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Abstract
Common for tree-shaped, space-filling flow-field plates in polymer electrolyte fuel cells is their ability to distribute reactants uniformly across the membrane area, thereby avoiding excess concentration polarization or entropy production at the electrodes. Such a flow field, as predicted by Murray's law for circular tubes, was recently shown experimentally to give a better polarization curve than serpentine or parallel flow fields. In this theoretical work, we document that a tree-shaped flow-field, composed of rectangular channels with T-shaped junctions, has a smaller entropy production than the one based on Murray's law. The width w0 of the inlet channel and the width scaling parameter, a, of the tree-shaped flow-field channels were varied, and the resulting Peclet number at the channel outlets was computed. We show, using 3D hydrodynamic calculations as a reference, that pressure drops and channel flows can be accounted for within a few percents by a quasi-1D model, for most of the investigated geometries. Overall, the model gives lower energy dissipation than Murray's law. The results provide new tools and open up new possibilities for flow-field designs characterized by uniform fuel delivery in fuel cells and other catalytic systems.
Highlights
PaperMurray[15] used a volume-filling condition as a constraint for flow in tree-shaped structures, and obtained as an outcome of the optimization his famous scaling law, saying that the diameters of the branches from one generation to the were scaling as eqn (1) shows: Xn d03 1⁄4 dj[3 ] (1)j1⁄41 where d0 is the diameter of the parent branch, and dj are the diameters of the n daughter branches belonging to the generation level.Eqn (1) characterises the fluid delivery system for which the total entropy production of the flow-field pattern by viscous dissipation is minimum, given the total volume available to flow.[15]
We studied the impact of the geometry and scaling properties on the total entropy production (TEP) (eqn (9)) and total specific entropy production (TSEP) (eqn (12)) of the flow-field pattern to answer the question: is Murray’s law the most efficient way to scale the pattern in terms of entropy production?
The temperature was set at 353 K, a common temperature in fuel cell experiments
Summary
Eqn (1) characterises the fluid delivery system for which the total entropy production of the flow-field pattern by viscous dissipation is minimum, given the total volume available to flow.[15] An optimization problem with minimum total volume at a given entropy production, has, the exact same solution Both formulations are beneficial to use in flow-field plate design. Minimum total volume at a constant channel depth means maximum gas–land contact area and, smaller total electric resistance of current collectors (smaller Ohmic losses). In this sense, it is logical to use constant volume as a constraint in the optimization problem
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