Some Simple Results for Two-Dimensional Jet-Flap Aerofoils

1958 ◽  
Vol 9 (4) ◽  
pp. 395-406 ◽  
Author(s):  
D. A. Spence
Keyword(s):  
High Velocity ◽  
Lift Coefficient ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Momentum Coefficient ◽  
Image Position ◽  
Derivatives Of

SummaryIt is shown from elementary considerations that the lift coefficient of a thin two-dimensional wing at zero incidence, with a narrow high-velocity jet of momentum coefficient Cj issuing from its trailing edge at a (small) downward inclination τ, is given byand the loading on the chord line (0<x<1) by(except in a certain neighbourhood of the trailing edge), for small values of Cj. These formulae agree well with known measurements. Interpolation formulae for derivatives of CL at larger values of CJ based on earlier work, are also given:

The aerodynamic performance of paragliders

1999 ◽  
Vol 103 (1027) ◽  
pp. 421-428 ◽  
Author(s):  
H. Babinsky
Keyword(s):  
Separation Bubble ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Wing Section ◽  
Two Factors ◽  
Performance Deterioration ◽  
Edge Separation

Abstract An analysis of paraglider performance has revealed that wing section drag is the most significant contribution to overall drag. Wind tunnel measurements performed on two-dimensional hollow models indicate that intake drag is less significant than previously thought. An experimental investigation into the characteristics of a ‘quasi ’ -two-dimensional flexible model consisting of solid ribs covered with a fabric skin was performed at realistic Reynolds numbers. The main cause of performance deterioration was found to be a significant reduction in section lift coefficient when compared to a similar solid wing section. This is believed to be mainly due to two factors: a large trailing edge separation and the deformation of the wing between ribs. The deformation was measured and it was shown that the deformed shape is less capable of generating high lift coefficients than the design section. It is thought that the extent of the trailing edge separation is increased due to the presence of streamwise grooves caused by the shape deformation of the wing. The shape of the separated region was found to be strongly three-dimensional with the separation point being about half a chord-length further upstream along the ribs. A small separation bubble was also observed immediately behind the lip of the intake, due to the fabric ‘flaring’ open. Based on the observations presented a number of suggestions for improved wings have been made.

The Effect of Intake and Exhaust on the Two-Dimensional Airfoil in a Distributed Propulsion System

2016 ◽  
Author(s):  
Yongsheng Wang ◽  
Ming Zhou ◽  
Quanyong Xu
Keyword(s):  
Lift Coefficient ◽  
Leading Edge ◽  
Jet Flow ◽  
Propulsion System ◽  
Two Dimensional ◽  
Original Design ◽  
Trailing Edge ◽  
Distributed Propulsion ◽  
Drag Ratio

A new distributed propulsion system in which micro-engines were embedded into the wings was proposed. To consider the effects of the intake and exhaust of the engines, the system was simplified as a two-dimensional airfoil with a surface ingestion and a trailing edge jet. The influence of the layout was comprehensively studied with CFD. Compared to the original design, the surface ingestion and trailing edge jet can increase the lift coefficient. The lift-drag ratio increases at smaller attack angles (< 3°) and decreases at greater attack angles (> 3°). The lift-drag ratio improvement with surface ingestion at the leading edge is mainly due to the drop in drag, while the increase with ingestion close to the trailing edge is primarily because of the augment of lift. Moreover, increasing the temperature of the jet flow can enlarge the range of the attack angles with a higher lift-drag ratio.

The High Subsonic Flow Around a Two-Dimensional Aerofoil with a Trailing Edge Control Surface

1973 ◽  
Vol 24 (4) ◽  
pp. 273-283 ◽  
Author(s):  
D Nixon
Keyword(s):  
Linear Theory ◽  
Subsonic Flow ◽  
Lift Coefficient ◽  
Integral Equation Method ◽  
Control Surface ◽  
Two Dimensional ◽  
Front Part ◽  
Trailing Edge ◽  
Moment Coefficient ◽  
Standard Linear

SummaryThe effect of the operation of a 15 per cent trailing edge control surface on the flow around a two-dimensional aerofoil in a high subsonic shock-free condition is investigated using the integral equation method developed by Nixon and Hancock. The effect of retaining the non-linearities in the transonic potential equation is to increase considerably the magnitude of the pressures over the front part of the aerofoil in comparison with the pressure found using a modified linearised theory in which significant second-order terms in the boundary conditions are retained. The magnitude of the lift coefficient and the pitching moment coefficient are increased by 10-15 per cent over the values found using the modified linear theory, and by 20 per cent over the values found using standard linear theory. However, the magnitude of the hinge-moment coefficient is decreased by the order of 20 per cent compared with the modified linear values and by 30 per cent when compared to the standard linear values.

An Extension of Two-Dimensional Sail Theory

1972 ◽  
Vol 16 (02) ◽  
pp. 148-152
Author(s):  
E. O. Tuck ◽  
M. Haselgrove
Keyword(s):  
Lift Coefficient ◽  
Direct Application ◽  
Two Dimensional ◽  
Optimum Length ◽  
Trailing Edge

The two-dimensional sail theory of Thwaites is extended to account for nonrigid attachment of the trailing edge (leach) of the sail. This extension enables direct application to foresails (jibs), and possible application to mainsails. Results for sail shape and lift coefficient are presented which suggest a possible optimum length for jib sheets.

An Experimental Investigation of a Low-Speed Circulation-Controlled Aerofoil

1968 ◽  
Vol 19 (2) ◽  
pp. 170-182 ◽  
Author(s):  
R. J. Kind ◽  
D. J. Maull
Keyword(s):  
Experimental Investigation ◽  
Angle Of Incidence ◽  
Pitching Moment ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Low Speed ◽  
Momentum Coefficient ◽  
Blunt Trailing Edge ◽  
Elliptic Section ◽  
Jet Blowing

SummaryExperiments performed on a low-speed circulation-controlled aerofoil are described. The aerofoil was of elliptic section with the circulation controlled by means of a jet blowing around the blunt trailing edge. Results for the lift, drag and pitching moment on the aerofoil are presented as functions of the blowing momentum coefficient and the angle of incidence. The results are for a two-dimensional aerofoil. Possible applications of this type of aerofoil are briefly discussed.

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

Word problems related to derivatives of the displacement map

1991 ◽  
Vol 110 (3) ◽  
pp. 569-579 ◽  
Author(s):  
J. Devlin
Keyword(s):  
Periodic Solutions ◽  
Word Problem ◽  
Word Problems ◽  
Abstract Word ◽  
Local Problem ◽  
Image Position ◽  
Derivatives Of

In [6], we considered the equationwhere z ∈ ℂ and the pi are real-valued functions; abstract word-problem concepts and techniques were applied to the local problem of the bifurcation of periodic solutions out of the solution Z ≡ 0. This paper is a sequel to [6]; we present an extension of certain concepts given in that paper, and give a global version of some of our word-problem results.

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