A Propeller Model Based on a Modern Numerical Lifting-Line Algorithm with an Iterative Semi-Free Wake Solver

Montgomery, Zachary S.; Hunsaker, Douglas F.

doi:10.2514/6.2018-1264

Cited by 4 publications

(2 citation statements)

References 6 publications

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“…Then, the work of Bliss et al is summarized. Substantial work in the field of circular arc vortex segments has been performed [10,11,[33][34][35][36][37][38], but will not be described herein because it does not provide a direct means of validation for this work.…”

Section: Previous Workmentioning

confidence: 99%

A General Approach to Lifting-Line Theory, Applied to Wings with Sweep

Reid

Hunsaker

2020

AIAA Scitech 2020 Forum

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Implementations of lifting-line theory predict the lift of a finite wing using a sheet of semi-infinite vortices extending from a vortex filament placed along the locus of aerodynamic centers of the wing. Prandtl's classical implementation is restricted to straight wings in flows without sideslip. In this work, it is shown that lifting-line theory can be extended to swept wings if, at the control points where induced velocity is calculated, the second derivative of the locus of aerodynamic centers is zero and the trailing vortices are perpendicular to the locus of aerodynamic centers. Therefore, a general implementation of lifting-line theory is presented that conditionally forces the second derivative of the locus of aerodynamic centers to zero at each control point and joints each trailing vortex such that there is a finite segment of the trailing vortex that lies perpendicular to the locus of aerodynamic centers. Consideration is given to modeling the locus of aerodynamic centers and section aerodynamic properties of swept wings. The resulting general formulation is analyzed to determine its sensitivity to closure parameters, accuracy, and numerical convergence.

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Section: Previous Workmentioning

confidence: 99%

A General Approach to Lifting-Line Theory, Applied to Wings with Sweep

Reid

Hunsaker

2020

AIAA Scitech 2020 Forum

Self Cite

View full text Add to dashboard Cite

show abstract

“…Then, the work of [5] is summarized. Substantial work in the field of circular arc vortex segments has been performed [3][4][5]7,12,18,23,26], but will not be described herein because it does not provide a direct means of validation for this work.…”

Section: Introductionmentioning

confidence: 99%

Application of the Biot-Savart Law to Parabolic Vortex Segments using Elliptic Integrals

Malmendier,

Reid

2019

Preprint

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The Biot-Savart law is used in aerodynamic theory to calculate the velocity induced by curved vortex lines. Explicit formulas are developed, using multivariate Appell hypergeometric functions, for the velocity induced by a general parabolic vortex segment. The formulas are derived by constructing a particular pencil of elliptic curves whose period integrals provide the solution to the induced velocity. We use numerical integration and a perturbation expansion to evaluate the validity of our formulas.

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Application of the Biot–Savart law to parabolic vortex segments using elliptic integrals

Malmendier

Reid

2020

Z. Angew. Math. Phys.

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A Propeller Model Based on a Modern Numerical Lifting-Line Algorithm with an Iterative Semi-Free Wake Solver

Cited by 4 publications

References 6 publications

A General Approach to Lifting-Line Theory, Applied to Wings with Sweep

A General Approach to Lifting-Line Theory, Applied to Wings with Sweep

Application of the Biot-Savart Law to Parabolic Vortex Segments using Elliptic Integrals

Application of the Biot–Savart law to parabolic vortex segments using elliptic integrals

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