Abstract



This chapter studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis in its impact on the scaling of the work per cycle curves using an asymptotic approach (Part I) and numerical simulations. A perturbation analysis of the linearized NavierStokes equations at low reduced frequency is presented and some conclusions are drawn (Part I of the corresponding paper). The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure field caused by the vibration of the airfoil. For lightly loaded airfoils the unsteady pressure and the influence coefficients scale linearly with the reduced frequency whereas the phase departs from ?/2 and changes linearly with the reduced frequency. As a consequence the workpercycle is proportional to the reduced frequency for any interblade phase angle and it is independent of its sign. For highly loaded airfoils the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero varies linearly with it. In this case only the mean value of the workpercycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and in first approximation of the modeshape. For symmetric cascades the workpercycle scales linearly with the reduced frequency irrespectively of whether the airfoil is loaded or not. Simulations using a frequency domain linearized NavierStokes solver have been carried out on a lowpressure turbine airfoil section, the NACA0012 and NACA65 profiles and a flat plate operating at different flow conditions to show the generality and correctness of the analytical conclusions. Both the travelingwave and influence coefficient formulations of the problem are used in combination to increase the understanding and explore the nature of the unsteady pressure perturbations.  
International

Si 

10.1115/GT201542439 
Book Edition


Book Publishing

American Society of Mechanical Engineers 
ISBN

9780791856772 
Series


Book title

ASME Proceedings. Structural Mechanics and Vibration 
From page

300 
To page

313 