Application of Unsteady Laminar Triple-Deck Theory to Viscous-Inviscid Interactions from an Oscillating Flap in Supersonic Flow

Abstract

The formal asymptotic triple-deck theory of unsteady free laminar viscousinviscid interactions for purely supersonic or subsonic inviscid flow has been developed in general by Ryzhov and Zhuk [401] as an extension of the steady flow theory due to Stewartson and Williams [232]. Their results for the leading approximation as Reynolds number Re → ∞ indicate that when the reduced frequency based on reference length L* and freestream velocity $\omega *L*/U_\infty ^* < 0(\operatorname{Re} ^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 4}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$4$}}} )$, the explicit unsteady effect remains only in the viscous lower-deck equations, the inviscid disturbance flow in the overlying middle (main) and outer decks being quasi-steady. Schneider [402] has also given a fundamental analysis of unsteady disturbances in purely supersonic outer flow for arbitrary amplitudes in which, unlike the aforementioned free-interaction case, the amplitude governs the streamwise interactive scale; he also found that the quasi-steady approximation fails near the wall.