A novel 2D analytical model for predicting single and multiple‐interacting wakes of horizontal‐axis wind turbines

Abstract

A 2D analytical model has been proposed for predicting the wind velocity distribution inside the wake by coupling the Jensen wake model and the Gaussian function using the conservation of mass and momentum. More realistic approaches were adopted in choosing the control volume and calculation of the wake initial radius at the formation and a new modified expression was employed for the wake turbulence intensity to be used for computation of the revised wake decay. Validation of the model was performed using a body of experimental and numerical data, where the model was thoroughly compared with five analytical models of the literature. The model was successful in predicting double-interacting wakes, and gave more accurate single wake velocity profiles at the far wake region, especially at downwind distances of x ≥ 7d t (d t is the rotor diameter), which are the economically-and power harvestingoptimized spacing between the turbines in wind farms.

A 3D analytical model for predicting horizontal‐axis wind turbines wake based on a 2D analytical wake model

“…In the present study, the model introduced in a previous study 27 has been used for obtaining the 2D wake velocity profile of a wind turbine (Figure 1). This 2D model 27 was obtained by proposing a new expression for the calculation of the wake turbulence intensity (), which was further used for calculation of the revised wake coefficient ( (Equations () and ()).…”

“…In the present study, the model introduced in a previous study 27 has been used for obtaining the 2D wake velocity profile of a wind turbine (Figure 1). This 2D model 27 was obtained by proposing a new expression for the calculation of the wake turbulence intensity (), which was further used for calculation of the revised wake coefficient ( (Equations () and ()). In the next step, an analytical 2D Gaussian model for calculation of the wake 2D velocity profile () at specified downstream distances () [Equation ()] was obtained through solving Equations ()–().…”

“…Moreover, Equations ( 5) and ( 6) were derived by considering the conservation of momentum, and Equations ( 7) and ( 8) were obtained by taking into account the conservation of mass in the wake boundary region. For further information please see Reference [27]…”

“…Two approaches that have been adopted for formulating the case of varying stand out. In one approach, was proposed to be dependent on the turbines hub height () and ground surface roughness () through the relationship 20 In the other approach, revision of was proposed by considering the effects arising from the incoming wind turbulence intensity () and the wake turbulence intensity () through the relationship 10,12,13,27 Application of this equation requires usage of expressions of that are functions of , , , induction factor (), and thrust coefficient () specific to the turbine. For obtaining these expressions experimental, 28 combined experimental and numerical 18 and engineering 9,13 methods have been employed.…”

“…A later improvement of this 2D model into a 3D one was obtained by inclusion of a modified anisotropic 10 As other examples of 3D analytical models one can point out (i) the model of Ishihara and Qian, 15 which included incorporation of the turbulence by a new mathematical approach, (ii) the model of Sun and Yang, 29 which utilized momentum conservation and an isotropic , and (iii) the model of He et al, 30 which employed an anisotropic and took into account the free stream wind shear effect by using mass conservation law. In our previous work, 27 we proposed a new 2D analytical model based on coupling Jensen's wake model and the Gaussian function by adopting a more realistic control volume to calculate the wake initial radius at formation, and provided a modified expression for computation of .…”