A Systematic Study on the Impact of Dimensionality for a Two-Dimensional Aerodynamic Optimization Model Problem

Harrison, A.; Roman, Dino; Jameson, Antony

doi:10.2514/6.2011-3176

Cited by 45 publications

(40 citation statements)

References 5 publications

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“…The upper branch of both of the aerofoils has a double shock flow structure with drag values approximately double the lower branch, which has a single shock. This is in agreement with the original problem set by Vassberg et al [2], where it was believed that this is the lowest Mach number at which a shock free optimized solution is not possible.…”

Section: B Hysteresis Studysupporting

confidence: 79%

“…This case has previously been investigated with a variety of different parameterisation methods: Bèzier Curves [1,2]; B-Splines [3,4,5,6,7]; NURBS [8]; Class/Shape Transformations (CSTs) [9]; Hicks-Henne bump functions [10]; Bèzier Surface FFD [11]; PARSEC [12]; Radial basis function domain element (RBF-DE) deformation [13,14] and Singular Value Decompositions (SVD) [14,15]. Due to the large range of factors influencing the results it is difficult to isolate contribution of the parameterisation method from these previous studies.…”

Section: Introductionmentioning

confidence: 99%

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Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

Masters

Poole

Taylor

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 paper presents an investigation into the influence of shape parameterisation and dimensionality on the optimisation of a benchmark case described by the AIAA Aerodynamic Design Optimisation Discussion Group. This problem specifies the drag minimisation of a NACA0012 under inviscid flow conditions at M = 0.85 and α = 0 subject to the constraint that local thickness must only increase. The work presented here applies six different shape parameterisation schemes to this optimisation problem with between 4 and 40 design variables. The parameterisation methods used are: Bèzier Surface FFD; B-Splines; CSTs; Hicks-Henne bump functions; a Radial Basis Function domain element method (RBF-DE) and a Singular Value Decomposition (SVD) method. The optimisation framework used consists of a gradient based SQP optimiser coupled with the SU 2 adjoint Euler solver which enables the efficient calculation of the design variable gradients. Results for the all the parameterisation methods are presented with the best results for each method ranging between 25 and 56 drag counts from an initial value of 469. The optimal result was achieved with the B-Spline method with 16 design variables. A further validation of the results is then presented and the presence of hysteresis is explored.

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Section: B Hysteresis Studysupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

Masters

Poole

Taylor

et al. 2016

54th AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

show abstract

“…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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“…Corresponding results for the JC6 airfoil are shown in Figures (10) to (12). In these cases stable asymmetric solutions are formed in the range of Mach numbers from 0.844 to 0.848.…”

Section: Iiid Jc6 Airfoilmentioning

confidence: 68%

“…The present authors have encountered another example as a consequence of a shape optimization study for symmetric airfoils in transonic flow, 12 in which an attempt was made to find a 12 percent thick airfoil with a shock free solution at Mach 0.84. The resulting airfoil, labelled NU4, has an almost shock free solution at its design Mach number, but also allows a lifting and non-lifting solution at zero angle of attack.…”

Section: Iia Nu4 Airfoilmentioning

confidence: 99%

Further Studies of Airfoils Supporting Non-Unique Solutions in Transonic Flow

Jameson

Vassberg

2012

AIAA Journal

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Non-unique solutions of the Euler equations were originally discussed by Jameson in 1991 for several highly cambered airfoils which were the result of aggressive shape optimization. In 1999 Hafez and Guo found non-unique solutions for a symmetric parallel sided airfoil, and subsequently Kuzmin and Ivanova have discovered some fully convex symmetric airfoils that provide non-unique solutions. In this article four new symmetric airfoils, all of which exhibit non-unique solutions in a narrow band of transonic Mach numbers, were studied. The first, NU4 was the result of shape optimization. The second, JF1 is an extremely simple parallel sided airfoil. The third JB1, is also parallel sided but has continuous curvature over the entire profile. The fourth, JC6, is convex and C∞ continuous. CL − α plots of these airfoils exhibit three branches of zero angle of attack, the P, Z and N-branches with positive, zero and negative lift respectively. At some Mach numbers no stable Z-branch could be found. When the P-branch is continued to negative α in some cases there is a transition to the Z-branch, while in other cases there is a direct transition from the P to N-branch.

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A Systematic Study on the Impact of Dimensionality for a Two-Dimensional Aerodynamic Optimization Model Problem

Cited by 45 publications

References 5 publications

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Further Studies of Airfoils Supporting Non-Unique Solutions in Transonic Flow

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