Topology optimisation for rotor-stator fluid flow devices

Multi-component devices such as flow machines, heat exchangers, and electric motors present parts with different physical properties and operating in different states. Optimisation algorithms may improve the performance of these devices, and the simultaneous optimisation of a set of parts may harness the interaction of these parts to generate improved designs. Particularly, rotating flow devices such as pumps and turbines present rotating and stationary components. If a description of the fluid flow between the rotating and stationary parts is desired, it is necessary to model solid at different velocities. However, the standard topology optimisation formulation for fluid flow problems considers only a single stationary solid or a single rotating solid in a rotating reference frame. Thus, this work proposes a topology optimisation formulation capable of solving fluid flow problems with different solid velocities. The idea is to add mutually exclusive Darcy terms to the linear momentum equation. Each Darcy term models a different rotation and only one term may be active at each element. The method uses two discrete design variable fields. The moving limits of the optimisation algorithm are adjusted to handle the two discrete design variable fields, and extra constraints are added to ensure proper phase transitions. The algorithm is applied to two design problems: a Tesla pump and a labyrinth seal. The governing equations are solved by the Finite Element Method, and the optimisation is solved by an approach based on the Topology Optimisation of Binary Structures (TOBS) algorithm, with each linearized subproblem being solved through integer linear programming with a branch-and-bound algorithm.