Topology optimization of a no-moving-part valve incorporating Pareto frontier exploration

No-moving-part (NMP) valves, such as Tesla valves, are engineered fluid channels whose flow resistance depends on the flow direction. They have no moving parts and do not deform, but rely on inertial forces of the fluid to preferentially allow flow in one direction while strongly inhibiting flow in the reverse direction. NMP valves have significant advantages over active valves in terms of their reliability and easy manufacturability. Several previous studies have explored optimum designs of NMP valves, and the most widely used indicator of NMP valve performance is diodicity, defined as the ratio of the pressure drop of reverse flow to that of the forward flow. However, higher diodicity does not necessarily imply a lower pressure drop for the forward flow, and if this pressure drop is too high, significant pumping power is required, which makes the NMP valve inefficient for use in pumping applications. Therefore, for the design NMP valves, treating the forward and reverse flow pressure drops independently in a multiobjective formulation is preferable to optimization of the diodicity alone. In this paper, we propose a bi-objective topology optimization method for an optimum design of an NMP valve. One objective function is to minimize the pressure drop in the forward flow, and the other is to maximize the pressure drop in the reverse flow. A numerical example is provided to illustrate the effectiveness of the proposed method.