Effects of flow instabilities on the linear analysis of turbomachinery aeroelasticity - Campobasso, MS; Giles, M (2003)
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.