Evaluating the Aerodynamic Damping At Shock Wave Boundary Layer Interacting Flow Conditions With Harmonic Balance

The aerodynamic damping of a stator vane located in a rear stage of a high pressure compressor is evaluated at transonic flow conditions by numerical means. The results of a solution method based on temporal linearization around a steady RANS state are compared to results generated by relying on a state-of-the-art harmonic balance solver. It is found that the time-linearized method is not capable to reproduce the damping behavior in a sufficient manner for the majority of assessed nodal diameters. The limitations of the time-linearized method consisting of expansion around an imperfect steady RANS state, neglecting nonlinear contributions, and considering turbulence to be frozen at its steady-state are evaluated and quantified. Furthermore, the presence of unsteady content induced by shock wave boundary layer interaction can be identified by performing a full-annulus URANS simulation based on time-integration. For a limited range of nodal diameters, this shock boundary layer interaction locks in to the assessed flutter motion and affects the damping behavior substantially. It is demonstrated that the mechanism of the shock wave boundary layer interaction can be reproduced with harmonic balance in accordance with the time-integration method. Coupling the eigenmode of interest and the identified shock boundary layer interaction via the harmonic balance method allows us to predict the aerodynamic damping for the affected nodal diameters.