On the Exact Solution of the Linearized Lifting-Surface Problem of an Elliptic Wing

Hauptman, A.; Miloh, T.

doi:10.1093/qjmam/39.1.41

Cited by 15 publications

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“…Equation (3.8) was solved for a rectangular region D of arbitrary aspect ratio with up to seven-digit accuracy. An explicit solution of equation (3.8) has been obtained for an elliptic region D by Hauptmann & Miloh (1986). A finite element method was used by Donguy et al (2000) to solve the threedimensional impact problem with respect to the displacement potential.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Three-dimensional theory of water impact. Part 1. Inverse Wagner problem

Scolan¹,

Korobkin

2001

J. Fluid Mech.

152

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The three-dimensional problem of blunt-body impact onto the free surface of an ideal incompressible liquid is considered within the Wagner theory. The theory is formally valid during an initial stage of the impact. The problem has been extensively studied in both two-dimensional and axisymmetric cases. However, there are no exact truly three-dimensional solutions of the problem even within the Wagner theory. At present, three-dimensional effects in impact problems are mainly handled approximately by using a sequence of two-dimensional solutions and/or aspect-ratio correction factor. In this paper we present exact analytical rather than approximate solutions to the three-dimensional Wagner problem. The solutions are obtained by the inverse method. In this method the body velocity and the projection on the horizontal plane of the contact line between the liquid free surface and the surface of the entering body are assumed to be given at any time instant. The shape of the impacting body is determined from the Wagner condition. It is proved that an elliptic paraboloid entering calm water at a constant velocity has an elliptic contact line with the free surface. Most of the results are presented for elliptic contact lines, for which analytical solutions of the inverse Wagner problem are available. The results obtained can be helpful in testing other numerical approaches and studying the influence of three-dimensional effects on the liquid flow and the hydrodynamic loads.

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Section: Methods Of Solutionmentioning

confidence: 99%

Three-dimensional theory of water impact. Part 1. Inverse Wagner problem

Scolan¹,

Korobkin

2001

J. Fluid Mech.

152

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“…The computations suggest that the convergence with respect to n is like n~l, so that the extrapolated estimate for (m, n) -(10, oo) from the above results is 1.790350. This is better than 4-figure agreement with the exact value 1.790750 of Hauptmann and Miloh [5], but this agreement is again perhaps a fluke, and less satisfactory extrapolation occurs at other n values. The nearly 3-figure accuracy obtained by the actual computation for the (10,20) panelisation of Figure 8 is perhaps representative of what is achievable by this naive procedure, and more work is needed if this method is to be competitive for general non-rectangular planforms.…”

Section: Rectangular Panels For Non-rectangular Wingsmentioning

confidence: 60%

“…The lifting surface equation (1.1) cannot be solved analytically for arbitrary B. However, an explicit solution has been obtained for elliptic B by Hauptmann and Miloh [5]. When B is a circle, this solution for y(x, y) is expressed in the form of a series of associated Legendre functions, and the lift coefficient (1.3) is found to be CJa = 32/(8 + n 2 ) = 1.7907503.…”

Section: W(x Y) = Y~2{\ + X/r) (12)mentioning

confidence: 99%

“…Obviously this change has a greater effect on the chordwise discretisation (3.3), (3.4) than the spanwise discretisation (3.5), (3.6), though it does make the latter appear to produce even closer to an O(«~3) rate. The effect on the chordwise discretisation is to increase the rate to slightly better than O(m~3 5 ). Figures 3 and 4 (for a flat square wing) illustrate the accuracy of the final method.…”

Section: Computational Experiencementioning

confidence: 99%

See 1 more Smart Citation

Some accurate solutions of the lifting surface integral equation

Tuck

1993

J. Aust. Math. Soc. Series B, Appl. Math

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This note describes a simple numerical method for solution of the lifting surface integral equation of aerodynamics, and provides benchmark computations of up to 7 figure accuracy for flat rectangular wings of arbitrary aspect ratio. The nature of the large aspect ratio limit is also investigated numerically and asymptotically. This enables determination of the limiting behaviour near the wing tips, which is compared to the predictions of lifting line theory. Generalisations to non-rectangular wings are discussed.

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“…The tip region of the thin, flat wing of elliptic planform has been studied in some detail by Jordan' 2627 '. The recent work by Hauptman and Miloh' 28 ' provides results for a wing of elliptic planform with some twist. At supersonic speeds, complete solutions within the framework of linearised theory can be obtained.…”

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confidence: 99%

Introductory remarks

Smith¹

1987

Aeronaut. j.

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On the afternoon of 14th April 1987, the Society held a half-day symposium on wing-tip flows and devices. Papers were presented by J. J. Spillman of Cranfield Institute of Technology on wing-tip sails, by A. C. Willmer of British Aerospace (in association with R. V. Barrett and J. D. Coleman of Bristol University) on the tip flow of part-span flaps, and by H. P. Horton of Queen Mary College on measurements in the viscous flow regions of streamlined tips. Written versions of two of these talks and a synopsis of the third* have been prepared and are being printed in the Journal following these introductory remarks. The contribution by J. S. Smith of RAE to the discussion session is appearing elsewhere.

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On the Exact Solution of the Linearized Lifting-Surface Problem of an Elliptic Wing

Cited by 15 publications

References 0 publications

Three-dimensional theory of water impact. Part 1. Inverse Wagner problem

Three-dimensional theory of water impact. Part 1. Inverse Wagner problem

Some accurate solutions of the lifting surface integral equation

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