Numerical study of Newtonian fluid in tree-shaped structures

Abstract

We address the effect of the network size-limiting constraints on the optimal design. The optimal design of a symmetrical dichotomous tree structure with several branching levels for laminar flow of a Newtonian fluid is studied numerically. For optimal flow design to emerge, it is necessary to include size constraints in the study. In several studies, only the volume occupied by the network is preferred [5,7-11]. Here, the volume of each branching level is fixed. Among other results, we showed that the network designed according to the Hess-Murray law does not represent the design with minimum resistance, but the network built on this law is the one with the most uniform resistances at the different levels of bifurcation. Another outcome of our study is that freedom inside a fixed size flow system is needed for preventing nonoptimal designs from appearing, which corroborates the constructal thinking of ”freedom is good for design.”