AN EXPLICIT ALGEBRAIC TURBULENT MODEL TO REPRODUCE THE ANISOTROPY OF THE MOMENTUM TURBULENT FLOWS IN A WIND TURBINE WAKE

摘要

The proposed model is based in a three-dimensional wake model (UPMWAKE) that solves the mass, momentum and energy equations and uses the k-ε method to calculate the Reynolds stress components. However, UPMWAKE cannot reproduce properly the anisotropy of the turbulent stress components in the wake, and it cannot even reproduce the anisotropy of the basic atmospheric flow. In many applications it is of interest to have reliable values of the turbulence stress tensor in the wake. In particular, to calculate the unsteady loads due to turbulence it is important to know the value of the turbulence intensity in the main flow direction. In this work, an explicit algebraic model for the components of the turbulent stress tensor is used. The conservation equations establish a balance between production and dissipation, so that the equations to solve are algebraic. The constants of the model have been adjusted, so that it will reproduce the logarithmic layer of the basic flow and the corresponding stress tensor, as obtained from classical experimental results. The model uses the same schemes and boundary conditions of UPMWAKE. The new model, called UPM-ANIWAKE, has a low computational cost. The numerical results are compared to experimental data from the Sexbierum wind farm, and a reasonable agreement is obtained. In general, the turbulence in the wake is more isotropic than in the outside flow, although, locally, there are some peaks of turbulence intensity of the component in the wind direction, that are not observed for the turbulence intensities in the other directions.