Range-Wide Aerodynamic Optimization of Darrieus Vertical Axis Wind Turbines Using CFD and Surrogate Models

The depletion of fossil fuel resources and the growing need for sustainable energy solutions have increased interest in vertical axis wind turbines (VAWTs), which offer advantages in urban and variable-wind environments but often exhibit limited performance at low tip speed ratios (TSRs). This study optimizes VAWT aerodynamic behavior across a wide TSR range by varying three geometric parameters: maximum thickness position (a/b), relative thickness (m), and pitch angle (β). A two-dimensional computational fluid dynamics (CFD) framework, combined with the Metamodel of Optimal Prognosis (MOP), was used to build surrogate models, perform sensitivity analyses, and identify optimal profiles through gradient-based optimization of the integrated Cp–λ curve. The Joukowsky transformation was employed for efficient geometric parameterization while maintaining aerodynamic adaptability. The optimized airfoils consistently outperformed the baseline NACA 0021, yielding up to a 14.4% improvement at λ=2.64 and an average increase of 10.7% across all evaluated TSRs. Flow-field analysis confirmed reduced separation, smoother pressure gradients, and enhanced torque generation. Overall, the proposed methodology provides a robust and computationally efficient framework for multi-TSR optimization, integrating Joukowsky-based parameterization with surrogate modeling to improve VAWT performance under diverse operating conditions.