Multiobjective Optimization of Pin-Type Flow Channels Using a Reinterpretation of Murray’s Law

Abstract

Biomimetics has been used to improve performance in several fields of engineering. For flow fields, Murray’s Law has been used to explore branching of channels that carry reactants and products. The applicability of Murray’s Law to flow fields was examined here. The pin-type flow field was used to explore variations and conflicting performance objectives: pressure drop, manufacturability, standard deviation of flow velocity, and channel area. NSGA-II was used to solve a multiobjective optimization problem. Two designs, 3 × 3 and 11 × 11, were analyzed. Results that were similar to previous single-objective studies were obtained, confirming the efficacy of Murray’s Law. Computational fluid dynamics simulations were used to compare optimized and unoptimized designs. The maximum velocity for the 3 × 3 and 11 × 11 cases was lower when Murray’s Law was followed, indicating that it effectively slowed down the flow. Similarly, the flow was much more uniform: the standard deviation of flow velocity in the channels was 94% and 57% lower, respectively, for both cases, compared to the unoptimized designed. Finally, a method to select one optimal solution from a front of non-dominated solutions, the nearest point method, was demonstrated.