Application of unsteady laminar triple-deck theory to viscous-inviscid interactions from an oscillating flap in supersonic and subsonic flow
Unsteady triple-deck theory is applied to analyze the local viscous-inviscid interaction of an idealized oscillating flap with a laminar boundary layer in either supersonic or subsonic external flow. For small flap amplitudes and small-to-moderate nondimensional frequencies, linearized analytical solutions by means of Fourier transformation are given for the pressure and shear distributions ahead of and behind the flap hinge. In the supersonic case, the predicted unsteady viscous effects reduce the pressure amplitude and spread it out upstream while causing it to lag the quasi-steady inviscid prediction (flap motion); this also results in an unsteady delay of incipient separation at the hinge to a higher flap amplitude. In contrast, the lowered unsteady viscous pressure distribution in purely subsonic flow slightly leads the flap motion, resulting in incipient separation at a smaller flap amplitude than the quasi-steady value. These trends are shown to be in qualitative agreement with available experimental data.