Theory of laminar boundary layer separation in supersonic flow

Neiland, V. Ya.

doi:10.1007/bf01094681

Cited by 130 publications

(81 citation statements)

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“…As may be seen from comparing figure 6 with figure 5, near the primary separation point the flow remains unaffected by an increase of α. All the fluid dynamic functions including the skin friction τ and pressure p follow universal laws here as predicted by Neiland (1969) and Stew & Williams (1969) in their early studies of self-induced separation of the boundary layer on a flat surface. The increase of α merely results in a displacement of the separation point further upstream from the corner O.…”

Section: Calculation Resultssupporting

confidence: 53%

“…The asymptotic theory of viscous-inviscid interaction, known now as the triple-deck theory, was formulated simultaneously by Neiland (1969) and Stewartson & Williams (1969) for the self-induced separation in supersonic flow and by Stewartson (1969) and Messiter (1970) for incompressible fluid flow near a trailing edge of a flat plate. Later it became clear that the triple-deck interaction region, while being small, plays a key role in many fluid flows.…”

Section: Introductionmentioning

confidence: 99%

“…Most notably, the theory remains predominantly restricted to incipient or small-scale separations where the entire recirculating region together with the separation and reattachment points 'fits' into the O(Re −3/8 ) region of interaction. Even in the studies specifically aimed at describing developed separations (see Neiland 1969;Stewartson & Williams 1969;Sychev 1972;Ruban 1974), the analysis is confined to the 'local' flow behaviour near the separation point. Meanwhile, the 'global' structure of the flow in the recirculating region remains unresolved.…”

Section: Introductionmentioning

confidence: 99%

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Once again on the supersonic flow separation near a corner

2002

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Laminar boundary-layer separation in the supersonic flow past a corner point on a rigid body contour, also termed the compression ramp, is considered based on the viscous-inviscid interaction concept. The 'triple-deck model' is used to describe the interaction process. The governing equations of the interaction may be formally derived from the Navier-Stokes equations if the ramp angle θ is represented as θ = θ 0 Re −1/4 , where θ 0 is an order-one quantity and Re is the Reynolds number, assumed large. To solve the interaction problem two numerical methods have been used. The first method employs a finite-difference approximation of the governing equations with respect to both the streamwise and wall-normal coordinates. The resulting algebraic equations are linearized using a Newton-Raphson strategy and then solved with the Thomas-matrix technique. The second method uses finite differences in the streamwise direction in combination with Chebychev collocation in the normal direction and Newton-Raphson linearization.Our main concern is with the flow behaviour at large values of θ 0 . The calculations show that as the ramp angle θ 0 increases, additional eddies form near the corner point inside the separation region. The behaviour of the solution does not give any indication that there exists a critical value θ * 0 of the ramp angle θ 0 , as suggested by Smith & Khorrami (1991) who claimed that as θ 0 approaches θ * 0 , a singularity develops near the reattachment point, preventing the continuation of the solution beyond θ * 0 . Instead we find that the numerical solution agrees with Neiland's (1970) theory of reattachment, which does not involve any restriction upon the ramp angle.

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Section: Calculation Resultssupporting

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Once again on the supersonic flow separation near a corner

2002

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“…Investigating the separation and its consequences is of particular importance in understanding flows at high Reynolds numbers. The explanation of the phenomena of separation lies in the theory of the boundary layer, in particular triple deck theory, see Stewartson & Williams (1969), Neiland (1969), Messiter (1970). In recent years, there has been an increasing interest in using micro-electro-mechanical-system (MEMS) devices to control the separation of flow at high Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

Subsonic flow past localised heating elements in boundary layers

Aljohani

Gajjar

2017

J. Fluid Mech.

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The problem of subsonic flow past micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface, where the MEMS devices have hump-shaped surfaces, is investigated using triple deck theory. The compressible Navier-Stokes equations supplemented by the energy equation are considered in the limit that the Reynolds number is large. The triple deck problem is formulated and the linear and non-linear analysis and results are presented. The current work is a generalisation of the problem discussed by (Koroteev & Lipatov 2012, 2013 where the MEMS devices have flat shaped surfaces. The results show the hump-shaped heating elements enhance large drops in pressure and peaks and troughs in the skin-friction over the centre of the hump as compared to the flat shaped devices which may be useful for controlling the flow.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfmkeywords.pdf for the full list)

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“…Stewartson was at the vanguard of the use of formal asymptotic methods, which for the triple-deck problem resolved the nature of high-Reynolds-number flow in the vicinity of the trailing edge of a flat plate; see for example [6,13] and [7]. These asymptotic methods were further developed for, and gave an enlightened view of, flow separation (see [15] for a review of early work in this area), flow instabilities and even early-stage transition (e.g.…”

Section: Introductionmentioning

confidence: 99%

A resolution of Stewartson’s quarter-infinite plate problem

Duck

Hewitt

2011

Theor. Comput. Fluid Dyn.

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We revisit a problem originally considered by Stewartson in 1961: the incompressible, high-Reynolds-number flow past a quarter-infinite plate, with a leading edge that is perpendicular to, and a side edge that is parallel to, an undisturbed oncoming freestream. Particular emphasis is placed on the key region close to the side edge, where the flow is (superficially) three-dimensional, although the use of similarity variables reduces the dimensionality of the problem down to two. As noted by Stewartson, this problem has several intriguing features; it includes singularities and is also of a mixed parabolic type, with edge conditions influencing the solution in both directions across the flow domain. These features serve to greatly complicate the (numerical) solution process (the problem is of course also highly non-linear), and computation was clearly infeasible in 1961. In the present paper, a detailed computational study is presented, answering many of the questions that arose from the 1961 study. We present detailed numerical results together with asymptotic analyses of the key locations in the flow.

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Theory of laminar boundary layer separation in supersonic flow

Cited by 130 publications

References 1 publication

Once again on the supersonic flow separation near a corner

Once again on the supersonic flow separation near a corner

Subsonic flow past localised heating elements in boundary layers

A resolution of Stewartson’s quarter-infinite plate problem

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