On laminar boundary layers near corners
01 May 1970-Quarterly Journal of Mechanics and Applied Mathematics (Oxford University Press)-Vol. 23, Iss: 2, pp 137-152
About: This article is published in Quarterly Journal of Mechanics and Applied Mathematics.The article was published on 1970-05-01. It has received 93 citations till now. The article focuses on the topics: Boundary layer thickness & Blasius boundary layer.
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TL;DR: The free interaction boundary layer was first observed by Ackeret and independently by Liepmann in their study of the interaction between a shock wave and a boundary layer and more extensively studied subsequently by LiePmann, Chapman, Hakkinen, and many others.
Abstract: Publisher Summary The chapter reviews subdivisions of the boundary layers that become necessary under the impact of sudden stream wise changes. If the boundary layer is supersonic, a new phenomenon occurs that appears to have no counterpart in subsonic flow. It leads to a greater ease of study of the flow properties and helps to overcome the barrier of separation that appears to hinder progress in the incompressible studies. The phenomenon is the free-interaction boundary layer, first observed by Ackeret and independently by Liepmann in their study of the interaction between a shock wave and a boundary layer and more extensively studied subsequently by Liepmann, Chapman, Hakkinen, and many others. These studies show that when a shock, sufficiently strong to provoke separation, strikes a laminar boundary layer, the boundary layer actually separates ahead of the foot of the shock and the flow features of the separation region are independent of the characteristics of the shock and depend only on the local properties of the flow. The chapter provides example for incompressible boundary layers when the fluid is compressible and explains the modifications necessary to allow this effect.
345 citations
TL;DR: By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) it was shown that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien-Schlichting wave as discussed by the authors.
Abstract: By using the triple-deck scaling of Stewartson (1969) and Messiter (1970) it is shown that small but relatively sudden surface geometry variations that produce only very weak static pressure variations can nevertheless produce strong, i.e. O(1), coupling between an externally imposed acoustic disturbance and a spatially growing Tollmien-Schlichting wave. The analysis provides a qualitative explanation of the Leehey and Shapiro (1979) boundary-layer receptivity measurements and is in good quantitative agreement with the Aizin and Poliakov (1979) experiment. It may also explain why small 'trip wires' can promote early transition.
334 citations
TL;DR: In this article, a boundary layer flows over a flat plate which has on it a small hump situated downstream of the leading edge, and the presence of the hump generates an interaction between the inviscid region just outside the boundary layer and the viscous region near the hump.
Abstract: A boundary layer flows over a flat plate which has on it a small hump situated downstream of the leading edge. The description of the boundary-layer flow, based upon a triple-deck structure, shows how the presence of the hump generates an interaction between the inviscid region just outside the layer and the viscous region near the hump. The pressure force dominant in the boundary layer and the connexion of the local flow with the main stream develop together and are self-perpetuating, and both remain of primary significance for a wide range of hump sizes, even for a hump buried well inside the boundary layer. By consideration of the limiting cases of very small and very large humps, a consistent account of the nature of the disturbances due to the various sizes of hump is produced. The forces and couples on the hump are also evaluated.
162 citations
118 citations
TL;DR: In this paper, the authors examined Sychev's (1972) proposal that the laminar separation and breakaway of an incompressible fluid streaming past a smooth surface (e.g. on a bluff body) takes place through a triple-deck structure around the separation point.
Abstract: Sychev's (1972) proposal, that in general the laminar separation and breakaway of an incompressible fluid streaming past a smooth surface (e.g. on a bluff body) takes place through a triple-deck structure around the separation point, is examined numerically in this paper. The proposed pattern for large Reynolds number ($Re$) flows is based on a modification of the classical Kirchhoff (1869) free streamline theory, in which a slight adverse pressure gradient is provoked in the inviscid motion immediately ahead of the breakaway. This pressure gradient is just enough to generate a triple-deck development closer to the separation point. The major task then is to decide whether or not a solution of the basic triple-deck problem exists, and is regular at separation, and if it is unique. The numerical investigation, an iterative calculation of the relevant boundary layer problem, together with the potential flow relation between the unknown pressure and displacement, points fairly firmly to both the existence and uniqueness of a solution. Thus, for the bluff body problem when $Re$ $\gg $ 1, the triple-deck determines exactly how far the separation point lies from the position implied by inviscid (Kirchhoff) theory. Comparisons with separating incompressible fluid motions determined numerically from the Navier-Stokes equations and measured experimentally give some support overall to the triple-deck description. For the flow past a circular cylinder the agreement in the variation of pressure and skin friction near separation is in general very encouraging, for Reynolds numbers as low as 30.
114 citations