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The Low Reduced Frequency Limit of Vibrating Airfoils. Part II: Numerical Experiments

Research Areas
  • Aeroacustics and vibrations,
  • Turbomachinery

This paper studies the unsteady aerodynamics of vibrating air- foils 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 Navier-Stokes 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 work-per-cycle is proportional to the reduced frequency for any inter-blade phase angle and it is independent of its sign. For highly loaded airfoils the unsteady pressure mod- ulus 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 work- per-cycle scales linearly with the reduced frequency. This be- havior is independent of the geometry of the airfoil and in first approximation of the mode-shape. For symmetric cascades the work-per-cycle scales linearly with the reduced frequency irre- spectively of whether the airfoil is loaded or not. Simulations using a frequency domain linearized Navier-Stokes solver have been carried out on a low-pressure 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 traveling-wave and in- fluence coefficient formulations of the problem are used in com- bination to increase the understanding and explore the nature of the unsteady pressure perturbations.
ASME Turbo Expo 2015: Turbine Technical Conference and Exposition
Montreal, Canada
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ASME Proceedings | Structural Mechanics and Vibration

Research Group, Departaments and Institutes related
  • Creador: Departamento: Mecánica de Fluidos y Propulsión Aeroespacial