Cascade flutter analysis with transient response aerodynamics

Abstract

Two methods for calculating linear frequency domain unsteady aerodynamic coefficients from a time-marching full-potential cascade solver are developed and verified. In the first method, the influence coefficient method, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the pulse response method, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier transforms of the blade motion and the response. Both methods are validated by comparison with the harmonic oscillation method, in which all the airfoils are oscillated, and are found to give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. Flutter calculations are performed for two examples over a range of subsonic Mach numbers using both flat plates and actual airfoils.