A Method to Evaluate the Sensitivity of Aerodynamic Damping to Mode Shape Perturbations

Abstract

Abstract Turbomachinery blade mode shapes are routinely predicted by finite element method (FEM) programs and are then used in unsteady computational fluid dynamic (CFD) analyses to predict the aerodynamic damping. This flutter stability assessment process is critical for the last-stage blades (LSBs) of modern heavy-duty gas turbines (HDGTs) which can be particularly susceptible to flutter. Evidences suggest that actual mode shapes may deviate from the FEM predictions due to changes in the FEM boundary or loading conditions, effects of the nonlinear friction contacts, and blade-to-blade variations (mistuning), among others. This uncertainty in the mode shape is accompanied by a general lack of knowledge on the sensitivity of the aerodynamic damping to a small change in mode shape. This paper presents a method to perturb a mode shape and estimate the corresponding change in aerodynamic damping in a framework enabled by linear theories and a rigid-body, quasi-3D treatment of mode shapes. This method is of low computational cost and is suitable for use in the preliminary design cycle. The numerical validation and applications of the method are demonstrated on two LSB blades. Results suggest that the mode shape sensitivity can be substantial and may even exceed the change in aerodynamic damping of a frictionally damped system when subjected to various levels of excitation.