The flow field near the centre of a rolled-up vortex sheet

1967 ◽  
Vol 30 (1) ◽  
pp. 177-196 ◽  
Author(s):  
K. W. Mangler ◽  
J. Weber
Keyword(s):  
Delta Wing ◽  
Present Report ◽  
Vortex Sheet ◽  
Slender Body ◽  
Two Dimensional ◽  
Slender Body Theory ◽  
Vortex Sheets ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Body Theory

Most of the existing methods for calculating the inviscid flow past a delta wing with leading-edge vortices are based on slender-body theory. When these vortices are represented by rolled-up vortex sheets in an otherwise irrotational flow, some of the assumptions of slender-body theory are violated near the centres of the spirals. The aim of the present report is to describe for the vortex core an alternative method in which only the assumption of a conical velocity field is made. An asymptotic solution valid near the centre of a rolled-up vortex sheet is derived for incompressible flow. Further asymptotic solutions are determined for two-dimensional flow fields with vortex sheets which vary with time in such a manner that the sheets remain similar in shape. A particular two-dimensional flow corresponds to the slender theory approximation for conical sheets.

Inviscid separated flow over a non-slender delta wing

1995 ◽  
Vol 305 ◽  
pp. 307-345 ◽  
Author(s):  
D. W. Moore ◽  
D. I. Pullin
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Delta Wing ◽  
Nonlinear Eigenvalue Problem ◽  
Vortex Sheet ◽  
Slender Body ◽  
Normal Velocity ◽  
Slender Body Theory ◽  
Closed Set ◽  
Body Theory

We consider inviscid incompressible flow about an infinite non-slender flat delta wing with leading-edge separation modeled by symmetrical conical vortex sheets. A similarity solution for the three dimensional steady velocity potential Φ is sought with boundary conditions to be satisfied on the line which is the intersection of the wing sheet surface with the surface of the unit sphere. A numerical approach is developed based on the construction of a special boundary element or ‘winglet’ which is effectively a Green function for the projection of ∇2Φ = 0 onto the spherical surface under the similarity ansatz. When the wing semi-apex angle γo is fixed satisfaction of the boundary conditions of zero normal velocity on the wing and zero normal velocity and pressure continuity across the vortex sheet then leads to a nonlinear eigenvalue problem. A method of ensuring a condition of zero lateral force on a lumped model of the inner part of the rolled-up vortex sheet gives a closed set of a equations which is solved numerically by Newton's method. We present and discuss the properties of solutions for γ0 in the range 1.30 < γ <89.50. The dependencies of these solutions on γ0 differs qualitatively from predictions of slender-body theory. In particular the velocity field is in general not conical and the similarity exponent must be calculated as part of the global eigenvalue problem. This exponent, together with the detailed flow field including the position and structure of the separated vortx sheet, depend only on γ0. In the limit of small γ0, a comparison with slender-body theory is made on the basis of an effective angle of incidence.

Boundary-Layer Flow Between the Attachment Lines on a Flat Plate Delta Wing at Incidence

1962 ◽  
Vol 13 (1) ◽  
pp. 1-16
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Delta Wing ◽  
Three Dimensional ◽  
External Flow ◽  
Two Dimensional ◽  
Conical Flow ◽  
Slender Body Theory ◽  
Layer Flow ◽  
Body Theory ◽  
Transition Fronts

SummaryA three-dimensional laminar-boundary-layer calculation is carried out over the area concerned. The external flow is simplified, being calculated by slender-body theory assuming conical flow, with two point vortices above the wing, their positions and strength being determined by experiment. Attempts are made to draw transition fronts both for two-dimensional and sweep instability from this calculation. The combination of these gives fronts similar to those observed in some experiments. Because there is little or no pressure gradient over the area in question it is suggested that it is a region where distributed suction might usefully be applied in order to maintain laminar flow and reduce drag.

Two-Dimensional Apparent Masses for Cross-Flow Sections of Wing-Store Configurations

1982 ◽  
Vol 49 (3) ◽  
pp. 471-475
Author(s):  
M.-K. Huang
Keyword(s):  
Approximate Method ◽  
Cross Flow ◽  
Slender Body ◽  
Two Dimensional ◽  
Aerodynamic Stability ◽  
Slender Body Theory ◽  
Rolling Moment ◽  
Stability Derivatives ◽  
The Cross ◽  
Body Theory

On the basis of the assumption that the external stores are small compared with the wing, an approximate method has been developed for estimation of two-dimensional apparent masses for the cross-flow sections of wing-store combinations. The results obtained may be applicable to the analysis of the effects of the stores on the aerodynamic stability derivatives in slender-body theory. The theory has also been applied to estimate the rolling moment due to sideslip for high-wing configurations. The presented results are in agreement with those of other investigations.

A generalized slender-body theory for fish-like forms

1973 ◽  
Vol 57 (4) ◽  
pp. 673-693 ◽  
Author(s):  
J. N. Newman ◽  
T. Y. Wu
Keyword(s):  
The Body ◽  
Slender Body ◽  
Slender Body Theory ◽  
Vortex Sheets ◽  
Flow Past ◽  
Longitudinal Orientation ◽  
Trailing Edges ◽  
Lifting Surfaces ◽  
Axisymmetric Bodies ◽  
Body Theory

A consistent slender-body approximation is developed for the flow past a fish- like body with arbitrary combinations of body thickness and low-aspect-ratio fin appendages, but with the fins confined to the plane of symmetry of the body. Attention is focused on the interaction of the fin lifting surfaces with the body thickness, and especially on the dynamics of the vortex sheets shed from the fin trailing edges. This vorticity is convected by the (non-lifting) flow past the stretched-straight body, and departs significantly from the purely longitudinal orientation of conventional lifting-surface theory. Explicit results are given for axisymmetric bodies having fins with abrupt trailing edges, and calculations of the total lift force are presented for bodies with symmetric and asymmetric fin configurations, moving with a constant angle of attack.

Two-Dimensional Flow of Polymer Solutions Through Porous Media

1999 ◽  
Vol 2 (3) ◽  
pp. 251-262
Author(s):  
P. Gestoso ◽  
A. J. Muller ◽  
A. E. Saez
Keyword(s):  
Porous Media ◽  
Polymer Solutions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow
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