New Actuator Disk Model for the Analysis of Wind Turbines Wake Interaction with the Ground

Document Type : Regular Article


1 EPST Centre De Développement Des Enregies Renouvelables, CDER, BP 62 Route de l'Observatoire, Bouzareah, 16340, Alger, Algeria

2 Thermodynamics and Energetical Systems Laboratory, Faculty of Physics, USTHB, B.P 32 El Alia, 16111 Bab Ezzouar-Algiers, Algeria

3 DynFluid, ENSAM, 151 bvd L’Hopital; 75013 Paris France



Wake models based on Actuator Disk theory are usually applied to optimize the wind farm layouts and improve their overall efficiency and expected AEP. Despite the effectiveness of the existing models, most Actuator Disk approaches are based on the flow axisymmetric assumption, without considering the ground effect on the wake behavior. However, it has been shown that the mast’s height, or distance from the wind turbine to the ground, has an influence on the wake expansion on both hub’s side and at downstream of the wind turbine. Therefore, in this study, a hybrid CFD-BEM-Actuator Disk approach is developed to address the lack of the existing models. In the proposed model, the 3D wind rotor is modeled by a set of blade elements. Then, the local lift and drag forces acting on each blade element are calculated using BEM theory and incorporated into the momentum equation. This BEM-AD model is implemented in a User Defined Function (UDF) that is loaded into the CFD software. Thereby, ground effects are considered to be a wall boundary and defining a wind boundary layer profile at the inlet boundary, which describes the Atmospheric Boundary Layer (ABL). For the validation of this new Actuator Disk model, an enhanced experimental study is conducted at the Dynfluid Laboratory wind tunnel (ENSAM School Paris Tech). The Particle Image Velocimetry (PIV) measurements are used for the experimental wake explorations applied to a miniature two-bladed wind turbine. The wake developments are analyzed at two different hub heights ratio, h/D = 0.7 and 1.0 (where h is the hub height, and D is the wind rotor diameter). The analysis of the outcomes showed that the numerical simulations are in good correlation with the experimental measurements of the ENSAM wind tunnel. The numerical results show that for h/D=0.7, the upper half of the rotor operates within the boundary layer whereas the lower tip vortices are mainly developed in the horizontal direction with lower intensity compared to the upper tip vortices. This effect was not observed for the case h/D=1.0 where the rotor operates outside of the boundary layer; however, the wake centerline is upward deflected at about 0.3D. The main conclusion is that a distance above 7D must be observed between wind turbines to optimize the wind farm performance and over 1D hub height be required to limit the influence of the ground boundary layer effect.


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  • Received: 02 June 2022
  • Revised: 13 September 2022
  • Accepted: 15 September 2022
  • First Publish Date: 13 November 2022