Topology optimization design of labyrinth seal-type devices considering subsonic compressible turbulent flow conditions

In this work, a topology optimization model for designing devices that operate with multiple relative velocities considering turbulent compressible flows is proposed. The model consists of the Favre-averaged Navier-stokes equations in an axisymmetric domain coupled with a continuous boundary propagation model. The propagation is used to impose different solid behaviors based on which wall it is connected to, for example, solid material in contact with a rotating shaft will have a rotational velocity, while material encrusted in the support will have zero absolute velocity. The implementation is composed of a segregated solver with steps for the FANS equations, the $k-ϵ$ turbulent equations, and the propagation model. The sensitivity is obtained with automatic differentiation of the adjoint method and an internal point optimizer is used to update the design variable. A study case of a labyrinth seal is defined to illustrate the methodology by using three different objective functions, maximization of radial velocity, static pressure change rate, and vorticity. The results are designs for small-scale labyrinth seals in real operation conditions.