Computational study of forced air-convection in open-cathode polymer electrolyte fuel cell stacks

doi:10.1016/j.jpowsour.2010.02.083

Journal of Power Sources

Volume 195, Issue 17, 1 September 2010, Pages 5550-5563

https://doi.org/10.1016/j.jpowsour.2010.02.083 Get rights and content

Abstract

A mathematical model for a polymer electrolyte fuel cell (PEFC) stack with an open-cathode manifold, where a fan provides the oxidant as well as cooling, is derived and studied. In short, the model considers two-phase flow and conservation of mass, momentum, species and energy in the ambient and PEFC stack, as well as conservation of charge and a phenomenological membrane and agglomerate model for the PEFC stack. The fan is resolved as an interfacial condition with a polynomial expression for the static pressure increase over the fan as a function of the fan velocity. The results suggest that there is strong correlation between fan power rating, the height of cathode flow-field and stack performance. Further, the placement of the fan – either in blowing or suction mode – does not give rise to a discernable difference in stack performance for the flow-field considered (metal mesh). Finally, it is noted that the model can be extended to incorporate other types of flow-fields and, most importantly, be employed for design and optimization of forced air-convection open-cathode PEFC stacks and adjacent fans.

Introduction

The operation of a polymer electrolyte fuel cell (PEFC) stack with an open-cathode manifold involves transport of both air to and from the ambient and fuel from storage or a reformer. The magnitude of the inlet flow and the type of device – fan, pump, compressor, and/or blower – that is employed to provide the flow depends on the size, power and operating conditions of the fuel cell stack. Broadly speaking, the flow rates for the anode and cathode require careful consideration of the flow rate: (i) a high flow rate provides a high stoichiometric oxidant or fuel supply, but may cause dehydration of the membrane, where the former is beneficial and the latter is detrimental to stack performance; (ii) a low flow rate may give rise to flooding or depletion of oxygen or fuel, resulting in a drop in stack performance. In addition, the flow rate has to be sufficiently large to prevent overheating of the stack if it is also to be used for cooling purposes.

Depending on the size of the PEFC stack, the air flow for the cathodes can be provided by either natural convection due to temperature and concentration differences between the stack and the ambient (PEFC stacks with a power rating $≲$ 100 W [1]) or by forced convection (stacks with a power rating of around 100–1000 W [1], [2]). If fans are chosen to provide the airflow, it is important to ensure that they not only provide an adequate air flow rate through the cathodes in the stack, but also require minimal power in order to reduce the parasitic load, a compatible voltage rating with the stack and, to a lesser extent, a high life expectancy and generate a minimum of audible noise. A typical PEFC stack with an open-cathode manifold and a fan is illustrated in Fig. 1, where the fan is placed at the front of the stack (blowing mode) as opposed to the exit of the stack (suction mode).

To date, various designs and operating conditions of PEFC stacks equipped with free-breathing or forced-convection open-cathode manifolds have been studied experimentally (see, for example [3], [4], [5], [6], [7], [8], [9], [10], [11]). While these experimental studies provide details and insight into overall stack behaviour, they cannot do so at a local level; that is to say, at any given point inside the stack. Mathematical modeling and numerical simulations, on the other hand, can resolve not only global behaviour, for example, in terms of polarization curves, but also local behaviour, provided the essential phenomena have been adequately captured in the model. Several computational studies have been carried out for PEFC stacks [12], [13], [14], [15], [16] and for single cells with the ambient included [17], [18], [19], [20], [21], [22], [23]. The latter studies focus on free-breathing PEFCs, where the supply of oxygen from the air and removal of water from the stack occurs by natural convection; none of these studies have considered an open-cathode manifold with one or several fans providing forced convection through the stack, where the fan is included in the model itself.

To extend the work on modeling and computational studies of open-cathode PEFC stacks, the aim of the work presented here is threefold: (i) to develop a coupled mathematical model for a PEFC stack, the ambient air, and the fan; (ii) to implement the mathematical model numerically with a one-domain approach, which is commonly used for single cell studies, see for example [24], [25], [26], [27], [28], [29], [30], [31]; (iii) to study the interaction between the stack and the fan in terms of placement, fan power and characteristic curves, as well as the size of the cathode flow-field, which can be expected to have a significant impact on the overall pressure drop and hence on the flow rate achieved by the fan.

The layout of the paper is as follows. First, the mathematical model is introduced. It is comprised of two-phase conservation of mass, momentum, species, charge and energy in a fuel cell stack, which is approximated by a repetitive unit cell with periodic boundary conditions. Here, the flow-fields in the anode and cathode are of a porous type (a metallic mesh) and are operating in a co-flow mode. The inherent electrochemistry is accounted for by an agglomerate model and a Butler–Volmer equation in the cathode and the anode catalyst layers, respectively; the membrane is treated with a phenomenological model. For the ambient, conservation of mass, momentum and energy is considered, whilst the fan is approximated with a parameter-adapted polynomial to represent the characteristic curve. Numerically, the mathematical model is then solved via a one-domain approach, that is, the governing equations are solved everywhere; it is therefore necessary to ‘suppress’ certain equations in domains where they should not be solved. Parameter studies for the system – fuel cell stack, ambient and fan – are then carried out. Finally, conclusions are drawn and extension of the work to include other types of flow-fields and an arbitrary number of fans are highlighted.

Section snippets

Mathematical formulation

The mathematical model comprises three components, viz., the fuel cell stack, the ambient, and the fan. The main transport phenomena and assumptions are summarized here, while the full set of equations, boundary and interface conditions, constitutive relations and submodels can be found in Appendix A Governing equations, Appendix B Boundary conditions, Appendix C Constitutive relations, Appendix D Phenomenological membrane model, Appendix E Electrochemistry and agglomerate model.

Numerics

The computational domains (see Fig. 2) were created and meshed in the commercial pre-processor software Gambit 2.3.16 [44]. After a mesh-independence test, the computational domain was resolved with $\sim$ 10⁵ elements: a fine structured mesh inside the PEFC stack and an increasingly coarser unstructured mesh in the ambient in order to reduce the computational cost.

The mathematical model for the stack, fan and ambient comprising 11 dependent variables – $p^{(g)}$ , $u^{(g)}$ , $v^{(g)}$ , $ω_{H_{2}}^{(g)}$ , $ω_{O_{2}}^{(g)}$ , $ω_{H_{2} O}^{(g)}$ , T, $ϕ^{(}$

Results and discussion

Simulations were carried out for typical conditions found in a PEFC with forced air-convection cooling; these base-case conditions together with the geometry and physical parameters are listed in Table 1. The electrochemical parameters were calibrated and validated with experimental polarization curves and local current density distributions obtained with a segmented PEFC equipped with a porous-type flow field [38], [45]; see [34] for more details. The representative computational unit cell for

Conclusions

A computational study of forced air-convection in a PEFC stack with an open-cathode manifold has been carried out, where the PEFC stack and ambient are resolved in detail, together with a simple model for the fan based on an interface condition. The computational cost is reduced by identifying a repetitive computational unit cell and by assuming an even flow from the fan, which allows for fast and efficient simulations of the interaction between the fan and the stack. It has also been

Acknowledgements

Financial support from the National University of Singapore (NUS) and the ASEAN University Network/South-East Asia Engineering Education Development-Network (AUN/SEED-Net) is gratefully acknowledged.

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