Abstract
The engineering wake models by Jensen [1] and Frandsen et al. [2] are assessed for different scenarios simulated using Large Eddy Simulation and the Actuator Line method implemented in the Navier-Stokes equations. The scenarios include the far wake behind a single wind turbine, a long row of turbines in an atmospheric boundary layer, idealised cases of an infinitely long row of wind turbines and infinite wind farms with three different spacings. Both models include a wake expansion factor, which is calibrated to fit the simulated wake velocities. The analysis highlights physical deficiencies in the ability of the models to universally predict the wake velocities, as the expansion factor can be fitted for a given case, but with not apparent transition between the cases.
Highlights
Today, industry continues to employ a number of engineering wake models for assessing the velocity deficits and power production behind single and multiple wind turbines
Jensen a√ssumes a linear expansion of the wake, while Frandsen et al suggests a wake expansion of D ∝ X, i.e. k = 2 which ensures a theoretical asymptotic flow speed for the infinite wind farm
The wake expansion factor is shown to depend on thrust coefficient in the case of single wind turbine
Summary
Industry continues to employ a number of engineering wake models for assessing the velocity deficits and power production behind single and multiple wind turbines. These models are based on simple single wake calculations and steady state considerations. The third regime models the equilibrium or infinite scenario, where the flow internally in the wind farm is in balance with the boundary layer created over the wind farm These engineering models are occasionally capable of giving good agreement, particular in terms of overall farm efficiency, the results are generally not consistent. The effects of thrust coefficient, turbine spacing, and vertical shear are investigated in the present work for the different scenarios. The aim is to assess and attempt to link the model performance in the different scenarios, and provide new calibrated parameters for the engineering models
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