Forced Vibration of a Turbine Cascade under Low and High Engine Order Excitation Predicted by Transformation Techniques

An improved forced response analysis for turbine blades is conducted in both frequency and time domains. For its aerodynamic analysis, a time domain vortex lattice method which can capture a detailed behavior of the vorticities and account for thickness effect of the airfoil is used. To deal with the complex aerodynamic coefficients and express an aeroelastic equation of motion into state-space form, two types of transformation techniques are invoked. First, the z transformation is used to convert the mixed time/frequency domain aerodynamics to frequency domain. The p transform technique is next used to convert the equation of motion back to time domain. The resulting aeroelastic model will be without aerodynamic states or lag equations and can be used to perform various aeroelastic analyses at reduced computational cost. Numerical results from the flutter analysis are presented in both frequency and time domains. For the cascaded blades, the present and the other existing results show a good agreement for aerodynamic analysis and flutter analysis. The forced vibration results are also presented in both domains. For a single airfoil, the transient responses obtained by the present method show a good agreement with those by the full order analysis. The transient response for a cascade shows similar trajectories for the present method and the full order model.