On the remarkable accuracy of the vortex lattice method

James, R. M.

doi:10.1016/0045-7825(72)90021-7

Cited by 49 publications

(16 citation statements)

References 3 publications

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“…5 This tendency remains to be explained, as do other aspects of the method, 9 but it suggests that a correcting scale factor be introduced into the spanwise distribution of induced drag that is based on the cross-flow energy in the wake (i.e., the total induced drag). The correcting scale factor is defined as the ratio CDiJCoiv where Coi W is the wake integral given by Eq.…”

Section: Applicationsmentioning

confidence: 98%

Spanwise distribution of induced drag in subsonic flow by the vortexlattice method

Giesing¹,

Kalman²,

Rodden³

1970

Journal of Aircraft

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Nomenclature A = aspect ratio Cot = total induced drag coefficient of surface CDW = total induced drag coefficient given by Vortex Lattice Method CD^ = total induced drag given by wake integral CL = total lift coefficient of surface c = chord length of strip c = average chord length of surface Cdi = induced drag coefficient of strip ci = lift coefficient of strip Dd = normalwash factor at bound vortex DC -normalwash factor at control point d = induced drag coefficient of box e = semiwidth of strip M = Mach number p = pressure coefficient of box S = reference area s = semispan of surface Wb = dimensionless normalwash at bound vortex w c = dimensionless normalwash at control point x,y,z = Cartesian coordinates a.= angle of attack ai = induced incidence at bound vortex 77 = dummy spanwise coordinate

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Section: Applicationsmentioning

confidence: 98%

Spanwise distribution of induced drag in subsonic flow by the vortexlattice method

Giesing¹,

Kalman²,

Rodden³

1970

Journal of Aircraft

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“…If the vortex filaments and control points are located at the local quarter and three-quarter chord points of the panel, respectively, the Kutta condition is implicitly satisfied, and no additional boundary condition is needed at the trailing edge. 18 ' 19 Although no left-hand superscript is given in Eq. (lOa) indicating the time index of the configuration or velocity step, it should be clear that the aerodynamic pressures are to be evaluated at the current configuration and velocity step at time t + At.…”

Section: Aerodynamic Problemmentioning

confidence: 99%

“…12 The use of a lattice of vortex filaments to model the lifting potential flow around thin wings has its historical origin and justification in work by James. 18 A description of the method in its modern form for wings of finite span may be found in Ref. 19.…”

Section: Aerodynamic Problemmentioning

confidence: 99%

Incremental Potential Flow Based Membrane Wing Element

Smith

Shyy

1997

AIAA Journal

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A new quadrilateral membrane wing element is presented that combines an incremental formulation of the elastic membrane problem with a vortex lattice formulation of the thin wing aerodynamic problem. The incremental formulation leads to an explicit/implicit velocity-stepping algorithm for solving the coupled aeroelastostatic membrane wing problem. The Stein-Hedgepeth wrinkle model is adopted as the constitutive relation for the membrane, which may develop slack or wrinkled regions. The element is shown to satisfy two limiting cases of the aeroelastic problem for which there are well-known analytic solutions. The algorithm is applied to two moderate aspect ratio membrane wing configurations with the second configuration being a model of a marine sail.

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“…So the solution is still not unique, and may become dependent on details of the numerical scheme. See for example [30].…”

Section: Introductionmentioning

confidence: 99%

A note on the Kutta condition in Glauert’s solution of the thin aerofoil problem

Rienstra

1992

Problems in Applied, Industrial and Engineering Mathematics

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SummaryGlauert's classical solution of the thin aerofoil problem (a coordinate transformation, and splitting the solution into a sum of a singular part and an assumed regular part written as a Fourier sine series) is usually presented in textbooks on aerodynamics without a great deal of attention being paid to the role of the Kutta condition. Sometimes the solution is merely stated, apparently satisfying the Kutta condition automatically. Quite often, however, it is misleadingly suggested that it is by the choice of a sine series that the Kutta condition is satisfied.It is shown here that if Glauert 's approach is interpreted in the context of generalised functions, (1) the whole solution, i.e. both the singular part and any non-Kutta condition solution, can be written as a sine-series, and (2) it is really the coordinate transformation which compels the Kutta condition to be satisfied, as it enhances the edge singularities from integrable to non-integrable, and so sifts out solutions not normally representable by a Fourier series.Furthermore, the present method provides a very direct way to construct other, more singular solutions.A practical consequence is that (at least, in principle) in numerical solutions based on Glauert's method, more is needed for the Kutta condition than a sine series expansion.

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On the remarkable accuracy of the vortex lattice method

Cited by 49 publications

References 3 publications

Spanwise distribution of induced drag in subsonic flow by the vortexlattice method

Spanwise distribution of induced drag in subsonic flow by the vortexlattice method

Incremental Potential Flow Based Membrane Wing Element

A note on the Kutta condition in Glauert’s solution of the thin aerofoil problem

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