Effect of roughness on the wake lenght of a wind turbine located on a Gaussian hill

Several factors influence the efficiency of power generation in wind farms, such as wind speed and direction, turbine size, distribution, and topography. In particular, the irregularity of the topography affects the wake characteristics of each turbine, and the wake length impacts the power generation of the downstream turbines. We evaluated different topographic configurations for a wind tunnel by combining a Gaussian function with a sinusoidal function to represent a hill with complex topography. This approach allows us to control the complexity characteristics of the terrain to correlate the topography with the length of the wakes. We used the commercial software ANSYS Fluent™️ to study the fluid mechanics of turbulent flow over a Gaussian hill with small-scale surface waviness using Reynolds Averaged Navier Stokes, utilizing the k-ω SST turbulence model with the Actuator Disk model to represent a wind turbine. We validated the numerical results with experimental data presented by Cao and Tamura (2006). For an area of interest downstream (7D), we found that a smaller sinusoidal amplitude and greater wavelength favor the recovery of the wakes. Larger sinusoidal amplitude thickens the Gaussian hill’s boundary layer upstream of the turbine, which we believe is responsible for a smaller airflow and a lower production of kinetic energy. The latter leads to larger wakes due to lower momentum entrainment.