A Three-Dimensional, Analytical Wind Turbine Wake Model: Flow Acceleration, Empirical Correlations, and Continuity

A new, three-dimensional, analytical, steady state wake model is presented which includes local flow acceleration near the rotor improving wake description compared to existing models. Wake structures such as the momentum deficit and regions of accelerated flow are concisely described with compound and normal Gaussian functions. Large-eddy simulations (LES) are used as training data to develop the model using two, inline turbines under various inflow conditions parameterized by hub height wind speed and turbulence intensity. Mass conservation is considered by fixing two components of the wake velocity model and optimizing the third to best satisfy continuity; after which, the model performs comparably if not better than existing work with regards to both relative error and mass consistency. The final model demonstrates a high degree of flexibility making use of empirical correlations to scale across different inflow conditions. This work will be transitioned into the open source, flow redirection and induction in steady state (FLORIS) wind farm modeling toolbox where it will be used to predict wake velocities in wind plant optimization processes. The inclusion of these effects is capable of revealing unutilized opportunities for enhanced power generation by aligning wake trajectories with these regions of accelerated flow.