On laminar separation at a corner point in transonic flow

Ruban, Anatoly I.; Türkyılmaz, İbrahim

doi:10.1017/s002211200000207x

Cited by 16 publications

(17 citation statements)

References 21 publications

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“…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%

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: Introductionmentioning

confidence: 99%

Once again on the supersonic flow separation near a corner

2002

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“…It is weaker than the pressure gradient (1.8) observed in transonic flow separating from a convex corner (Ruban & Turkyilmaz 2000), but stronger as compared to the pressure gradient (1.7) in the analogous subsonic flow (Ruban 1974). As a result of the action of the pressure gradient (5.1), the gas in the boundary layer experiences an extreme acceleration.…”

Section: Discussionmentioning

confidence: 71%

“…The transonic version of this problem was considered by Ruban & Turkyilmaz (2000). They found that when the gas speed at the separation point coincides with the speed of sound, the pressure gradient upstream of the interaction region becomes even stronger, that is, dp…”

Section: Re -1/2mentioning

confidence: 99%

“…Experimental observations show that unlike incompressible fluid flows which always separate from a convex corner, a perfect gas flow may assume two different forms. The first one is a flow with separation from the corner point; it was considered earlier by Ruban & Turkyilmaz (2000). The second possibility is that the flow remains fully attached to the body contour.…”

Section: Re -1/2mentioning

confidence: 99%

“…We note that near the body surface upstream of point O, the similarity variable (2.17) is large and negative. As shown in Ruban & Turkyilmaz (2000) the corresponding asymptotic solution of equation (2.22) may be written in the form …”

Section: Properties Of the Inviscid Transonic Flowmentioning

confidence: 99%

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Viscous–inviscid interaction in transonic Prandtl–Meyer flow

Ruban

Pereira

2006

J. Fluid Mech.

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This paper presents a theoretical analysis of perfect gas flow over a convex corner of a rigid-body contour. It is assumed that the flow is subsonic before the corner. It accelerates around the corner to become supersonic, and then undergoes an additional acceleration in the expansion Prandtl-Meyer fan that forms in the supersonic part of the flow behind the corner. The entire process is described by a self-similar solution of the Kármán-Guderley equation. The latter shows that the boundary layer approaching the apex of the corner is exposed to a singular pressure gradient, dp/dx ∼ (−x) −3/5 , where x denotes the coordinate measured along the body surface from the corner apex. Under these conditions, the solution for the boundary layer also develops a singularity. In particular, the longitudinal velocity near the body surface behaves as U ∼ Y 1/2 . Here Y is the normal coordinate scaled with the boundary-layer thickness Re −1/2 ; Re being the Reynolds number, assumed large in this theory. As usual, the boundary layer splits up into two parts, a viscous near-wall sublayer and a locally inviscid main part of the boundary layer. The analysis of the displacement effect of the boundary layer shows that neither the viscous sublayer nor the main part determines the displacement thickness. Instead, the overlapping region situated between them proves to be responsible for the shape of the streamlines at the outer edge of the boundary layer. This leads to a significant simplification of the analysis of the flow behaviour in the viscous-inviscid interaction region that forms in a small vicinity of the corner. In order to describe the flow behaviour in this region, one has to solve the Kármán-Guderley equation for the inviscid part of the flow outside the boundary layer. The influence of the boundary layer is expressed through a boundary condition, that relates the streamline deflection angle ϑ at the outer edge of the boundary layer to the pressure gradient dp/dx acting upon the boundary layer. The boundary-layer analysis leads to an analytical formula that relates ϑ and dp/dx (unlike in previous studies of the viscous-inviscid interaction). The interaction problem was solved numerically to confirm that the solution develops a finite-distance singularity.

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Incipient separation over wall irregularities in transonic flow

Türkyılmaz

2010

Applied Mathematical Modelling

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On laminar separation at a corner point in transonic flow

Cited by 16 publications

References 21 publications

Once again on the supersonic flow separation near a corner

Once again on the supersonic flow separation near a corner

Viscous–inviscid interaction in transonic Prandtl–Meyer flow

Incipient separation over wall irregularities in transonic flow

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