Tree-shaped flow structures with local junction losses

This paper is a fundamental study of the effect of junction losses on the optimized geometry of tree-shaped flows. Several classes of flows are investigated systematically in a T-shaped construct with fixed internal and external size: laminar with non-negligible entrance and junction losses, and turbulent in tubes with smooth and rough walls. It is shown that in all cases junction losses have a sizeable effect on optimized geometry when Sv2 < 10, where the svelteness Sv is a global property of the entire flow system: Sv = external length scale/internal length scale. The relationship between the global Sv and the slenderness of individual channels is discussed. The study shows that, in general, the duct slenderness decreases as the tree architecture becomes finer and more complex. In conclusion, miniaturization pushes flow architectures not only toward the smaller, finer and more complex, but also toward the domain in which junction losses must be taken into account in the optimization of geometry.