Near Critical Phenomena in Laminar Boundary Layers

Abstract

Recent developments in the construction of airfoils and rotorblades are characterized by an increasing interest in the application of so-called smart structures for active flow control. These are characterized by an interplay of sensors, actuators, real-time controlling data processing systems and the use of new materials e.g. shape alloys with the aim to increase manoeuvrability, reduce drag and radiated sound. The optimal use of such devices obviously requires a detailed insight into the flow phenomena to be controlled and in particular their sensitivity to external disturbances. In this connection locally separated boundary layer flows are of special interest. Asymptotic analysis of boundary layer separation in the limit of large Reynolds number Re→ ∞ has shown that in a number of cases which are of importance from a practical point of view solutions of the resulting interaction equations describing two-dimensional steady flows exist up to a limiting value Γ _c of the relevant controlling parameter Γ only while two branches of solutions exist in a regime Γ < Γ _c . The present study aims at a better understanding of near critical flows ǀ Γ — ǀ _c ǀ → 0 and in particular the changes of the flow behaviour associated with the passage of Γ through Γ _c .