Polhamus Langley Research Center SUMMARY A concept for the calculation of the vortex lift of sharp-edge delta wings is pre­sented and compared with experimental data. The concept is based on an analogy between the vortex lift and the leading-edge suction associated with the potential flow about the leading edge. This concept, when combined with potential-flow theory modified to include the nonlinearities associated with the exact boundary condition and the loss of the

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A concept of the vortex lift of sharp-edge delta wings based on a leading-edge-suction analogy

This paper seeks to clarify what is meant by the ‘social construction of nature’, which has become a crude but common term used to describe very different understandings of nature, knowledge and the world. I distinguish two broad varieties of construction talk in the social sciences: construction-as-refutation and construction-as-philosophical-critique. The first uses the construction metaphor to refute false beliefs about the world and is consistent with orthodox philosophical stances, such as positivism and realism. By contrast, I identify four other, more radical sorts of construction-as-philosophical-critique that use the construction metaphor to question the culture/nature, subject/object and representation/reality dualisms that provide the conventional philosophical foundation for distinguishing true conceptions of nature from false ones. Another source of confusion has been the question of precisely what is meant by the term ‘nature’. Making distinctions among different senses of that term can prov...

What is the ‘social construction of nature’? A typology and sympathetic critique

Two problems involving the unsteady motion of two-dimensional vortex sheets are considered. The first is the roll-up of an initially plane semi-infinite vortex sheet while the second is the power-law starting flow past an infinite wedge with separation at the wedge apex modelled by a growing vortex sheet. In both cases well-known similarity solutions are used to transform the time-dependent problem for the sheet motion into an integro-differential equation. Finite-difference numerical solutions to these equations are obtained which give details of the large-scale structure of the rolled-up portion of the sheet. For the semi-infinite sheet good agreement with Kaden's asymptotic spiral solution is obtained. However, for the starting-flow problem distortions in the sheet shape and strength not predicted by the leading-order asymptotic solutions were found to be significant.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112078002189

The large-scale structure of unsteady self-similar rolled-up vortex sheets

A point-vortex representation is used to study numerically the evolution of an initially plane vortex sheet. By introducing a tip vortex to represent the tightly rolled portion of the vortex sheet, the chaotic motion which was a feature of some earlier studies is eliminated and the details of the outer portion of the spiral are calculated. The rate of rolling up is calculated and is shown to be governed by the analytically predicted similarity law of Kaden during the initial stages of the rolling up. The calculations are continued until 99% of the vorticity has been rolled up, at which stage the spiral displays a marked ellipticity.

A numerical study of the roll-up of a finite vortex sheet

*† ‡ Vortex control concepts employed for slender and nonslender delta wings were reviewed. Important aspects of flow control include flow separation, vortex formation, flow reattachment, vortex breakdown, and vortex instabilities. The occurrence and relative importance of these phenomena strongly depend on the wing sweep angle. Various flow control methods were discussed: multiple vortices, control surfaces, blowing and suction, low-frequency and high-frequency excitation, feedback control, passive control with wing flexibility, and plasma actuators. For slender delta wings, control of vortex breakdown is achieved by modifications to swirl level and external pressure gradient acting on the vortex core. Effects of flow control methods on these two parameters were discussed, and their effectiveness was compared whenever possible. With the high-frequency excitation of the separated shear layer, reattachment and lift enhancement in the post-stall region is observed, which is orders of magnitude more effective than steady blowing. This effect is more pronounced for nonslender wings. Re-formation of vortices is possible with sufficient amplitude of forcing at the optimum frequency. Passive lift enhancement on flexible wings is due to the self-excited wing vibrations, which occur when the frequency of wing vibrations is close to the frequency of the shear layer instabilities, and promote flow reattachment.

Review of flow control mechanisms of leading-edge vortices

In previous calculations (Mangler & Smith 1959) of the vortex-sheet model of leading-edge separation, only qualitative agreement was found with experimental observations. Because the numerical treatment of the model was then necessarily incomplete, it was uncertain how far the lack of quantitative agreement was to be attributed to the limitations of the model. The use of an automatic digital computer has now made it possible to reduce the uncertainties in the calculation to a negligible level. The features of interest in the real flow are more accurately predicted and the remaining discrepancies can be ascribed to the deficiencies in the model. The paper describes the method used to locate the vortex sheet and determine its strength in terms of the two boundary conditions on it; assesses the credibility of the results; and relates them to the observations. It is concluded that the model successfully predicts the observed height of the vortex above the wing, though the predicted lateral position is in error by up to 6% of the semi-span of the wing. This error falls as the incidence increases and is less when transition occurs in the boundary-layer upstream of secondary separation. Normal force is predicted accurately as is the distribution of pressure on the lower surface and the inboard part of the upper surface. The observed suction peak below the vortex changes its character when transition occurs in the boundary-layer upstream of secondary separation. The model predicts the suction peak in the turbulent case fairly well, but it is clear that detailed prediction of the suction peak is not possible by a model which is wholly inviscid.

Improved calculations of leading-edge separation from slender, thin, delta wings

The flow at incidence to a slender delta wing with a sharp leading edge usually separates along this edge, i.e. a vortex layer extends from the edge into the main flow. This layer rolls up above and inboard of the leading edge to form a region of high vorticity which strongly influences the flow pattern. This paper gives a theoretical treatment, more complete than those hitherto available, of this type of flow. A potential flow model is constructed, in which the vortex layer is replaced by a vortex sheet of spiral form, and the problem is then reduced to a two-dimensional one by the use of slender-body theory and the assumption of a conical velocity field. The boundary conditions expressing that the vortex sheet is a stream surface and sustains no pressure difference determine, in principle, its shape and strength. In practice, the inner part of the spiral and the finite, outer part of the spiral, which joins the inner part to the leading edge, are treated separately. The inner part is regarded as small and a solution is given for it which is asymptotically correct as the centre of the spiral is approached. The outer part is replaced by a sheet whose shape and strength depend on a finite number of parameters; these parameters are determined by applying the boundary conditions at isolated points. Results are given for the shape of the sheet and the pressures, loadings and forces on the wing, as functions of the ratio of the incidence to the aspect ratio.

J. H. B. Smith

Papers

Improved calculations of leading-edge separation from slender, thin, delta wings

A Theory of the Flow Past a Slender Delta Wing with Leading Edge Separation