A Fast Influence Coefficient Method for Linearized Flutter and Forced-Response Analysis

Abstract

Flutter assessments of turbomachinery rotor designs are often based on linearized unsteady flow equations instead of nonlinear flow equations which are computationally more expensive. Typically, a flow model with only one flow passage is used to calculate the linear perturbation of the steady flow field due to the vibration of the blade. From this calculation the aerodynamic damping value for a particular nodal-diameter (ND) value is obtained. However, this traditional method can still be time-consuming if the entire aero-damping versus ND curve needs to be generated, as the linearized flow model has to be repeatedly simulated to predict the aero-damping values for many different ND values. An alternative is the influence coefficient (IC) method, which requires a full-annulus unsteady flow model and thus is also time-consuming. A quicker IC method which replaces the full-annulus model with a multi-blade model to save the computational cost was investigated. This multiblade model is simulated only once to calculate the entire aerodynamic damping-ND curve, thus the required total computational work is less if the blade number on the rotor is high. For example, if there are twenty-four blades on the disk and a 5-blade model was employed in the IC method, then the CPU time saving is about 80%. However, as one reduces the number of blades on the multi-blade model, the prediction accuracies decrease. To balance between the computational cost and the prediction accuracy, investigations were made on how many diagonal lines should be kept in the approximated IC matrix and how many blades the multi-blade flow model should posses.