Improved order of magnitude estimate of rotational effects on HAWTs

Abstract

This work proposes an improved order of magnitude estimate methodology of rotational effects on wind turbines, by applying the partial pressure field concept to the case of rotating wind turbine blades, which allows isolating acceleration that rises as a result of the rotation of the blades; then an order of magnitude scaling is performed to estimate the partial pressure due to rotation for both fully attached flow and massively separated flow. In the case of fully attached flow, it was found that rotational effects are negligible; while in the case of massively separated flow, rotational effects were found to be important. The pressure reduction was found to scale linearly with the aspect ratio inside the separated boundary layer, while it scales quadratically with the aspect ratio in the outer inviscid flow. A new estimate of the Rossby number is proposed, which is found to be the inverse of the pressure reduction coefficient estimate in the outer inviscid flow. Then, a semi-empirical model of the pressure reduction is proposed based on the order of magnitude estimate in the outer inviscid flow. The proposed semi-empirical model is then compared against the reference data of three wind turbines, namely, MEXICO, NREL phase VI, and AVATAR 10 MW rotors; along with the already known centrifugal pumping model. The results showed that the centrifugal pumping alone, inside the separated boundary layer, is not sufficient to produce the large force augmentation observed in experimental data. In contrast, the improved semi-empirical model provided a good agreement with experimental data, thanks to the quadratic scaling of the aspect ratio. And, the new estimate of the Rossby number proved to be advantageous over the existing Rossby number estimate in terms of the dependency on the angle of attack. Furthermore, the tangential and drag force coefficients were found to be strongly dependent on the airfoil type and its corresponding pressure shape. In contrast, the normal and lift force coefficients were found to be less dependent on the airfoil type. The proposed semi-empirical model is still strongly empirical, future work needs to account for the complex effect of airfoil type and its consequent interaction with the outer inviscid flow through the boundary layer.