Thermodynamic optimization of geometry: T- and Y-shaped constructs of fluid streams

This paper presents a series of examples in which the global performance of flow systems is optimized subject to global constraints. The flow systems are assemblies of ducts, channels and streams shaped as Ts, Ys and crosses. In pure fluid flow, thermodynamic performance maximization is achieved by minimizing the overall flow resistance encountered over a finite-size territory. In the case of more complex objectives such as the distribution of a stream of hot water over a territory, performance maximization requires the minimization of flow resistance and the leakage of heat from the entire network. Taken together, these examples show that the geometric structure of the flow system springs out of the principle of global performance maximization subject to global constraints. Every geometric detail of the optimized flow structure is deduced from principle. The optimized structure (design, architecture) is robust with respect to changes in some of the parameters of the system. The paper shows how the geometric optimization method can be extended to other fields, e.g., urban hydraulics and, in the future, exergy analysis and thermoeconomics.