Fundamentals of tree-shaped networks of insulated pipes for hot water and exergy

This paper outlines recent thermodynamic optimization work on the geometric layout of schemes for distributing hot water and exergy over a large system. Constrained are the amount of insulation material, the volume of all the pipes, and the amount of pipe wall material. Unknown are the distribution of insulation over all the links of the network, and the configuration of the network itself. The main focus is on how the geometric configuration may be selected in the pursuit of maximized global performance, and how closely a non-optimal configuration performs to the highest level. Maximum global performance means minimum heat loss to the ambient, minimum pressure loss, and minimum exergy destruction. Three configurations are optimized: (a) an area covered by a coiled steam, where all the users are aligned on the same stream, (b) a sequence of tree-shaped flows on square areas in which each area construct is made up of four smaller area constructs, and (c) a sequence of tree-shaped flows where each area construct is made up of two smaller area constructs. It is shown that the tree-shaped designs (b), (c) outperform significantly the coiled stream design (a). The tree designs obtained by pairing (c) are better than the square tree constructs (b) and, in addition, they deliver water at the same temperature to all the users spread over the territory. The fundamental trade off between minimum heat loss and pressure drop, in the pursuit of minimum exergy destruction, pinpoints the optimal size of each duct and insulation shell.