Topology optimization of labyrinth seals using interface identification techniques

Labyrinth seals are mechanical devices that reduce the leakage between moving components of rotating machines. They are crucial for determining the performance of these machines and essential for reducing greenhouse gas emissions. Therefore, mathematical optimization algorithms for labyrinth seals are of high interest. This work concerns the topology optimization of labyrinth seals, which is a challenging task because the optimizer must distribute solids at different velocities to properly model the flow in the cavity of the labyrinth seal. Also, the model must not allow the optimizer to close the fluid channel or to leave free-floating islands of solid elements in the final design. Therefore, the interface identification method based on a series of erosion-dilate projection filters is used to model the fluid channel as the interface between the rotor and stator, allowing the representation of different velocities and avoiding the channel closure. The virtual temperature method is employed as a connectivity constraint to avoid free-floating islands of solid material. Still, thin structural members appear in the optimized designs, so geometric constraints are used to impose the minimum length scale on rotor and stator components. The final topology optimization results are labyrinth seals with contorted channels constricted to the minimum allowed gap size (as expected for low Reynolds flows), showing the success of the proposed formulation. The staggered and stepped labyrinth seal configurations are optimized to show the generality of the method.