Effects of flow instabilities on the linear analysis of turbomachinery aeroelasticity

The linear analysis of turbomachinery aeroelasticity is based on the linearization of the unsteady How equations around the mean flow field, which can be determined by a nonlinear steady solver. The unsteady periodic flow can be decomposed into a sum of harmonies, each of which can be computed independently by solving a set of linearized equations. The analysis considers just one particular frequency of unsteadiness at a time, and the objective is to compute a complex How solution that represents the amplitude and phase of the unsteady How. The solution procedure of both the nonlinear steady and the linear harmonic Euler/Navier-Stokes solvers of the HYDRA suite of codes consists of a preconditioned fixed-point iteration. The numerical instabilities encountered while solving the linear harmonic equations for some turbomachinery test cases are documented, their physical origin highlighted, and the implementation of a GMRES algorithm aiming at the stabilization of the linear code summarized. Presented results include the flutter analysis of a two-dimensional turbine section and a civil engine fan