The transition to renewable energy sources is essential to mitigate climate change, and floating wind turbines (FOWTs) present a promising solution to harness offshore wind resources. Light Detection and Ranging (LiDAR) systems mounted on nacelles provide a cost-effective and efficient means to measure wind fields, critical for turbine performance, control and load simulation. However, FOWT's motion introduces complexities in LiDAR measurements due to velocity and positional changes. This thesis focusses on developing a correction method for LiDAR measurements on FOWTs, addressing the influence of motion on wind velocity, position, and direction. The accuracy and uncertainty of these corrected measurements are quantified.

Simulated six degrees of freedom (6DOF) motion and a power law wind field are inserted in a numerical LiDAR model, in which corrected and uncorrected measurement position, direction and line of sight velocity are constructed. The corrected outputs are validated through reconstructed wind fields and the uncertainty of the correction is quantified. In this study, significant motion-induced bias is identified in the reconstructed wind fields. The dominant motion affecting measurement accuracy was identified as pitch motion, especially when it exhibits a non-zero mean. The relative error of the reconstructed power law wind field parameters is reduced by 3 orders of magnitude. Despite an increase in uncertainties associated with the correction method applied, the correction remains effective in reducing the error in LiDAR measurements induced by FOWT motions. The findings highlight the necessity and feasibility of motion correction for LiDAR measurements, offering substantial improvements in the accuracy and reliability of reconstructed wind fields for floating wind turbine applications.

Solving the incompressible Navier-Stokes equations is computationally heavy, with the pressure Poisson equation being the most time-consuming step. Iterative linear solvers are typically utilized to solve this equation. Since most solvers are iterative and rely on an initial guess, an opportunity emerges to use machine learning to improve this initial guess, such that fewer iterations are needed, consequently saving time.
A novel graph neural network is designed that employs a custom convolution algorithm, message-passing scheme, and pooling algorithm to maximize its performance. First, a convolution algorithm is proposed that uses interpolation to make a discrete (3x3) CNN kernel continuous. Then, instead of directly computing the kernel weight from the function, an integral over specified bounds is applied to account for the geometrical inhomogeneous distribution of the source nodes. The integral is embedded as the weighted sum of a vector containing learnable parameters, computed through a dot product with the edge attribute vectors. Next to the convolution operation, a message-passing scheme is designed that is compatible with the data format of the finite volume method whilst performing well in terms of the distance information can travel over the mesh. To conclude the design of the model, a custom pooling algorithm is designed that is equivalent to average pooling in CNNs.
A normalization procedure is established that ensures consistency in the model's magnitude. Notably, the ground truth output pressure is normalized using its standard deviation, which is unknown. To estimate this normalization factor, a correction model is established that uses the same convolution algorithm but employs an architecture inspired by classification CNNs.
The model's performance is evaluated based on the reduction in number of iterations required to reach convergence. This is done for both the Preconditioned Conjugate Gradient (PCG) solver and the multigrid Geometric Agglomerated Algebraic Multigrid (GAMG) solver
Across the various tests conducted, the number of iterations needed to reach convergence is reduced by approximately 40%, with the PCG solver performing slightly better than the GAMG solver. However, the PCG solver yields less consistent results, performing very well at samples that closely align with the training data, leading to a reduction of up to 60%. However, its performance drops significantly when tested on data that does not closely resemble the training data, sometimes even increasing the number of iterations. The GAMG solver demonstrates consistent performance, with almost no difference between the training and evaluation data.
In terms of generalization, the model demonstrates promising results, achieving similar performance across datasets with varying levels of complexity. This is interesting as the root mean square error differs significantly across the datasets and individual samples. This suggests that there is no direct relationship between the reduction in the number of iterations and the accuracy of the prediction. Furthermore, the model performs well on unseen meshes, showing that it can handle the unstructured nature of the meshes used throughout this research. This demonstrates the model's ability to be trained on a diverse dataset, after which it can be applied to unseen cases.

This thesis explores the use of Bayesian Deep Learning to improve uncertainty quantification in Reynolds-Averaged Navier-Stokes (RANS) turbulence models. While RANS models are commonly used in computational fluid dynamics due to their efficiency, they are often criticized for inaccuracies in certain flow conditions, primarily due to the challenges in modeling the Reynolds stress term. The thesis acknowledges the limitations of traditional turbulence models, which rely heavily on empirical parameters and often fail to generalize across different flow scenarios, leading to significant uncertainties.

To address these issues, the research introduces a data-driven approach, leveraging Bayesian Neural Networks (BNNs). BNNs are particularly suitable for this task because they not only improve prediction accuracy but also provide a mechanism to quantify uncertainties arising from both the model and the data. This dual uncertainty quantification is critical, as it helps to address the inherent ”black box” nature of machine learning models, which can introduce additional uncertainties into the predictions.

The methodology involves correcting traditional turbulence models and integrating them with BNNs to capture both aleatoric (data-driven) and epistemic (model-driven) uncertainties. The thesis demonstrates the effectiveness of this approach through various flow case studies, comparing the results against more accurate but computationally expensive methods like Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS).

The research concludes that the integration of Bayesian Neural Networks into RANS turbulence models not only enhances predictive accuracy but also provides a more comprehensive uncertainty quantification, making it a promising direction for future work in turbulence modeling.

Reynolds averaged Navier Stokes (RANS) models are the industry standard when it comes to computational fluid dynamics (CFD). RANS models have notable shortcomings as the
Reynolds stress is modelled locally and does not include temporal behaviour. Therefore,
current RANS models fail to make accurate predictions in areas of out-of-plane straining,
high streamline curvature and significant anisotropic Reynolds stresses.
Data augmented RANS models have shown promise to improve accuracy, with sparse regression and machine learning algorithms being able to train models between high fidelity
data and RANS. The current data driven models have problems, as they lack generalisability between data-sets, are difficult to interpret and only provide a local, non-temporal
correction or prediction for the Reynolds stresses.
The current work will explore sparse regression routines, in particular PDE FIND, for
the purpose of creating a non-local, temporal transport equation from data. Rather than
using high-fidelity turbulence data, a self-developed model problem, dubbed the ψ − ϕ
system, is created to replicate the uncertainties related to turbulence modelling. Multiple
candidate libraries for PDE FIND are tested, with the greatest emphasis on libraries
lacking a part of the true functional form, known as incomplete candidate libraries.
Incomplete candidate libraries are found to benefit from using highly correlated replacement functions for the missing function with an exception being a candidate library lacking
the correct production term. Even if models were trained poorly, PDE FIND was able to
identify the most important functions with an accurate coefficient.
PDE FIND could potentially create an universal transport equation to model the residual
between high fidelity data and RANS, but only if there are enough highly correlated
candidate functions and the production terms are well known or well represented in the
candidate library.

In recent years, computational fluid dynamics (CFD) has become an essential design tool across various industries, allowing engineers to tackle complex fluid dynamics problems that would otherwise require costly and time-consuming real-life experiments. For Formula 1 teams, who must experiment within strict time limits in the wind tunnel and on track, the ability to simulate airflow around their race cars under various conditions is crucial for maintaining competitiveness in the fast-paced world of Formula 1 racing. Reynolds-Averaged Navier-Stokes (RANS) simulations remain the industry standard for simulating turbulent flows, as they allow engineers to conduct simulations efficiently. However, this efficiency comes at the expense of accuracy, as RANS cannot resolve all turbulence scales, leading to uncertainties.

Recent advances in data-driven RANS turbulence modeling have enabled partial correction of these uncertainties. However, obtaining a correction that is generalizable under different geometries and flow conditions remains a challenge. Turbulence models are calibrated to fit specific flow regimes, so correcting these models across the entire domain can disturb these calibrations, worsening performance. A solution is to divide the domain into regions based on identifiable physical phenomena and apply local corrections without disturbing calibrated regions. In Formula 1 race car design, the most critical region is the shear layer, where RANS shows the largest discrepancies.

In this thesis, a classifier was developed to distinguish the shear layer from the rest of the domain based on the ratio between turbulent kinetic energy production and destruction, as well as turbulence intensity. Within this classifier region, corrections to the k-ω SST turbulence model are made by extracting model form errors from high-fidelity data using k-corrective-frozen RANS. These corrections include a residual term added to both the k and equations and a term for the anisotropy of the Reynolds stress tensor. The Spars Regression of Turbulent Stress Anisotropy (SpaRTA) framework, based on elastic-net regularization, was used to regress symbolic expressions for the corrections, enabling their application to simulations of unseen test cases.

The models discovered with the SpaRTA framework for the shear layer show promising results, improving the prediction of separation and reattachment positions. These models were tested on various geometries and simulations at different Reynolds numbers, demonstrating a certain level of generalizability. While there is room for further improvement, this thesis shows that integrating targeted model corrections into RANS simulations, informed by isolated shear layer data, can enhance the understanding and prediction of shear layer dynamics in 2D-separated flows.

Reducing anthropogenic climate change is a significant challenge requiring a global response to prevent tipping points in the climate system, such as the disintegration of ice sheets, and thawing of permafrost, among others. The rapidly growing air transport sector, which carried 4.5 billion passengers in 2019, is projected to emit nearly 2 Gt CO2 by 2050—about 2.6 times the emissions in 2021. Decarbonising aviation is challenging due to its reliance on fossil fuels, and while technological, operational, and regulatory measures have reduced fuel consumption, they are insufficient to mitigate aviation’s overall climate impact. The non-CO2 effects are significant, accounting for about two-thirds of aviation’s warming impact in terms of Effective Radiative Forcing (ERF). These effects include contrails, contrail-induced cirrus clouds, nitrogen oxides (NOx ), and water vapour emissions, collectively contributing to approximately 4% of anthropogenic forcing since the pre-industrial era. Given their spatio-temporal variability, climate-optimised flight planning canmitigate these impacts by avoiding sensitive regions, but this faces several challenges. These include the inherent chaos of weather, low scientific understanding of non-CO2 effects, and the large computational expense of calculating sensitive regions using climate change functions (CCFs).

To address these issues, this thesis first analyses algorithmic climate change functions (aCCFs), a simple surrogate model obtained by regressing the CCFs against local atmospheric variables. The aCCFs are computationally inexpensive to run since they only use few meteorological inputs to estimate climate impact, enabling real-time flight trajectory optimisation on arbitrary days. However, aCCFs are applicable only in parts of the Northern Hemisphere and require thorough verification before implementation. The focus is narrowed down on local aviation NOx effects on climate change, which largely causes warming via short-term increase in tropospheric ozone (O3) and is characterised by large variability. This necessitates a detailed investigation of NOx-O3 effects in isolation and its mitigation, which is a previously unexplored area. After verifying the O3 aCCFs through complex climate-chemistry model simulations, it is concluded that while it enables a reasonable first estimate, there are a few discrepancies.

TheO3 aCCFs are replaced by using a more comprehensive dataset comprising global NOx-O3 impacts, identifying additional physical variables that influence this impact, and using this information to train stochastic surrogates based on homoscedastic and heteroscedastic Gaussian processes. These models provide mean and uncertainty estimates for the climate impact of NOx on O3, for the first time. The heteroscedastic model more accurately reproduces the data distribution and its ease of use in predicting the climate impact of individual flights is demonstrated. Defined as probabilistic aCCFs (paCCFs), these models demonstrate superior accuracy over aCCFs, provide valuable insights for aviation’s non-CO2 effects, and offer broader implications for climateoptimised flight planning. The thesis concludes with limitations and recommendations to furthermitigate aviation’s environmental impact. @en

Site analysis to determine the loads experienced by wind turbines based on site-specific environmental conditions is typically done using either coupled aero-servo-elastic simulations for onshore wind turbines or coupled aero-servo-hydroelastic simulations in the case of offshore wind turbines. These simulations become computationally expensive when multiple load cases are needed to be taken into account, together with the numerous possible combinations of turbulence inflow patterns that result in the same mean inflow conditions. Probabilistic surrogate models offer a cheap alternative to these expensive simulations for predicting load statistics. This thesis explores a type of neural network called Conditional Generative Adversarial Networks (CGANs) as a potential candidate for such a surrogate model. Originally developed for image generation, CGANs have seen success in other applications. However, most applications of GANs to date are high-dimensional, with relatively low research focused on low-dimensional problems such as wind turbine load statistics. Multiple experiments are conducted using various multimodal and heteroscedastic datasets to assess its ability to model such characteristics
accurately. The conditional log-likelihood andWasserstein-1 distances were used as metrics. The results show that CGANs can indeed model such low-dimensional datasets. Finally, the CGANs are trained on data from simulations of onshore and offshore wind turbines in OpenFAST and compared with predictions from Mixture Density Networks (MDNs). The results from CGANs are comparable to MDNs, showing its potential as another alternative surrogate method, although more research needs to be performed.

Unsteady numerical simulation has been proven to be an essential tool for research. The quality of the results can be improved by using mesh adaptation. Mesh adaptation uses error indicators to refine the mesh in regions with high errors. The error indicators used are output errors with the most accurate output error estimation method being adjoint-based error estimation. However, for this method, the primal solution needs to be stored, which is storage intensive, especially for large unsteady simulations. The method proposed in this thesis uses a neural network autoencoder to compress and reconstruct the primal solution. This solution is compared to a reconstructed solution using Proper Orthogonal Decomposition (POD).

The one-dimensional unsteady Burgers equation is used as validation for the methods using a manufactured solution while the lid-driven cavity flow is investigated using the proposed method. The manufactured solution of the one-dimensional Burgers case could be exactly reconstructed using two POD modes. For the autoencoder a small latent space was used. For low resolutions, the small latent space did not prove to be a problem as the primal and residual could be captured accurately. However, for higher resolutions, the reconstruction error of the autoencoder became dominant for the residuals and resulted in erroneous adjoint-based error estimates while the primal remained qualitatively similar.

For the lid-driven cavity flow, the POD was still able to capture the solution using a low number of modes due to the smoothness of the solution. This resulted in an unfair comparison between the POD and autoencoder reconstructed solutions. The reconstructed autoencoder error estimates for lower resolutions were more accurate due to the latent space being large enough to capture the residual of the discrete primal accurately enough. When moving to higher resolutions, the autoencoder was not able to reconstruct the residual accurately enough leading to erroneous error estimates. Therefore, the latent space of autoencoders should be sufficiently large in order to gain an accurate reconstruction of the residual. If the latent space is large enough, the error estimate is accurate and the local error estimates can be used as a first iteration error indicator for mesh refinement.

Considering the goals set by the international community, the implementation of new energy sources has to increase considerably in the next seven years. In this thesis, the focus is on the acceleration and improvement of the application of offshore wind turbines. The power produced using this technology should become 3.6 times more before the end of this decade to comply with the set goals.

To achieve this target, new solutions have to be developed. To this aim, the implementation of model predictive control for wind turbines in the last years has been investigated. This would allow to optimize different parameters at the same time, such as maximization of energy production while minimizing the perceived loads. For this application, it is necessary to have forecasts of different features of the turbine, especially loads, with a higher frequency. As a result, the main research topic is defined as 'Can data-driven surrogate models be used for forecasting load time series on offshore wind turbines?'.

To answer this question, first environmental conditions are sampled within limits deducted from real data through Halton sequencing, and next simulations are run through OpenFAST to determine the resulting loads acting on the turbine. Within all the features resulting from the simulation, only five inputs and five target outputs are selected. This is the result of various considerations. Given the desire to develop a realistic methodology, the input variables are first filtered by assessing their availability from measurement devices. Next, the relationships between the variables are analyzed through cross-correlation to determine the degree of influence of each input on the output.

Using this data, a training database is created. It is used to train two different types of surrogate models, one linear and one non-linear, respectively ARIMAX and LSTM. These are implemented to generate a 30-second forecast of the moments acting at the root of the blade. To do so, the algorithms are trained using different variables as exogenous inputs to assess the models' performance in different cases. Given the wide range of target features, for LSTM two different behaviors are identified and the blade edgewise and flapwise moments are taken as examples. The hyper-parameters are tuned on the blade edgewise moment and lead to overfitting when applied to the blade flapwise and out-of-plane moment.

The obtained results show that the RMSE in ARIMAX is up to seven times larger than the one obtained from the application of LSTM. Within the non-linear models, the one resulting in the lowest percentage error for the blade edgewise, pitching, and in-plane moment considers the wind reference speed, the wind speed time series, and the corresponding tip deflection as exogenous inputs. Very low RMSE errors are obtained for all variables. Furthermore, it is concluded that while it is possible to implement LSTM in real-life, this is not achievable for ARIMAX.

Classical RANS (Reynolds-Averaged Navier-Stokes) turbulence models have limited accuracy in the prediction of the flow over the wing-body geometry. Therefore, this work focuses on improving the prediction accuracy of the classical k-ω SST turbulence model for the junction flow by means of the data-driven method SpaRTA. In the SpaRTA methodology higher-fidelity data, in this work LES (Large Eddy Simulation) data, is leveraged to find correction models
that enhance the baseline turbulence model. These correction models aim at correcting the Reynolds stress anisotropy and the turbulent kinetic energy (k) equation. The correction models are obtained by sparsely regressing flow features to the correction fields that are found by the k-corrective frozen approach.

The results showed that the correction fields determined by the frozen method are very effective. Direct propagation of these fields resulted in a solution very similar to the LES data. In contrast to the model search for the k correction, finding a model for the anisotropy correction by means of sparse regression was difficult. The latter is reflected in the CFD (Computation Fluid Dynamics) propagation of the found models on the same flow case as the training of the models. This model propagation showed an improvement in the placement of the horseshoe vortex, however, the vortex topology in the corner region was unsatisfactory. Which is linked to the poor model fit of the anisotropy correction field.

Besides the search for an improved turbulence model, this work also encapsulates an evaluation of the drag reduction by the anti-fairing geometry for the wing-body junction flow. This evaluation was achieved by comparing available wall-resolved LES data sets. The evaluation revealed that the anti-fairing reduces the drag force by a propulsive pressure mechanism over the bottom wall for a specific geometry over which the drag is computed. This geometry included only 5% of the complete wing span, for larger wing spans the drag reduction was not evident.

Computational fluid dynamics (CFD) is an important tool in design involving fluid flow. Scale-resolving CFD methods exist, but they are too computationally expensive for practical design. Instead, the relatively cheap Reynolds-averaged Navier-Stokes (RANS) approach is the industry standard, specifically models based on the Boussinesq hypothesis, which are unable to represent the effect of turbulence anisotropy. Development of RANS models based purely on physical arguments has stagnated; however, data-driven turbulence modeling presents a paradigm shift for improved predictions. Though this technique has produced successful models tailored to specific flows, it has yet to produce a successful general turbulence model, which is the focus of this work.

In this work, models consist of corrections to the classical k-omega SST turbulence model; bijDelta to correct the Reynolds stress anisotropy and R to correct the turbulent kinetic energy. High fidelity data combined with the k-corrective-frozen technique is used to obtain exact correction fields, which are validated. Then, the SpaRTA framework is used to regress symbolic expressions for the corrections. Using a newly developed solver, models are injected into a full RANS solver to assess a-posteriori performance for various test cases. SpaRTA identifies a good R model, but only after a-posteriori optimization of coefficients, this model holds promise for generalization. Meanwhile, SpaRTA is unable to find a good bijDelta model due to its reliance on linear regression. A new framework based on non-linear regression is introduced which identifies a much better bijDelta model, though this model is Reynolds number dependent.

The most used RANS-model in relation to wind farms, k−epsilon, has significant shortcomings. It over-predicts the eddy viscosity in the near-wake and fails to model the anisotropy of the turbulence quantities. The Sparse Regression of the Turbulence Stress Anisotropy (SpaRTA) method could remedy these shortcomings. This method uses temporally averaged fields from LES data together with sparse regression methods to learn corrections for the anisotropy tensor and turbulence production terms.

This thesis extends the SpaRTA method to wind farms in stable atmospheric boundary layer conditions through an additive correction term for the turbulent heat flux. This extended SpaRTA method is applied to a stably stratified parcel of air with and without a turbine.

The simulations with implemented correction models show significant improvement over the baseline simulations. However, it is also concluded that the effects of the additional turbulent heat flux correction could be incorporated in the turbulence production correction.

Studies revolving around data-driven methods have been on a rise in recent years to improve highly modelled methods such as the two-equation turbulence models of Reynolds-averaged Navier-Stokes (RANS). Similarly, such data-driven methods are implemented into partially-averaged Navier-Stokes (PANS). PANS is a young bridging method that fulfils the requirements of bridging methods set by Speziale [1]. It can be adjusted according to the fraction of a flow field that is desired by the user to be resolved and modelled by changing the value of fk, a parameter that takes a value between 0 and 1. In this thesis, PANS is extended via a combination of two data-driven methods: k−corrective frozen RANS [2] and data-driven stochastic closure simulation (DSCS) [3]. The k−corrective frozen RANS method aims to correct for the model errors in the k−equation and the anisotropy of the Reynolds
stress tensor derived from the Boussinesq approximation. While DSCS also aims to correct for the anisotropy of the Reynolds stress tensor, it considers that PANS solves for the unresolved part of the flow field and thus corrects for the unresolved anisotropy. While PANS and the two data-driven methods have independently been proved to work as they were theoretically desired, combining these ideas has not yet been attempted. As any turbulence kinetic energy solving RANS turbulence model can be developed into PANS form, the k − ω SST model was chosen for the best initial prediction. This SST model for PANS is extensively derived and then reformulated to produce the target correction terms. The correction terms are analysed at various values of fk and they show good agreements with fk.

When simulating fluids the industry standard is Reynolds averaged Navier-Stokes (RANS). However, the results for certain flows are inaccurate. The main source of error in popular RANS turbulence models is the Boussinesq approximation, assuming a linear relationship between the Reynolds stress anisotropy and the mean rate of strain. Experiments show this is simply not correct. Most state of the art research in data driven turbulence modelling is focused on replacing or augmenting this linear relationship.

The research presented in this report implements two corrections, one to the Reynolds stress anisotropy and another to account for the modified production of turbulent kinetic energy by the modified anisotropy tensor. The magnitude of the required corrections is found by comparing RANS simulations to more detailed CFD algorithms such as large eddy simulation and direct numerical simulation.

A state of the art symbolic regressions framework named deep symbolic regression (DSR) is used to find explicit algebraic Reynolds stress models. DSR uses a recurrent neural network to create expressions and is able to find complex expressions that fit the data very well.

The expressions found with DSR are implemented in a custom k-omega SST turbulence model and validated in CFD. Large improvements over the standard turbulence model are achieved. The results are compared to results of the SpaRTA framework where the same method of corrections is applied. DSR is able to produce better fitting expressions and these result in improved flow fields over the best models found with SpaRTA.

The best model is also tested in a true prediction of a flow at a Reynolds number that is roughly three times as large as values encountered during training. The results are good, showing generalisability of the model outside training conditions.

To this date, simulating the dynamics of a fluid remain extremely expensive for most practical design prob- lems. The large range of length and time scales to be resolved makes it especially computationally heavy. In engineering applications, the standard is still the RANS approach for CFD modelling. Most commonly the so- called two-equation models are used. The use of CFD in the aerospace design process is still severely limited by the inability to accurately and reliably predict turbulent flows with significant regions of separation. More accurate modelling approaches including LES are often not practical to use in engineering applications.
In the recent work of Deltares, such problems also arise. Research has been performed on water flow be- hind an underflow gate. The flow phenomenon that occurs closely resembles that of a wall-bounded jet. The reason such research has been performed is to better predict the turbulent behaviour of the jet downstream to predict possible damage to sediment. Seven weirs on the Meuse are planned to be renovated or replaced. Currently, bed protection is designed using physical scale models. Ultimately numerical models are to be the new standard for designing bed protection behind an underflow weir.
In their work experiments have been performed to acquire PIV data of the velocity field. This has been compared to their results of multiple CFD simulations which have been performed with different levels of fidelity. Several gate openings, changing the effective Reynolds number, have been used to compare the experimental results with the simulations. They concluded that although the velocity field solution of the simulations is good enough for engineering practices, all simulations show a mismatch in the area of the shear layer between the jet and the main flow.
In recent years more and more research has been done in the applications of machine learning. The capabilities of ML have increased rapidly and are now also used in closure modelling. Alongside this are the continuously improving experimental capabilities which allow for much higher resolution information. The combination can be used for data-driven techniques to improve upon current RANS models.
In recent work, the paradigm of field inversion has been proposed. Here instead of calibrating the mod- elling coefficients, a corrective field is used to effectively address the modelling deficiency. The correction field has been applied to the production term of the specific turbulent dissipation rate transport equation. To infer the values of the highest probability for the corrective field inverse methods are proposed. The method proposed uses Bayesian inversion, which includes an optimisation process. As the problem consists of a large number of variables normal optimisation processes are too expensive. Therefore, the adjoint method is proposed to compute gradients efficiently.
In this work, the goal is to extend upon the recent work on field inversion. The paradigm will be applied to the underflow weir case of Deltares. The experimental data will be used to infer a spatially varying corrective field used to correct the simulations to improve their predictive capabilities. As the density of data points is often far smaller than the density of simulation cells, and often data sets do not cover the whole simulation domain the paradigm is extended to accept imperfect data.
It was found that with these extensions a correction field could be found that can lower the cost function by a factor of two. The prediction of flow features behind the weir were predicted more accurately using the newly found corrected model.

A wall resolved LES simulation of the Anti-Fairing wing/body junction introduced by Belligoli et al. [6] to reduce interference drag is performed. The LES mesh is composed of 61.7 million cells with a C-fitted grid around the wing . The simulation is performed using the pimple solver of Open- Foam 4 with a time and space varying inlet boundary condition obtained thanks to a precursor. This simulation will be used to assess the impact of the Anti-Fairing by comparing the result to the wall resolved baseline case of Alberts [2] and to serve as a training data for data driven techniques applied to junctions flows. Using the wall resolved LES we apply the data driven algorithm method Sparse Regression of Turbulent Stress Anisotropy (SpaRTA) developed by Schmelzer et al. [38] in the case of junction flows. It is shown that the first step of the method, namely the k-corrective frozen RANS, is able to produce corrective fields to the Reynolds tensor and the turbulent kinetic energy equations in this case. The corrective fields once added in a k-omega SST simulation make it possible to obtain the exact location, strength and shape of the main horseshoe vortex. The upstream boundary layer is also subject to corrections indicating RANS-LES mismatch in the inflow. Mutual Information (MI) is calculated to identify the relevant tensors, physical features and invariants that correlate with the junction flow data. Finally, algebraic models for the corrective fields are obtained. They are compared to the true values of these fields. It is possible to see that the performance of SpARTA models is good upstream of the wing. However, models found and tested in the vicinity of the wing, where the separation and horseshoe vortex are located, are not fully able to capture the relevant corrections. Additional constraints or steps to the ones performed in the time of this study may be necessary in order to use SpaRTA to generate models giving improved predictions compared to classic RANS turbulence models.

Recent years have seen an increase in studies focusing on data-driven techniques to enhance modelling approaches like the two-equation turbulence models of Reynolds-averaged Navier-Stokes (RANS). Different techniques have been implemented to improve the results from these simulations. In particular, the main focus has been on overcoming the limitations implied by the Boussinesq assumption. This has been approached by using machine learning techniques as a way of discovering new formulations that could overperform when compared to traditional models.
Despite promising results for steady RANS simulations, little has yet been investigated in URANS applications. In this dissertation, this lack of research will be addressed. The main ideas are then, first, to see how the available information in URANS simulations can be used to improve the anisotropic Reynolds stress tensor prediction, and second if and how this can be done by using a sparse regression technique, whose framework is known as SpaRTA. A procedure involving the triple decomposition of High-Fidelity velocity fields is applied, aiming at finding a model exclusively for the stochastic component of the anisotropy. The test case which is considered is the flow around a cylinder at Re=3900. The High-Fidelity data was collected by running Large Eddy Simulations in OpenFOAM, after which the velocity was split into its different components through Proper Orthogonal Decomposition.
A priori results have shown good performance of the trained models, outperforming the Boussinesq assumption both in the prediction of turbulence componentiality and also on the values of the single anisotropy components.

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.

A wall-resolved Large Eddy Simulation (LES) of a wing-body junction is performed. The aim is to generate high-fidelity junction flow data to be used in a data-driven turbulence modelling approach, specifically to improve the accuracy of RANS-simulations in junction flows. The simulation is performed on a 61.5 million C-grid body fitted mesh in the pimpleFoam solver of OpenFOAM, with a turbulent channel flow precursor providing the unsteady inlet boundary condition. Analysis of the wall-resolved LES shows that the simulation accurately captures the complex flow phenomena in the wing-body junction flow including intermittency for the present inflow condition. Comparisons of the wall-resolved LES with a coarse-grid RANS simulation and the wall-modelled LES of Srikumar [2019] show that the wall-resolved LES in the present study is an improvement over the other two numerical methods. Most notably, an improvement in terms of the prediction of the location and magnitude of the mean spanwise vorticity and the mean turbulent kinetic energy of the horseshoe vortex systems was observed. Especially the RANS-simulation was unable to accurately capture the complex flow physics in the junction due to the limitations of RANS-methods, which are unable to accurately capture Reynolds stress anisotropy due to the Boussinesq hypothesis. An analysis of the high-fidelity junction flow data was performed to indicate regions where the Boussinesq hypothesis breaks down. The most notable region where the Boussinesq hypothesis was found to be not valid, was the region in close proximity to the wing-body junction upstream of the wing. Due to the breakdown of the Boussinesq hypothesis in the junction region, significant improvements of the accuracy of junction flow RANS-simulations can potentially be achieved by using the high-fidelity data from the present study in a data-driven turbulence modelling approach.