An extended K-ɛ model for wake-flow simulation of wind farms

TY - JOUR

T1 - An extended K-ɛ model for wake-flow simulation of wind farms

AU - Zehtabiyan-Rezaie, Navid

AU - Abkar, Mahdi

PY - 2024/2

Y1 - 2024/2

N2 - The Reynolds-averaged Navier–Stokes approach coupled with the standard k−ɛ model is widely utilized for wind-energy applications. However, it has been shown that the standard k−ɛ model overestimates the turbulence intensity in the wake region and, consequently, overpredicts the power output of the waked turbines. This study focuses on the development of an extended k−ɛ model by incorporating an additional term in the turbulent kinetic energy equation. This term accounts for the influence of turbine-induced forces, and its formulation is derived through an analytical approach. To assess the effectiveness of the proposed model, we begin by analyzing the evolution of normalized velocity deficit and turbulence intensity in the wake region, and the normalized power of the waked turbines. This investigation involves a comparison of the predictions against results from large-eddy simulations in three validation cases with different layouts. We then simulate a wind farm consisting of 30 wind turbines and conduct a comparative analysis between the model-predicted normalized streamwise velocity and wind-tunnel measurements. Finally, to conclude our assessment of the proposed model, we apply it to the operational wind farm of Horns Rev 1 and evaluate the obtained normalized power with the results from large-eddy simulations. The comparisons and validations conducted in this study prove the superior performance of the extended k−ɛ model compared to the standard version.

AB - The Reynolds-averaged Navier–Stokes approach coupled with the standard k−ɛ model is widely utilized for wind-energy applications. However, it has been shown that the standard k−ɛ model overestimates the turbulence intensity in the wake region and, consequently, overpredicts the power output of the waked turbines. This study focuses on the development of an extended k−ɛ model by incorporating an additional term in the turbulent kinetic energy equation. This term accounts for the influence of turbine-induced forces, and its formulation is derived through an analytical approach. To assess the effectiveness of the proposed model, we begin by analyzing the evolution of normalized velocity deficit and turbulence intensity in the wake region, and the normalized power of the waked turbines. This investigation involves a comparison of the predictions against results from large-eddy simulations in three validation cases with different layouts. We then simulate a wind farm consisting of 30 wind turbines and conduct a comparative analysis between the model-predicted normalized streamwise velocity and wind-tunnel measurements. Finally, to conclude our assessment of the proposed model, we apply it to the operational wind farm of Horns Rev 1 and evaluate the obtained normalized power with the results from large-eddy simulations. The comparisons and validations conducted in this study prove the superior performance of the extended k−ɛ model compared to the standard version.

KW - Power losses

KW - Reynolds-averaged simulation

KW - Turbine wakes

KW - Turbulence modeling

KW - Wind-farm modeling

UR - http://www.scopus.com/inward/record.url?scp=85181762378&partnerID=8YFLogxK

U2 - 10.1016/j.renene.2023.119904

DO - 10.1016/j.renene.2023.119904

M3 - Journal article

SN - 0960-1481

VL - 222

JO - Renewable Energy

JF - Renewable Energy

M1 - 119904

ER -