Contents lists available at ScienceDirect Journal of Wind Engineering and Industrial Aerodynamics journal homepage: www.elsevier.com/locate/jweia Modeling of wind turbine wakes under thermally-stratified atmospheric boundary layer W.A. El-Askary ⁎ , I.M. Sakr, Ali M. AbdelSalam, M.R. Abuhegazy Mechanical Power Engineering Department, Faculty of Engineering, Shebin El-Kom, Menoufia University, Egypt ARTICLE INFO Keywords: Wind turbine wakes Actuator disk Atmospheric thermal stratification Atmospheric boundary layer RANS k-ε model Wind power ABSTRACT In the present work, the wake behavior of wind turbines, operating under thermally-stratified atmospheric boundary layer (ABL), is numerically investigated. The steady state three dimensional Reynolds-Averaged Navier–Stokes (RANS) equations, combined with the actuator disk approach, are used in the simulation. The standard k-ε turbulence model as well as a modified one namely El Kasmi model are adopted. Two different methods are used and compared, for representing the atmospheric stratification flow conditions: In the first one (direct method), the energy equation is considered along with mass, momentum, and turbulence model equations. In the second one (indirect method), stratification is modeled by means of additional buoyancy production and dissipation terms. Such terms are added to the turbulent kinetic energy and dissipation rate equations, instead of solving the energy equation. The results obtained from both methods show a reasonable agreement with the experimental data available from the literature. Moreover, it is concluded that, there is no significant difference between the predicted results from both methods. Further, the effect of the atmospheric stability class on the wake deficit and the available wind power in the wake region has been also investigated using the indirect method. It has been found that, there is a significant influence of the different atmospheric conditions on the wake behavior. In particular, the wake region becomes smaller with the decreasing of atmospheric stability, and hence a higher wind power in the wake region is observed for unstable conditions. 1. Introduction Wind turbine wakes have attracted a lot of attention of the research community in recent years because of their effect on power production of wind farms. These wakes are characterized by a reduction of wind speed which in turn reduces the available wind power, and an increase of turbulence levels that generate fatigue loads on downstream wind turbines. Therefore, the investigation of wind turbine wakes becomes important to construct a suitable wind turbines farm. Wind turbines operate in the lowest region of the atmospheric boundary layer (ABL). Therefore, the evolution and recovery of wind turbine wakes are strongly affected not only by the turbine character- istics and complexity of terrain, but also, by the ambient wind speed and turbulence levels related to the different thermal stratifications of ABL. A proper modeling of all these factors becomes mandatory for detailed understanding and accurate prediction of wind turbine wakes and their effects on the performance of the whole wind farm. According to the thermal conditions, the atmospheric boundary layer can be classified into three types, which are neutral (NBL), stable (SBL), and unstable or convective (CBL). In NBL, the mean potential temperature is approximately constant with height, so that the generated turbulence is mainly due to the ground surface. It is observed only during windy weather with clouds. In SBL, the ground surface is colder than the ambient air, therefore the generated turbulence by wind shear is suppressed by negative buoyancy resulted from vertical downward heat flux. This atmospheric condition usually occurs at night time. The third type, CBL, occurs during day time when the ground surface is warmer than ambient air. The vertical upward heat flux generates a positive buoyancy, which in turn enhances the ambient turbulence. It is observed that, the turbulence level varies in descending order of magnitude in CBL, NBL and SBL, respectively. Full-scale field measurements as well as wind tunnel experiments of small-scaled models of wind turbines showed significant effects of thermal stratification on wind power production and structure of wind- turbine wakes, as reported in Van den Berg (2008), Wharton and Lundquist (2010), Chamorro and Porté-Agel (2010), Zhang et al. (2013), Hancock and Pascheke (2014). Baker and Walker (1984) used a kite anemometer to measure wake deficits of two MOD-2, 2.5 MW, 91 m diameter wind turbines. The measurements were obtained at different ambient turbulence levels under stable condition at Goodnoe http://dx.doi.org/10.1016/j.jweia.2016.11.001 Received 29 April 2016; Received in revised form 31 October 2016; Accepted 5 November 2016 ⁎ Corresponding author. E-mail addresses: wageeh_elaskary@yahoo.com, Wageeh.Elaskary@sh-eng.menofia.edu.eg (W.A. El-Askary). Journal of Wind Engineering & Industrial Aerodynamics 160 (2017) 1–15 Available online 16 November 2016 0167-6105/ © 2016 Elsevier Ltd. All rights reserved. MARK