Three-Dimensional Boundary Layers on Cones at Small Angles of Attack

1968 ◽  
Vol 35 (4) ◽  
pp. 634-640 ◽  
Author(s):  
O. Pinkus ◽  
S. B. Cousin
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Equivalent Radius ◽  
Wind Tunnel Model ◽  
Boundary Layer Equations ◽  
Tunnel Model ◽  
Dimensional Boundary ◽  
Heat Transfer Effects ◽  
Incipient Separation

Based on an expression given by Cooke, an equation is derived for a three-dimensional “equivalent radius” for cones at a small angle of attack. This function when used in any of the available axisymmetric boundary-layer equations yields corresponding solutions for yawed cones. Expressions for the streamlines along which the above equations are to be integrated are also derived. The method yields a line of possible incipient separation or wake formation in addition to the boundary-layer properties in both the longitudinal and circumferential direction. Numerical solutions including heat transfer effects are presented for a wind tunnel model and compared with experimental results.

Boundary layer at a swept stagnation line of semi-infinite extent

1970 ◽  
Vol 41 (4) ◽  
pp. 737-750 ◽  
Author(s):  
Paul A. Libby ◽  
Karl K. Chen
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Cross Flow ◽  
Differential Analysis ◽  
Eigenvalues And Eigenfunctions ◽  
Stagnation Line ◽  
Infinite Extent ◽  
Dimensional Boundary ◽  
Upstream Flow

A three-dimensional boundary layer developing along a semi-infinite swept stagnation line from a starting edge and evolving into that associated with such a line of infinite extent is calculated. A series solution useful for assessing the counteracting effects of cross-flow and mass transfer near the starting edge and for providing initial data for a subsequent streamwise, numerical solution is developed. The asymptotic behaviour far from the starting edge is examined and shown to involve only eigenfunction contributions associated with the far upstream flow. However, it is not presently possible to determine the relevant eigenvalues and eigenfunctions. Numerical solutions based on a difference-differential analysis yield the entire development of the boundary layer and indicate the streamwise length required for the case of the boundary layer at an infinite stagnation line to be obtained.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

On three-dimensional boundary layer flow over surface irregularities

1980 ◽  
Vol 373 (1754) ◽  
pp. 311-329 ◽  
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Solution Technique ◽  
Parabolic Boundary ◽  
Boundary Layer Equations ◽  
Surface Irregularities ◽  
Dimensional Boundary ◽  
Layer Flow

The three-dimensional pipeflow boundary layer equations of Smith (1976) are shown to apply to certain external flow problems, and a numerical method for their solution is developed. The method is used to study flow over surface irregularities, and some three-dimensional separated flows are calculated. Upstream influence in the form of so-called ‘free interactions’ requires an iterative solution technique, in which the initial conditions for the parabolic boundary layer equations must be determined to satisfy a downstream condition

Singularities in solutions of the three-dimensional laminar-boundary-layer equations

1985 ◽  
Vol 160 ◽  
pp. 257-279 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
New Type ◽  
Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

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