Development of tree-shaped flows by adding new users to existing networks of hot water pipes

This paper describes the optimization of a tree-shaped system of insulated pipes for the distribution of a stream of hot water over an area. The area is covered uniformly by users who must receive the same flow rate of hot water. The network of pipes is developed in steps. Each step consists of attaching to an existing network an extension (one new user) that is placed in the position that maximizes the temperature of the water received by the new user. The network grows `one-by-one', i.e., by one new user at a time. Networks with up to 16 users are optimized in this manner, and their geometric features and thermo-fluid performance are documented. These one-by-one trees of hot water flows are compared with corresponding `constructal' trees that are obtained in steps of pairing (doubling), i.e., connecting together two identical area constructs of the same size. It is shown that although the constructal trees perform the best (uniform water delivery at the highest temperature), the one-by-one trees approach the same level of performance as they become more complex. It is also shown that the geometry of the insulated tree structure is relatively insensitive to how the insulation is distributed over all the pipes. The thermal performance of the structure is relatively insensitive to how finely the distribution of pipe sizes and insulation radii is optimized.