The absolute instability of joukowski-type airfoils

In this paper an investigation is undertaken to explore the nature of the flow in the vicinity of the trailing edge of Joukowski-type airfoil configurations. Making use of the asymptotic interactive boundary layer theory, the basic flow profiles in the attached and detached flow regions are computed numerically through integrating the interactive boundary layer equations governing the flow motion for sufficiently large Reynolds numbers. Employing a Spectral Chebyshev collocation numerical integration scheme, boundary layer features corresponding to a number of thickness-to-chord ratio parameter cases are produced. The analysis carried out over the interaction region of the trailing edge shows that flow separation always takes place beyond certain critical value of the thickness-to-chord ratio parameter under the action of a self-induced pressure gradient. In addition, reversed flow regions of a sufficiently large size are found to be absolutely unstable, within the framework of linear spatio-temporal stability analysis in combination with the Briggs-Bers branch point criterion.