Study of the influence of imposed turbulence on the asymptotic wake deficit in a very long line of wind turbines

The influence of imposed turbulence on the development of the flow along a long row of wind turbines is studied, in search for an asymptotic wake deficit state. Calculations are performed using EllipSys3D, a CFD code that solves the Navier–Stokes equations in their incompressible form using a finite volume approach. In this code, the Large-Eddy Simulation technique is used for modeling turbulence, and the wind turbine rotors are represented as actuator discs whose loading is determined through the use of tabulated airfoil data by applying the blade-element method.Ten turbines are located along a row and separated from each other by seven rotor diameters, which is representative of the distance used in today's offshore wind farms. Turbulence is pre-generated with the Mann model, with imposed turbulence intensity levels of 4.5% and 8.9%. The aim with this study is to investigate features of the flow that depend solely on imposed turbulence and the presence of wind turbine rotors. For this reason, the turbines are isolated from their environment, and no effect from the presence of the atmospheric boundary layer is modeled, i.e., a non-sheared inflow is used. Analysis of the characteristics of the flow as a function of the position along the row of turbines is performed in terms of standard deviation of the velocity components, turbulence kinetic energy, mean velocity, and power spectra of the axial velocity fluctuations. The mean power production along the row of turbines is also used as an indicator.Calculations are performed below rated power, where a generator torque controller implemented in EllipSys3D renders it possible for the turbines to adapt to the flow conditions in which they operate.The results obtained for the standard deviation of the velocity components, turbulence kinetic energy, power and mean velocity as functions of downstream distance show that an asymptotic wake state seems close to be reached, in the conditions tested, near the end of the 10 turbine row. Significant changes towards this state are seen to happen faster when imposing turbulence in the domain. Power spectra of the axial velocity fluctuations are shown to provide interesting information about the turbulence in the flow, but are found not to be useful in determining if an asymptotic wake state is reached.