Modelling wind farms as forests

Abstract

The increasing size of wind turbines, the expansion of wind farm areas, and the growing offshore space occupied by wind warms highlight the need for accurate modelling of wake interactions between wind farms. These interactions can significantly influence power production and the optimal layout of wind farms in densely developed offshore regions. This thesis modifies and expands existing forest canopy models by introducing a wind-farm induced momentum sink, a turbulent kinetic energy source and a turbulent kinetic energy dissipation source in the transport equations that represent the effect of the turbines within the wind farm. Wind farms are parametrised and modelled using a 𝑘 − 𝜀 RANS approach in which a neutrally stable atmospheric boundary layer is simulated under offshore conditions. Different modelling approaches and wind turbine spacings within the wind farm are investigated, considering a range of spacings representative of modern offshore wind farm layouts to evaluate their influence on wake recovery and turbulence generation. The results are first verified with higher-fidelity LES results and subsequently validated against wind speed and power production measurements from operational offshore wind farms. The study shows that a modelling approach inspired by forest canopies agrees well with high-fidelity simulations. Moreover, a relationship between wind turbine spacing and the Wind Farm Canopy model coefficients is found. The results indicate that as turbine spacing increases, relatively more turbulent kinetic energy dissipation than turbulent kinetic energy needs to be added to the 𝑘 − 𝜀 transport equations. As a result, increased turbulent kinetic energy dissipation is required to reproduce the observed velocity deficit. This indicates that larger turbine spacings correspond to lower background turbulence levels, leading to a weaker and slower recovery of the velocity deficit. These findings provide guidance for selecting Wind Farm Canopy model coefficients based on turbine spacing, thereby improving the predictive capability of RANS-based simulations for large offshore wind farm clusters and their wake interactions.