the geometry and meshing it, assigning governing equations and boundary conditions, to solving and postprocessing. As a result, we were able to build and solve a stack consisting of 400 single cells within 15 minutes and 2.3GB of RAM required, without any e¤ort and human errors made in implementation of the code. The low computa- tional cost coupled with the level of resolution (in terms of transport phenomena that are solved locally throughout the stack) opens up avenues for wide-ranging parameter studies, fully automated optimization of stacks and detailed system models.
Finally, the single-phase reduced model was successfully extended to include liquid water transport in a multi-phase counterpart. The model has been validated against three di¤erent sets of experimental data with good agreement achieved. The thermal e¤ect on operating condition has been analyzed and decoupled from the rest of governing equations.
11.2 Recommendations for future work
Based on the results obtained, some potential areas for further investigation related to PEMFC modeling are highlighted below.
1. Porous medium approach –The key advantage of the reduction method employed in this thesis is that the fuel cell equipped with a porous ‡ow …eld allows a re- duction from the three-dimensional model to two-dimensional counterpart. As a
…rst step to generalize this methodology to other types of ‡ow …elds, we have applied the porous medium approach to reduce the three-dimensional parallel- channel ‡ow …eld to a two-dimensional porous one. Practically, many other types of ‡ow …eld have been developed, e.g. serpentine, parallel serpentine, integrated, interdigitated ‡ow …elds, etc.[23]. The main purpose of the development of these designs is to enhance the mass transfer between the ‡ow …elds and gas di¤usion
194 11. Conclusions and Future Work
layers. However, modeling these ‡ow …eld in three-dimensional model results in a high computational cost; even for a single cell model, a multi-processor system and/or multi-core parallel computing system is required to handle the computation [53]. Hence, modeling a stack equipped such ‡ow …eld may be prohibitive. The aforementioned methodology can be extended to reduce such channel-type ‡ow
…eld in three dimensions to porous-type ‡ow …eld in two dimensions, providing an additional consideration of the corner e¤ects in such channel-type ‡ow …eld.
2. Multi-phase stack model –For the single-phase models, we have developed a stack consisting of arbitrary number of cells. The drawback of this model is that when the number of cells in the stack becomes large, e.g. more than 10 cells, with high perturbations of inlet conditions between cells, error in local solutions of charge and heat transport will occur, larger and larger as moving away from the central cell of the stack. To overcome this issue, a hybrid model –consisting of the conservation of energy and charge of electrons with the full set of equations and the remaining transport equations with the reduced counterpart –can be considered to capture the perturbations in a stack with large number of cells. The procedure can base on the two-phase single cell model developed in this thesis; a stack model can be developed with the aid of automated model generation.
3. Validation of liquid water – So far, we have provided a global validation based on the polarization curves of three experimental data. At the local level, we have validated the local current density local current densities measured with the segmented cell [79]. Although, in the multi-phase model, we have solved the liquid water in the ‡ow …elds, gas di¤usion layers, and catalyst layers, no validation of the local liquid water have been carried out in this thesis. This requires additional experimental information so that the multi-phase parameters, e.g. wetting angles
11.2. Recommendations for future work 195
and Leverett functions, can be calibrated. Then, the multi-phase model, which locally captures a liquid level of water, will be a useful aid in water management in fuel cell system.
4. Optimization – This is one of the main purposes that the research aims towards.
With the aid of the automatic code generator, we are able to carry out optimiza- tions. The operating conditions and design parameters can be the …rst target of the optimizing processes. Di¤erent optimization techniques such as direct search, ge- netic algorithm, simulated annealing and evolutionary strategy can be employed to identify the best possible operating conditions as well as design for PEMFC stack. This optimization process will play an essential role to bring the fuel cell technology to the energy market.
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