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. ... Read more

Adverse pressure gradients, separation and other forms of non-equilibrium flows are often encountered in flows of interest. In these type of flows, the Boussinesq hypothesis does not hold and often leads to erroneous predictions by eddy viscosity models. In an attempt to capture these non-equilibrium effects, lag parameter models introduce a lag parameter, which is derived from an elliptic blending Reynolds stress model. A novel deterministic machine learning algorithm, referred to as Sparse Regression of Turbulent Stress Anisotropy (SpaRTA), has been used with the objective of developing a data-driven turbulence model based on the elliptic blending k − ω lag parameter model and evaluating its performance in terms of generalizability, interpretability and its ability to infer the quantities of interest. Corrective terms are introduced and computed directly from high-fidelity data to account for the model-form error by using the k-corrective-frozen-RANS approach. SpaRTA is then used to infer algebraic stress models for these corrective terms using a Galilean invariant integrity basis. It was shown that the k-corrective-frozen-RANS framework has the ability of representing the mean flow features by propagating the corrective terms through a CFD model in OpenFOAM and comparing its result to high-fidelity data. Cross-validation is used to test the performance of the models on unseen data using three flow cases that involve separation, namely periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). In order to assess the impact of the additional transport equation of the lag parameter, the same data-driven approach was applied to the conventional two-equation k − ω model. Utilizing an additional transport equation for the lag parameter in this data-driven approach did not result in any significant improvements in terms of predictive capability or generalizability, as both data-driven approaches showed a similar performance, although the data-driven k − ω models were more numerically stable. It was found that corrective terms formulated using a reduced integrity basis yields data-driven models that have a similar predictive capability compared to models that used the full integrity basis to construct the corrective terms. A significant portion of the resulting data-driven models showed an improvement in predictive capability over the standard (non-data-driven) k − ω model. Furthermore, most of the models were able to generalize their predictions to two-dimensional flow cases that had different complexity and showed a significant improvement over the baseline k − ω model. ... Read more