Analyzing the effects of airfoil camber on flutter suppression using Rogers approximation technique and Timoshenko theory

摘要

In this paper, gas turbine blades are modeled analytically and numerically as Timoshenko beams by considering rotary inertia and shear deformation. The natural frequencies and relevant mode shapes are then determined by using this theory. On the other hand, the 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, and quasi-elastic and higher order terms. Having the structure and the aerodynamic model, the final aeroelastic equations are established by bending/torsion and aerodynamics/structure coupling. Thus, an eigenvalue problem is formulated 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 and the imaginary component of the corresponding eigenvalue is the flutter frequency. Then the flutter characteristics of such blade with an uncambered airfoil are also determined by the same procedure, and the effect of a specified camber on flutter is investigated.