A Beddoes-Leishman-type model with an optimization-based methodology and airfoil shape parameters

Abstract

Floating offshore wind turbines operate in a highly unsteady environment; thus, many flow transients occur at the blade cross-sectional level, which affect the rotor aerodynamics. In every rotor aerodynamics modelling technique requiring the blade element theory, the blade cross-sectional aerodynamics need to be predicted accurately on the basis of the flow conditions. At reduced frequencies of 0.01 and greater, the flow unsteadiness can be considered significant and cannot be treated as quasisteady. Floating offshore wind turbines can be expected to consistently operate in some degree of yaw or pitch, which may result in reduced frequencies greater than 0.01 over most of the blade when operating at rated wind speeds and rotor RPM. The Beddoes-Leishman model is a comprehensive but complex model for predicting unsteady airfoil aerodynamics, containing 8 dimensionless time constants. In the present study, the Beddoes-Leishman model was compared with experimental results of 10 different airfoil profiles, each performed under a range of Reynolds numbers, motion frequencies, mean, and amplitudes of angle of attack. An optimization was performed for all time constants in the model, the results of which were used to formulate a simplified model with fewer equations, without any reduction in accuracy. Further, optimizations were performed against the experimental results of each airfoil, and the optimized constants were compared with shape parameters of the airfoils, yielding possible correlations, which were then applied in the simplified Beddoes-Leishman model to yield improved accuracy, measured as a 5% reduction in accumulated error between experimental and predicted coefficients of lift.