Three‐dimensional Boundary Layers

Eichelbrenner, E. A.

doi:10.1111/j.1749-6632.1968.tb15221.x

Cited by 5 publications

(3 citation statements)

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“…The main controversy about Is in the literature centers on whether it is an envelope of limiting streamlines,ie.skin-friction lines, (Eichelbrenner and Oudart 1954, 1973, Maskell 1955 or is itself a limiting streamline (Lighthlll 1963). The distinction is not academic.…”

Section: The Separation Line When a 60mentioning

confidence: 99%

Three-dimensional laminar boundary layers and the ok of accessibility

1981

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An investigation is carried out into the structure of the laminar boundary layer originating from the forward stagnation point of a prolate spheroid at incidence in a uniform stream, assuming that the external velocity distribution is given by attached potential theory. The principal new results of the study are: A new transformation of the body co-ordinates is devised which facilitates the computation of the solution near the nose.Two variations of the standard box method of solving the equations are devised to enable solutions to be computed in regions of cross-flow reversal. They are referred to as the zigzag box and the characteristic box.Whereas in two-dimensional flows the effect of the boundary layer approaching separation on the external flow may be represented by a blowing velocity, in the present study we find that this is only true near the windward line of symmetry. Near the leeward line of symmetry the blowing velocity must be replaced by a suction velocity even though the boundary layer is being significantly thickened.The boundary layer over the whole of the spheroid cannot be computed in an integration from the forward stagnation point. The accessible region is largely bounded by the separation line, if α ≤ 6°, and develops a wedge-like shape whose apex is named the accessibility ok, pointing towards the nose of the spheroid. On the windward side of this line the solution develops a singularity; on the leeward side the situation is less clear but it is also believed to occur there.For α ≥ 15° the accessible region on the leeward side of the ok is largely determined by the external streamline through the ok.

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Section: The Separation Line When a 60mentioning

confidence: 99%

Three-dimensional laminar boundary layers and the ok of accessibility

1981

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“…A review of boundary layers in three dimensions during that active period has been given by Cooke and Hall (1962). A review of numerical methods for solving generalized three-dimensional boundary layer flows has been given by Eichelbrenner (1973). The basic feature of similarity flows of this type, valid asymptotically far downstream from the origin of the streamwise motion, is that the primary streamwisevarying flow is described by a single nonlinear ordinary differential equation, while the secondary fully-developed cross flow is described by a linear ordinary differential equation which has, for its variable coefficients, terms involving the primary flow solution.…”

Section: Introductionmentioning

confidence: 99%

New solutions for laminar boundary layers with cross flow

Weidman

1997

Z. angew. Math. Phys.

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In some three-dimensional laminar boundary layer problems a coordinate decomposition reduces the governing equations to a primary nonlinear ordinary differential equation describing the streamwise flow in a semi-infinite domain and a secondary linear equation coupled to the primary solution describing the cross flow of infinite spanwise extent. Five new cross-flow problems of this type are investigated within the confines of laminar boundary layer theory. First, the equation for uniform flow transverse to a planar laminar wall jet is found and solved exactly. Second, two solutions for motion transverse to a uniform shear flow along a flat plate are given. A third problem considered is the transverse motion over a flat plate aligned with the uniform mainstream and advancing toward or receding from the mainstream. In the fourth problem, a family of solutions for transverse uniform streams above and below a planar laminar jet is given in closed form. This solution depends on the momentum J of the planar jet and the velocity ratio κ of the transverse streams. The last problem addresses the motion of transverse uniform streams above and below a planar laminar wake. At leading order the cross flow depends only on the velocity ratio κ and not on the drag D produced by the body forming the wake. The influence of the drag first appears at O(x −1 ln x) in the streamwise coordinate expansion of the cross-flow solution.Mathematics Subject Classification (1991). 35C05, 76D10, 76D25.

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“…Separation in Three Dimensions. Among the major contributors to the understanding of three-dimensional boundary-layer separation are Moore (1956), Eichelbrenner andOudart (1954 , 1973) , Maskell (1955), Lighthill (1963), Brown and Stewartson (1969), Wang (1972) , and Smith (1975. As indicated earlier , a majority of the previous work has centered around correla ting the occurrence of~~~~~…”

Section: Security Classification Of This Page (Wbin D~~~ Ef L Trd)mentioning

confidence: 99%

Flow-Visualization of Three-Dimensional Boundary-Layer Separation on Bodies of Revolution at Incidence.

Han¹,

Patel²

1977

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Three‐dimensional Boundary Layers

Cited by 5 publications

References 5 publications

Three-dimensional laminar boundary layers and the ok of accessibility

Three-dimensional laminar boundary layers and the ok of accessibility

New solutions for laminar boundary layers with cross flow

Flow-Visualization of Three-Dimensional Boundary-Layer Separation on Bodies of Revolution at Incidence.

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