Application of enforced motion to study 2-D cascade lock-in effect
The vortex lock-in effect has been well-studied for an oscillating cylinder and numerous experimental and computational data are available. However, only recently has this phenomenon been observed for two-dimensional isolated airfoils as well as turbine cascades. This paper investigates a flow instability about a two-dimensional airfoil tip section of a modern front stage compressor blade operated at an off-design condition. The governing nonlinear, unsteady Navier-Stokes equations are solved using a novel harmonic balance (HB) method. For periodic unsteady flows, such as the transonic flow through a turbomachinery cascade, this method requires one to two orders of magnitude less computational time than conventional time-accurate solvers. The vortex shedding frequency is obtained using a unique phase error method. Enforced motion is then used to encourage lock-on of the frequency of the blades' motion to the natural shedding frequency. In particular, it is assumed that the airfoils vibrate harmonically in pitch about their elastic axis at a given frequency and amplitude. Analogous to the circular cylinder, a V-shaped lock-in region is observed. The aeroelastic stability of the rotor is determined and the results indicate that the largest limit cycle oscillation (LCO) amplitude is not at the natural shedding frequency. Furthermore, the system is always stable at the natural shedding frequency. This is contrary to conventional thought in which the most significant response is assumed to be when the blade frequency and the frequency of the fluid instability are coincident. Therefore, the results indicate how both the natural shedding frequency and blade frequency should be considered in design analysis. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc.
