Tree-shaped flow structures designed by minimizing path lengths

摘要: Abstract This paper outlines a direct route to the construction of effective tree-shaped flow structures. Dendritic structures dominate design natural and engineered systems, especially in thermal fluid systems. The starting point is optimization shape each elemental area or volume, such that length path housed by element minimized. Proceeding toward larger more complex – from elements, first constructs, second etc. develops between one straight line, plane, circle its center, many points distributed uniformly over an area. In latter, method applied configuration with laminar fully developed flow. constructions reveal several features are supported empirical observations flows: asymmetry, rate imbalance, pairing bifurcation, angles branches, Y-shaped constructs lie plane. It shown these basic necessary because “packing”, i.e., assembling optimized elements into fixed space, filling space completely. For point, best regular hexagon. emergence string-shaped links connect two features, which also required packing. Strings cover some inner zones tree network, particularly large trees. Dichotomous structure, peripheral canopy. practical importance simplified discussed.