Scaling of Turbine Blade Unsteady Pressures for Rapid Forced Response Assessment

High Cycle Fatigue caused by high vibration levels continues to be a major concern in gas turbine design. The use of Computational Fluid Dynamics methods is becoming more commonplace for calculating the vibration amplitude of turbomachinery blades during the design process. A typical calculation approach would be to calculate the unsteady aerodynamic loads at the resonance condition for each vibration mode of interest. In this paper it is proposed that, for a choked high pressure (HP) turbine, an unsteady flow prediction can be scaled across a wide engine operating range using a few simple parameters. There is a fixed relationship between the turbine inlet pressure and the HP shaft speed (when expressed non-dimensionally) which can be used to scale the flow conditions. The effects of altitude variation in the ratio of shaft speeds, compressor bleed flows and schedule of the variable vanes are secondary, having only a small influence on the behaviour. This paper demonstrates that the steady flow distribution around both stator and rotor is virtually constant across the speed range of the engine and the rotor unsteady surface pressure distribution shows only small differences. Further, the parameter which is of prime interest for vibration assessment, the modal force, can be scaled very well using turbine inlet pressure. For modes of vibration with high amplitudes the errors introduced by scaling are of the order of 6% which is considered acceptable for design predictions.