Fast flutter and forced response analyses using a cubic-B-spline-based time collocation method

Flutter and forced response, as two main branches of aeroelasticity, can lead to high-cycle fatigue failure of turbomachinery blades. Efficiently and accurately assessing aeroelastic performance of turbomachinery blades is essential in the routine design. In this work, the Time Collocation Method (TCM) which uses the cubic B-spline to approximate flow variables is first thoroughly studied and then combined with the moving grid technique to analyze aeroelastic flow fields. To showcase its advantage over the Harmonic Balance (HB) method which uses a truncated Fourier series to approximately represent flow variables, a matrix analysis of the one-dimensional advection equation is first performed. The results of stability analysis are verified by two test cases: the Durham linear oscillating turbine cascade and a two-blade-row transonic compressor. The vibration of the blade of the first case is driven by a motor while the excitation force of the second case comes from blade row interaction. The results show that the time collocation method has a faster convergence rate and is more stable than the harmonic balance method, especially for cases with a large maximum grid reduced frequency. More importantly, the time collocation method is capable of accurately predicting aeroelastic performance of turbomachinery blades.