Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

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

doi:10.2514/6.2016-1544

Cited by 30 publications

(27 citation statements)

References 43 publications

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“…This is the inviscid drag reduction of a NACA0012 at M = 0.85 and α = 0. A considerable number of papers have been published on this case [1,2,46,47,48,49,50,51,52,53,54] and it has been shown to be a particularly difficult problem to optimise due to a range of characteristics such as multiple local minima [52], non-symmetric solutions [53] and hysteresis [54].…”

Section: Rae2882 Viscous Drag Reduction (Vgk)mentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

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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. Department of Aerospace Engineering, University of BristolThis work presents a shape parameterisation method based on multi-resolutional subdivision curves and investigates its application to aerodynamic optimisation. Subdivision curves are defined as the limit curve of a recursive application of a subdivision rule, which provides an intrinsically hierarchical set of control polygons that can be used to provide surface control at varying levels of fidelity. This is used to construct a progressive aerofoil parameterisation that allows an optimisation to be initialised with a small number of design variables, and then periodically increased in resolution through the optimisation. This brings the benefits of a low dimensional design space (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 progressive refinement technique is tested on a variety of optimisation problems. For each problem a range of 'static' (non-progressive) subdivision schemes (equivalent to cubic B-splines) are also used as a control group. For all the optimisation cases the progressive schemes perform comparably or better than the static methods, often providing a significant computational advantage, and in many cases allowing a solution to be found when the static method would otherwise finish prematurely in a local optimum.

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Section: Rae2882 Viscous Drag Reduction (Vgk)mentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

Self Cite

View full text Add to dashboard Cite

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“…A considerable number of papers have been published on this case 1,2,52-60 and it has been shown to be a particularly difficult problem due to a range of characteristics such as multiple local minima 58 , non-symmetric solutions 59 and hysteresis 60 . In this previous work, results ranging from 100 to 25 drag counts have been reported with the best cases produced by Lee Due to the symmetry of the problem a symmetry plane was aligned with the aerofoil chord and just half the mesh was solved.…”

Section: Symmetric Naca0012mentioning

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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“…The NACA aerofoil library has been created by taking all the possible integer combinations of the three input parameters t * , m * and p * for the NACA 4-series definition (Appendix B) in the ranges t * ∈ [6,24], m * ∈ [0, 9] and p * ∈ [3,7]. The aerofoils were then normalised and discretized as described in appendix A producing a final library of 874 unique aerofoils.…”

Section: A Aerofoil Librariesmentioning

confidence: 99%

“…With optimisation becoming more common in aerodynamic design, a significant effort is being made to improve the effectiveness and efficiency [1][2][3][4][5] of the full optimisation process. A typical CFD-based aerodynamic optimisation consists of four stages: shape parametrisation/control; mesh creation/deformation; flow solution; and optimisation.…”

Section: Introductionmentioning

confidence: 99%

Geometric Comparison of Aerofoil Shape Parameterization Methods

et al. 2017

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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. Department of Aerospace Engineering, University of BristolA comprehensive review of aerofoil shape parameterisation methods that can be used for aerodynamic shape optimisation is presented. Seven parameterisation methods are considered for a range of design variables: CSTs; B-Splines; Hicks-Henne bump functions; a Radial Basis function (RBF) domain element approach; Bèzier surfaces; a singular value decomposition modal extraction method (SVD); and the PARSEC method. Due to the large range of variables involved the most effective way to implement each method is first investigated. Their performance is then analysed by considering the geometric shape recovery of over 2000 aerofoils using a range of design variables, testing the efficiency of design space coverage with respect to a given tolerance. It is shown that, for all the methods, between 20 and 25 design variables are needed to cover the full design space to within a geometric tolerance with the SVD method doing this most efficiently. A set transonic aerofoil case studies are also presented with geometric error and convergence of the resulting aerodynamic properties explored. These results show a strong relationship between geometric error and aerodynamic convergence and demonstrate that between 38 and 66 design variables may be needed to ensure aerodynamic convergence to within one drag and one lift count.

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Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

Cited by 30 publications

References 43 publications

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Geometric Comparison of Aerofoil Shape Parameterization Methods

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