Modeling the effect of wind shear into a Vortex Particle-Mesh method for wind turbines

A model for the effect of a shear velocity profile on a wind turbine flow for the Lagrangian vorticity form of the 3-D Navier-Stokes equation is proposed, based on the assumption that vorticity from the shear velocity profile and the turbine do not interact. The model is implemented as part of the Vortex-Particle Mesh method developed by the Thermodynamics and Fluid mechanics Lab at the Universite Catholique de Louvain. Turbines are modeled using the lifting lines method, which is corrected in this work to operate with chosen wind velocity profiles. Simulations of wind turbines operating in linear velocity, power law and atmospheric boundary layer wind profiles are carried out and analyzed in detail. A partial version of the model corresponding to its definition in a 2-D environment is created to study the influence of the model’s different terms. The results show that the partial model has little influence on the near wake of the turbine, but slows down the flow below the turbine’s hub in the far wake. Reference cases corresponding to the exact phenomenon of a turbine operating under a shear wind profile are created. When compared to the latter, the model yields physically incorrect results. The model produces a flow which generates too much vorticity above hub height and too light below, creating an incorrect upwards deflection of the wake center. An exaggerated power law profile highlights the proportional correlation between the steepness of the profile and the inaccuracy of the model.