Daniel J Poole

Free-form aerodynamic wing optimization using mathematically-derived design variables

Aerodynamic shape optimizations of aerofoils and wings using mathematically-derived design variables are presented. A novel approach is used for deriving design variables using a proper orthogonal decomposition of a set of training aerofoils to obtain an efficient, reduced set of deformation ‘modes’ that represent typical design parameters such as thickness and camber. A major advantage of this extraction method is the production of orthogonal design variables, and this is particularly important in aerodynamic shape optimization. These design parameters have previously been tested on geometric shape recovery problems and been shown to be efficient at covering a large portion of the design space, hence the work is extended here to consider their use in aerodynamic shape optimization in two and three dimensions. Using these mathematically-extracted design variables allows the use of global search algorithms for the optimization process in two dimensions, since a small number of parameters are required and these are also orthogonal. In three dimensions a parallel gradient-based optimiser is used. It is shown for two-dimensional inviscid compressible test cases, fewer than 10 aerofoil modes are required to obtain shock free solutions from initial strong shock, highly-loaded aerofoils. In three dimensions, a small number of local and global deformation modes are compared to a section-based application of these modes and to a previously-used section-based domain element approach to deformations, and applied to a transonic wing optimisation. The modal approach is shown to be particularly efficient with, again, fewer than 10 design variables required to achieve an effective optimisation.

Metric-Based Mathematical Derivation of Efficient Airfoil Design Variables

Within an aerodynamic shape optimization framework, an efficient shape parameterization and deformation scheme is critical to allow flexible deformation of the surface with the maximum possible design space coverage. Numerous approaches have been developed for the geometric representation of airfoils. A fundamental approach is considered here from the geometric perspective; and a method is presented to allow the derivation of efficient, generic, and orthogonal airfoil geometric design variables. This is achieved by the mathematical decomposition of a training library. The resulting geometric modes are independent of a parameterization scheme, surface and volume mesh, and flow solver; thus, they are generally applicable. However, these modes are dependent on the training library, and so a benchmark performance measure, called the airfoil technology factor, has also been incorporated into the scheme to allow intelligent metric-based filtering, or design space reduction, of the training library to ensure eff...

Application of Control Point-Based Aerodynamic Shape Optimization to Two-Dimensional Drag Minimization

An investigation is presented that considers various aspects of an aerodynamic shape optimization framework. A two-dimensional aerofoil transonic zero-lift drag minimization test case is used to investigate the effect of dimensionality, shape deformation parameters, and optimizer on the results from the shape optimization process. A flexible control point-based parameterization is implemented which decouples the design variables from the surface, such that control point deformations determine the surface and volume mesh deformations in a unified manner. A gradient-based optimizer (feasible sequential quadratic programming) and global search algorithm (gravitational search algorithm) are tested on the constrained optimization case. The results show, as expected, that an increase in the number of dimensions produces a greater design space coverage and better optimization results, and the gradient-based method is prone to terminating in local optima or at constraint boundaries, so the global search algorithm is more reliable at locating optima. Efficient, reduced, and orthogonal shape deformation parameters are defined here by singular value decomposition extraction, and are shown to be particularly effective, demonstrating a 99.7% drag reduction for the case considered.

AIAA paper 2015-0761, Proceedings AIAA Science and Technology Forum, Kissemee, Florida

This paper presents a review of aerofoil shape parameterisation methods that can be used for aerodynamic shape optimisation. Six parameterisation methods are considered for a range in design variables: Class function/Shape function Transformations (CST); B-splines; Hicks-Henne bump functions; a domain element approach using Radial Basis functions (RBF); Bezier surfaces; and a singular value decomposition modal extraction method (SVD); plus the PARSEC method. The performance of each method is analysed by considering geometric shape recovery on over 1000 aerofoils using a range of design variables, testing the efficiency of design space coverage. A more in-depth analysis is then presented for three aerofoils, NACA4412, RAE2822 and ONERA M6 (D section), with geometric error and convergence of the resulting aerodynamic properties presented. In the large scale test it is shown that, for all the methods, a large number of design variables are needed to achieve significant design space coverage. For example at least 25 design variables are needed to cover 80% of the design space regardless of the method used; this is often higher than is desired for two-dimensional studies, suggesting that further work may be required to reduce the number of design variables needed.

A geometric comparison of aerofoil shape parameterisation methods

A comprehensive review of aerofoil shape parameterization methods that can be used for aerodynamic shape optimization is presented. Seven parameterization methods are considered for a range of desi...

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

This 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: Bezier 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 SU2 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.

Volumetric Shape Parameterisation for Combined Aerodynamic Geometry and Topology Optimisation

A novel mesh based volume geometry parameterisation method is presented that allows for optimisation of shape and topology simultaneously: a topology inclusive parameterisation. This uses a volume of solid (VOS) technique to describe the geometry by reconstructing surfaces from the volume fraction that solid in each parameterisation mesh cell. The parameterisation is applied to the shape recovery of the NACA 0012 and RAE 2822 aerofoils and is used in the optimisation for minimum drag of a constrained thickness body in Mach 2 and Mach 4 flow using two optimisation methods, one gradient based and the other agent based. The parameterisation achieves excellent shape recovery of the target aerofoils, and allows a number of multi-body solutions to the drag minimisation problem to be generated, demonstrating the utility of topology inclusive parameterisations in bringing topological changes within easy access of the optimiser.

A Constrained Global Optimization Framework

Agent-based global search algorithms employ a set of search agents to traverse a given design space in pursuit of an optimum solution, and are normally accepted as the most reliable methods for finding a global optimum in a complex design space. However, when non-linear constraints are present in the optimization problem, modifications have to be made to such algorithms to allow the handling of these constraints. The gravitational search algorithm (GSA) is a recent addition to the family of global search methods but, to date, little research has been presented focussed on dealing with the handling of constrained optimization using GSA. To that end, this paper presents a constraint handling method specifically for use with GSA called separation-sub-swarm (3S), that splits the primary swarm into a feasible and infeasible swarm where the sub-swarms optimize either the constraints or the true objective function, which has the advantage of being algorithmically independent so is applicable to any agent-based search algorithm. This algorithm is applied here first to constrained analytical optimizations, and shown to be very effective and efficient. It is further applied to a transonic aerodynamic shape optimization problem and a problem that is subject to research by the AIAA Design Optimization Discussion group, again showing impressive results.

Influence of Shape Parameterization on a Benchmark Aerodynamic Optimization Problem

This paper presents an investigation into the influence of shape parameterization and dimensionality on the optimization of a benchmark case described by the American Institute of Aeronautics and A...

Optimal Domain Element Shapes for Free-Form Aerodynamic Shape Control

When performing aerodynamic shape optimization, a suitable method of parameterizing the surface geometry, and subsequently deforming the geometry and CFD mesh during the optimization, must be selected. The control point-based approach, where an interpolation links control point deformations to surface and mesh deformations, is a common method. However, dening the control point deformations and the location of the control points are dicult problems that often rely on user intuition. The work presented here considers this from an optimization point of view where linear solutions are used to dene control point deformations, and an objective function is used to improve control point locations. Inverse shape design results prove that the application of this preprocessing step in advance of aerodynamic shape optimization improves shape recovery.