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.

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.

Induced Curved-Flow Effect in the Lifting-Surface Theory of the Widely Bladed Propellers

1967 ◽  
Vol 11 (01) ◽  
pp. 61-70
Author(s):  
Tetsuo Nishiyama ◽  
Takao Sasajima
Keyword(s):  
Present Theory ◽  
Surface Theory ◽  
Flow Effect ◽  
Lifting Surface ◽  
Line Theory ◽  
Lift Curve ◽  
Lifting Line ◽  
Lifting Line Theory ◽  
Good Agreement ◽  
Blade Element

The present paper is aimed to develop a more accurate lifting-surface theory of widely bladed propellers by applying the Scholz' technique. Curved-flow effect, which is of essential importance in the theory of widely bladed propellers, is analyzed and clarified in detail in the forms of correction coefficients to the lift-curve slope and zero lift angle of the blade element. Further, curved-flow correction to the lifting-line theory and the corresponding factor to the Ginzel's camber correction are shown by the present theory. The theoretical characteristics seem to be in good agreement with the experiment, so far as the assumption of linearization holds.

Some Remarks on Vortex Drag and its Spanwise Distribution in Incompressible Flow

1968 ◽  
Vol 72 (691) ◽  
pp. 623-625 ◽  
Author(s):  
H. C. Garner
Keyword(s):  
Theoretical Data ◽  
Leading Edge ◽  
List Type ◽  
Surface Theory ◽  
Lifting Surface ◽  
Line Theory ◽  
Lifting Line ◽  
Swept Wings ◽  
Lifting Line Theory ◽  
Drag Factor

Summary Theoretical data from lifting-surface theory are presented to illustrate (i) that the vortex drag factor is closely related to the half-wing spanwise centre of pressure on simple planforms without camber or twist, (ii) that lifting-line theory is useless for predicting the spanwise distribution of vortex drag on swept wings, (iii) that recent numerical improvements in lifting-surface theory help to reconcile the concepts of wake energy and leading-edge suction in relation to vortex drag.

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.

A New Approach to Lifting Line Theory: Hub and Duct Effects

2006 ◽  
Vol 50 (02) ◽  
pp. 138-146
Author(s):  
Victor G. Mishkevich
Keyword(s):  
Mathematical Model ◽  
Singular Integrals ◽  
Jacobi Polynomials ◽  
New Approach ◽  
Improve Design ◽  
Propeller Design ◽  
Line Theory ◽  
Circulation Distribution ◽  
Lifting Line ◽  
Lifting Line Theory

This paper deals with a new approach to lifting line theory in which the presence of a hub and/or duct is taken into account by introducing the generalized induction factors. The proposed mathematical model is built on the assumption that the hub and/or duct are simulated with infinite cylinders. The circulation distribution function is represented in the form of a series of orthogonal Jacobi polynomials that covers all cases that can occur in practical propeller design, including both zero and nonzero gap conditions. The integral equation of the lifting line theory is solved numerically by applying the highest accuracy quadrature formula for singular integrals. Propellers with optimum and arbitrary circulation distribution are considered. The proposed theory is intended to improve design of the near hub and duct blade sections, cavitation control, and integral propeller characteristics. Numerical results are presented for the purpose of comparison with different methods and to illustrate the developed approach.

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.

Sign in / Sign up

Export Citation Format

Share Document