Aerodynamic Shape Optimization of Wings Using a Parallel Newton-Krylov Approach

Leung, Timothy; Zingg, David W.

doi:10.2514/1.j051192

Cited by 63 publications

(17 citation statements)

References 35 publications

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“…Applications of CFD-based ASO to wing design have, up until recently, largely focused on the Euler equations [21][22][23][24][25][26][27][28]. Contrary to circulation-distribution and panel methods, the Euler equations do not require the user to prescribe the starting location and shape of the wake.…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

Euler-Equation-Based Drag Minimization of Unconventional Aircraft Configurations

Gagnon

Zingg

2016

Journal of Aircraft

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“…Such techniques have been developed by Zingg and colleagues (Hicken and Zingg 2010;Leung and Zingg 2012), and have shown that these types of methods can be flexible enough to allow the moulding of a sphere into an aircraftlike shape under certain optimization conditions (Gagnon and Zingg 2012). Further work has been performed by Martins and others (Mader and Martins 2013;Lyu and Martins 2014) who showed results for blended-wing-body optimizations, and Yamazaki et al (2010) who further reduced the number of design variables by considering the direct manipulation method for wing optimization.…”

Section: Shape Parameterizationmentioning

confidence: 99%

Wing aerodynamic optimization using efficient mathematically-extracted modal design variables

2018

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract Aerodynamic shape optimization of a transonic wing using mathematically-extracted modal design variables is presented. A novel approach is used for deriving design variables using a singular value decomposition of a set of training aerofoils to obtain an efficient, reduced set of orthogonal 'modes' that represent typical aerodynamic design parameters. These design parameters have previously been tested on geometric shape recovery problems and aerodynamic shape optimization in two dimensions, and shown to be efficient at covering a large portion of the design space; the work is extended here to consider their use in three dimensions. Wing shape optimization in transonic flow is performed using an upwind flow-solver and parallel gradient-based optimizer, and a small number of global deformation modes are compared to a section-based local application of these modes and to a previously-used section-based domain element approach to deformations. An effective geometric deformation localization method is also presented, to ensure global modes can be reconstructed exactly by superposition of local modes. The modal approach is shown to be particularly efficient, with improved convergence over the domain element method, and only 10 modal design variables result in a 28% drag reduction.

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“…30 Further implementations of these types of methods have a http://www.optimalsolutions.us/ (2008) also been adopted by Zingg and colleagues. [31][32][33] Reviews of a range of parameterization methods have also been presented, and the reader is guided towards the work of Samareh 34, 35 and Nadarajah. 36,37 An effective parameterization must be i) flexible enough to allow sufficient design space investigation, ii) robust enough to be applicable to any geometry or design surface, and iii) efficient enough to cover the design space with a small number of design parameters.…”

Section: Surface Representation and Perturbationmentioning

confidence: 99%

Metric-Based Mathematical Derivation of Aerofoil Design Variables

Poole

Allen

Rendall

2014

10th AIAA Multidisciplinary Design Optimization Conference

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Derivation of fundamental geometric aerofoil design variables is considered. An efficient parameterization and deformation scheme is important in an aerodynamic shape parameterization framework to allow flexible deformation of the surface and volume mesh with full design space coverage attainable. To allow full design space coverage a method has been developed to allow the derivation of aerofoil geometric design variables, which is done by the mathematical decomposition of a training library. The resulting geometric modes are independent of parameterization scheme, surface and volume mesh, and flow solver, thus are generally applicable. Furthermore, a benchmark performance measure, the aerofoil technology factor, has been incorporated into the scheme, to allow intelligent, metric-based selection of the training library, to ensure high performance aerofoil modes are extracted. Three criteria for the selection of the training library are considered: high performance; varied performance; random selection. Results are presented for several geometric shape recovery problems, and these show that having a wide variety of aerofoil profiles in the training data produces modes that have greater design space coverage and are able to reconstruct target aerofoils to a greater accuracy than only having a high performance training library. I. Background and IntroductionNumerical simulation methods are now used routinely in industrial design, and increasing computer power has resulted in their integration into the optimization process being widely accepted. Integrating an effective geometry control method with an aerodynamic model and a numerical optimization scheme can result in an aerodynamic shape optimization approach, which is invaluable during design. The quality and applicability of results gained by numerical optimization are inherently dependent on the fidelity of the analysis tool used, and so developing a modular approach means that the complexity and cost of each module required at various stages of the design process can be changed, in terms of aerodynamic or fluid dynamic fidelity, number of surface shape design degrees of freedom, and the complexity of the optimization scheme. Computational fluid dynamics (CFD) is at the forefront of aerodynamic analysis capabilities, and application of numerical optimization algorithms with compressible CFD has been used in numerous optimizations of two-dimensional aerofoil sections, 1, 2 three-dimensional aircraft, 3-5 and three-dimensional aeroelastic aircraft, 6 and there has been a recent increase in activity in the rotor area. 7-11 The authors have also presented work in this area, having developed a modularised, generic optimization tool, that is flow-solver and mesh type independent, and applicable to any aerodynamic problem. [12][13][14] The key aspect of a flexible optimization and design process is an effective geometry parameterization and surface control technique. The effectiveness of these techniques can be measured in terms of being i) flexible enough to allow suff...

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Aerodynamic Shape Optimization of Wings Using a Parallel Newton-Krylov Approach

Cited by 63 publications

References 35 publications

Euler-Equation-Based Drag Minimization of Unconventional Aircraft Configurations

Euler-Equation-Based Drag Minimization of Unconventional Aircraft Configurations

Wing aerodynamic optimization using efficient mathematically-extracted modal design variables

Metric-Based Mathematical Derivation of Aerofoil Design Variables

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