Bi-global stability analysis in curvilinear coordinates

A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability. Published under license by AIP Publishing.