Design and scaling laws of ramified fluid distributors by the constructal approach
Résumé
The present paper contributes to theoretical advances in the conception, modelling and design of multi-scale fluidic elements, namely fluid distributors. The function of such fluid distributors is to deliver a controlled amount or rate of fluid to an array of distributing ports, in order for example to feed uniformly the channels of a multi-tubular heat exchanger, or of a catalytic monolith, or any other fluid-handling engineering apparatus. In recent years, distributors based on multi-scale channel networks, of fractal tree type, have been developed. The theoretical approach presented allows to design such distributors optimally, within certain constraints. The basis of the optimization is a compromise between “costs” related to pressure drop and viscous dissipation on one hand, and hold-up volume of the pore structure on the other hand. The calculations lead to geometric scaling laws, that is to relations between the dimensions of the channels at the different scales. Scaling relations are also established for different characteristic quantities, such as pressure drop, viscous dissipation power, volume fractions, wall surfaces, cost functions. An example of design procedure is given, and examples of distributors fabricated by stereolithography is shown.