FD Wake Modelling with a BEM Wind Turbine Sub-Model

Abstract

Modelling of wind farms using computational uid dynamics (CFD) resolving the ow eld around each wind turbine’s blades on a moving computational grid is still too costly and time consuming in terms of computational capacity and eort. One strategy is to use sub-models for the wind turbines, and sub-grid models for turbulence production and dissipation to model the turbulent viscosity accurately enough to handle interaction of wakes in wind farms. A wind turbine sub-model, based on the Blade Momentum Theory, see Hansen (2008), has been implemented in an in-house CFD code, see Hallanger et al. (2002). The tangential and normal reaction forces from the wind turbine blades are distributed on the control volumes (CVs) at the wind turbine rotor location as sources in the conservation equations of momentum. The classical k turbulence model of Launder and Spalding (1972) is implemented with sub-grid turbulence (SGT) model, see Sha and Launder (1979) and Sand and Salvesen (1994). Steady state CFD simulations were compared with ow and turbulence measurements in the wake of a model scale wind turbine, see Krogstad and Eriksen (2011). The simulated results compared best with experiments when stalling (boundary layer separation on the wind turbine blades) did not occur. The SGT model did improve turbulence level in the wake but seems to smear the wake ow structure. It should be noted that the simulations are carried out steady state not including ow oscillations caused by vortex shedding from tower and blades as they were in the experiments. Further improvement of the simulated velocity defect and turbulence level seems to rely on better parameter estimation to the SGT model, improvements to the SGT model, and possibly transient- instead of steady state simulations.