Vascularization with trees that alternate with upside-down trees

This article describes the generation of dendritic flow architectures that provide maximum side-to-side flow access, across a vascularized body. The flow architecture consists of trees that alternate with upside-down trees (a,b,a,b,…). If in tree “a” the flow is from root to canopy, in tree “b” the flow is from canopy to root. This means that the flow proceeds in the same direction through all the trees, i.e., the flow is oriented side-to-side, or line-to-line. The channel cross sections are rectangular, and they all have the same depth. The article shows under what conditions the tree vascularization offers greater flow access than parallel single-scale channels oriented perpendicularly to the two parallel lines. The analytical part of the work is based on the assumption of fully developed laminar flow in every channel. The numerical part consists of simulations of three-dimensional laminar flow through the entire tree architecture and its many bifurcations. It is shown that tree vascularization is more attractive than parallel channels when the number of bifurcation levels increases, the global porosity of the vascularized body decreases, and the global svelteness (Sv) of the flow architecture increases. The nonuniformity (maldistribution) of flow rates through ramifications of the same rank becomes nonnegligible when the pressure drop number (Be) exceeds 109. The optimal step in the sizes of cross-sectional areas from one channel to the channel of the next rank is closely approximated by 22∕3 even when the cross section is not square or round. The agreement between analysis and numerical simulation and optimization is good.