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The Reynolds-averaged Navier-Stokes approach coupled with the standard$k-\varepsilon$ model is widely utilized for wind-energy applications. However,it has been shown that the standard $k-\varepsilon$ model overestimates theturbulence intensity in the wake region and, consequently, overpredicts thepower output of the waked turbines. This study focuses on the development of anextended $k-\varepsilon$ model by incorporating an additional term in theturbulent kinetic energy equation. This term accounts for the influence ofturbine-induced forces, and its formulation is derived through an analyticalapproach. To assess the effectiveness of the proposed model, we begin byanalyzing the evolution of normalized velocity deficit and turbulence intensityin the wake region, and the normalized power of the waked turbines. Thisinvestigation involves a comparison of the predictions against results fromlarge-eddy simulations in three validation cases with different layouts. Wethen simulate a wind farm consisting of 30 wind turbines and conduct acomparative analysis between the model-predicted normalized streamwise velocityand wind-tunnel measurements. Finally, to conclude our assessment of theproposed model, we apply it to the operational wind farm of Horns Rev 1 andevaluate the obtained normalized power with the results from large-eddysimulations. The comparisons and validations conducted in this study prove thesuperior performance of the extended $k-\varepsilon$ model compared to thestandard version.

An extended $k-\varepsilon$ model for wake-flow simulation of wind farms