Transonic Airfoils and Wings Design Using Inverse and Direct Methods

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.

Section: Rae2882 Viscous Drag Reduction (Vgk)mentioning

confidence: 99%

Progressive Subdivision Curves for Aerodynamic Shape Optimisation

Masters

Taylor

Rendall

et al. 2016

“…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%

Impact of Shape Parameterisation on Aerodynamic Optimisation of Benchmark Problem

Masters

Poole

Taylor

et al. 2016

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.

“…In equations (14) and (15) N is the order of the Bernstein polynomial used to describe the airfoil surface and the terms Au i and Al i are the i th design parameter on the upper and lower surface respectively used to scale the i th S i (x) term in the Bernestein polynomial defined in equation (16).…”

Section: Iiia Case 1: Shape Optimization Of the Modified Naca-0012 mentioning

confidence: 99%

Adjoint-Based Aerodynamic Design On Unstructured Meshes

Fabiano

Mavriplis

2016

This work presents initial optimization results for the Aerodynamic Design Optimization Discussion Group Cases 1 and 3 on unstructured meshes. A sequential quadratic programming algorithm is used to drive the constrained optimizations and the objective and constraint functional sensitivities are computed with the discrete adjoint method. After introducing the aerodynamic flow solvers employed, optimization results are discussed. The two dimensional optimization delivers an optimal solution, but yields higher drag values than other participants, most likely due to the airfoil parameterization employed in this work. The three dimensional optimization converges to a feasible optimum and is in good agreement with the workshop results.