Keywords: aerodynamic optimisation, shape parameterization, mesh deformation, radial basis functions, rotor aerodynamics, computational fluid dynamics.

Constrained aerodynamic shape optimization of a helicopter rotor in hover is presented, using compressible computational fluid dynamics (CFD) as the aerodynamic model. The key aspect of a flexible optimization and design process is an effective geometry parameterization approach, that is flexible enough to allow sufficient design space investigation and robust enough to be applicable to any geometry or design surface. Furthermore, a small number of design parameters is desirable, particularly if using a finite-difference gradient evaluation. Related to the surface control is the required volume mesh deformation or regeneration once the design surface has been deformed, and mesh deformation is much prefered, to avoid introducing differing discretization error. An efficient domain element shape parameterization method is used here as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh, which is deformed in a high-quality fashion, and so both the geometry control and volume mesh deformation problems are solved simultaneously. This method is independent of mesh type (structured or unstructured) or size, and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient-based algorithm by finite-difference. The optimizer has also been parallelized, in a data sense, such that each CPU can spawn its own parameter perturbation, mesh deformation, and call to the flow-solver, so each parameter sensitivity can be computed independently, and results returned to the master for optimizer updates. This has resulted in a flexible and versatile modular method of 'wrap-around' optimization. Previous work has applied the methods to hovering rotors using only twist parameters, using minimum torque as the objective, with strict constraints on thrust, internal volume and pitching moments applied. The effects of global and local twist parameters were investigated, and showed that significant torque reductions could be achieved using only three global and 15 local twist parameters. This paper extends the parameterization to allow more flexibility, by incorporating local planform changes; the three global twist variations used previously, are combined with local dihedral, sweep, chord, and thickness variations, to give a total of 63 local and global parameters. Results are presented for two transonic tip speeds, and large geometric changes are demonstrated in both cases, resulting in significant torque reductions, along with reductions in the other two root moments.

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