Periodic adjoints and anisotropic mesh adaptation in rotating frame for high-fidelity RANS turbomachinery applications

Highlights: • Anisotropic mesh adaptation is applied successfully to turbulent flows in turbomachinery, it becomes a reality. • High-fidelity turbulent flow predictions can be obtained with unstructured meshes composed only of tetrahedra. • Mesh-converged solutions are achieved guaranteeing that the numerical solution is independent of the mesh. • The solution-adaptive process automatizes the mesh generation stage ; the human disappears from the loop. • These high-fidelity simulations have helped to understand how the stall occurs on the transonic NASA Rotor 37. The scope of this paper is to demonstrate the viability and efficiency of metric-based unstructured anisotropic mesh adaptation techniques to turbomachinery applications. The main difficulty in turbomachinery is the periodicity of the domain that must be taken into account in the mesh-adaptive solution process. The periodicity is strongly enforced in the flow solver using ghost entities to minimize the impact on the source code. For the mesh adaptation, the local remeshing is done in two steps. First, the inner domain is remeshed with frozen periodic frontiers, and, second, the periodic surfaces are remeshed after moving geometric entities from one side of the domain to the other. One of the main goal of this work is to demonstrate that mesh-independent certified numerical solutions can be obtained thanks to anisotropic mesh adaptation and that it is possible to run high-fidelity CFD on unstructured adapted meshes composed only of tetrahedra. This paper demonstrates how mesh adaptation, thanks to its automation, is able to generate meshes that are extremely difficult to envision and almost impossible to generate manually, leading to highly accurate numerical solutions. This study considers feature-based error estimate based on the standard multi-scale $L^p$ interpolation error estimate and goal-oriented error estimate using an adjoint state to control the error on turbomachinery output functionals. A description of the flow solver and the adjoint solver is given in this work, as they are very different from what is encountered in the turbomachinery community. We also present all the specific modifications that have been introduced in the adaptive process to deal with periodic simulations used for turbomachinery applications. The periodic mesh adaptation strategy is then tested and validated on the LS89 high pressure axial turbine vane and the NASA Rotor 37 test cases.