CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation

Morris, AM; Allen, Christian B; Rendall, Thomas

doi:10.1002/fld.1769

Cited by 128 publications

(106 citation statements)

References 37 publications

Supporting

Mentioning

106

Contrasting

Order By: Relevance

“…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], Hicks-Henne 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]. A whole variety of options are available, however all are subject to the 'curse of dimensionality'.…”

Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

54th AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

show abstract

“…The deformation method itself differs however, preserving the exact movement of a set of control points then creating a deformation field defined by radial basis function interpolation. The general theory of RBFs is outlined by Wendland 50 and Buhmann 51 ; the formulation used here is then presented extensively in Rendall and Allen 15 and its use as a parametrisation technique in Morris et al 34 . They define that an aerofoil X initial , deformed relative to the position of a set of RBF domain element control points P i , is given by…”

Section: Radial Basis Function Domain Elementsmentioning

confidence: 99%

“…The RBF domain element method also allows the local fidelity of movement to be controlled through the proximity and density of the point distribution. Both of these methods have shown promising optimisation results 16,[34][35][36] . A range of other comparative shape parameterisation studies have been previously investigated [37][38][39][40] .…”

Section: Introductionmentioning

confidence: 99%

Geometric Comparison of Aerofoil Shape Parameterization Methods

et al. 2017

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…For suitable surface control and mesh deformation, an efficient domain element shape parameterization method has been developed by the authors and presented previously for CFD-based shape optimization [8,51]. The parameterization technique, surface control and volume mesh deformation all use radial basis functions (RBFs), wherein global interpolation is used to provide direct control of the design surface and the CFD mesh, which is deformed in a high-quality fashion [52,53].…”

Section: Iiib Shape Controlmentioning

confidence: 99%

“…Numerous advanced optimizations using compressible computational fluid dynamics (CFD) as the aerodynamic model have previously been performed [3][4][5][6][7]. 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 [8,9].…”

Section: Introductionmentioning

confidence: 99%

Global Optimization of Wing Aerodynamic Optimization Case Exhibiting Multimodality

Poole

Allen

Rendall

2018

Journal of Aircraft

Self Cite

View full text Add to dashboard Cite

An investigation into an aerodynamic optimization benchmark case that exhibits multimodality is presented using a global optimization approach. The recently suggested case 6 of the AIAA Aerodynamic Design Optimization Discussion Group involves the drag minimization of a rectangular NACA0012 wing subject to lift and root bending moment, as well as other geometric constraints. In this paper, optimization of that case using a state-of-the-art constrained population-based global optimization framework is presented.Shape control is achieved via a hierarchical application of the radial basis function domain element approach. Three different fidelity of optimization cases are performed to investigate the multimodality of various aspects of the full problem, with four independent runs of each case being performed. When considering chord optimization, the optimizer converges to two independently identifiable minima with very similar performance. When adding dihedral and sweep variation, further multimodality is introduced, though this multimodality is reasonably well defined, with minima including forward and rearward sweep, and an upward and downward winglet. Introducing thickness variables leads to a highly multimodal problem due to the coupling between the chord and thickness variables. The theoretical minimum drag for this case is 24.7 counts, which a number of the runs get close to achieving.

show abstract

CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation

Cited by 128 publications

References 37 publications

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Geometric Comparison of Aerofoil Shape Parameterization Methods

Global Optimization of Wing Aerodynamic Optimization Case Exhibiting Multimodality

Contact Info

Product

Resources

About