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 Analysis of the 3D unsteady aerodynamics of a Darrieus wind turbine blade in motion  Highly spatially and temporally refined time-dependent simulations carried out with the COSA code  One month calculation time on more than 16.000 processors on a IBM BG/Q cluster  Detailed description of: tip losses, dynamic stall, vortex propagation and blade/wake interaction ACCEPTED MANUSCRIPT Energized by the recent rapid progress in high-performance computing and the growing The reported CFD results provide a valuable and reliable benchmark for the calibration 36 of lower-fidelity models, which are still key to industrial design due to their very high execution 37 speed.

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SUMMARYIn recent years, there has been rapid progress in aerodynamic optimization methods which use adjoint ow analysis to e ciently calculate the sensitivity of steady-state objective functions to changes in the underlying design variables. This paper shows that the same adjoint approach can be used in turbomachinery applications in which the primary concern is blade vibration due to harmonic ow unsteadiness.The paper introduces the key engineering concepts and discusses the derivation of the adjoint analysis at the algebraic level. The emphasis is on the algorithmic aspects of the analysis, on the iterative solution method and on the role played by the strong solid wall boundary condition, in particular. The novel ideas are exploited to reveal the potential of the approach in the minimization of the unsteady vibration of turbomachinery blades due to incident wakes.