Constructal Design of a Porous Structure for Gas Transport from one Opening to a Surface

Abstract

In this paper we address the general problem of finding the optimal flow structure for gas transport from opening to surface. In Nature, lungs are an example of such optimal structure while porous electrode of fuel cells are among the many examples that can be encountered in engineered systems. We pursued this analysis in the framework of Bejan’s Constructal Theory that is a simple and powerful tool for optimising flow trees. Two limiting possibilities were envisaged for accomplishing the purpose of gas transport from opening to surface: (I) a duct system that ends with an alveolar volume from which gas diffuses onto the surface or (II) a unique volume in which the incoming gas reaches the surface only by diffusion. We focused on the first one as we showed that the second was clearly noncompetitive. In this way, for prescribed surface area A, and under the constraints of total length of the gas pathway L, and volume allocated to the system V, we calculated the overall flow resistance of a tree composed of ducts with alveoli at the end. We found that the duct flow resistance increases with the branching level of the tree while the diffusive resistance decreases, therefore existing a point of minimal resistance. An optimal branching level exists for every non-dimensional number AL/V. In addition, was found a relationship between the number AL/V and the length defined by the ration of the square of the diameter of the first duct and its length, which is a characteristic of the flow tree. We propose to apply these results to the design of porous electrodes, which are components that are crucial to the performance of fuel cells.