Abstract
A topology optimization approach is applied to the design of a compact fluid distribution device that achieves uniform flow distribution among parallel channels while minimizing the mean residence time under a pressure loss constraint. Such devices are widely used in applications including parallel microreactors, thermal management systems, and energy devices, where both compactness and precise flow control are required. The design problem is formulated using a density-based method in which the design variable represents the local void fraction of a fictitious porous medium. The governing equations are based on the incompressible Navier-Stokes equations with an additional Darcy-type resistance term. The objective function is defined as the spatially averaged design variable, corresponding to the minimization of the effective flow passage volume and thus the mean residence time. Constraints are imposed on both flow rate uniformity among parallel channels and the total pressure loss. A two-stage topology optimization strategy is proposed to obtain physically realizable geometries. The results show that the proposed strategy effectively removes non-functional regions while preserving flow uniformity, leading to compact designs. Furthermore, numerical investigations reveal that designs with fewer early-stage bifurcations tend to achieve smaller flow passage areas under identical pressure loss conditions. These findings demonstrate that topology optimization provides a rational and flexible framework for the systematic design of compact fluid distribution devices.