Load evaluation of horizontal-axis wind turbine rotor using coupled Beddoes near-wake model and free-wake method

Bouatem et al. International Journal of Energy and Environmental Engineering 2013, 4:35 http://www.journal-ijeee.com/content/4/1/35 ORIGINAL RESEARCH Open Access Load evaluation of horizontal-axis wind turbine rotor using coupled Beddoes near-wake model and free-wake method Abdelfattah Bouatem1*, Ahmed Almers2 and Noureddine Boutammachte2 Abstract Wind turbines operate mostly in yaw conditions that give rise to cyclic variations in aerodynamic forces applied on the blade. This induced load fluctuation is closely related to the upstream velocity field of the rotor and can be a significant source of fatigue and vibration. An accurate prediction of blade loading is considered the key in designing reliable and efficient wind turbines. The related calculation remains a complicated task to perform and requires enormous computing time. In this context, a numerical method is presented, aimed at evaluating the azimuthal fluctuation of the normal force. This method is obtained by coupling the Beddoes near-wake model and the free-wake method: the near-wake-induced velocities are calculated using Beddoes near-wake model with the far-wake contribution evaluated using the free-wake method. In addition, the unsteady effects on the aerodynamic coefficients are taken into account using the Beddoes-Leishman dynamic stall model. A computer code was developed, and numerical values were obtained in acceptable computational time. Results are compared with measurements performed in the NASA Ames wind tunnel. Keywords: Wind turbine; Yaw; Skewed wake; Stall delay; Free wake; Near wake; Far wake Background To reach satisfactory levels of performance, the horizontalaxis wind turbine requires accurate predictions of the aerodynamic forces acting on the blades. However, in non-steady conditions, these aerodynamic load predictions remain a complicated task to perform because of the complex nature of the flow around the blades. To model the wind turbine, a variety of mathematical models exist, such as the blade element method (BEM), computational fluid dynamics (CFD) method, and vortex method, each with different levels of accuracy and complexity. The classical BEM method is obtained by coupling blade element theory with momentum theory [1]. This method assumes that the blade can be divided into several elements. The study is performed for each element by applying the momentum theory in the axial and tangential direction. The BEM method includes several approximations and * Correspondence: 1 Department of Mechanical Engineering, Moulay Ismail University, ENSAM-MEKENS, PO. BOX. 4024, Meknes 50003, Morocco Full list of author information is available at the end of the article limitations. Its validity may be extended using empirical corrections to take into account the finite number of blades, blade tip losses, and the cyclical variation of the axial induction factor in yaw conditions. Currently, the use of the CFD techniques has experienced significant progress thanks to the improved performance of computers. Despite the accurate results obtained in most cases, CFD methods require huge computational resources and large memory. The aim of the vortex theory is to model the wind turbine taking into account the geometry of the wake behind the rotor and its effect on the velocity field upstream [2]. The vortex theory principle is derived from the lifting line and lifting surface theories, which have been developed for airplane wings to determine wing loads and wake geometry. The flow is replaced by inviscid and incompressible fluid through an equivalent vortex system. The methodology is based on the Biot-Savart law to compute induced velocities and the vorticity transport theorem to shape the wake which is generally divided into near wake and far wake. The near wake consists of the trailing vortices issuing from the trailing © 2013 Bouatem et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Bouatem et al. International Journal of Energy and Environmental Engineering 2013, 4:35 http://www.journal-ijeee.com/content/4/1/35 edges. The far wake is reduced in two intense tip and root vortices. The vortex method gives more accurate results than the BEM method and is relatively easy to implement compared with CFD methods. Consequently, the vortex theory can be a better choice for predicting the aerodynamic performance of a wind turbine. This methodology requires a perfect determination of the wake geometry. There are two main approaches to shape the wake. The first is known as ‘prescribed wake.’ According to this method, the wake geometry is known a priori. The second is the ‘free-wake method,’ which is based on the following steps: first, trailing vortices are detached from the blade and represented by Lagrangian markers; then, the wake-induced velocities are calculated using the Biot-Savart law at each Lagrangian marker to determine their new positions; finally, the Lagrangian markers are connected by a straight line to form the wake [3]. This method requires huge computational time, basically at the near-wake region. This can be explained by the large number of trailing vortices and straight lines which form the wake. The main objective of this paper is to develop a numerical procedure that can predict aerodynamic loads without using great amounts of computer time which are generally required in the free-wake method. This procedure is obtained by combining the Beddoes near-wake model with the free-wake method. The Beddoes near-wake model is used to calculate the near-wake-induced velocities at the rotor plane. The free-wake method is used to shape the far wake in a simpler and faster way; the calculation begins with a generation of a rigid wake which is corrected to take into account the effect of wake-induced velocities. The near-wake-induced velocities are added to the farwake-induced velocities to calculate the circulation distribution along the blade. This iterative procedure continues until the rotor flow field takes a constant value. The wind turbine is assumed to be operating in yaw conditions. To take into account the unsteady aerodynamic effect on the blade loading, the Beddoes-Leishman dynamic stall model has been used. In this model, the deficiency in lift arising from the circulatory effect of shed vorticity is modeled using the indicial response function. To validate this numerical simulation, a comparison is made with measurements performed in the NASA Ames wind tunnel. Page 2 of 11 in the calculation using the Beddoes-Leishman dynamic stall model. As shown in Figure 1, the vortex element of length ds, strength Г, and originating from the point B, induces the velocity dw at point A. Assuming that the geometry of the near-wake vortices can (...truncated)