Several 2D and 3D Navier-Stokes computations performed with the compressible elsA solver, developed at ONERA, on the wind turbine tested by NREL in the NASA Ames large wind tunnel are presented. After a brief description of the tools and methods used, the predictions of the S809 aerofoil performance are first discussed. Full 3D computations are then presented, analysed and compared with the experimental results. The successes and failures of the computations are highlighted and explained. The analysis focuses in particular on the 3D and unsteady effects.

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. To improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction was investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low-speed and high-speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart-Allmaras-type models to state-of-the-art, seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall. Nomenclatureb span, m c chord, m c d , c d drag coefficient, difference in drag coefficient c l , c l lift coefficient, difference in lift coefficient c m , c m pitching moment coefficient, difference in pitching moment coefficient f frequency, Hz M Mach number r radius, m Re Reynolds number s, s LE , s max cell size, cell size at airfoil leading-edge, maximum cell size, m T period, s v ∞ freestream velocity, m/s x, y coordinates, m y + normalized wall distance α, α angle of attack, difference in angle of attack, deg t timestep, s ω * reduced frequency, ω * = 2πfc/v ∞

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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 )

A multi-objective strategy adapted to the aerodynamic concurrent optimization of helicopter rotor blades is developed. The present strategy is based on Nash Games from game theory, where the objective functions are minimized by virtual players involved in a non-cooperative concurrent game.A method is presented to split the design vector into two sub-spaces, defined to be the strategies of the players in charge of the minimization of the primary and the secondary objective functions respectively. This split of territory allows the optimization of the secondary function while causing

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