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.

The sea and the shoreline form a complex ecosystem driven by tides. So far, studies often ignore the moving boundary caused by these tides. The focus of this thesis to incorporate this boundary by using a coordinate transformation and a time-explicit numerical method. To achieve this, first the one-dimensional shallow water equations are derived from the 3D Navier Stokes equations. Then these 1D equations are non-dimensionalized and the coordinate transformation is done. This results in a system of non-linear equations. The seabed is modelled as a straight line. At the seaward side there is a periodic forced wave and at the landward side the water depth is 0. The time-explicit numerical method of Lax-Friedrichs is used. This method is stable under a more restricted Courant-Friedrichs-Lewy condition and is convergent for refined grids. For the Ameland inlet system the water depth, velocity and length of the basin results are calculated and compared to a simplified model and complemented by a Fourier analysis. The results are realistic (constant in the beginning of the basin with visible non-linearities at the landward side). An analysis is done to understand how the model behaves for dierent physical parameters, such as: the amplitude of the periodically forced wave, the undisturbed water depth, the length of the basin and the resistance. The model remains stable and the results are realistic.

Hydrogen, as an energy carrier, is of paramount importance in the energy transition. At the industrial level, it can be derived from various sources, including fossil fuels, biomass, or electrolysis. In Alkaline Water Electrolysis (AWE), the growth of hydrogen bubbles directly impacts system efficiency. Understanding and simulating this growth, attributed to the diffusion of dissolved hydrogen in the supersaturated electrolyte near nucleation sites via diffusive and convective mass transfer, is a crucial step towards advancing knowledge in this field and unlocking new possibilities.

This research focuses on simulating the growth of a single hydrogen bubble in a supersaturated domain, both far from and near the cathode, in a 30 wt% KOH solution. Bubble growth, a mesoscale phenomenon, is investigated using the Lattice Boltzmann Method (LBM). A comprehensive comparison of the Shan-Chen (SC), Colour Gradient (RK), and Interface Tracking Phase-Field (HZC) methods was conducted to measure the intricacies of the multiphase system accurately. The Laplace Law equation served as a benchmark, demonstrating that the HZC method produced the most accurate results.

A continuous species transfer method is employed to track hydrogen transport from the supersaturated electrolyte into the bubble, validated with Newman's analytical solution of mass transfer controlled by pure diffusion inside a sphere. Two cases are then analyzed: one of a single bubble far from an electrode in a supersaturated domain and another of a single bubble near an electrode with a constant hydrogen flux. For the first case, bubble growth follows a power law equivalent to R ∼ t^0.5, while in the second case, growth follows R ∼ t^0.7, matching results from previous studies. Finally, this method is extended to a 3D model; however, the results cannot be directly compared to the 2D model due to the shorter runtime resulting from computational cost.

Understanding the dynamics of bubbles in broth is crucial for various biotechnological processes conducted in bubble columns, such as the manufacturing of cultured meat. In this study, the drag coefficient of individual bubbles ascending in sodium chloride, sodium sulphate, albumin, and egg-white protein solutions was determined. This was accomplished by extracting bubble characteristics, such as the equivalent diameter and terminal velocity, from images captured by a camera system, utilizing bubble detection by a software suite. The obtained terminal velocities and computed drag coefficients were then compared to existing predictive models developed by Clift, Fan and Tsuchiya, Ishii and Zuber, and Peebles and Garber. This comparative analysis was conducted to assess the accuracy of these models in predicting bubble behavior in contaminated water. The results indicated that the drag coefficient of single bubbles rising in salt and protein solutions is higher compared to when ascending in demineralized water. The drag coefficient of single bubbles rising in protein solutions predicted by the drag model of Ishii and Zuber aligned well with the experimentally derived drag coefficients. However, both drag models tended to underpredict the drag coefficient of bubbles ascending in protein solutions. In the case of salt solutions, the drag coefficient predictions by Peebles and Garber approached the experimentally derived drag coefficients more closely although both models tended to overpredict the drag coefficient of bubbles ascending in salt solutions. Additional data acquisition of bubbles within the same size distribution rising in the examined salt and protein solutions is needed to validate and further refine these observations.

Photosensitizers play a key role in photodynamic therapy as a drug that is activated by light. In this thesis, the effect of ionizing radiation on the generation of singlet oxygen when using photosensitizers (Chlorin e6) and photocatalysts (titanium dioxide) was studied. By using radionuclides and photosensitizers (PS), cells can be killed with reactive oxygen species (ROS) which are produced by PS under influence of radiation that is emitted by radioactive decay. ROS are produced naturally in cells, but an excess of ROS can lead to damage to proteins, nucleic acids, lipids, membranes and organelles, which can lead to activation of cell death processes such as apoptosis. The focus of this thesis is the production of singlet oxygen which is a type of ROS.
Indium-111, lutetium-177 and yttrium-90 which decay by different types of radiation have been used as radiation sources. In this research, the influence of these different radiation sources have been tested on Ce6 and TiO2 and their ability to produce singlet oxygen. Results show that Ce6 and TiO2 have increased production of singlet oxygen when exposed to ionizing radiation. Ce6 generates singlet oxygen when irradiated by both low energy gamma sources
and high energy beta-minus radiation, while TiO2 generates singlet oxygen when irradiated by high energy beta-minus radiation.

The salinity profile in a coastal sea-river system is the result of balancing of salt transport due to mixing of the water by tides and the freshwater discharge from the river. When for example during times of drought freshwater discharge suddenly declines, the salinity in the river may increase significantly and threaten drinking water supplies and agriculture. The time it takes for the salinity to reach the new equilibrium may be considerable. Thorough understanding of the adaptation process is essential for taking appropriate prevention measures. However, much about this adjustment process is still unknown, in particular regarding the interaction between the river and the adjacent sea. In this study, a simplified linear model is developed to describe a well-mixed river and the adjacent sea where the water flows radially away from the mouth of the river. The unique assumptions, most notably a time-independent intrusion length, allow for a unique analytical approach using the method of eigenfunction expansion. The smallest eigenvalues are found to define a time scale of the adjustment process. The eigenfunctions provide insight about how the salinity adjustment time varies within the system. The adjustment time does not only depend on the parameters that describe the new equilibrium, but also on the initial salinity. The eigenvalue time scales corresponding to the sea and to the river can then be used to determine the time scale of the coupled system. It is found that when the sea adjusts much faster than the river, the time scale of the river is leading the adjustment. When the eigenvalue time scale of the sea is similar to or larger than the eigenvalue time scale of the river, the adjustment time is significantly increased by the sea. When salinity is increasing, the sea restricts the inflow of salt in the river, while for decreasing salinity, the sea keeps transporting salt to the river by mixing which delays the adjustment. The model is applied to analyse a sudden decrease in freshwater discharge in the Rotterdam Waterway, which is part of the Dutch Rhine-Meuse delta. Results show that the salinity response is delayed compared to freshwater discharge, indicating that the adjustment time of the river indeed plays an important role. Further research should consider a more general dispersion relation or an extra vertical dimension to better describe estuaries that are not well-mixed. Using numerical methods there are many other possibilities to extend the model. The effect of tides on the presence and dynamics of the fresh water bulge in the sea is of specific interest.

In dit verslag is een eolisch sedimenttransport model geformuleerd en het model van De Vries geïmplementeerd en geanalyseerd. Na de afleiding van de eendimensionale advectie-diffusievergelijking vanuit de driedimensionale continuïteitsvergelijking is eerst het model van De Vries zonder diffusie onderzocht. In het model kan er onderscheid gemaakt worden tussen 3 verschillende situaties: Geen (toevoer van) sediment, Sediment-gelimiteerd en Erosie-gelimiteerd. In elke situatie zijn voor lange tijd\-schalen de toestanden van het model afgeleid vanuit de advectievergelijking. In de resultaten kwam naar boven dat de theoretische toestanden sterk overeenkwamen met de toestanden in de numerieke simulatie. Verder is het effect van numerieke diffusie van het model van De Vries geconstateerd en de grootte van dit effect afgeleid. Om het effect van numerieke diffusie te verminderen is diffusie in het model geïntroduceerd samen met het Lax-Wendroff numerieke schema. Dit schema gebruikt de gewogen upwind methode samen met de gewogen centrale Euler methode om de nauwkeurigheid van het model te verbeteren. In de resultaten is aangetoond dat numerieke diffusie kan worden gecompenseerd door het juist kiezen van dit gewicht. Uit een stabiliteitsanalyse blijkt dat de Lax-Wendorff methode een betere stabiliteitcriterium heeft dan de upwind methode. Hierdoor kan een grotere tijdstap gekozen in een numerieke simulatie. De maximale tijdstap is getest door het model te runnen met verschillende tijdstappen rondom het theoretische maximum. Uit de resultaten bleek dat het model op tijdstap die een fractie kleiner was dan de theoretische maximale tijdstap, stabiele oplossingen simuleerde. Zodra de tijdstap de maximale waarde behaalde werden de oplossingen instabiel. Door het toevoegen van diffusie aan het model is een extra voorgeschreven randvoorwaarde nodig. Door implementatie van verschillende randvoorwaarden aan het einde van het domein is gebleken dat de randvoorwaarde 'extrapoleren tweede orde' het best is. De dimensie-analyse van de advectie-diffusievergelijking wijst uit de eolischsedimenttransport gedomineerd wordt door advectief transport en het effect van diffusie verwaarloosd mag worden.

A phenomenon that compromises the health of city inhabitants is the urban heat island (UHI) effect. This effect is mainly driven by thermal radiation and designates the typically higher air temperature in cities compared to the surrounding rural areas. Over 55% of the world’s population lives in cities, and with this percentage set to rise to more than 65% by 2050, it is vital to model the urban climate to be able to mitigate the UHI-effect. In this study, the surface energy balance (SEB) is modeled in urban environments using a one-way coupled RANS 𝑘 − 𝜖 approach in order to gain fundamental insights into the influence of thermal radiation on the UHI-effect. The SEB model is built mechanism-by-mechanism, adding in different physical mechanisms one at a time and validating the model at each step with literature- or theoretical values. The SEB model showed a good agreement with experimentally found values for the effect of surface irregularity of an urban structure on the absorption and reflection of incident solar radiation. A good agreement was also found with theoretical values for the longwave radiation and conductive heat flux part of the SEB model. Subsequently, a study was done on a 2D street canyon to compare the model with literature results. This study showed a good agreement for the radiative fluxes, but a lesser agreement for the conductive- and sensible heat fluxes. A more complex scenario of an intersection between buildings was studied. It was shown that the longwave trapping effect is highly correlated with building height. Finally, the effect of wall heating on flow characteristics in a 2D street canyon was examined. For homogeneously heated walls, the SEB model showed a relatively good agreement with literature results. A study was also done with non-homogeneously heated walls. This study showed less realistic results and should be further investigated in further research.

Fluidized bed reactors are catalytic multiphase reactors capable of processing large volumes with relatively high mass and heat transfer, which is appealing to a variety of industries. The presence of voids, in this case gas bubbles, within these systems can be detrimental to the efficiency and are desired to be minimized. Further fundamental understanding of the bubbles is necessary to model, design, and control them. However, the study of bubbles is difficult, as these beds are typically opaque and 3D. Current studies of bubbles within fluidized beds are often limited to use of quasi-2D set ups, specialized particles, or internal measuring devices. This research utilizes a newly constructed experimental setup consisting of three x-ray source and flat panel detector pairs that produce 2D projections. This setup allows for investigation into the bubble dynamics inside a 3D cylindrical column with industrial particles. The possibilities and limitations of the use of 2D projections to obtain fully 3D time-resolved reconstructions were explored through simple 3D reconstructions of injections of single bubbles. These 3D reconstructions showed the potential of the setup for 3D time-resolved studies of the bubble dynamics and laid the groundwork for future studies. Apart from the ability to obtain 3D reconstructions, the 2D projections can be used to study the dynamics of the bubbles. In this research, 2D projections of an injection of a single bubble were used to develop a deeper fundamental understanding of the shape, motion, and dynamics of an individual bubble traversing through a bed. The bubble shape and size were obtained through a horizontal slicing technique, which assumes axis-symmetry around the vertical axis. Different background fluidization levels, injection volumes, injection velocities, particles, and column diameters were investigated. An analysis of the individual bubble trajectories and the statistical averages provided insight into the interconnection of these factors. The two previously studied bubble stages, formation and rising, were observed. The rising stage was observed to have two regions, stable and unstable. The stable region, following the formation stage, occurs when the motion of the bubble is essentially rectilinear. The unstable region, following the stable region, occurs when the bubble moves sideways while traversing the column in an irregular motion. A simple analogy to gas bubbles in a liquid was drawn, suggesting the bubble cloud, or particles surrounding the bubble, plays a vital role, especially in the formation of the bubble. Standard correlations for the bubble rise velocity based on a constant bubble Froude number were found to be insufficient at accurately describing the bubble velocity and dynamics. The Froude number for individual bubbles appears to be non constant and dependent on parameters that have not been previously considered, like the level of background fluidization.

In the human body calcium is the most abundant mineral and is involved in a lot of vital processes. Calcium deficiency occurs when there is not enough calcium present in the bloodstream. In the Netherlands one in three women will face this problem in their lifetime. A major factor contributing to this problem is that the intake of calcium on average is below the recommended amount which is around 950 mg/day for adults in the Netherlands. Calcium deficiency when left unattended can lead to osteoporosis. Therefore it is important to consume enough calcium rich products or take calcium supplements. Milk is a good source of calcium and is considered a staple food. This makes bovine milk a good candidate for calcium fortification. Milk can be fortified by using calcium salts to increase the bioavailability the calcium present. In this thesis in vitro methods were used to study the effects of calcium salt fortification on the phase distribution of calcium in bovine skimmed milk under different pH conditions and by using the radioactive isotope 45Ca to track the exchange between the phase casein micelles, serum proteins and the soluble phase when fortifying the milk. For unfortified milk it was found that 36.0±0.9% was present in the soluble phase, 3.7±2.9% was present in the serum proteins phase and 60.3±3.0% in the casein micelles. Acidifying the milk to simulate the gastric environment resulted in an increase of the soluble phase from 55.1±2.7% to 97.0±3.3% which corresponds to a decrease in pH from pH 6 to pH 2. For the fortification of the milk, five calcium salts were selected for synthesis. The salts were calcium carbonate, tricalcium di-citrate, calcium gluconate, calcium lactate and tri-calcium phosphate. The fortification was performed with all of the synthesized salts except calcium lactate and tri-calcium phosphate. The starting material for the syntheses, calcium chloride, was also used for fortification. It was found that for the fortification of CaCO3 under gastric conditions a bioavailability of 100% could be achieved. However the acidic environment also resulted in coagulation of the milk and therefore the bioavailability could not be accurately assessed. Calcium gluconate had the only increase in bioavailability under normal conditions. In conclusion a better understanding of fortification with calcium salts was achieved and the influence of pH on the bioavailability of calcium in milk and the effects on the salt fortification.

This thesis is aimed at developing a fundamental understanding of the key physical mechanisms associated with swirling gas-liquid flow in a vertical pipe, in order to construct a mechanistic model for predicting the flow behaviour. The model is based on quasi-1D reasoning, in analogy to the classical models for gas-liquid flow without swirl. As a benchmark case, it is used to investigate the onset of columnar flow patterns that are characteristic to swirling multiphase flow, for low gas input flows.

The study of adhesion mechanisms in animals such as the gecko has helped mankind with the understanding and development of novel adhesives. The adhesion mechanism of the tree frog is not fully understood, it is a wet adhesion mechanism which works differently than the dry adhesion mechanisms of animals, such as the gecko, studied previously. The wet adhesion mechanism of the tree frog may be based on the capillary force present in liquids. Researching the adhesion mechanisms of the tree frog could help develop new capillary based
adhesives. Although there are several capillary measurement methods and devices used to study the interactions between small volumes of liquids and surfaces, they would require the frog to be immobilized for accurate measurements, which constitutes as harm. This thesis begins the design and development of a system to measure the capillary force created by tree
frogs without harming them. The selected concept functions with the use of a pressure sensor connected to the capillary pressure source with capillary channels. This concept allows for a precision of 12Pa determined by the pressure sensor and a responsiveness of 30 ms determined by fluidic circuit while allowing the frog to roam free around the system input. The components were tested to verify their functionality. A controlled pressure source is used to verify the calibration of the sensor, the time constant and hydraulic capacitance; which are
the parameters that determine the accuracy and responsiveness of the system. The sensor was successfully calibrated to measure pressure linearly up to 10 kPa but the time constant and hydraulic capacitance were experimentally measured to be three orders of magnitude larger than the estimated parameters of the components. In order to solve the disparity between the experimental and theoretical values, different tubing and connections were suggested to reduce the hydraulic capacitance and a method verifying the presence of air bubbles was advised. A Sesille drop experiment was performed on the pressure sensor in order to support the principle of measurement, the results suggests the principle of measurement is valid but the issues surrounding the fluidic circuit needs to be resolved in order to complete the system.

In this work neural networks are used to approximate the solutions of multiple differential equa- tions. Three main differential equations are investigated: the mass-spring equation, the heat equation and the Navier-Stokes equations coupled with the continuity equation. Each of these equations are approached differently with the current methods, therefore these equations test the applicability of the newly proposed method on a general differential equation. The results of various experiments performed in this work show that the method is able to approximate to great precision the mass-spring equation as well as the heat equation. However, the method does not perform well on the Navier-Stokes equations coupled with the continuity equation. The main advantage of this method is that meshes used by this method can often be very small compared to other approximation algorithms. When a slight decrease in performance is allowed, the method can be made completely mesh free. A huge drawback of the method is that there is no guarantee that the method will generate a reasonable approximation, for a given neural network configuration. This makes it necessary to look for a good configuration of the neural network. At this moment, this can only be done using trial and error and is therefore very time-consuming. Sometimes no good configuration is found at all. Another drawback is that the generated approximation does not satisfy the boundary and initial conditions. Multiple ways are proposed in this work to tackle this problem, but they introduce much more complexity and a performance decrease. The neural networks used in this work are generated using software called PyTorch, which comes with an automatic analytic differentiation tool. This part of PyTorch makes it possible to approximate differential equations using neural networks.