Multiscale optimization of flow distribution by constructal approach

International audienceConstructal approach is a recent concept allowing to generate and optimize multi-scale structures, in particular, branching structures, connecting a microscopic world to a macroscopic one, from an engineer's point of view. Branching morphologies are found in many types of natural phenomena, and may be associated to some kind of optimization, expressing the evolutionary adaptation of natural systems to their environment. In a sense, the constructal approach tries to imitate this morphogenesis while short-cutting the trial-and-error of nature. The basic ideas underlying the constructal concept and methodology are illustrated here by the examples of fluid distribution to a multi-channel reactor, and of the design of a porous material and system for gas adsorption and storage. In usual constructal theory, a tree branching is postulated for the channels or flow-paths or conductors, usually a dichotomic tree (every branch is divided into two “daughters”). The objective function of the optimization is built from the resistances to mass or heat transport, expressed here as “characteristic transport times”, and the geometric result is expressed as a shape factor of a domain. The optimized shape expresses the compromise between the mass or heat transport characteristics at adjacent scales. Under suitable assumptions, simple analytical scaling laws are found, which relate the geometric and transport properties of different scales. Some challenging geometric problems may arise when applying the constructal approach to practical situations where strong geometric constraints exist. The search for analytical solutions imposes simplifying assumptions which may be at fault, calling for less constraining approaches, for example making only weak assumptions on the branching structure. Some of these challenges are brought forward along this text