Physics of Vibrating Turbine Airfoils at Low Reduced Frequency

Resumen

The unsteady aerodynamics of low-pressure turbine vibrating airfoils in flap mode is studied in detail using a frequency-domain linearized Navier–Stokes solver. Both the traveling-wave and influence coefficient formulations of the problem are used to highlight key aspects of the physics and understand the trends of the modulus and phase of unsteady pressure with the reduced frequency and Mach number. The study is focused in the low reduced-frequency regime, which is of paramount relevance for the design of aeronautical low-pressure turbines and compressors. It is concluded that the variation of the influence coefficient phase with the reduced frequency is linear, whereas the effect of the Mach number can be neglected in the first order approximation; moreover, the unsteadiness of the vibrating and adjacent airfoils is driven by vortex shedding mechanisms. Finally, a simple model to estimate the work per cycle as a function of the reduced frequency and Mach number is provided for bending modes. The edgewise and torsion modes are presented in less detail, but it is shown that acoustic waves are essential to explain its behavior. The nondimensional work per cycle of the edgewise mode shows a weak dependence with the Mach number, whereas in the torsion mode, a large number of airfoils is needed to reconstruct the work per cycle departing from the influence coefficients, and the mean value is Mach independent.