Local separation on a slender cone preceding the appearance of a vortex sheet

Zametaev, V. B.

doi:10.1007/bf01050720

Cited by 3 publications

(4 citation statements)

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“…As shown by Zametaev (1987), solutions to equations (4.33) for x -+ O can be expressed in terms of the similarity variable y = X l / 5 (fi: T = X l / 5 A. Starting with the similarity solut ion equation (4.33) was then integrated numerically by marching in the x-direction for the two cases A = 0.5 , r = -2 and A = 0.5, r = 2.…”

Section: Incompressible Flow Past Cones At Incidencementioning

confidence: 84%

“…Comparison of the induced pressure gradient 8pj8(rcP) = 0(o-Re-l / 2 ) and the viscous term 8 2 wj8r 2 = 0(c0-7 / 4 Re-l ) entering the second order momentum equation following from the local analysis of the classical boundary-Iayer equations, indicates that the parameter range covered by the interaction concept is a = O(C 2 / 5 Re-l / 5 ). The appropriate asymptotic interaction theory has been formulated by Zametaev (1987). According to the similarity solution (4.26) the radial velocity component at the outer edge of the boundary layer is proportional to X-l / 2 .…”

Section: Incompressible Flow Past Cones At Incidencementioning

confidence: 99%

“…In order to determine B(x, <pd it is necessary to derive the solvability condition for the second order equations holding in the viscous sublayer. Using suitably scaled variables A, (fi in place of B, <P this condition can be expressed in the form, Zametaev (1987) …”

Section: Incompressible Flow Past Cones At Incidencementioning

confidence: 99%

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Interacting Laminar and Turbulent Boundary Layers

Kluwick

1998

CISM International Centre for Mechanical Sciences

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This chapter deals with the properties of viscous wall layers in the high Reynolds number limit which are subjected to rapid changes of the boundary conditions. Classical, e.g. hierarchical boundary layer theory in which the driving pressure is imposed by the extern al inviscid· ftow then typically leads to difficulties which of ten can be overcome by an interaction strategy. Examples include ftows past bodies of finite length and shock boundary layer interactions. The interaction concept is formulated first for laminar flows but extended later also to the case of turbulent boundary layers.A. Kluwick (ed.), Recent Advances in Boundary Layer Theory © Springer-Verlag Wien 1998 232 A. Kluwick

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Section: Incompressible Flow Past Cones At Incidencementioning

confidence: 84%

Section: Incompressible Flow Past Cones At Incidencementioning

confidence: 99%

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Interacting Laminar and Turbulent Boundary Layers

Kluwick

1998

CISM International Centre for Mechanical Sciences

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“…First, one can extend the analysis of Ruban and Stewartson et al by considering the local properties of a three-dimensional boundary layer with (or without) additional symmetry conditions near the point (line) of vanishing wall shear, e.g. Brown (1985), Zametaev (1987), Duck (1989), and Vilenskii (1991), see also Smith (2000). But then the question arises of if and how these local structures are embedded in a global flow field, which has not been addressed in sufficient depth so far.…”

Section: Introductionmentioning

confidence: 99%

The effect of three-dimensional obstacles on marginally separated laminar boundary layer flows

Braun

Kluwick

2002

J. Fluid Mech.

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We consider the steady viscous/inviscid interaction of a two-dimensional, nearly separated, boundary layer with an isolated three-dimensional surface-mounted obstacle, for example in the large Reynolds number flow around the leading edge of a slender airfoil at a small angle of attack. An integro-differential equation describing the effect of the obstacle on the wall shear stress valid within the interaction regime is derived and solved numerically by means of a spectral method, which is outlined in detail. Typical solutions of this equation are presented for different values of the spanwise width B of the obstacle including the limiting cases B → 0 and B → ∞. Special emphasis is placed on the occurrence of non-uniqueness. On the main (upper) solution branch the disturbances to the flow field caused by the obstacle decay in the lateral direction. Conversely a periodic flow pattern, having no decay in the spanwise direction, was found to form on the lower solution branch. These branches are connected by a bifurcation point, which characterizes the maximum (critical) angle of attack for which a solution of the strictly plane interaction problem exists. An asymptotic investigation of the interaction equation, in the absence of any obstacle, for small deviations of this critical angle clearly reflects the observed behaviour of the numerical results corresponding to the different branches. As a result we can conclude that the primarily local interaction process breaks down in a non-local manner even in the limit of vanishing (three-dimensional local) disturbances of the flow field.

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