Frozen-RANS Turbulence Model Corrections for Wind Turbine Wakes in Stable, Neutral and Unstable Atmospheric Boundary Layers

Abstract

Computational Fluid Dynamics based on RANS models remain the standard but suffer from high errors in complex flows. In particular, turbulent kinetic energy is over-produced in high strain rate regions, such as the near wake of wind turbine flows. Data-driven turbulence modelling methods aim to derive novel turbulence models with lower uncertainties, which generalize well to a certain class of flows. These state-of-the-art constitutes to first derive model-form corrections of a selected baseline model from high fidelity reference data, followed by regressing the corrections in terms of RANS-known flow features. For data-driven wind turbine wake modelling, industrial-scale wind turbines and non-neutral atmospheric boundary layers have yet to be considered. In this thesis, the first steps are made to address this research gap. First, Large-Eddy Simulation data is generated and validated against literature. The considered cases are under neutral, convective and stable atmospheric conditions. The frozen-RANS methodology, a technique used to derive turbulence model corrections given the high fidelity data, is then extended to for non-neutral conditions. The new framework now provides corrections to both the Boussinesq eddy viscosity hypothesis for the Reynolds stress and the gradient-diffusion hypothesis for the turbulent heat flux. By injecting the obtained corrections into dynamic RANS simulation, the baseline turbulence model deficiencies are corrected. In particular, high rate-of-strain regions now no longer show an overproduction of mechanical turbulence. Similarly, the lack of buoyant turbulence production in the free-stream atmosphere under convective conditions is solved. In the stable case, buoyant destruction is too large in the free-stream but not large enough in the wake. For the neutral and stable case, the corrected models produce wake velocity profiles that show excellent agreement with the large-eddy simulation reference data. Issues in the wall stress solution of the convective large-eddy simulation propagate to issues in the corrected RANS solutions, proving the necessity of high-quality data. Furthermore, it is shown that for most cases a single scalar correction to the turbulent heat flux, as opposed to the full vector correction, is sufficient for improving the error introduced by the gradient-diffusion hypothesis. This result is considerable since the simpler correction would be much easier to regress in terms of mean RANS-known quantities. The computational cost of the corrected RANS models is around the same as that of baseline RANS models; only 2\%-5\% of the large-eddy simulation computational cost.