A pressure-corrected double-Gaussian analytical wake model for wind turbines

Analytical wake models play a crucial role in assessing wake effects, optimizing wind farm layouts, and enabling active wake control. However, conventional models primarily focus on the far-wake region and show limited accuracy in the near wake, restricting their applicability in modern compact wind farms. To address this, this study proposes a pressure-corrected double-Gaussian analytical wake model to improve prediction accuracy across the entire wake. Time-averaged wakes under different thrust coefficients and yaw angles are simulated using large-eddy simulation coupled with an actuator disk model with rotation. Based on the near-wake pressure distribution obtained from large-eddy simulation (LES), a pressure correction term is incorporated into the momentum conservation equation to construct the pressure-corrected double-Gaussian wake model. An analytical expression for the position of the minimum velocity in the wake is derived from mass conservation. The model requires only the wake expansion coefficient as an adjustable parameter. Comparison with LES data indicates that, relative to the uncorrected double-Gaussian model, the normalized root mean square error of wake velocity in the near-wake region, particularly near the rotor, is reduced from approximately 40% to below 13% of the inflow wind speed. The model successfully captures wake velocity distributions across different turbulence intensities, yaw angles, and tip speed ratios, demonstrating strong robustness and general applicability.