Lift and drag characteristics of a delta-wing-half-cone configuration with subsonic leading edges, using slender-body theory

1968 ◽  
Vol 2 (2) ◽  
pp. 187-205
Author(s):  
W. J. Bannink ◽  
J. W. Reyn
Keyword(s):  
Delta Wing ◽  
Slender Body ◽  
Slender Body Theory ◽  
Leading Edges ◽  
Lift And Drag ◽  
Body Theory ◽  
Half Cone

The Slender Wing with a Half Body of Revolution Mounted Beneath

1968 ◽  
Vol 72 (693) ◽  
pp. 803-807 ◽  
Author(s):  
H. Portnoy
Keyword(s):  
Supersonic Flow ◽  
Slender Body ◽  
Meridian Plane ◽  
Pitching Moment ◽  
Body Of Revolution ◽  
Slender Body Theory ◽  
Lift And Drag ◽  
Body Theory ◽  
Slender Wing

Summary The slender-body theory of Ward is applied to a configuration consisting of a slender, pointed wing, carrying directly beneath it a pointed half-body of revolution divided along a meridian plane. Expressions for lift and drag due to incidence are found which are valid in both subsonic and supersonic flow if the flow is attached. The lift result can be used to find pitching moment. For the supersonic case the drag at zero incidence is also found and the expressions for a conical configuration are developed so that a limiting form of these can be compared with the results of ref. 3.

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.

Note on the swimming of slender fish

1960 ◽  
Vol 9 (2) ◽  
pp. 305-317 ◽  
Author(s):  
M. J. Lighthill
Keyword(s):  
Swimming Speed ◽  
Critical Value ◽  
Slender Body ◽  
Vortex Wake ◽  
Frictional Drag ◽  
Slender Body Theory ◽  
Propulsive Efficiency ◽  
Deformable Bodies ◽  
Work Done ◽  
Body Theory

The paper seeks to determine what transverse oscillatory movements a slender fish can make which will give it a high Froude propulsive efficiency, $\frac{\hbox{(forward velocity)} \times \hbox{(thrust available to overcome frictional drag)}} {\hbox {(work done to produce both thrust and vortex wake)}}.$ The recommended procedure is for the fish to pass a wave down its body at a speed of around $\frac {5} {4}$ of the desired swimming speed, the amplitude increasing from zero over the front portion to a maximum at the tail, whose span should exceed a certain critical value, and the waveform including both a positive and a negative phase so that angular recoil is minimized. The Appendix gives a review of slender-body theory for deformable bodies.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Application of Slender-Body Theory

1957 ◽  
Vol 1 (04) ◽  
pp. 40-49
Author(s):  
Paul Kaplan
Keyword(s):  
Slender Body ◽  
Vertical Force ◽  
Regular Waves ◽  
Slender Body Theory ◽  
Surface Theory ◽  
Surface Ship ◽  
Submerged Body ◽  
Dynamic Forces ◽  
Body Theory

The vertical force and pitching moment acting on a slender submerged body and on a surface ship moving normal to the crests of regular waves are found by application of slender-body theory, which utilizes two-dimensional crossflow concepts. Application of the same techniques also results in the evaluation of the dynamic forces and moments resulting from the heaving and pitching motions of the ship, which corrected previous errors in other works, and agreed with the results of specialized calculations of Havelock and Has-kind. An outline of a rational theory, which unites slender-body theory and linearized free-surface theory, for the determination of the forces, moments and motions of surface ships, is also included.

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