Effects of Geometric and Structural Parameters on Coupled Bending Torsion Flutter in Turbo Machinery Blades

TLDR: In this paper, the critical flutter speed with respect to both the torsion and the bending modes as a function of the interblade phase angle as well as dominant vibration frequencif s at flutter was analyzed.

Abstract: The development o f propulsion system technology over the last few decades has encountered and overcome several technological barriers. A large number o f problems were resolved resulting in considerably higher component efficiencies and reduced fuel consumption. These advances led to lighter overall designs and higher power densities compared to earlier designs. The accomplishment of lighter designs for the turbomachinery components also led to some drawbacks due to the reduced margins on the design factor-of-safety. Consequently, aeroelastic stability has become a major concern, and is often the limiting design constraint. So a careful and systematic study of coupled bending-torsion flutter o f a cascade in incompressible flow was carried out which requires estimation of unsteady aerodynamic loads, and a structural model o f the cascade. Unsteady aerodynamic loads were evaluated using Whitehead's solution for incompressible flow through a cascade of arbitrary geometry and interblade phase angle. The lift and moment coefficients calculated were found to match within the four decimal place accuracy with the results given by Whitehead and other literature. The blades were modeled as an equivalent 2-D section at 75% of span, and structural and inertial couplings were lumped into an effective CG-EA offset. Structural damping was included in the equations of motion. The resulting complex eigenvalue problem was solved recognizing the fact that there are two parameters in the eigenvalue problem, namely the reduced frequency k and the interblade phase angle β. The critical flutter speed was determined by minimizing it with respect to β, keeping the constraint on β as suggested by Lane. The solution provided the critical flutter speed with respect to both the torsion and the bending modes as a function of the interblade phase angle as well as dominant vibration frequencif s at flutter. Various structural and aerodynamic parameters of the cascade were varied and the effect of the variations on the coupled bending torsion flutter was studied. A jump was observed in the flutter boundary near frequency ratio of I, which was explained by the change in the mode shape of the vibration, which is represented by interblade phase angle. The developed technique can be used as a preliminary design tool for the aeroelastic flutter analysis of turbo-machinery blades.