The Effects of Airfoil Camber on Flutter Suppression Regarding Timoshenko Beam Theory

Abstract

The application of Timoshenko beam theory is presented, thereby the effects of airfoil camber can be investigated analytically and numerically by considering rotary inertia and shear deformation in addition to moment of inertia, aerodynamic loading and bending/torsion coupling. Regarding a tuned blisk, the analysis is simplified to a single blade with plunge and pitch DOF. Pressure distribution of the airfoil surfaces and the resulting aerodynamic forces are calculated with ‘ANSYS/FLOTRAN’ during one-cycle time marching at several reduced frequencies. A parametric relation is then achieved by Roger’s approximation including quasi-inertia, quasi-damping, quasi-elastic and lag terms. The final aeroelastic equations are established by bending-torsion and aerodynamics-structure coupling which is solved by state space approach. This procedure is repeated at several free stream velocities until the real component of an eigenvalue equals zero. The latest velocity is the flutter speed. Following this procedure, flutter characteristics of two similar aeroleastic cases are determined considering only one difference in blade configuration; one with cambered and the other with uncambered airfoil. Comparison of these two cases shows the considerable suppression effect of airfoil camber on flutter.