Three-dimensional multi-scale fluid distributor assembly minimizing total viscous dissipation

In this paper, a novel multi-scale transport network geometry has been addressed by means of constructal theory. The channel dimensions are given and justified with an engineering criterion into the design itself. The first stage of this work consists of assembly optimization, which is formulated as follows: find the distribution of channel radii and angle that minimizes total viscous dissipation (or pumping power, pressure drop) under the constraints of fixed total volume of channels and tube material consumed. Analytical resolutions of the problem of optimal channel size distribution for tree-like networks used as flow distributors are obtained. In the subsequent stages, a large number of flow configurations are constructed based on the optimal channel size. The resulting structure is an optimized multi-scale flow distributor. Furthermore, for such configuration, the equality of pressure drops ensuring flow rate uniformity at the outlet ports of the distributor is demonstrated theoretically. Finally, CFD simulations are employed to investigate fully developed smooth turbulent flow on different branch junctions. Numerical results are found to be in good agreement with predicted analytical results and support the relationship between the pressure drop and the liquid flow rate at the inlet port of the constructal liquid distributor.