Multi-phase model

Fig. 4. Sample history of a collisional multizone multi-phase model with stripping at...

Averaged Eulerian-Lagrangian Multi-Phase Models... 

The macroscopic multi-phase models resulting from the local averaging procedures must be supplemented with state equations, constitutive equations, boundary and initial conditions. The constitutive equations specify how the phases interact with themselves and with each other. The closure laws or constitutive laws can thus be divided into three types [16] Topological, constitutive and transfer laws, where the first type describes the spatial distribution of phase-specific quantities, the second type describes physical properties of the phases and the third type describes different interactions between the phases. 

The second objective for model applications is the test of complex chemical mechanisms used for multi-phase model applications related to chamber experiments. An established chemical code for interpretation of chamber studies that can be applied to all facilities increases the quality of the whole infi-astructure and offers new possibilities for solving open questions of interest for the European researchers community. 

Using as a basis the single-phase model presented in section 3, a multi-phase model has been developed that accounts for both the gas and liquid phase in the same computational domain and thus allows for the implementation of phase change inside the gas diffusion layers. The model includes the transport of liquid water within the porous electrodes as well as the transport of gaseous species, protons, energy, and water dissolved in the ion conducting polymer. 

Water transport across the membrane is also described by two physical mechanisms electro-osmotic drag and diffusion. The balance between the electro-osmotic drag of water from anode to cathode and back diffusion from cathode to anode yields the net water content through the membrane. The present multi-phase model is capable of identifying important parameters for the wetting behavior of the gas diffusion layers and can be used to identify conditions that might lead to the onset of pore plugging, which has a detrimental effect of the fuel cell performance. 

The assumptions made in this multi-phase model are basically identical to the ones stated in section 3. In order to implement the phase change of water, the following additional assumptions were made ... 

Results with and without phase change for the cell operates at nominal current density of 1.4 A/cm are discussed in this section. The selection of relatively high current density is due to illustrate the phase change effects, where it becomes clearly apparent between single and multi-phase model in the mass transport limited region. 

Figure 4.6. Oxygen molar fraction distribution in the cathode side predicted in single-phase model (upper) and multi-phase model (lower) at a nominal current density of 1.4 PJcvii. Bar chart shows the average oxygen molar fraction at the cathode CL.

The water vapor molar fraction distribution in the cell is shown in Figure 4.7. The molar water vapor fraction, however, remains almost constant throughout the gas diffusion layer in multi-phase model. In the absence of phase change, this is not being the case, since the nitrogen and water vapor fraction would increase as the oxygen fraction decreases. 

The variations of the cathode and anode diffusion overpotentials are shown in Figures 4.8 and 4.9 respectively. For both single and multi-phase models, the distribution patterns of diffusion overpotentials have similar profiles, but their magnitudes differ. 

It can be seen from the figures that, the diffusion overpotentials predicted in multi-phase model is quantitatively higher than that predicted in single-phase simulations, due to the presence of liquid water inside GDL. This water reduces the limiting current density in the cell by increasing the acciunulation of liquid water at the GDL, which decreases its permeability to reactant gas flow and lead to the onset of pore plugging by liquid water. 

Gurau, V. and Mann, J.A. (2009) A critical overview of computational fluid dynamics multi-phase models for proton exchange membrane fuel cells. SIAM J. Appl. Math., 70, 410-454. 

N. Zamel, X. Li, 2009. Non-isothermal, multi-phase modeling of PEM fuel cell cathode. International Journal of Energy Research. DOl 10.1002/er.l572. 

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