Turbulence effects in the topology optimization of compressible subsonic flow

Turbulence significantly influences fluid flow topology optimization, and this has already been verified under the incompressible flow regime. However, the same cannot be said about the compressible flow regime, in which the density field now affects and couples all of the fluid flow and turbulence equations and makes obtaining the adjoint model, which is necessary for topology optimization, extremely difficult. Up to now, the turbulence phenomenon has still not been considered in compressible flow topology optimization, which is what is being proposed and analyzed here. Rather than being based in the Reynolds-Averaged Navier-Stokes (RANS) equations which are defined only for incompressible flow, the equations are now based on the Favre-Averaged Navier-Stokes (FANS) equations, which are the counterpart of the RANS equations for compressible flow and feature different dependencies and terms. The compressible turbulence model being considered is the compressible version of the Spalart-Allmaras model, which differs from the usual Spalart-Allmaras model, since now there are some new spatially varying density and specific heat terms that depend on the primal variables and that act over some of the turbulence terms of the overall model. The adjoint equations are obtained by using an automatic differentiation scheme through a coupled software platform. The optimization algorithm is IPOPT, and some examples are presented to show the effect of turbulence in the compressible flow topology optimization. This paper highlights the impact and importance of including turbulence effects on topology optimization of compressible flow. The study proposes a novel approach based on Favre-Averaged Navier-Stokes equations and the compressible version of the Spalart-Allmaras model and solves first the compressible turbulent adjoint model by coupling dolphin adjoint from FEniCS and OpenFOAM software. Examples demonstrate the effects of turbulence on compressible flow and analyze industrial cases such as pipes, diffusers and mixers chambers where non-intuitive and efficient designs are presented. image