This paper deals with the aeroelastic instability of vibrating multiple blade rows under aerodynamic coupling with each other. A model composed of three blade rows, e.g., rotor-stator-rotor, in which blades of the two rotor cascades are simultaneously vibrating, is considered. The generalized aerodynamic force on a vibrating blade consists of the component induced by the vibrating motion of the blade itself and those induced by vibrations not only of other blades in the same cascade but also of blades in another cascade. To evaluate the aerodynamic forces, the unsteady lifting surface theory for the model of three blade rows is applied. The equations describing motions of blades are coupled via the aerodynamic forces. The so-called k method is applied to determine the critical flutter conditions. A numerical study has been conducted. The flutter boundaries are compared with those for a single blade row. It is shown that the effect of the aerodynamic coupling significantly modifies the critical flutter conditions.
The unsteady lifting surface theory for a model composed of five bladerows is developed to predict unsteady aerodynamic forces on oscillating blades of aerodynamically coupled multistage annular bladerows. The theory is formulated to calculate generalized aerodynamic forces which appear in Lagrange's equations of blade motions, so that it can be used as the aerodynamic tool for the inter-row coupling flutter analysis of multistage bladerows. Numerical studies were also conducted to investigate the mutual aerodynamic influences among bladerows. The simultaneous effects of co-rotating upstream and downstream bladerows located at next to the next position significantly modify the aerodynamic response of oscillating blades. The aerodynamic force induced by the oscillating bladerow is not very small even on the bladerows remoter than the next-to-the-next bladerow. Vol. 53, No. 181, pp. 215-222, 2010 ðÞ: abbreviation for ( 1 ; 2 ; . . . ; 5 ), and stands for frequency component identified by five integral mode parameters 1 , 2 , . . ., 5 in frame of reference fixed to ductThe signs of the rotational speeds are assumed to be j > 0 (clockwise looking from downstream) and j < 0 (counterclockwise).
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