Numerical Implications of Spanwise Camber on Minimum Induced Drag Configurations

Liersch, Carsten M.; Streit, Thomas; Visser, Kenneth D.

doi:10.2514/6.2009-898

Cited by 10 publications

(14 citation statements)

References 6 publications

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“…6 demonstrates. Liersch et al [14] found that an elliptical planform does not achieve the theoretical minimum induced drag, unless a twist is also applied. While this may explain why the present planforms are not elliptical, it does not adequately explain why the lift distributions are not elliptical.…”

Section: B Planform Optimizationmentioning

confidence: 99%

“…Two notable investigations of induced drag in the ASO literature are the works of Yamazaki et al [13] and Liersch et al [14]. Yamazaki et al [13] used drag decomposition and a genetic algorithm to explore the tradeoffs between minimizing different components of drag, including induced drag.…”

mentioning

confidence: 99%

“…Yamazaki et al [13] used drag decomposition and a genetic algorithm to explore the tradeoffs between minimizing different components of drag, including induced drag. Liersch et al [14] were interested in whether or not nonplanar wings outperform planar wings when both have the same unfolded span (i.e., equal spanwise arclength). They used a lifting-line method to probe the design space initially, while Euler-based inverse design and drag minimization were used to refine the twist in some cases.…”

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confidence: 99%

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Induced-Drag Minimization of Nonplanar Geometries Based on the Euler Equations

Hicken

Zingg

2010

AIAA Journal

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Section: B Planform Optimizationmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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Induced-Drag Minimization of Nonplanar Geometries Based on the Euler Equations

Hicken

Zingg

2010

AIAA Journal

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“…Smith [14] and Smith and Kroo [15] confirmed that beneficial nonlinear wing-wake interaction can indeed lead to lower induced-drag values, provided that the shape of the rolled-up forcefree wake is accurately modeled. More recently, Liersch et al [16] concluded that higher-order effects such as induced lift explained why a spanwise cambered elliptical wing produced less induced drag than the same unfolded wing.…”

Section: Introductionmentioning

confidence: 98%

Euler-Equation-Based Drag Minimization of Unconventional Aircraft Configurations

Gagnon

Zingg

2016

Journal of Aircraft

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This study investigates the potential of unconventional aircraft transports through numerical optimization. Three distinct configurations are investigated: a box wing, a C-tip blended wing-body, and a braced wing. Each transport is sized for the same regional mission and is subjected to the same optimization strategy based on the Euler equations. The figure of merit is inviscid pressure drag at transonic speed; the nonlinear constraints are lift, pitching moment, and internal volume. The design variables include the section shape and twist distribution of the main lifting surfaces. It is found that the box-wing, C-tip blended-wing-body, and braced-wing configurations investigated here are, respectively, 34.1, 36.2, and 40.3% more efficient than a similarly optimized conventional tube-and-wing configuration. Each optimization revealed, in one way or another, the importance of accounting for flow nonlinearity during the early stages of unconventional aircraft design. For the blended wing-body, the C tip does not appear to provide a drag benefit over a purely vertical winglet, presumably as a result of the compressibility effects prevalent in the C opening. For the braced wing, compressibility effects also lead to a curious result, where the supporting strut finds itself carrying negative lift at the optimum. Nomenclature= span efficiency L = lift, N n = normal force (section), m q ∞ = freestream dynamic pressure, N∕m 2 W = weight, N x, y, z = chordwise, spanwise, and vertical coordinates, m α = angle of attack, deg

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“…Ideally, the contribution of numerical dissipation to the flux balance should be minimized to obtain an accurate solution; however, practitioners sometimes increase the dissipation to assist the solution algorithm at the expense of accuracy. 30 This practice suggests that a dissipation-based continuation strategy may be useful.…”

Section: B Dissipation-based Continuationmentioning

confidence: 99%

Globalization Strategies for Inexact-Newton Solvers

Hicken

Zingg

2009

19th AIAA Computational Fluid Dynamics

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Globalization strategies are necessary in practical inexact-Newton flow solvers to ensure convergence when the initial iterate is far from the solution. In this work, we present two novel globalizations based on parameter continuation. The first continuation method parameterizes the boundary conditions while the second parameterizes the numerical dissipation. In both cases, a continuation parameter is used to create a sequence of modified nonlinear equations. The solution of each equation in the sequence provides an initial estimate for the subsequent problem until the desired convergence tolerance is reached. When applied to benign inviscid flows, the proposed globalization methods have similar efficiency compared with the more common pseudo-transient continuation. They are significantly more robust on difficult inviscid problems. Moreover, the continuation-based methods require less tuning.

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Numerical Implications of Spanwise Camber on Minimum Induced Drag Configurations

Cited by 10 publications

References 6 publications

Induced-Drag Minimization of Nonplanar Geometries Based on the Euler Equations

Induced-Drag Minimization of Nonplanar Geometries Based on the Euler Equations

Euler-Equation-Based Drag Minimization of Unconventional Aircraft Configurations

Globalization Strategies for Inexact-Newton Solvers

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