Presentations

Abstract

Global blockage is known as the interaction of a wind farm with the atmospheric boundary layer (ABL) and the free atmosphere. As the density of wind farms increases, this phenomenon and its impact on power production must be properly modelled and accounted for in yield calculations. While computational fluid dynamics methods can solve for global blockage implicitly, they generally remain too computationally expensive for energy yield assessments and layout optimization. Thus, there is a need for simple and practical, yet physically consistent, global blockage models.   In this study, we focus on the PyWake implementation of a 2-layer model that is based on the work of Smith (2010) and Stipa (2024). The model describes the pressure gradients and gravity waves associated with a temperature inversion at the top of the ABL and a weekly stratified atmosphere aloft. The pressure disturbance arises from the wind farm drag force in combination with the confinement associated with the presence of the ABL. This disturbance is estimated by an iterative coupling of a micro-scale wind farm model calculating the wind farm drag and a macro-scale wind farm model calculating the pressure perturbation.  The response of the atmosphere to the presence of the wind farm is primarily dependent on the Brunt-Väisälä frequency (N) describing the strength of the upper layer stratification and the Froude number (Fr) describing the inversion strength. In the extreme cases where the stability aloft is very strong (N is large), leading to a small inversion displacement, the inversion acts as a rigid lid. Conversely, when N and Fr are both small, the pressure perturbation plays a small role compared to the wind farm drag.  In this study, we have varied the two aforementioned numbers in combination with three different inflow models prescribing the ABL height, the geostrophic wind in the upper layer, and the bulk wind speed in the wind farm layer. The two first models, proposed by Liu and Stevens (2022) and Narasimhan et al. (2024), are both describing the vertical velocity profile by applying a coupling of the Ekman boundary layer theory with a Monin-Obukhov Similarity Theory description of the surface layer for conventional neutral and stable boundary layers.  Lastly, we used the steady-state Reynolds-averaged Navier–Stokes inflow model of the neutral and stable ABL described in van der Laan et al. (2024) where the ABL height is implicitly obtained by a simple buoyancy parametrization assuming a constant temperature gradient over the ABL.  The modelling is performed at the Dudgeon wind farm including two neighboring wind farms: Sheringham Shoal and Race Bank. In addition to representing the reduction of the wind upstream of the wind farm, the speed-up fields resulting from the pressure perturbation show a significant interaction between the wind farms, and the gradients over the farms are clearly dependent on the Fr number. The results are also compared to measurements from the OWA GLOBE project where the reduction in wind speed upstream of a farm and the acceleration between two adjacent farms have been measured.