This paper describes the work performed by ONERA and Airbus to solve several aerodynamic optimization problems proposed in 2013 by the AIAA Optimization Discussion Group (ADODG). Three of the four test cases defined by this group have been addressed, respectively a 2D invicid, non-lifting, transonic airfoil optimization problem, a 2D RANS transonic airfoil optimization problem and a 3D RANS transonic wing optimization problem. All three problems have been investigated using local, gradient-based, optimization techniques and the elsA[1][2] CFD software and its adjoint capability. Through these three optimization exercises, several generic issues introduced by aerodynamic gradient-based optimization have been investigated. Among the investigated aspects are the impact of the geometry parameterization (nature and dimension), of the accuracy of the gradient calculation method, optimization algorithm and presence of constraints in the optimization problem. NomenclatureC p = pressure coefficient CD = total drag coefficient CDp = pressure drag coefficient CDf = friction drag coefficient CDw = wave drag coefficient CDvp = viscous pressure drag coefficient CL = lift coefficient CM = pitching moment coefficient c ref = chord reference d.c. = drag counts (0.0001) Ma = Mach number Re = Reynolds number AoA = Angle of attack f = objective function g = inequality constraint 1

A gradient-based method using a discrete adjoint of the Reynolds-averaged Navier-Stokes (RANS) equations is applied to the problem of helicopter blade shape optimization in hover. First, the RANS equations expressed in a specific coordinate system, adapted to the problem of a hovering rotor, are introduced. Then the numerical scheme used to solve the flow equations and the discrete adjoint equation is presented. They are then used within a gradient-based optimizer to perform rotor shape optimizations. The method is applied to the planform optimization of two different rotor blades: a classical rectangular blade and an innovative double swept blade planform. Design variables define the twist, chord, anhedral, and sweep distributions over the blade span, and the objective of the optimization is to improve the rotor figure of merit. The method demonstrated its efficiency in terms of central processing unit time and memory requirement and succeeded in providing interesting rotor blade shapes. The main interest of the present method is its ability to perform local optimization of isolated rotor in hover using an accurate computational fluid dynamics model and accounting for a large number of shape parameters. T turbulent heat flux vector ϕ rotation of a blade section generated by twist (deg) rotor rotational speed (rad·s −1 )

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Results of the elsA software package, the ONERA multipurpose tool for applied aerodynamics and multiphysics, are presented for a well-known NACA0012 configuration proposed by the turbulence modeling resource website of NASA Langley Research Center and on the ONERA-M6 wing. ONERA proposed new computer-aided design models for the turbulence modeling resources to make ONERA-M6 a reference test case. Results and solver performance are presented and discussed.