Stability and separation of freely interacting boundary layers
The triple-deck theory to describe boundary-layer free interaction and separation is carefully investigated from the viewpoint of how it predicts stability properties of a viscous flow. The linearized version of this theory gives the same results as the linear stability theory based on the Orr-Sommerfeld equation if the flow is incompressible and the wave number of small disturbances goes to zero. Hence, a rather general criterion results to fix limits for a subsonic boundary layer to be stable. On the contrary, the linear approximation to the triple-deck theory leads to discouraging conclusions when the velocity of the oncoming stream exceeds the speed of sound, since it fails to reveal the boundary-layer instability. The Prandtl equations with a self-induced pressure gradient included are used to formulate a nonlinear approach for elucidating stability properties of freely inter acting boundary layers both for subsonic and supersonic cases. The shock-wave boundary-layer interaction and separation on a moving wall is numerically studied, the formation of two recirculation bubbles being the most striking feature. With the shock strength increasing, both bubbles tend to divide into smaller vortex cells whence the nonsteady process of velocity field “breathing” stems.
KeywordsInternal Wave Linear Stability Theory Recirculation Bubble Interact Boundary Layer Prandtl Equation
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