A generalised Gaussian wake model based on extended actuator disc theory

Abstract. Engineering wake models have been widely used for wind farm design and optimization due to low computational cost. Recent work suggests that the key to improving the wake models lies in the prediction of the transition point between the 'near-wake' and 'far-wake' regions. This study proposes an analytical model for this transition point based on a relationship between the wake-centreline pressure gradient and the divergence of Reynolds shear stresses. Using this relationship together with an extended actuator disc analysis for a turbine in a laterally confined flow, the proposed model also predicts the initial wake profile at the start of the far-wake region for any practical inflow turbulence conditions and local blockage ratios. In addition, a new Gaussian far-wake model considering the local blockage effect is formulated to form a complete engineering wake model. The model is validated against a series of Reynolds-averaged Navier-Stokes (RANS) simulations of an actuator disc over a wide range of inflow turbulence intensities, thrust coefficients and local blockage ratios. The model predictions are in good agreement with the simulation results.