Boundary-Layer Separation in Unsteady Flow

Abstract

Extension of the familiar concept of boundary-layer separation to flow along moving walls and unsteady flows is a subject that attracted some interest in the 1950's and has been investigated further in the past few years. The well-known criterion of vanishing wall-shear does not apply in such flows, and therefore the definition of the phenomenon becomes more difficult than in the simpler types of flow considered by Prandtl. The practical importance of extending the concept is discussed and arguments in favor of its definition in terms of Goldstein's singularity are reviewed. The model proposed by the present authors in 1971 is described, together with available numerical and experimental evidence that supports it. Numerical studies of steady and unsteady separating boundary-layer flows are reported, in which singularities of Goldstein's type are detected and comparisons can be made between the position-vs.-time curves of the singularity and of the point of vanishing wall-shear. One of these studies involves the classic case of the circular cylinder started impulsively, which was treated by Blasius and by Goldstein and Rosenhead and for which detailed numerical results are available. The distinction between vanishing wall-shear and separation is dramatic. This review closes with some remarks about the mathematical state of this subject.

On the Lagrangian description of unsteady boundary-layer separation. Part 1. General theory

“…Tlic t t r m 'sepRrat.ion' will in this paper be used to refer to the 'breakaway' of a thin layer of vorticity from the surface of a body. This definition of separation is close to that of both Prandtl (1904) and Sears & Telionis (1975). In particular, Sears & Telionis speak only of separation when the penetration of the boundary-layer vorticity away from the wall becomes too large to be described on the usual O(Re-3) boundary-layer scale (Re is the Reynolds number of the flow, and is assumed large).…”

Unsteady laminar separation: an experimental study

“…Such a layer would be necessary if a saddle-point pattern were to exist in this neighborhood , as Sears and Telionis (15 ] point out. An overall flow pattern emerges now which together with the distorted separation bubbles is shown in Fig.…”

Unsteady separation in vortex-induced boundary layers

“…This has become known as the Moore-Rott-Sears (MRS) criterion, as it was also arrived at independently by Rott and Sears. Because the steady flow over a moving wall is analogous to a special case of unsteady flow over a fixed wall, the development of a singular boundary-layer solution could also be an indication of separation for an unsteady flow [20,21]. The singularity would again show up as a drastic thickening of the boundary layer.…”