Is Julia suited for chemical process analyses? Yes.
This thesis investigates solving ordinary differential equations (ODEs) in programming language Julia, which it does firstly through a simple example of algae populations, and secondly through complex chemical simulations. A progressively more complex framework describing chemical combustion and diffusion is established and implemented. Problems of great stiffness and containing 200+ variables have been integrated in less than 20 seconds, showing the promise this new, open-source and accessible code language.

The thermochemical model that was developed could be improved upon: it has the problem of unexpectedly low flame temperatures because of heat lost to dissociative effects, the current solution for preventing variables overshooting into the negative, it is is ugly and there is ever more optimisation possible. What the program does is run, and it approximately simulates the kinetics and thermochemistry of combustion within acceptable runtimes, thus proving the technical feasibility but lacking the complete implementation of graph-based chemical analysis in Julia.

The Korteweg-de Vries equation is a partial differential equation that can be used to describe water waves. A few years back, a modified version of this equation was derived, to take Coriolis forces into account. Before that, the Korteweg-de Vries equation had also been found in the realm of Lie theory, as an equation of motion on the Virasoro-Bott group.
This paper aimed to find a relation between the two equation, through studying the equations themselves, as well as through the Lie algebras in which they also appear. This way, two similar transformations from solutions of one equation, to solutions of the other have been found. Both of these come down to a vertical shift, though different ones. Another transformation was also found for the equation, but no similar transformation between the Lie algebras was found.

This thesis investigated, for the first time, the possibilities and limitations of tomography-based real-time control of multiphase flows. The investigation was performed in a gas-liquid axial cyclone separator, chosen as representative of quasi-1D multiphase flow processes. The analysis performed has a multidisciplinary aspect, combining swirling gas-liquid flow physics, tomography, system dynamics and real-time control.
In relation to the swirling gas-liquid flow physics, the vertical upward swirling gas-liquid pipe-flow patterns were experimentally mapped in the axial cyclone for different swirl intensities. Mechanistic models were proposed based on the identified physics to predict the upward vertical swirling gas-liquid flow pattern transitions for pipe diameters in the order of centimeters and swirl numbers in the order of 1. The proposed models were able to successfully predict the flow pattern transitions observed in the axial cyclone and reported in literature.
Tomographic measurements are usually too slow for real-time control, due to the computationally demanding inverse problem of the image reconstruction step. To overcome this limitation, a fast real-time application-specific Electrical Resistance Tomography (ERT) algorithm was proposed to measure the phase distribution in axial cyclones. The proposed algorithm reconstructs the cyclone phase distribution via simple correlations based on raw ERT data instead of solving the inverse problem, resulting in measurements three orders of magnitude faster and up to five times more precise than general non-iterative traditional ERT algorithms based on the inverse problem.
Regarding system dynamics and control, this thesis showed that the phase distribution dynamics in axial cyclones can be split into two components: (i) the intrinsic dynamics due to the swirling gas-liquid flow patterns, and (ii) the phase distribution response to external process disturbances, e.g., changes in the flow rates in the cyclone inlet. The intrinsic dynamics are too fast compared to typical flow actuators, such as control valves, and cannot be controlled. A system dynamics model of the phase distribution in the cyclone was proposed, and used to design a tomography-based controller to suppress external process disturbances in the phase distribution much slower than the intrinsic dynamics. Despite the successful suppression of slow external disturbances, the controller did not significantly improve the efficiency of separation of the process due to the high impact of the (uncontrolled) intrinsic dynamics on the cyclone performance.
The results obtained with the axial cyclone suggest that suppressing external disturbances in the phase distribution of multiphase flows is insufficient to control the efficiency of the process. Therefore, the way forward towards tomography-controlled multiphase flows relies on the development of fast sensors and actuators to attempt to control the intrinsic dynamics, something challenging due to its chaotic nature.

To optimally use wind farms, thorough understanding of wind patterns is needed. Recently, a lot of attention in the scientific community is turned to the Current FeedBack effect, where oceanic currents influence the atmosphere above. It has been shown that this also applies to tidal currents in the English Channel where the induced tidal winds have an amplitude of one-third of the underlying current. In this report focus is moved to the Dutch coast. Using a numerical integration model of a vertical grid, the horizontal wind speeds above a small area of the Dutch coast are modelled. The model is based on the 1-dimensional Navier-Stokes equations in combination with Prandtl's mixing length model to account for turbulence. The horizontal wind speeds are found to reach up to one-fourth of the amplitude of the tidal currents at a height of z = 10 m above the sea surface and 1/20 at z = 50 m. This is similar to what was found in earlier research, but a lot of assumptions were made in this model. Therefore, further research could focus on addressing some of these assumptions such that the understanding of tidal induced wind velocities can be even better understood.

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.

This thesis focuses on the influence of tides on flow behaviour and salt intrusion in a semi-infinite channel ending at the sea, with a specific focus on the effects of adding a side channel. Tide causes variations in the flow behaviour, which in turn affects salt concentrations in the channel. Adding a side channel has an impact on the flow pattern, mainly because of reflections of the tidal wave, leading to changes in the salt intrusion. The effect investigated is the influence of varying the distance from the sea to the junction, and the length of the side channel. A 1-dimensional exploratory model based on the shallow water equations for the flow behaviour is developed, analysing only the bidaily M2 tide caused by the gravitational pull of the moon. The flow pattern is solved analytically, while the salt balance is solved analytically in time but numerically in space. The salt balance contains an advection term and an effective dispersion term. The effect of adding a branching channel is compared to the same situation without a branching channel. It is found that the addition of a side channel affects the salt intrusion in the order of 1 km compared to a single channel. Moreover, both positive and negative changes occur in the shift of the intrusion length. The results of this study can be used to understand and explain the behaviour in more complex geometries.

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.

In the realm of fluid dynamics and particle transport, the control of particle trajectories represents a formidable challenge. It would be useful to be able to optimally navigate an oceanographic float from one pre-set location to another by solely changing its buoyancy. In this thesis, a first step in discovering whether this is possible and what optimization strategy can be used is taken.
To do so, first, the physical situation is translated into a mathematical model. Then, an optimization strategy for changing the buoyancy to optimally travel to a set location is constructed. The strategy is based on gradient descent and implemented in Python. Four different definitions of an optimal trajectory to a target location are considered, those are 1) any trajectory that leads to the target location, 2) the most time-efficient trajectory, 3) the most energy-efficient trajectory, and 4) a trajectory that is both time and energy-efficient.
The optimization strategy is tested for five different starting and target locations for a small spherical float in an idealized two-dimensional linear flow field. It is concluded that it is possible to use the optimization strategy to navigate a float using buoyancy changes for all four optimization objectives, although the current implementation is not efficient enough for targets far away.
The first objective of future research should be to increase the coding efficiency. Thereafter, other steps toward a more realistic situation can be taken, such as testing for non-linear flow fields, three-dimensional fields, and bigger floats.

Geothermal energy can be promising to help the energy transition. Warm water is pumped up from a geothermal well and after it is cooled down, the cold water is reinjected into the hot aquifer underground. The temperature change could cause chemical balances to be disturbed and result in precipitation on the porous medium of the aquifer. This process of clogging of an aquifer is not desirable since it re- duces the efficiency of the production of warm water. This research is a stepping stone for modelling these reactions and clogging of the aquifer. The reactions rates depend on the temperature and the concentration of the reactants in the aquifer. For this reason the temperature distribution of the aquifer was numerically derived with finite difference methods. The velocity field is important for modelling both the temperature and the concentrations. Therefore the pressure and velocity field were modelled with use of mass conservation and the Darcy model. The models were solved numerically with finite difference methods and some results were compared to the analytical solution of the model. It was concluded that the numerical model for the velocity field is accurate when compared to analytical solu- tions of the model equations. In the model used, an increase in porosity resulted in a delay of cooling the aquifer. This is because there was no relation between porosity and permeability implemented in the model. A lower flow rate in the aquifer delays the cooling of the aquifer as well. For further research it is recommended to implement the chemical reactions into the model and use this model to look into how to prevent the clogging in the aquifer.

In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’, while the other argues that phoretic activity due to attractive or repulsive surface interactions on the enzyme are responsible for the enhanced diffusivity. At the moment of writing, no consensus has been reached on the mode of enhancement. A novel agent-based lattice model for the diffusion of enzymes was derived in this Bachelor’s Thesis in accordance to the phoretic theory of enhanced diffusion. The model that was developed is a stochastic model which describes the interactions at the particle level. The model showed that phoresis produces enhanced diffusion in the order that was expected for the enzyme urease. Furthermore, the model showed pattern formation in the case of repulsive interactions between enzyme and substrate. The instability of this phase transition was investigated using linear stability analysis on the continuum limit of the lattice model. This yielded a restriction on the strength of the interactions for which pattern formation could occur.

Due to climate change, the sea temperature is rising. This temperature change has an effect on the phytoplankton population. Phytoplankton is responsible for more than 50 percent of the oxygen production on earth, and is therefore crucial for life on earth. In this report, the research question is: is the temperature increase of the water important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean?

To investigate this, first a 2D model for a coastal area of an ocean is formed. As a basis for this model the 0D model of Steele and Henderson is used to describe the predator-prey model for zooplankton and phytoplankton. Due to this model a repeating pattern in time arises, which is called a limit cycle. This predator-prey
model is expanded to a 2D model by applying convection (v) and diffusion (D) to it, representing the current and dispersion in the water. The chosen parameters and boundary conditions are inspired by the coastal area of the west coast of Portugal.

To evaluate the effect of the water temperature rising, first, the effect of diffusion and convection are studied by answering the following questions: is the convection important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean? And: is the diffusion important for the development in space and time of the plankton population in a 2D model of a coastal area of an ocean?

The diffusion is dominant in the direction perpendicular to the coast. Due to the diffusion the limit cycle of the predator-prey model is suppressed. Its range gets smaller until the plankton population is completely constant for D > 2.5 m^2/s. This critical value is included in the realistic value of D, which varies from 1 to 2000 m^2/s.

Due to convection, the limit cycle corresponding to the boundary condition occurs in the direction parallel to the coast, making every point in the domain steady state. The higher the velocity v corresponding to the convection is, the less oscillations in phytoplankton density there are in the domain, thus the larger the wavelength of the oscillation is. For v > 0.06 m/s the current is so fast that the predator-prey model has little time to develop before it reaches the right boundary, making the left boundary value more important. This critical value is included in the realistic value of v, which varies from 0.03 to 0.28 m/s.

The model experiences both diffusion and convection more or less equally when the Péclet number vH^2/DL≈1, resulting in D/v≈50 m. If this number is significantly larger than 50 m, diffusion dominates the solution. If the number is significantly smaller than 50 m, convection dominates the solution.

Now the main research question can be answered. By increasing the temperature of the water the growth rate of phytoplankton increases. Due to this increase, the timescale of the predator-prey (τpp ) decreases. The value of D and v for which the predator-prey model and diffusion and convection all influence the solution
equally depends on the timescale with the factor 1/τpp . A smaller time scale means that the predator-prey model contributes more to the model. However, this change is very small in comparison to the scale of the realistic values. In conclusion, in the formed 2D model the temperature increase of the water is not important for the development of the plankton population in space and time.

The results of this report are influenced by the assumptions and approximations made. In this study, several processes, both physical and biological, are described with constants and simplifications. Improving the models of these processes is left for further research.

To mitigate climate change, carbon capture is necessary. In addition to the energy transition towards renewable sources and green house gasses emission reduction, CO2 capture from flue gas and its sinks, including air and the ocean, must be promoted. By 2030, in less than 8 years, the global carbon capture capacity must increase 100 × (from the current ca. 40 MtCO2 yr−1 to 4 GtCO2 yr−1). To meet the net zero carbon goals of 2050, sustainable, scalable, inexpensive technologies that fit in an electrified industry and have a small footprint are needed for carbon capture. Currently, such technologies do not exist. In the framework of the necessary carbon capture, and the opportunities for electrochemical (ocean) CO2 capture, five research questions are defined and addressed in this thesis...

Physical Vapor Deposition (PVD) is the resublimation of a substance on a cold surface coating it with a thin solid layer. PVD coatings are utilized in industry to modify surface properties and appearance. Since the industrial process requires vacuum conditions, it has been mainly conducted in a batch process. Recently, PVD is considered a promising alternative coating technology to the hot-dip galvanization in order to apply a corrosion protective coating on steel. However, a continuous process is missing to manufacture protective coatings for strip steel on an industrial scale using PVD.

First approaches suggest the following process: The steel strip is pulled into a vacuum chamber through air-tight seals to ensure a non-reactive coating atmosphere and avoid impurities; then its surface is treated to obtain high adhesion during the coating process; afterwards it passes a Vapor Distribution Box (VDB) from which vapor jets (or plumes) emerge and coat the steel surface; eventually the strip leaves the vacuum chamber again via air-tight seals, is coiled and shipped.

To make this process usable on a large scale - or even superior to galvanization - multiple challenges need to be overcome: ensuring the tightness of the seals, cleaning the strip, preventing stray coating of the vacuum chamber, guaranteeing a uniform coating thickness, and providing a uniform high vapor mass flow to maintain a high speed of the production line.

This thesis tackles the last challenge by modeling the vapor transport both inside the VDB and inside the vacuum chamber.

First the flow inside the VDB is modeled using a SIMPLE-/PISO-based algorithm for transsonic flows. To account for the evaporation at the melt surface, a boundary condition for the inlet pressure is implemented based on the Hertz-Knudsen equation. The total mass flow rate for different melt temperatures is compared to experimental values as well as an analytical, isentropic estimation. Furthermore, the sensitivity of the model to material properties and process conditions is studied.

The total mass flow rate of the system is found to depend on evaporation and choking. With higher melt temperatures the total mass flow rate increases. The trend found in the simulations resembles the one from the experiment. Both yield only 33%-54% of the mass flow rate estimated by the analytical isentropic relation. This low efficiency improves with higher melt temperature. A comparison of the pressure loss across the VDB reveals that the main losses appear due to the viscous boundary layer in the nozzles connecting the VDB with the vacuum chamber. The simulation overpredicts the experimental result by a factor of 1.3. This may be due to the used assumption of an idealized value of unity for the evaporation coefficient; a value of approximately 0.3 would produce a better match between simulations and experiments. Impurities found in the experiment may cause this reduction of the evaporation coefficient.

When expanding from the nozzles into the vacuum chamber, the flow accelerates to supersonic speeds and rarefies. We study the interaction of two planar sonic plumes that causes a shock next to the interaction plane. This in turn produces peaks in deposition rate and thus in the coating. Direct Simulation Monte Carlo (DSMC) method is applied for the flow which ranges from continuum at the nozzles to rarefied and free molecular flow downstream. The results are compared to the analytical effusion solution and the inviscid continuum solution from a Riemann solver. The expansion and shock regions of the DSMC simulation are visualized by the Method of Characteristics (MOC). The mass flow distribution as a function of the degree of rarefaction, the nozzle-separation-distance and the inclination of the nozzles is studied.

The DSMC result of plume interaction outside the VDB closely resembles the inviscid continuum solution at low degrees of rarefaction. The flow structure with expansions and shocks coincides, deviations are apparent in the actual number density, velocity and temperature especially in the shock region. With higher rarefaction, the shock structure diminishes and the flow field approaches the free molecular flow field. However, the rarefied flow field is not within the limits of the inviscid continuum and the free molecular flow field, but may exceed them in both deposition peaks and temperature peak in the shock region.
Using the MOC for visualization reveals that with higher rarefaction the shock bends away from the interaction plane which can be explained by the increased temperature in the secondary expansion. While the shock location shifts with the nozzle-separation distance, it merges to one location when scaling it with the nozzle-separation distance. Bending the nozzle outlets towards each other produces a stronger shock starting further upstream, which in turn causes a stronger secondary expansion and thus smoother deposition.

In addition to studying the impact of geometry changes in the PVD setup, the effect of adding a light, inert carrier gas on the plume interaction and the resulting deposition uniformity is investigated. To this end, the carrier-gas mole fraction is varied at a given Knudsen number. Species separation focuses the heavy species along the primary axes, whereas the light inert carrier gas is scattered towards the periphery. Due to the higher mean molecular weight, the speed of sound decreases and consequently the interaction shock occurs farther downstream, is less bent and weaker producing a more uniform deposition profile. Desirable side effects of the carrier-gas are less stray deposition and a higher conductance of the coating material from the inlet nozzle.

The last part of the thesis focuses on the numerical method, since DSMC is accurate but computationally costly. The substitution of the collision step in DSMC with a kinetic relaxation using the Bhatnagar-Gross-Krook (BGK) operator is implemented in order to speed up the algorithm. The choice of the target distribution for the relaxation is crucial. The Maxwellian velocity distribution produces an incorrect Prandtl number; the Ellipsoidal-Stochastical BGK (ES-BGK) corrects for the Prandtl number by taking the stress into account; the Shakov model (S-BGK) corrects by considering the heat flux vector. The implemented models are verified against literature data and evaluated for their accuracy in simulating the interacting plumes case. In addition, we evaluated a hybrid coupling of the various kinetic relaxation models in dense, near-continuum regions with DSMC for rarefied and non-continuum regions. The switching criterion for the hybrid coupling was the gradient-length local Knudsen number. The implemented kinetic models compare well to literature data for rarefied Poiseuille flow. The lower resolution criteria lower the computational cost to approximately 30% of the one of DSMC. For the planar jet interaction, the BGK model (using the Maxwellian target distribution) overestimates the shock strength, the S-BGK model overpredicts the diffusion of the shock, whereas the ES-BGK models results are in good agreement with the DSMC results. This indicates that the velocity sorting and breakdown of temperature isotropy in the expansions have a more significant influence on the flow field than the shock, which skews the velocity distribution. Coupling the kinetic models with DSMC in the highly rarefied regions improves the flow field for the BGK and S-BGK model, but not significantly.

In short, this thesis examines the influence of process conditions, geometry and carrier-gas use on the mass flow rate and deposition uniformity in continuous PVD for coating steel strips with anti-corrosive coatings. It provides modeling tools for the mass transport both inside and outside the VDB which can be used for further investigation and optimization.

The growing demand for manufactured products with complex geometries requiring advanced fusion-based manufacturing techniques emphasises the importance of process development and optimisation to reduce the risk of adverse outcomes, which is currently impeded with traditional approaches (trial and error experiments). Development, optimisation and qualification of such procedures are often expensive and time-consuming, particularly when new materials or new material combinations are involved. Process stability is intrinsically linked to the stability of the molten metal melt-pool, which ideally should solidify in a smooth and continuous manner to produce a consistent product, free of undesirable geometric and metallurgical defects. The influence of material properties and process conditions on melt-pool stability are generally difficult to derive from experimental observations; hence process optimisation is often reliant on a trial-and-error approach, mitigated to a large extent by a considerable body of industrial experience.
The challenge addressed in this research is to develop a simulation-based approach to assess the stability of oscillating melt-pools in fusion welding and additive manufacturing, to minimise the number of trial-and-error experiments required for process development and optimisation, which ultimately will lead to shortening the time between design and production. The computational model developed in the present work has a generic construction with specific process influences addressed through appropriate boundary conditions, avoiding the necessity to integrate melt pool and detailed process descriptions in a single simulation. The model is therefore capable of representing a wide range of welding and additive manufacturing technologies through selection of appropriate material properties and boundary conditions. The robustness of the present computational model in predicting the melt-pool behaviour is demonstrated by comparing the numerical predictions with experimental, analytical and numerical data.
Focusing on numerical simulations of solidification and melting using the enthalpy-porosity method, the influence of the permeability coefficient (also known as the mushy-zone constant) on the numerical predictions, which is employed to dampen fluid velocities in the mushy zone and suppress them in solid regions, is systematically analysed for both isothermal and non-isothermal phase-change problems. For isothermal phase-change problems, reducing the cell size diminishes the influence of the mushy-zone constant on the results and the solution becomes independent of the mushy-zone constant for fine enough meshes. Numerical predictions of non-isothermal phase-change problems are inherently dependent on the mushy-zone constant. A method is proposed, based on a Péclet number, to predict and evaluate the influence of the permeability coefficient on numerical predictions of solidification and melting problems.
In many numerical studies in the literature, the transport coefficients of the material, specifically thermal conductivity and viscosity, are artificially increased by a so-called `enhancement factor' to achieve agreement between experiments and numerically predicted melt-pool sizes and solidification rates. However, the use of an enhancement factor has little physical meaning, does not represent the physics of complex transport phenomena and can significantly affect the numerical predictions. The effects of using enhancement factors on the numerical predictions of melt-pool behaviour in fusion welding and additive manufacturing are studied in detail. Moreover, the effects of employing temperature-dependent material properties on the numerical predictions are discussed in the present thesis.
Melt pools in fusion welding and additive manufacturing exhibit highly non-linear responses to variations of process parameters and are very sensitive to imposed boundary conditions. Temporal and spatial variations in the energy-flux distribution, which are often neglected in numerical simulations, are taken into account in the present work. It is shown how deformations of the melt-pool surface, due to fluid motion as well as changes in the system orientation, affect the numerical predictions of thermal and fluid flow fields. The effects of joint shape design on melt-pool behaviour during fusion welding is also studied in the present work.
Changes in power-density and force distributions affect the thermal and fluid flow fields on the melt-pool surface, which in turn can influence the pool shape. Oscillations strongly relate to shape and size of the melt-pool and the surface tension distribution on the molten material surface. Using the simulation-based approach developed in the present work, the frequency and amplitude of melt-pool oscillations and changes in the oscillation modes are predicted, which are not accessible using published analytical models and are generally difficult to measure experimentally. Additionally, using the proposed simulation-based approach, the need for triggering of the melt-pool oscillations is obviated, since even small surface displacements are detectable, which are not sensible to the current measurement devices employed in experiments.
The dynamic features of the oscillation signals cannot easily be derived employing conventional Fourier transform (FT) analysis since the oscillation signals are assumed to be stationary (i.e. the behaviour of the system is linear and time-invariant), which is often not the case in fusion welding and additive manufacturing. The continuous wavelet transform (CWT) has been employed in the present work to overcome the shortcomings of the conventional fast Fourier transform (FFT) analysis in characterising the non-stationary features of the surface oscillation signals received from the melt pool. Employing the continuous wavelet transform, the time-resolved melt-pool surface oscillation signals obtained from the numerical simulations can be decomposed into time and frequency spaces simultaneously.
The simulation-based approach developed in the present work addresses some of the significant challenges involved in assessing the melt-pool stability for process development and optimisation. The numerical predictions of the present computational model enhances the current understanding of the process behaviour, which is often very challenging to achieve from experiments alone. Moreover, the present simulation-based approach can be employed to explore the design space and reduce the costs associated with process development and optimisation.

Welding is an extensively used technology by different industries such as aerospace, automotive and marine industry. Welding involves the temporal melting of materials in order to join them together. The quality of the weld is known to depend on the fluid flow and heat transfer in the material. A way to influence the heat transfer and fluid flow, and thus the quality of the weld, is by using different power-density distributions. However, the current literature falls short when combining the different power-density distributions with weld pool behaviour. The aim of this thesis is to study the effects of laser power-density distribution on heat and fluid flow in molten metal melting pools. This will be done by running weld pool simulations using a 2D axisymmetric, flat surface model. These simulations use a top-hat, Gaussian or doughnut laser power-density distribution. Besides, the cases have been simulated for a 20 ppm and a 150 ppm sulfur concentration. That the sulfur concentration has an influence on the weld pool shape was already shown in previous studies. However, it was not known how much the influence of sulfur concentrations varied for different laser power-density distributions. The laser power-density distributions are found to have a significant influence on the weld pool shape. The doughnut power-density distribution created a three times deeper weld pool than the Gaussian and top-hat power-density distribution. The maximum temperature of the weld pool was also influenced by the power-density distribution. In the case with a sulfur concentration of 20 ppm a discrepancy of 1000 K has been found between the Gaussian and doughnut distribution. The influence of sulfur concentrations varied for different laser power-density distributions. This influence of the sulfur concentrations has been measured through the difference in aspect ratio for different sulfur concentration cases. For both the top-hat and Gaussian power-density distribution, the aspect ratio differed 0.02 when using a 20 ppm versus a 150 ppm sulfur concentrations. The doughnut power-density distribution reached a higher difference in aspect ratio of 0.1 when using a 20 ppm versus a 150 ppm sulfur concentrations. The use of different power-density distributions in weld pool simulations results in different weld pool behaviour. Besides, the combination of different sulfur concentrations with power-density distributions largely influenced shape, temperature and fluid flow of the weld pool, which results in a great variation of weld pool shapes and sizes. Because there are different requirements for different welding cases, these results are useful in order to construct a quality weld.

Thin liquid films are fluid structures with perpendicular length scale, typically of the O(< 10 μm), being much smaller than the lateral length scale, typically of the O(> 1 mm). From foams and emulsions to tear films on eyes, they widely occur in industrial processes and natural phenomena. Depending on the wetting energies between its different interfaces, it is susceptible to developing an instability which can lead to its subsequent rupture. It is a great example of how dynamics at microscopic scale influence large scale physical behaviour, with instabilities at micron scale influencing a foam collapse or the blinking action of an eye. The subject of this thesis focuses on non-planar thin liquid films that are found, for instance, in between two foam bubbles or in partial wetting systems in microfluidic channels. The dynamics of such non-planar films is governed by two thinning mechanisms. The first mechanism involves drainage due to curvature differences, and results in a localized depression, commonly referred to as a dimple, at the connection between the planar and curved regions. The second thinning mechanism involves growth of a fluctuation originated instability arising from the competition between a stabilizing surface tension and destabilizing van der Waals forces. For this second thinning mechanism to manifest, the film’s lateral length (radius) needs to be large enough to accommodate unstable waves to fit within the film. We study thin film dynamics, by performing numerical simulations that incorporate all these crucial physical processes in the thin film equation...

Steel is commonly coated to protect it from corrosion. One method of applying this is by using Physical Vapor Deposition, which can be done by using multiple jets. In this process jets next to each other interact. This paper's main aim is to investigate the interaction effect of two rarefied two-dimensional vapor jets in vacuum and how this is influenced by the distance between jets and inlet density. Furthermore, the analytical solution for the collisionless case for a single jet is extended to dual jets. Additionally, the objective is to maximize the processing speed for the use of coating, with a certain uniformity for the parameters researched in this paper and finding an optimal method in doing so. This study is done by using the Direct Simulation Monte Carlo (DSMC) method.
The analytical solution gave the same results as the collisionless DSMC method for both single and dual jets. Simulations with a strong interaction effect resulted in a shock. These behaved similar compared to three-dimensional jets, in the plane of the jets. The shock results in a secondary jet, which has a lower density in the middle. The interaction effect depends primarily on the inlet density. Multiple regimes are observed for different inlet density ranging from small change in properties to a shock wave, with a transitional regime inbetween. The influence of the distance between the jets is found to result in a higher density at the axis of the inlet behind the shock, for bigger distance between jets. However, for very small distances between jets compared to the inlet size the shock is weak. For the optimization, it resulted in the conclusion that the optimal coating in general is applied with the smallest distance between jets. This generally gives a better uniform coating and increased performance. However, this is not always the case when constraining the distance between the jets and sheet, as it only holds if the shock between the jets for this distance. Furthermore, an approximation is found for the optimization, which results in fewer simulations needed.

The transport of a solute dissolved in a fluid flowing trough porous media is, next to advection and diffusion, determined by hydrodynamic dispersion. This be- haviour is commonly characterized using the longitudinal and transverse dispersion coefficients. Laboratory and field measurements of these coefficients tend to differ, which might be attributed to heterogeneities found in field porous media. To investigate this, a stratified porous medium consisting of two layers is con- sidered. Each layer has different physical properties, resulting in a different average fluid velocity. As a consequence of the difference in velocity, transport of the solute occurs between the two layers. Under certain circumstances the layers start to be- have as one single layer, with one single effective dispersion coefficient, explaining the discrepancy between field and laboratory measurements. The two-layer stratified porous medium is characterized using a dimensionless number. It is investigated for which values of this number the porous medium acts as one single layer, and for which values the medium behaves as two separate layers. This is done by introducing an index, which effectively measures the behaviour of the medium in terms of these two limit cases. The calculation of the index is done using a numerical simulation of flow and dispersion in the stratified porous medium. It was found that the dimensionless number was in general a good predictor of the behaviour of the stratified porous medium. The system behaved as one single layer if the dimensionless number (after a correction with a certain factor) was much greater than unity. Similarly, the system behaved as two separate layers if the number was much less than unity. However, this number failed if the ratio of the two layer thicknesses was varied. A correction to the dimensionless number was suggested, taking the ratio into account.

The accurate approximation of the surface tension force is paramount for continuum surface models in the field of computational fluid dynamics for multiphase flow where surface tension is relevant. This involves being able to accurately calculate the curvature at the interface. This study focuses on the use of convolution in smoothing the VOF colour field in order to obtain better approximations of the curvature. Given the sudden jump in values of the VOF colour field, the calculation of its derivative for the curvature is sensitive to errors, given the large values of high order terms that determine the truncation error. To deal with this problem, convolution of this abruptly varying field can be used to create a smoother transition. The curvature approximation of a circular interface improved as the support of the convolution was increased.
It was proven analytically that, for these interfaces, the original curvature is retrieved from the convoluted field. Interfaces along which the curvature varies were also considered, and it was found that there is a critical convolution support that minimizes the error in the curvature, given that the choice of the support length can modify the curvature that is estimated.
An algorithm was implemented in OpenFOAM that calculates the convolution of the VOF colour field. The resulting smoothed field was then used to calculate the curvature, which is needed for the surface tension force of the system. The simulations of a two-dimensional rising bubble resulted in more accurate results for the circularity and the rising velocity, when compared to the original OpenFOAM implementation with no smoothing. With the convolution algorithm, the terminal velocity deviated only 0.01% from a well-accepted benchmark case, a great improvement when compared to the 4.2% difference when no smoothing was used. However, simulations of a static bubble in zero-gravity rapidly resulted in unphysical flow, manifested as a wavy interface, when a convolution support larger than 2 cells was chosen. An improvement of the estimation of the surface tension force direction may be needed for this behaviour to disappear.

Brain aneurysms cause almost 500,000 deaths in the world every year. A better understanding of brain aneurysm genesis and rupture may open new opportunities to prevention and treatment. In this study, a part of the cerebral vascular system, the so called circle of Willis including an aneurysm, was analyzed with Computational Fluid Dynamics (CFD). The importance of boundary conditions in an aneurysm simulation was assessed by comparing the results to 7T MRI velocity data, obtained from the Academic Medical Center (AMC) in Amsterdam. Adequate similarities were found in velocity values, together with qualitative agreement in wall shear stress (WSS) values.
We found that in a patient-specific case with an aneurysm, the velocity profile was able to develop to a parabolic profile because of its location; the aneurysm existed far downstream of the circle of Willis. This implies that it is possible to use a cropped arterial system to simulate the aneurysm and to use parabolic inlet velocity profiles for patients with this aneurysm phenotype.
In previous studies, it proved hard to locate the precise location of rupture in an aneurysm. A risk assessment of the rupture location in an aneurysm can be used as a more accurate tool to assess the need for surgery. The aneurysm geometry of the CFD Rupture challenge from 2013 was simulated to predict the location of a rupture site. This rupture location was predicted by combining the following hemodynamic criteria: the time-averaged wall shear stress (WSSTA), oscillatory shear index (OSI) and vortex-saddle point structure during systole with accompanying low pressure values. A sensitivity study was performed on these criteria and a critical threshold for rupture risk was proposed. Based on these criteria it was possible to predict the exact rupture site for two analyzed aneurysm geometries. It is concluded that a CFD model could be used to assess the hemodynamics in intracranial aneurysms. Future research should focus on repeating this study on more patient specific aneurysm geometries to verify this hypothesis further.