A novel ordered-path criterion based topology optimization framework for filtration channel design

To ensure the functional stability and structural safety of the increasingly common flow channel structures in engineering applications, the issue of how to achieve effective filtration of random particles through channel design has received much attention. However, directly applying local projection constraint methods, widely used in solid mechanics, poses significant challenges due to fluid dynamics complexities. Therefore, we present a topology optimization framework for flow channels achieving precision filtration with minimal hydrodynamic penalty. In this study, an omnidirectional maximum length scale control method is proposed for density-based fluid topology optimization based on an ordered-path criterion. The solid-phase impurities are abstracted as geometric projections for local search to evaluate the flow path connectivity where multiple directions are taken into consideration. A computational method based on morphological operations is applied to simplify the local search process. Additionally, an ordered-path criterion is established to propagate geometric constraint along entire flow paths. This criterion involves calculating the sequence in which the fluid flows through the design elements, and a min-approximation function is employed to govern constraint relaxation intensity, enabling modulation of both blocking structure placement and flow channel complexity. Validated through EDEM-COMSOL co-simulations and industrial benchmarks, the method maintains radius-insensitive performance and resolves the fundamental trade-off between geometric control and flow efficiency in closed-loop systems.