Global Linear Stability Analysis of the Flow over Rotating Blades

An OVERFLOW simulation of a four-bladed rotor in hover is performed, and the resulting steady-state solution for the boundary layer over a rotating blade is analyzed by means of linear stability methods. The techniques employed are the Linear Stability Theory, the Parabolized Stability Equation, and the spanwise BiGlobal analysis. The unstable modes in the boundary layer of the rotating blade are analyzed in comparison with those typically observed in swept wings. The effect of the Coriolis force and the spanwise gradient of the free stream velocity are taken into account, and their influence on the instabilities is evaluated. It is shown that periodic boundary conditions in the spanwise BiGlobal analysis work adequately for a sufficiently small fraction of the length of the blade (∼ 1.2%), while increasing the domain would require an alternative approach to the boundary conditions.