A generalised Gaussian wake model based on extended actuator disc theory

Abstract. As both the turbine and the wind farm sizes grow, the local blockage effect and the robustness of the wake model become increasingly important for wind farm design. One of the main challenges that affects the generality of conventional wake models is to find the start of the far wake region where the velocity field can be assumed to be self-similar. This work derives a wake model based on the actuator disc theory that considers the local blockage effect by considering the global mass conservation and predicts the start of the far wake with a mathematical condition. We define that the far wake starts around the point where the divergence of the Reynolds shear stresses is equal to its streamwise integration. The model is validated against a series of Reynolds-averaged Navier-Stokes (RANS) simulations. The proposed condition for the start of far wake applies to a wide range of turbine thrust coefficients, blockage ratios and inflow turbulence intensities, except for low turbulence intensity around 1 % for the cases examined in this study. The velocity increase induced by the blockage effect becomes non-negligible at 5 % for the examined cases, which can be lower than that induced by the real atmosphere. Thus, the blockage effect should be considered in the wake modelling for large turbines.