Boundary conditions in flutter simulations of subsonic, transonic and supersonic blade cascades

Abstract

Simulations of blade flutter are highly sensitive to undesired wave reflections at inlet and outlet boundaries. A careful treatment of boundary conditions is required to prevent the generation of perturbations. This study is motivated by the need to perform flutter analysis of low-pressure steam turbine blades, for which supersonic inflow conditions may occur in the near-tip region. The exact steady non-reflecting boundary condition (NRBC), the spectral NRBC and a simple isentropic boundary condition are implemented in a time-marching flow solver and applied to turbomachinery flutter simulations covering a wide range of operating conditions. For the first time, the spectral NRBC is applied to a blade flutter simulation with a supersonic inlet and its performance is analysed and compared with other boundary condition formulations. It is shown that an effective non-reflective treatment in the design of the boundary condition is essential for an accurate aeroelastic prediction at all operating conditions, including the subsonic flow regime. The limitation of the exact steady NRBC to spatial modes causes it to perform poorly in some unsteady flow simulations, whereas the spectral NRBC achieves a satisfactory suppression of undesired wave reflections in all investigated cases.