Turbulence modeling of the flow around horizontal axis wind turbines

This paper proposes and describes a promising way for performance prediction of an arbitrary array of wind turbines. It is based on the solution of the time-averaged, steady-state, incompressible Navier-Stokes equations with an appropriate turbulence closure model. The actuator disk model, together with blade element theory, are used to model the turbines as a distribution of surficial forces. The k-ε model has been chosen for the closure of the time-averaged, turbulent flow equations and the properties of the incident flow correspond to those of a neutral atmospheric boundary layer. An additional term in the turbulent kinetic equation is proposed to model tip vortices' contribution to turbulence. In this paper, the applicability and viability of the proposed methodology is demonstrated using an axisymmetric implementation. The proposed mathematical model is solved using a Control-Volume Finite Element Method (CVFEM). Detailed results have been obtained using the proposed method for an isolated wind turbine and for two turbines one behind another. Accurate wake velocity deficit predictions are obtained and an increase in power due to atmospheric turbulence is found in agreement with measurements. In the case of two turbines, the proposed methodology provides a realistic prediction of the performance degradation of the downstream turbine.