed.
Machines 2026, 14(9), 1067; https://doi.org/10.3390/machines14091067 (registering DOI)
Submission received: 26 July 2026 / Revised: 12 September 2026 / Accepted: 15 September 2026 / Published: 17 September 2026
(This article belongs to the Topic Mobility Engineering and Sustainability)

Abstract

To reduce greenhouse gas emissions, fuel cell powertrains represent a promising alternative for heavy-duty transport. Such demanding applications require an extended operational lifespan, which calls for models able to accurately map internal states as a function of system architecture and control strategy. This work presents a pseudo-2D macro-homogeneous proton exchange membrane fuel cell model, discretized along the flow channels, in which the various transport phenomena are resolved between layers but not within their thickness. This choice reflects the model’s purpose: integration into complete system models to support system architecture studies, which requires a suitable trade-off between computation time and representativeness of system-imposed operating conditions. Kulikovsky’s analytical approximation is used to compute the voltage losses in the catalyst layer, preserving an accuracy close to a model with a fully discretized catalyst layer thickness. The model is integrated into a system featuring anode recirculation and no cathode humidification to study the sensitivity of humidity distribution to operating parameters. Simulations show that the anode recirculation rate and the temperature difference between inlet and outlet are the two main operating conditions governing spatial humidity distribution, while coolant inlet temperature, pressure, and cathode stoichiometry predominantly affect the absolute humidity within the stack.
Keywords: PEM fuel cell; model; anode recirculation; pseudo-two-dimensional model; humidity distribution; system architecture; automotive; hydrogen; OpenModelica PEM fuel cell; model; anode recirculation; pseudo-two-dimensional model; humidity distribution; system architecture; automotive; hydrogen; OpenModelica

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MDPI and ACS Style

Labeyrie, N.; Salameh, G.; Chalet, D.; Deligant, M. A Computationally Efficient Pseudo-2D PEM Fuel Cell Model for Studying Humidity Distribution Without External Humidification: The Role of Anode Recirculation. Machines 2026, 14, 1067. https://doi.org/10.3390/machines14091067

AMA Style

Labeyrie N, Salameh G, Chalet D, Deligant M. A Computationally Efficient Pseudo-2D PEM Fuel Cell Model for Studying Humidity Distribution Without External Humidification: The Role of Anode Recirculation. Machines. 2026; 14(9):1067. https://doi.org/10.3390/machines14091067

Chicago/Turabian Style

Labeyrie, Noé, Georges Salameh, David Chalet, and Michael Deligant. 2026. "A Computationally Efficient Pseudo-2D PEM Fuel Cell Model for Studying Humidity Distribution Without External Humidification: The Role of Anode Recirculation" Machines 14, no. 9: 1067. https://doi.org/10.3390/machines14091067

APA Style

Labeyrie, N., Salameh, G., Chalet, D., & Deligant, M. (2026). A Computationally Efficient Pseudo-2D PEM Fuel Cell Model for Studying Humidity Distribution Without External Humidification: The Role of Anode Recirculation. Machines, 14(9), 1067. https://doi.org/10.3390/machines14091067

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