A new RANS-based wind farm parametrization and inflow model for wind farm cluster modeling

Abstract. Offshore wind farms are more commonly installed in wind farm clusters, where wind farm interaction can lead to energy losses; hence, there is a need for numerical models that can properly simulate wind farm interaction. This work proposes a Reynolds-averaged Navier-Stokes (RANS) method to efficiently simulate the effect of neighboring wind farms on wind farm power and annual energy production. First, a novel steady-state atmospheric inflow is proposed. This inflow model is well suited for RANS simulations of large wind farms because it does not lead to the development of nonphysical wind farm wakes. Second, a RANS-based wind farm parametrization is introduced, the actuator wind farm (AWF) model, which represents the wind farm as a forest canopy and allows to use of coarser grids compared to modeling all wind turbines as actuator disks (ADs). When the horizontal resolution of the RANS-AWF model is increased, the model results approach the results of the RANS-AD model. A double wind farm case is simulated with RANS to show that replacing an upstream wind farm with an AWF model only causes a deviation less than 1 % in terms of wind farm power of the downstream wind farm. Most importantly, a reduction in CPU hours of 74.4 % is achieved, provided that the AWF inputs are known, namely, wind farm thrust and power coefficients. The reduction in CPU hours is further reduced when all wind farms are represented by AWF models; namely 89.3 % and 99.9 %, for the double wind farm case and for a wind farm cluster case consisting of three wind farms, respectively. For the double wind farm case, the RANS models predict different wind speed flow fields compared to output from simulations performed with the mesoscale Weather Research and Forecasting model (WRF), but the models are in agreement with the inflow wind speed of the downstream wind farm. The double wind farm case is also simulated with the TurbOPark engineering wake model. Similar wake shapes are reproduced by TurbOPark but the model predicts a larger wind farm wake magnitude compared to RANS and WRF. TurbOPark predicts much better results when its ground model is switched off and a wake expansion coefficient of 0.06 is used. The RANS-AD-AWF model is also validated with SCADA measurements in terms of wind farm shape; the model captures the trend of the measurements for a wide range of wind directions, although the SCADA measurements indicate more pronounced wind farm wake shapes for certain wind directions.