An Alternative Approach to the High Aspect Ratio Wing With Jet Flap by Matched Asymptotic Expansions

1978 ◽  
Vol 29 (4) ◽  
pp. 227-250 ◽  
Author(s):  
T. Kida ◽  
Y. Miyai
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Matched Asymptotic Expansions ◽  
Alternative Approach ◽  
Line Theory ◽  
Physical Insight ◽  
Lifting Line ◽  
Lifting Line Theory

SummaryAn alternative method is described for solving the problem of a three-dimensional jet-flapped wing with a high aspect-ratio. This method is similar to the lifting-line theory of Kerney6 or Tokuda7, but differs in that the method of matched asymptotic expansions is applied to an integral equation, derived from the lifting surface theory, rather than a partial differential equation. The advantage of the present method over those used previously is that the necessary outer solutions are obtained directly; it is not necessary to rely upon physical insight or considerable ingenuity. The final results are different from those obtained by the previous authors; it is shown that the present result is correct, by noting some errors in the earlier theories.

Unsteady lifting-line theory by the method of matched asymptotic expansions

1988 ◽  
Vol 186 ◽  
pp. 303-320 ◽  
Author(s):  
P. Wilmott
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Principal Result ◽  
Matched Asymptotic Expansions ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory ◽  
General Motion

An unsteady lifting-line theory is presented for a general motion of a wing of high aspect ratio. Our matched-asymptotic-expansions analysis parallels that of Van Dyke (1964) in his solution for the steady lifting line, but is complicated by the shedding of transverse vortices associated with variation of circulation with time. The principal result is an expression for the downwash due to three-dimensional effects. Numerical calculations are presented for a wing of elliptic planform following a curved path.

A New Approach To High-Aspect-Ratio Supercavitating Hydrofoils

1979 ◽  
Vol 23 (03) ◽  
pp. 218-227
Author(s):  
Teruhiko Kida ◽  
Yoshihiro Miyai
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Present Theory ◽  
Cavitation Number ◽  
New Approach ◽  
Surface Theory ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

A three-dimensional cavity hydrofoil with a high aspect ratio is analyzed by a new lifting-line theory. Unlike Leehey's (1971) approach, which formulates the lifting-line theory from differential equations, the present theory has extracted the similar lifting-line theory from integral equations derived from the lifting-surface theory. The chief advantage of this method is that it is not necessary to match the inner and outer solutions. This lifting-line theory seems to be close to experimental results for the elliptic planform with aspect ratio 3 and 5, and for the rectangular planform with aspect ratio 6, in the case of δ/α ≥ 1, where σ is the cavitation number and α the incidence of the foil.

scholarly journals Aeroelastic behaviour of a wing with over-the-wing mounted UHBR engine

2020 ◽  
Vol 11 (4) ◽  
pp. 1045-1055 ◽  
Author(s):  
N. Neuert ◽  
D. Dinkler
Keyword(s):  
Three Dimensional ◽  
High Lift ◽  
Reduced Order ◽  
Aerodynamic Loads ◽  
Flow Simulations ◽  
Dimensional Effects ◽  
Line Theory ◽  
Lifting Line ◽  
Bypass Ratio ◽  
Lifting Line Theory

Abstract The aeroelastic behaviour of a wing with an over-the-wing pylon-mounted ultra-high bypass ratio engine and high-lift devices is studied with a reduced-order model. Wing, pylon and engine structures are reduced separately using the modal approach and described by their natural frequencies and modes. The characteristic aerodynamic loads are investigated with steady and unsteady flow simulations of a two-dimensional profile section. These results indicate possible heave instabilities at strongly negative angles of attack. Three-dimensional effects are taken into account using an adapted lifting line theory according to Prandtl. Due to high circulations resulting from the high-lift systems, the effective angles of attack are in the range of the potential instabilities. The substructures and aerodynamic loads are coupled in modal space. For the wing without three-dimensional effects, the bending instability occurs at the corresponding negative angles of attack. Even though there is potential for improvement, including the three-dimensional effects shifts the endagered area to possible operation points.

An asymptotic theory of the jet flap in three dimensions

1971 ◽  
Vol 46 (4) ◽  
pp. 705-726 ◽  
Author(s):  
Naoyuki Tokuda
Keyword(s):  
Order Approximation ◽  
Three Dimensional ◽  
Outer Region ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Simple Method ◽  
Aspect Ratios ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory

A uniformly valid asymptotic solution has been constructed for three-dimensional jet-flapped wings by the method of matched asymptotic expansions for high aspect ratios. The analysis assumes that the flow is inviscid and incompressible and is formulated on the thin airfoil theory in accordance with the well-established Spence (1961) theory in two dimensions.A simple method emerges in treating the bound vortices along the jet sheet which forms behind the wing with the aid of the following physical picture. Three distinct flow regions—namely inner, outer and Trefitz—exist in the problem. Close to the wing the flow approximates to that in two dimensions. Therefore, Spence's solution in two dimensions applies. In the outer region a wing shrinks to a line of singularities from which the main disturbances of flow in this region arise. In particular, we find that the shape of the jet sheet, hence the strength of vortices, is now predetermined by the strength of the singularities there. Hence a complete flow field in the outer region can now be determined first by evaluating the flow due to various degrees of singularities along this line and then adding the effect of the jet bound vortices which is now known. Far removed from the wing, the well-known Trefftz region exists in which calculations of aerodynamic forces can be most easily done.The result has been applied to various wing planforms such as cusped, elliptic and rectangular wings. The present result breaks down for rectangular wings. However, we can apply Stewartson's (1960) solution for lifting-line theory for semi-infinite rectangular wings, because, to this second-order approximation it is established that the jet sheet in the outer region makes no contribution to lift, with the direct contribution of the deflected jet at the exit being cancelled by the reduced circulation in the jet vortices. This result for the rectangular wing gives excellent agreement with the experiments made on a rectangular wing, while the result for elliptic wings underestimates them considerably.

scholarly journals Unsteady lifting-line theory and the influence of wake vorticity on aerodynamic loads

2021 ◽  
Author(s):  
Hugh J. A. Bird ◽  
Kiran Ramesh
Keyword(s):  
Aspect Ratio ◽  
Oscillation Frequency ◽  
Cost Model ◽  
Computational Cost ◽  
Streamwise Vorticity ◽  
Aspect Ratios ◽  
Line Theory ◽  
Lifting Line ◽  
Lifting Line Theory ◽  
Low Computational Cost

AbstractFrequency-domain unsteady lifting-line theory (ULLT) provides a means by which the aerodynamics of oscillating wings may be studied at low computational cost without neglecting the interacting effects of aspect ratio and oscillation frequency. Renewed interest in the method has drawn attention to several uncertainties however. Firstly, to what extent is ULLT practically useful for rectangular wings, despite theoretical limitations? And secondly, to what extent is a complicated wake model needed in the outer solution for good accuracy? This paper aims to answer these questions by presenting a complete ULLT based on the work of Sclavounos, along with a novel ULLT that considers only the streamwise vorticity and a Prandtl-like pseudosteady ULLT. These are compared to Euler CFD for cases of rectangular wings at multiple aspect ratios and oscillation frequencies. The results of this work establish ULLT as a low computational cost model capable of accounting for interacting finite-wing and oscillation frequency effects and identify the aspect ratio and frequency regimes where the three ULLTs are most accurate. This research paves the way towards the construction of time-domain or numerical ULLTs which may be augmented to account for nonlinearities such as flow separation.

scholarly journals AN ALTERNATIVE APPROACH TO INDUCED DRAG REDUCTION

Aviation ◽  
2021 ◽  
Vol 25 (3) ◽  
pp. 202-210
Author(s):  
Nikolaos Kehayas
Keyword(s):  
Aspect Ratio ◽  
Drag Reduction ◽  
Structural Constraints ◽  
Induced Drag ◽  
Alternative Approach ◽  
Body Design ◽  
Line Theory ◽  
Drag And Lift ◽  
Lifting Line ◽  
Wing Tip

Induced drag constitutes approximately 40% of the total drag of subsonic civil transport aircraft at cruise conditions. Various types of winglets and several non-planar concepts, such as the C-wing, the joined wings, and the box plane, have been proposed for its reduction. Here, a new approach to induced drag reduction in the form of a combination of an elliptical and an astroid hypocycloid lift distribution is put forward. Lift is mainly generated from high circulation in the center part of the wing and fades away along the semi-span towards the wing tip. Using lifting line theory, the analysis shows that for fixed lift and wingspan the combined lift distribution results in an induced drag reduction of 50% with respect to the elliptical distribution. Due to its wing planform the combined lift distribution leads to a 51.5% higher aspect ratio. If structural constraints are placed, then the higher aspect ratio may affect wing weight. Although any substantial increase of wing weight is not envisaged, further study of the matter is required. Zero-lift drag and lift-dependent drag due to skin friction and viscosity-related pressure remain unaffected. The proposed lift distribution is particularly useful in a blended wing-body design.

A Three-Dimensional Theory for Calculating Circulation in Axial Turbomachines (Direct Problems)

1974 ◽  
Vol 96 (4) ◽  
pp. 365-371
Author(s):  
E. Lumsdaine ◽  
A. Fathy
Keyword(s):  
Finite Length ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Two Dimensional ◽  
Line Theory ◽  
Large Length ◽  
Circulation Distribution ◽  
Direct Problems ◽  
Lifting Line ◽  
Lifting Line Theory

In this work the steady-state spanwise circulation distribution of thin, slightly cambered radial blades of finite length is calculated using the method of singularities. The analysis extends the method of Scholz [1] for two-dimensional cascades to the three-dimensional case of radial blades of finite length. The effect of the casing enclosing the cascade is introduced by the method of images. The present analysis uses the generalized cylindrical coordinates without the restriction of the Prandtl lifting line theory. Comparisons show that for large hub-tip ratios, the use of the lifting line approximation will result in large errors. For small tip clearance or large length-chord ratio the present results reduce to the two-dimensional cascade solution.

A generalized lifting-line theory for curved and swept wings

1990 ◽  
Vol 211 ◽  
pp. 497-513 ◽  
Author(s):  
Jean-Luc Guermond
Keyword(s):  
Three Dimensional ◽  
Approximation Order ◽  
Total Force ◽  
Line Context ◽  
Line Theory ◽  
Carleman Type ◽  
Yaw Angle ◽  
Lifting Line ◽  
Swept Wings ◽  
Lifting Line Theory

A generalized lifting-line theory is developed in inviscid, incompressible, steady flow for curved, swept wings of large aspect ratio. It is shown in this paper that by using the integral formulation of the problem instead of the partial differential equation formulation, it is possible to circumvent the algebraic complications encountered by the previous approaches using the method of the matched asymptotic expansions. At each approximation order the problem is reduced to inverting a classical Carleman type integral equation. The asymptotic solution in terms of circulation is found up to A−1 and A−1 In (A−1). It is very convenient for illustrating the major three-dimensional effects induced on the flow by curvature and yaw angle. The concept of the finite part integrals, introduced by Hadamard (1932), is shown to be very useful for handling elegantly singularities like 1/x|x| or 1/|x| which occur in the course of our developments. Comparisons of the new, simple approach with lifting-surface theories reveal excellent agreements in terms of circulation. Furthermore, a consistent calculation of the three components of the total force acting on the wing is done in the lifting-line context without re-introducing the inner geometry of the wing.

scholarly journals Unsteady Lifting Line Theory Using the Wagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings

Aerospace ◽  
2018 ◽  
Vol 5 (3) ◽  
pp. 92 ◽  
Author(s):  
Johan Boutet ◽  
Grigorios Dimitriadis
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Test Case ◽  
Lattice Method ◽  
Linear Ordinary Differential Equations ◽  
Numerical Predictions ◽  
Line Theory ◽  
The Time Domain ◽  
Lifting Line ◽  
Lifting Line Theory

A method is presented to model the incompressible, attached, unsteady lift and pitching moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory through the unsteady Kutta–Joukowski theorem. The results are a set of closed-form linear ordinary differential equations that can be solved analytically or using a Runge–Kutta–Fehlberg algorithm. The method is validated against numerical predictions from an unsteady vortex lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.

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