Topology optimisation of transient turbulent compressible flow

Purpose The purpose of this paper is to present the first topology optimisation formulation for transient turbulent compressible flow modelled with the unsteady Favre-averaged Navier–Stokes equations. Design/methodology/approach The topology to be designed is incorporated in each of the momentum balance, the energy balance and the turbulence closure. The forward and adjoint equations are implemented with different discretisations: the forward model with a finite volume method and the adjoint model with a discontinuous Galerkin finite element scheme, since the former is very robust and the latter can be adjoined automatically. Once discretised, the topology optimisation problem is solved with an integer linear programming algorithm. The authors demonstrate the capability of the approach in the design of a U-bend, a pipe joint and a double pipe joint. Findings The formulation is developed and demonstrated through numerical examples, showcasing the developed approach. Originality/value No previous topology optimisation formulation was available for transient turbulent compressible flow modelled with the unsteady Favre-averaged Navier–Stokes equations.