Abstract
This paper investigates the application of topology optimization to enhance the flow field of circular Proton Exchange Membrane Fuel Cells (PEMFCs) by considering a water management model. Given the high computational demands of such a method, the model is simplified to a two-dimensional form, focusing on the cathode flow field. A multi-objective function is used to simultaneously maximize power generation, and minimize both energy dissipation and average saturation. The impacts of each objective function are deeply analyzed in different scenarios. The addition of the average saturation in the objective is pivotal for mitigating water accumulation issues providing valuable insights into effective water management designs. Through this innovative approach, topology optimization emerges not only as a theoretical concept but also as a practical tool for enhancing the performance and water management of PEMFCs, paving the way for future advancements in fuel cell technology.
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Acknowledgements
We gratefully acknowledge the support of the RCGI - Research Centre for Greenhouse Gas Innovation, hosted by the University of São Paulo (USP) and sponsored by FAPESP - São Paulo Research Foundation (2014/50279-4 and 2020/15230-5) and Shell Brasil, and the strategic importance of the support given by ANP (Brazil’s National Oil, Natural Gas, and Biofuels Agency) through the R &D levy regulation. The authors also thank FAPESP under Grant Numbers 2020/01177-5, 2022/14475-0, 2014/22130-6, and 2023/10333-9. E.C.N. Silva is pleased to acknowledge the support by CNPq (National Council for Scientific and Technological Development) under Grant 302658/2018-1.
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F.R., L.F.N.S., and D.S.P. wrote the main manuscript text, implemented the software, and collected the results; F.R., L.F.N.S., and T.L. are responsible for the modeling and analysis of the results; F.R., L.F.N.S., J.M., and E.C.N.S. are responsible for the conceptualization and conclusions; All authors reviewed the manuscript.
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The implementation in this work considers the commercial software COMSOL. However, all state equations and algorithm are described in the text to be implemented in other environments. In order to reproduce the results, the following steps are needed: (1) Define a mesh; (2) Define the function spaces of the state variables; (3) Define the function spaces of the design variable (\(\gamma\)); (4) Define the boundary conditions; (5) Define the state equations (NS, Species, and Current Density); (6) Define the objective function; (7) Solve the state equations, which enables COMSOL to calculate the sensitivities; (8) Calculate the initial objective function value; (9) Start the optimization loop: − Solve the state equations for current \(\gamma\); − Calculate the current objective function value; − Solve the adjoint model; − Pass the sensitivity to the optimizer (GCMMA); − Update the design variable (\(\gamma\)): \(\bullet\) If the convergence criteria is met return; \(\bullet\) Else: restart the optimization loop;
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Appendix
Appendix
1.1 Mesh independence analysis
The volume constraint used in this work considers the overall volume as the element-weighted sum of the design variable, thus, the mesh refinement should not change the final topology. Additionally, the filtering scheme in topology optimization formulation (Helmholtz-like filter and hyperbolic tangent projection) contributes to the mesh independence solution. To investigate this visually, two different mesh sizes of \(50\times 50\) and \(100\times 100\) (radial \(\times\) angular elements) are depicted for the case Sc8 in Fig. 12. The topologies at every 200 iterations are shown to have a better comparison of the resolution effect on the optimization procedure.
In Fig. 12, it can be seen that the influence of the number of elements is not prevalent. The final topologies (Fig. 12e, j) are very similar with a small difference near the outlet, where the lower resolution case has a split channel. However, by comparing the objective function, the final values are almost equal (− 0.0747). For the sake of completeness, the partial values for each term composing the multi-objective function are shown in Table 4. The value for each term is also very similar at the final topology.
FEA resolution effect on the topology of Sc8 at every 200 iteration, first row: 50 \(\times\) 50 elements, second row: 100 \(\times\) 100 elements
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Razmara, F., Sá, L.F.N., Prado, D.S. et al. Topology optimization of radial flow field PEM fuel cells for enhancing water management. Struct Multidisc Optim 67, 68 (2024). https://doi.org/10.1007/s00158-024-03788-w
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DOI: https://doi.org/10.1007/s00158-024-03788-w