Interaction Theory and Non-Uniqueness of Separated Flows Around Solid Bodies

Королев, Г. Л.

doi:10.1007/978-3-642-84447-8_18

Cited by 11 publications

(2 citation statements)

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“…in situations where a fully attached boundary layer is forced to separate owing to the presence of a large adverse pressure gradient. Examples displaying such a branching behaviour include supersonic flows past flared cylinders (Gittler & Kluwick 1987), subsonic flows past expansion ramps and subsonic trailing edge flows (Korolev 1990). Current work indicates that this indeed leads to phenomena similar to those described here.…”

Section: Discussionsupporting

confidence: 62%

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

Braun

Kluwick

2004

J. Fluid Mech.

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Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter $\Gamma$ characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value $\Gamma_c$ of $\Gamma$ only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near $\Gamma_c$. Specifically, it is shown that the integro–differential equation which governs these disturbances if $\Gamma_c\,{-}\,\Gamma\,{=}\,O(1)$ reduces to a nonlinear partial differential equation – known as the Fisher equation – as $\Gamma$ approaches the critical value $\Gamma_c$. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.

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Section: Discussionsupporting

confidence: 62%

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

Braun

Kluwick

2004

J. Fluid Mech.

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“…Figure 3 shows the circulation ¡ 1 as a function of c and it shows that when c exceeds c ¤ = 1:95 § 0:05, the problem has no solution. Another characteristic feature of the solution is the existence of a second lower branch, which is charac-terized by decrease in ¡ 1 and an increase in the extent of the reverse-®ow region associated with a decrease in c. It should be noted that a non-unique solution was also obtained in the theory of interaction between boundary layers and external streams in earlier studies of laminar incompressible ®ow past the leading edge of a slender airfoil in Brown & Stewartson (1983) and Ruban (1982), jet ®ows past a curved surface in Zametaev (1986) and the trailing edge of a slender airfoil in Korolev (1989), incompressible ®ow past the vertex of an obtuse angle in work of Korolev (1991), and supersonic viscous ®ow past an axially symmetric surface in Gittler & Kluwick (1987). Figures 4 and 5 compare the skin friction and the pressure distributions on the surface of the elliptic cylinder obtained for c = 1:82 and two di¬erent values of ¡ 1 and the curves 1 and 2 represent the upper and, respectively, lower branches of the solution.…”

Section: Resultsmentioning

confidence: 81%

A direct method for constructing periodic boundary–layer solutions

Королев

2000

Philosophical Transactions of the Royal Society of London. Seri

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Fluid Dynamics

Ruban¹

2017

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This is Part 3 of a book series on fluid dynamics. This is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture courses, and then progressing through more advanced material up to the level of modern research in the field. This book is devoted to high-Reynolds number flows. It begins by analysing the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory. These analyses include the Blasius boundary layer on a flat plate, the Falkner-Skan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers first the so-called ‘self-induced separation’ in supersonic flow that was studied in 1969 by Stewartson and Williams, as well as by Neiland, and led to the ‘triple-deck model’. It also presents Sychev’s 1972 theory of the boundary-layer separation in an incompressible fluid flow past a circular cylinder. It discusses the triple-deck flow near the trailing edge of a flat plate first investigated in 1969 by Stewartson and in 1970 by Messiter. It then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It concludes by covering the Marginal Separation theory, which represents a special version of the triple-deck theory, and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.

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Interaction Theory and Non-Uniqueness of Separated Flows Around Solid Bodies

Cited by 11 publications

References 4 publications

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

A direct method for constructing periodic boundary–layer solutions

Fluid Dynamics

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