Keywords: optimisation, aerodynamic, CFD, shape parameterisation, domain element, radial basis functions.

Optimisation is currently playing a key role in the aerospace industry, improving aerodynamic and structural designs within pre-specified limits and constraints. The objective of the research presented here is to provide a generic and versatile method for the high-fidelity aerodynamic optimisation of three-dimensional wings. This involves a novel domain element parameterisation technique, and an advanced gradient based optimiser, both of which can be combined with any CFD solver (inviscid, viscous or aeroelastic).

A novel domain element shape parameterisation method has been developed and presented recently for CFD-based shape optimisation [1,2]. The method provides a generic 'wrap around' optimisation tool that is independent of both flow solver and grid generation package and allows high-fidelity aerodynamic optimisation of two- and three-dimensional bodies with a very low number of design variables.

The parameterisation method links a set of aerodynamic mesh points to a domain element that controls the shape of the design. The domain element is automatically located around the exterior of the design. At the centre of this parameterisation technique is a multivariate interpolation using radial basis functions providing an inverse mapping between the domain element, the surface geometry and the locations of grid points in the volume mesh. Only an initial mesh is required and updates to the geometry and the corresponding mesh are provided simultaneously by application of multivariate interpolation; this is extremely fast and efficient and results in very high quality mesh deformation [3]. The domain element has design variables created in a hierarchical manner; these can range from gross three-dimensional planform changes to fine detailed surface changes.

In this paper, the methods are extended to the optimisation of a large modern transport aircraft wing in transonic cruise flight condition. Flow solutions are provided by an invicid Euler solver [4], with the initial mesh being a high-quality structured multiblock mesh. The initial wing geometry is parameterised with a domain element with 388 active design variables; these provide free-form control over aerofoil geometries together with planform design variables affecting angle of attack together with sweep, twist, and anhedral/dihedral distributions. The objective of the optimisation is the minimisation of drag at the cruise Mach of 0.85, with four stringent constraints placed on total wing lift, internal wing volume and the magnitude of both the root torsion and root bending moments. The optimisation results in a completely shock-free wing, and this achieves over 18% reduction in drag.

1

Morris A.M., Allen C.B., Rendall T.C.S., "Development of Generic CFD-Based Aerodynamic Optimisation Tools for Helicopter Rotor Blades", AIAA-2007-3809, 25th AIAA Applied Aerodynamics Conference, Miami, Florida, June 2007.

2

Morris A.M., Allen C.B., Rendall T.C.S., "CFD-based Optimisation of Aerofoils using Radial Basis Functions for Domain Element Parameterisation and Mesh Deformation", In Press to the International Journal for Numerical Methods in Fluids, Jan 2008. doi:10.1002/fld.1769

3

Rendall T.C.S., Allen C.B., "Unified Approach to Fluid-Structure Interpolation and Mesh Motion Using Radial Basis Functions", In press, International Journal for Numerical Methods in Engineering, 2007. doi:10.1002/nme.2219

4

Allen C.B., "Parallel Simulation of Unsteady Hovering Rotor Wakes", International Journal for Numerical Methods in Engineering, Vol. 68, pp. 632-649, 2006. doi:10.1002/nme.1723

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