The aerodynamic analysis and optimization of wind turbine based on a full free vortex wake model is presented. Instead of a simplification of the vortex wake structure, this model predict an adequate free-wake extension which can accurately take into account the profound influence of vortex sheet downstream on the aerodynamic performance of wind turbine. The problem that the model suffers from high computational costs is solved by combining the Fast Multipole Methods (FMM) for an efficient evaluation of the Biot–Savart law with the parallel processing. The model is applied to the aerodynamic analysis of wind turbine and a stable convergent numerical solution is achieved using the pseudo-implicit technique (steady) and predictor-corrector PC2B scheme (unsteady). The optimization based on this analysis is also efficiently carried out using a Fourier series representation of the bound circulation as optimization variables, using a given thrust coefficient as a constraint. The chord and twist distributions that completely define the geometry are produced from the obtained optimal bound circulation distribution. The optimization is capable of quickly finding an optimum design using a few optimization variables. The validations of presented methods are performed through comparisons with the National Renewable Energy Laboratory (NREL) wind turbine experiment.

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