Entropy generation minimization as a design tool. Part 1: Analysis of different configurations of branched and non-branched laminar isothermal flow through a circular pipe

The paper presents three examples of a solution of a simple multi-variable optimization problem: the "optimal configuration" of a branch of a pipe of circular cross-section with a given initial radius r0 and delivering a given mass flow rate m0. Three cases, two presented in previous papers and a novel one, are used to illustrate two theses: first, that for a given design "task", the configurations (shapes) displaying the minimal entropy generation are compatible with the shapes observed in nature; second, that an EGM analysis not only leads to the identification of a thermodynamically optimal solution, but offers substantial additional insight into the flow characteristics even in simple -but realistic- cases as the ones discussed here, for which an analytical solution to the Navier Stokes equations exists. The entropy generation rate is due-in all three examples- only to viscous flow effects within the tubes, and several simplifying assumptions are made to reduce the problem to a multi-variable optimization in 2 (for the tube with wall suction) or 3 (for the branchings) independent variables: the aspect ratio of the domain served by the flow, the diameter ratio of the primary and secondary branches, and the length of the secondary branch (the location of both the "source" of the fluid and the "sink", i.e. the place of desired delivery of the fluid, being a datum). It is shown that the solution is strongly dependent both on the aspect ratio and on the diameter ratio, and in the case of wall suction, to the wall porosity. The study is divided in two parts: the analysis presented in this first paper is useful from a theoretical point of view, because it sheds some light on the phenomenology of the configurations studied here. The final purpose is twofold: the a priori identification of more efficient geometries for the channels of heat exchangers and flow devices through a preliminary EGM analysis, and a better understanding of the teleology of some of the structures observed in nature. The present study and its conclusions are still preliminary, but since the procedure can be easily "falsified", and all numerical experiments on more complex flow geometries to date do not disprove the present findings, it is indeed a topic that warrants further investigation.