Quantification of the Influence of Unsteady Aerodynamic Loading on the Damping Characteristics of Airfoils Oscillating at Low Reduced Frequency—Part II: Numerical Verification

Abstract

This paper numerically investigates the correlation between the so-called unsteady loading parameter (ULP), derived in Part I of the corresponding paper, and the unsteady aerodynamics of oscillating airfoils at low reduced frequency with special emphasis on the work-per-cycle curves. Simulations using a frequency-domain linearized Navier–Stokes solver have been carried out on rows of a low-pressure turbine airfoil section, the NACA65 section, and a flat plate, to show the correlation between the actual value of the ULP and the flutter characteristics, for different airfoils, operating conditions, and mode shapes. Both the traveling wave and influence coefficient formulations of the problem are used in combination to increase the understanding of the ULP influence in different aspects of the unsteady flow field. It is concluded that, for a blade vibrating in a prescribed motion at design conditions, the ULP can quantitatively predict the effect of unsteady loading variations due to changes in both the incidence and the mode shape on the work-per-cycle curves. It is also proved that the unsteady loading parameter can be used to qualitatively compare the flutter characteristics of different airfoils.