The Beddoes-Leishman dynamic stall model: Critical aspects in implementation and calibration

Abstract

Dynamic stall is a phenomenon of primary interest in the design of modern wind turbines, whose long, and unprecedently flexible blades are exposed to continuous variations of the angle of attack due to the incoming non-uniform flow. Despite the importance of an accurate modelling of dynamic stall for a proper aeroelastic design of the rotor and the definition of its operational boundaries, consensus on a single formulation able to combine versatility and robustness has not been reached yet. The Beddoes-Leishman model, among the many engineering-type ones, is currently the most exploited solution adopted by the majority of state-of-the-art wind turbine simulation tools, but its capabilities have been under-exploited over the years due to both the uncertainty related to its implementation and, above all, the lack of calibration for different airfoils and operating conditions. The present study aims at providing an exhaustive review on the Beddoes-Leishman model that could serve as a future reference for either properly tuning the model case by case or benchmarking this formulation to novel dynamic stall models for wind turbine applications. The impact of different implementations and calibration strategies are assessed for two historical pitching-airfoil cases, using the NACA0012 and the S809 profiles, over a wide range of oscillation mean angles, amplitudes, and reduced frequencies. Results prove that, when calibrated with a physics-oriented approach instead of relying on current malpractices, the model provides good estimation of the unsteady loads even for an airfoil that is deemed to be outside its range of validity such as the S809.