Topology optimization for transient turbulent compressible flow using an equal-order discontinuous Galerkin formulation and Runge-Kutta methods

Abstract

This work is inserted in the project "Design of smart labyrinth seals to reduce GHG emissions in pneumatic machines (compressors and turbines)", which is being developed in the Research Centre for Greenhouse Gas Innovation (RCGI), under FAPESP grant 2014/50279-4. One important source of GHG (greenhouse gases) emission is turbomachine leakage, which is directly related to sealing. In particular, labyrinth seals are noncontact seals that are widely used in the industry. When considering higher-speed rotational motions and higher operating pressures, which means higher effects of swirling motion, turbulence and compressibility, it becomes increasingly hard to restrict the leakage flow, and also becomes a challenge for the simulation and the topology optimization formulation. Also, transient effects may be present in the fluid flow dynamics, which always happens when there are rotating and stationary parts, adding to the complexity. Furthermore, from being a complex problem, it is important to make it efficient. Thus, this proposal aims to initially investigate whether an equal-order Discontinuous Galerkin formulation would be more interesting for the finite element model for turbulent compressible flow in the FEniCS TopOpt Foam framework (ALONSO et al., 2021), which uses OpenFOAM® for the efficient fluid flow simulation and FEniCS/dolfin-adjoint for the efficient adjoint model. Note that this would make the connection between OpenFOAM® and FEniCS more efficient and less approximated. Next, it is proposed to consider transient turbulent compressible flow through stable Runge-Kutta methods, by extending FEniCS TopOpt Foam, which currently only works for steady state flow. Finally, the numerical implementation should also include adding compatibility for FEniCS TopOpt Foam to use Firedrake as well, rather than only FEniCS, because using Firedrake should enable more extensibility and flexibility for the topology optimization framework. (AU)