New insights into creeping fluid flow through dendritic networks: A constructal view

Abstract

Flow networks with dendritic tube organization are common in natural systems. Although the Hess-Murray law has been extensively reported in the literature, there have also been reports of systems that deviate from this law. Using 3D dendritic flow networks of tubes, this study compares designs with various homothety reduction factor for diameters and lengths of tubes. The geometric constraint that is applied to these networks is equal tube volume at each branching level. The assessment is based on the flow resistance of networks calculated based on the Computational Fluid Dynamics (CFD) results. This study shows, among other things, that the performance of dendritic designs is highly dependent on the geometric features such as the svelteness of the network, and on tube alignment at different levels of bifurcation. It is also worth mentioning that flow asymmetry can develop in the dendritic networks that are symmetrical in terms of design. These findings should be considered while designing networks for engineering systems.