Geometric Comparison of Aerofoil Shape Parameterization Methods

Masters, Dominic; Taylor, N. J.; Rendall, Thomas; Allen, Christian B; Poole, Daniel J

doi:10.2514/1.j054943

Cited by 135 publications

(91 citation statements)

References 47 publications

(61 reference statements)

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“…Other work by the authors 42 has shown that for aerofoil approximations the errors in drag coefficient prediction for transonic Euler flow relative to a target aerofoil are roughly equivalent to the maximum geometric error. These results therefore suggest that if the eight subdivision level is used for an inviscid drag reduction case, the design space should include aerofoils within the order of a thousandth of a drag count of any optimum.…”

Section: A Geometry Matchingmentioning

confidence: 99%

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Masters

Taylor²,

Rendall

et al. 2017

AIAA Journal

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Subdivision curves are defined as the limit of a recursive application of a subdivision rule to an initial set of control points. This intrinsically provides a hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This work presents a shape parameterisation method based on this principle and investigates its application to aerodynamic optimisation. The subdivision curves are used to construct a multi-level aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then be periodically increased in resolution throughout. This brings the benefits of a low fidelity optimisation (high convergence rate, increased robustness, low cost finite-difference gradients) while still allowing the final results to be from a high-dimensional design space. In this work the multi-level subdivision parameterisation is tested on a variety of optimisation problems and compared to a control group of single-level subdivision schemes. For all the optimisation cases the multi-level schemes provided robust and reliable results in contrast to the single-level methods that often experienced difficulties with large numbers of design variables. As a result of this the multi-level methods exploited the high-dimensional design spaces better and consequently produced better overall results.

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Section: A Geometry Matchingmentioning

confidence: 99%

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Masters

Taylor²,

Rendall

et al. 2017

AIAA Journal

Self Cite

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“…The method is based on perturbations, so is independent of the initial geometry and can fit into any of the three categories outlined above; the deformative formulation is used in this work, to allow a unified application of the design variables to control both the surface and volume mesh within the ASO framework. Previous work has considered the method's ability to represent a wide-range of aerofoil shapes (Poole et al 2015;Masters et al 2017b), and their effectiveness in aerofoil optimisation (Poole et al 2017;Masters et al 2017a), wherein the efficiency of this modal approach was clearly demonstrated. Hence, the aim of the work presented here is to develop an effective method to apply these novel mathematically-extracted design variables, which have been extracted as two-dimensional quantities, in three dimensions, and determine their effectiveness when applied to aerodynamic optimization, in particular drag minimisation of wings in transonic flow.…”

Section: Shape Parameterizationmentioning

confidence: 99%

“…Methods are classified as either constructive, deformative or unified. In-depth reviews have been presented by Samareh (2001b), Castonguay and Nadarajah (2007), Mousavi et al (2007) and Masters et al (2017b).…”

Section: Shape Parameterizationmentioning

confidence: 99%

“…The design variables used here are derived by a mathematical technique that is based on singular value decomposition (SVD), that extracts an orthogonal set of geometric 'modes'. The method itself has been presented recently by the authors (Poole et al 2015), and has been shown to outperform other commonly-used parameterization schemes (Masters et al 2017b) when considering geometric inverse design in two dimensions, often requiring fewer than a dozen variables to represent a large design space (Poole et al 2017). …”

Section: Introductionmentioning

confidence: 99%

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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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“…A substantial amount of research has been published for a number of decades in the field of ASO; reviewlike works have been presented in parameterization [10], and optimizer performance [11,12]. One primary issue on the development of the research field has been a lack of consistent benchmarking of individual ASO frameworks on unified test cases.…”

Section: Introductionmentioning

confidence: 99%

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

Poole

Allen

Rendall

2017

35th AIAA Applied Aerodynamics Conference

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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. An investigation into a multimodal aerodynamic optimization benchmark case using an approximate global optimization approach is presented. A new benchmark case of the AIAA Aerodynamic Design Optimization Discussion Group that involves the drag minimization of a rectangular NACA0012 wing subject to lift and root bending moment, as well as other geometric constraints, that is currently believed to be multimodal has been suggested. In this paper, optimization of that case using a constrained populationbased global optimization framework is presented, with three independent runs of the optimizer (each with different starting locations) having been performed. The runs are all coarsely-converged to give approximately converged solutions such that rapid run-times can be achieved and used to demonstrate any pitfalls that may be encountered when using a gradient-based optimizer. All three of the runs converged onto drag values close to the theoretical optimum, however with substantially different final shapes. This likely indicates the presence of a flat optimum region within the design space, where a substantial number of wing shapes are able to obtain the theoretical optimum span loading.

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Geometric Comparison of Aerofoil Shape Parameterization Methods

Cited by 135 publications

References 47 publications

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Wing aerodynamic optimization using efficient mathematically-extracted modal design variables

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

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