Divergence‐Free Correction for Synthetic Wind Fields

Abstract

Synthetic wind fields generated for wind turbine simulations do not satisfy incompressibility condition, thus, are not divergence-free. This results in spurious pressure fluctuations when input as a boundary condition to, for example, incompressible large eddy simulations (LES). This study investigates the impact of divergence-free correction on synthetic wind fields and their influence on wind turbine loads. Although divergence-free correction methods exist, they often modify the wind field energy spectrum and unsteady characteristics. Ongoing research addresses these challenges, but the acceptability of such changes and their impact on wind turbine loads has not been adequately studied. This work enforced incompressibility using the Helmholtz–Hodge decomposition, solved through spectral and spatial methods. An efficient Fourier-based spectral method was implemented, validated, and tested against the traditional finite difference method used for the spatial approach. Synthetic wind fields based on three coherence models were analyzed under three turbine operating conditions. An aeroelastic analysis of the IEA MW wind turbine was performed in the wind fields before and after divergence correction. Spectral analysis revealed a reduction in energy at specific frequencies after the correction for incompressibility. Additionally, the standard deviations of the wind velocities changed (despite similar means), consequently affecting the aeroelastic turbine response. A new iterative correction method is proposed to mitigate these effects, which preserves first- and second-order statistics while enforcing a divergence-free condition. This method is recursively applied, maintaining RMSE changes to the wind field within user-specified bounds. Key findings show that the iterative method yields an excellent match in the longitudinal wind field energy spectrum and a closer match in wind field standard deviation across the rotor, reducing discrepancies in turbine response. Some discrepancies in the lateral and vertical velocity components' higher order statistics were observed. Standard divergence correction (without RMSE constraints) led to a decrease of up to 20% in the tower fore-aft moment, while the proposed method reduces this change to −10%. The tower top side-side moment was found to increase by % by using the former approach, while the proposed correction reduced this increase to %. Blade root flap-wise bending moment was less affected (up to 5% reduction). Divergence-free wind fields, even with similar statistical properties, influence aeroelastic loads. The proposed method aims to achieve physically consistent and more comparable wind field analyses and resulting wind loads.