A harmonic balance solver for the aeroelastic analysis of turbomachinery components on unstructured grids

The harmonic balance method has proven to be an efficient tool for the study of aeroelastic phenomena associated with blades in turbomachinery components. In the turbomachinery industry it is used, for example, to predict the flutter susceptibility of blades using structured meshes. For the analysis of more complex geometries, like cavities or labyrinth seals, unstructured grids are easier to create than structured ones to accurately model geometric details of these components. With this application in mind, specifically the flutter analysis of labyrinth seals, an existing harmonic balance solver for the unsteady Reynolds averaged Navier-Stokes equations on structured grids has been extended to work efficiently on unstructured grids. Although the harmonic balance algorithm itself is agnostic to the spatial discretization method, as it is only related to the discretization in time, some adaptations are necessary for an efficient implementation. To verify the extensions for unstructured grids, the harmonic balance solver is applied to the flutter analysis of a NACA airfoil exhibiting an oscillating shock-induced separation region. To demonstrate the ability to handle unstructured mixed-element grids, a flutter analysis of a generic labyrinth seal test case on an unstructured grid is performed.