Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables

Poole, Daniel J; Allen, Christian B; Rendall, Thomas

doi:10.2514/1.j053427

Cited by 97 publications

(60 citation statements)

References 47 publications

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“…Consequently the choice of shape parameterisation method can have a significant impact on the effectiveness and efficiency of the overall procedure 3 . Many different methods have been used within an aerodynamic optimisation framework, from standard geometric curve definitions such as B-splines 4 or NURBS 5 to aerospace-specific methods such as CST 6,7 , HicksHenne bump functions 8,9 or PARSEC 9,10 to Free-Form Deformation [11][12][13][14] , proper orthogonal decomposition 2,15,16 or the discrete method 17 . All of these approaches are subject to the 'curse of dimensionality'; in the context of aerodynamic optimisation this refers to the problems associated with increasing the number of design variables used in the optimisation procedure.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Masters

Taylor²,

Rendall

et al. 2017

AIAA Journal

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“…New aerofoil shapes can then be constructed as a linear combination of these modes where the fidelity of the construction is determined by the number of modes used. This technique was first employed by Toal et al 30 then by Ghoman et al 31 and Poole et al 32 . Ghoman et al 31 used a series of supercritical aerofoils to derive the modes and showed that other supercritical aerofoils could efficiently be reconstructed.…”

Section: Singular Value Decomposition (Svd)mentioning

confidence: 99%

“…Poole at al. 32 then extended this to show that a broad range of aerofoils could be represented given a wide choice of training aerofoils.…”

Section: Singular Value Decomposition (Svd)mentioning

confidence: 99%

“…This is typically done through proper orthogonal decomposition (POD) of a set of training aerofoils which will create a set of optimal orthogonal shape modes based on a range of training data. Studies of this nature have been produced by Toal et al 30 , Ghoman et al 31 and then by Poole et al 32 who used a large, varied collection of aerofoils and singular value decompositions to produce a universal set of modes representing the deformation of aerofoil shapes.…”

Section: Introductionmentioning

confidence: 99%

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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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“…The consideration of a global optimization approach necessitates the requirement for a minimum number of design variables to reduce computational burden as much as possible. The design variables used are from a singular value decomposition (SVD) approach, 29 which decomposes a training library of aerofoils into constituent modes and this has the advantage of producing an optimal reduced set of deformation modes according to the optimality theory of SVD.…”

Section: Iia Shape Controlmentioning

confidence: 99%

Objective Function and Constraints for Robust Transonic Aerofoil Optimization

Poole

Allen

Rendall

2017

58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials 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. Construction of the aerodynamic optimization problem is considered within the context of robustness. The most common aerodynamic optimization problem considered is a liftconstrained drag minimization problem (also subject to geometric constraints), however, point-design at transonic flow conditions can produce shock-free solutions and therefore the result is highly localised, where the gains obtained at the design point are outweighed by the losses at off-design conditions. As such, a range optimization problem subject to a constraint on fixed non-dimensional lift with a varying design point is considered to mitigate this issue. It is shown, first from an analytical treatment of the problem, and second from inviscid optimizations, that more robust solutions are obtainable when considering range optimization against drag minimization. Furthermore, to effectively capture the trade-offs that exist in three-dimensional aircraft design between range, lift, drag and speed, it is shown that an induced drag factor is required and this is sufficient to produce optimal solutions exhibiting shocks.

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Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables

Cited by 97 publications

References 47 publications

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Multilevel Subdivision Parameterization Scheme for Aerodynamic Shape Optimization

Geometric Comparison of Aerofoil Shape Parameterization Methods

Objective Function and Constraints for Robust Transonic Aerofoil Optimization

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