Extension of a Harmonic Balance Method to the Analysis of the Separated Shear Layer Instability

Abstract

Incoming wakes can induce separated boundary layer instability, and cause performance losses in turbine cascades of a gas turbine. An efficient numerical method that can analyze unsteady incoming wake effects is desirable from practical point of view. In the present study, an extended harmonic balance method (Chebyshev-based harmonic balance, C-HB) is introduced to the analysis of the incoming wake effect on the separated boundary layer. Convection of a one-dimensional wake-like profile and the flow around the flat plate whose front part is replaced by the NACA0012 with the incoming wake at a Reynolds number Re = 92,000 are computed by the C-HB method. The result shows that the C-HB method can resolve the transient phenomenon of wake convection and the associated linear instability of the flow around the blade.