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.

This thesis investigates the behaviour of one-dimensional blood flow in the human arterial tree. It focuses on modeling the change in velocity, cross-sectional area, and concentration. The equations governing this flow are derived using the physical laws of conservation of mass, conservation of momentum, and the
advection-diffusion equation. To solve this set of equations numerically, the Finite Volume Method in combination with a flux difference splitting approach is employed. The study begins with an examination of a single artery, revealing wave-like behavior in pressure and concentration. Pressure propagates along the vessel, while concentration gradually dilutes over time. This
behaviour is also visible when expanding to the 55-artery model of the entire human body. The results of this model were found to be very comparable to the literature. Additionally, the propagation of a chemical
species injected into an artery near the heart is investigated. It takes around 25 seconds to propagate to
the legs but the amount of concentration is greatly reduced. The strength of this wave upon reaching the
legs is investigated for different values of the diffusion coefficient. It is found that when
D = 0.02 cm2/s, the strength is around the 80% of its original value while a value of D = 2 cm2/s reduces
it to 40%. Further research should focus on expanding this model and improving its accuracy. Especially
the exact concentration waves in single arteries are very prone to spurious oscillations. By optimizing the
numerical code, the accuracy can be greatly increased. Moreover, more realistic additions can be made to
this model. Such as expanding to a two-way model enabling to inject at various points around the arterial
tree. Nevertheless, this model provides insight into the propagation of blood and concentration in the
human circulatory system, highlighting the need for refinement.

Fermentation processes are considered to be essential to decrease our reliance on fossil fuel based products. However, the scale-up from lab-scale to industrial-scale has proven to be difficult. Computational Fluid Dynamics (CFD) has the potential to be a tool to optimize the scale-up and to help engineers understand the relevant hydrodynamics inside such reactors. However, traditional CFD simulations are computationally intensive and it is not uncommon that simulations can take several months to compute a few minutes of flow-time. Due to the recent development of GPU-based hardware, the Lattice-Boltzmann method (LBM) has been gaining much interest as this meant an orders-of-magnitude decrease of needed computational time compared to conventional CFD methods. In order to calibrate the models underlying the simulations, the obtained results of said simulations should be validated against experimentally obtained data, which is exceptionally scarce for industrial-scaled reactors. Hence the aim of this thesis is to to investigate the applicability of the LBM in high gas-flow, industrial sized reactors by studying three benchmark cases. Using Large Eddy Simulations (LES) and Euler-Lagrangian tracking of bubble parcels, the models provided by M-Star (MStar Simulations, LLC) are validated by replicating a small-scale reactor of which the LBM has already been successfully applied to. The industrial-scaled case consists of the simulation of the 22m3 industrial reactor located in Stavanger, which is an exception regarding the scarcity of experimental data for industrial sized reactors. As this data set did not encompass all the relevant data for aerated stirred tanks, the suitability of the LBM and provided models are also tested for a smaller scaled tank of which the Bubble Size Distribution (BSD) throughout the vessel is known. The applicability of the provided models will be tested by comparing the obtained gas hold-up, BSD and power consumption with experimental data sets. Although the LBM is suitable for industrial-scaled reactors, the provided models by M-Star are not sufficient to predict the gas hold-up and power consumption at high superficial gas velocities. The provided Free Particle drag correlation is not sufficient to describe the dispersion of bubbles throughout the vessel, leading to a significantly under-estimated gas hold-up. In addition, the parcel approach leads to the formation of large bubbles in the vessel. And although enforcing a maximum coalescence diameter does improve the BSD, the gas hold-up is not significantly influenced by the presence of large bubbles. Furthermore, the Euler-Lagrangian way of modeling bubble particles did not lead to the formation of gas cavities, which resulted in an insignificant drop in power consumption. Nevertheless, the current work provides a foundation for subsequent research.

Reducing the concentration of hydrogen and oxygen dissolved in the electrolyte helps to increase the efficiency of alkaline water electrolysis. This thesis provides an account of the evolution of dissolved concentration in the vicinity of the electrode surface for alkaline water electrolysis for the bubble size, the electrode height, the dissolved gas uptake by bubbles, and the bubble generation at the electrode surface. Included are an analytical and numerical model that not often include local electrokinetic effects coupled with a gas-liquid flow model. As is commonly found for experimental data on dissolved hydrogen and oxygen, the dissolved species is either an average concentration measured relatively far from the electrode surface or an average concentration at the electrode surface without any local effect of the electrode kinetics. In this thesis an agreement is found for the analytical derived natural convection up to an height of 0.01 [m] with the numerical model. The fraction of dissolved hydrogen and oxygen taken up by the gas bubbles is enhanced for smaller bubbles, a high frequency of bubbles generated, and an increased mass transfer of dissolved gas at the electrode. Moreover, a clear difference is found for the dissolved hydrogen and oxygen evolution near the electrode for horizontal and vertical electrodes. Horizontal electrodes have more dissolved gas at the electrodes, likely due to the dissolved gas not being able to transfer to the gas bubbles as easily for vertical electrodes. Also, for both vertical and horizontal electrodes the dissolved gas concentration flattens for increased current density, likely due to homogeneous nucleation. For an increasing electrode height a lowering of the dissolved gas was observed, associated with an increased dissolved gas uptake by the bubbles. Most of these local effects are able to be modelled using an analytical and numerically combined model. These simulations greatly improve the understanding of dissolved hydrogen and oxygen evolution in the vicinity of electrodes.

A one-dimensional model of respiratory deposition is developed based on an Eulerian approach. The model simulates aerosol deposition in all generations of the respiratory tract by numerically solving the aerosol general dynamics equation (GDE) for a range of aerosol diameters. The lung geometry is described by Weibel’s morphometric model, with a time varying alveolar geometry to accommodate inhalation dynamics. The model is first valuated by comparing it with numerical and experimental results. Afterwards a series of parameter studies is performed by changing breathing conditions, particle parameters and lung geometries. An increase in Tidal volume and decrease of breathing period resulted in an increase of the total deposition fraction for coarse particles and a decrease of the total deposition fraction for ultrafine particles. An increase in the particle density resulted in an increase in the total deposition fraction. A decrease in the airway diameter generally resulted in an increase of the total deposition fraction. This difference was most noticeable in the tracheobronchial region. Decreasing the airway diameter in the tracheobronchial region mostly effects coarse particles while decreasing the airway diameter in the alveolar region mostly effects ultrafine particles.

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.

In this work we investigate neural networks and subsequently physics-informed neural networks. Physicsinformed neural networks are away to solve physical models that are based on differential equations by using a neural network. The wave equation, Burgers’ equation, Euler’s equation, and the ideal magnetohydrodynamic equations are introduced and solved with physics-informed neural networks. The solutions to the first equations were captured well. The solution to the ideal magnetohydrodynamic equations contained some problems. These problems include transitions between different types of behaviour and exact values of constant sections. On the other hand, general shape and behaviour of the curve and locations of contact discontinuities were predicted well.

In this thesis, a model for air flow and temperature in urban areas is studied. In particular, the influence of vegetation in a street canyon is investigated. This includes the effect of vegetation on air flow and the cooling property of vegetation to lower temperature in street canyons. Computational Fluid Dynamics simulations with vegetation in a street canyon (green facades and trees) are performed. To model this, the Reynolds Averaged Navier Stokes equations in 3D are closed using the k-e turbulence model with source and sink terms to account for the effects of vegetation on air flow. In the thermal equation, the Simple Gradient Diffusion Hypothesis is used to close the equations and a cooling power term is introduced to account for the transpirational cooling property of vegetation. The results regarding the vertical velocities in the street canyon are compared with earlier simulations by Gromke et al. The simulations involving temperature showed significant effects of the vegetation in the street canyon. At street level, the green facades yielded a stronger cooling effect than trees. However, the cooling effect of trees is stronger halfway the canyon and just above the canyon in comparison with green facades. An important note is that the temperature drop inside the tree canopy strongly suggests that the cooling power in the simulation is modelled stronger than one would expect in reality. Another part of this research is the implementation of a Higher Order Scheme. This is done with the Van Leer limiter. The simulations with this new numerical method yielded very similar results compared with the UDS simulations. One outlier is noticed in the velocity in the 푦-direction for the empty street canyon. A possible explanation could be the sensitivity of the method near the ground. The study of the effect of vegetation in a street canyon could be extended in the future by comparing combinations of vegetation and adjusting the parameters of the green facades. Furthermore, the Van Leer limiter could be extended to the temperature part of the simulations in the future, since sharper gradients are expected here, so the improvement with respect to UDS and QUDS could be more significant. Finally, also other flux limiters, such as the Koren scheme, could be tested.

Knowledge of particle deposition is important in clinical settings or when discussing environmental effects of aerosols on humans.
Particle deposition in the human respiratory tract is determined by breathing patterns and lung morphology, as well as particle properties and deposition mechanisms.
In this study we develop a 1-dimensional model that numerically solves the general dynamic aerosol equation in the human respiratory tract.
The model can be used to calculate deposition fractions for a range of initial parameters.
We use Weibel's morphometric model to describe the lung geometry.

The model is validated by comparing it with previous numerical results, and running sensitivity tests to examine its consistency with parametric variations.
The model proved to be computationally efficient, requiring just seconds to run a simulation.
We use this to perform a number of parametric studies, most notably changing the tidal volume and the breathing rate.
For both of these, an increase in either the volume or the rate decreased the deposition fraction across the spectrum of particle sizes, apart from at the tails of the distribution.
We also examine the effect of particle density on the deposition fraction, which increases with an increasing density.
The source code is published along with this thesis, allowing anyone to perform arbitrary parametric studies of their own.

In this thesis, the behaviour and application of a one-dimensional model describing blood flow through compliant vessels is investigated. The one-dimensional model is derived using the physical laws of conservation of momentum and conservation of mass and uses a Finite Volume Method in combination with a high resolution flux difference splitting. First, the behaviour of the model is compared with established models in a network of 55 main arteries and then in a network of 111 main arteries including in vivo results. Finally, the model with the 111-artery network as a baseline is combined with inflow boundary conditions and a scaling factor provided by MRI blood flow data
to make it patient-speciffic. The adapted model is used to investigate how well characteristics in the distal part of the network can be predicted. It is found that the Finite Volume Method in combination with the high resolution flux difference splitting produces results that are highly comparable to those of established models both in the 55- and 111-artery network. The patient-speciffic model proves to be capable of predicting the pressure value in the arm to a reasonable degree. The flow in distal parts in the aorta is underestimated for all patients, but the degree of this underestimation varies per patient. Combining the results with a novel colour representation of pressure and velocity, it is possible to show patient speciffic evolution of pressure and velocity in their arteries. Further research should focus on adapting baseline networks with different key characteristics to increase the accuracy of the predictions for patients with different characteristics than the baseline model used in this study. Such characteristics include the number of bifurcations in the aortic arch (three or two) and the tapering of the aorta.

The third biggest cause of death in the western world is the stroke which is often caused by an aneurysm. Recent literature proposes the Wall Shear Stress (WSS), the Time-Averaged Wall Shear Stress (TAWSS), the Oscillatory Shear Index (OSI) and the Transverse WSS (Trans-WSS) as possible factors influencing the initiation, growth and rupture of intracranial aneurysms (IA). Currently, scientist and doctors are still in disagree on the biggest factors of rupture of an IA. In this research project, Tomographic Particle Image Velocimetry (TPIV) is used to acquire data to calculate these before mentioned hemodynamic quantities. The experiment captured 2040 images during one simulated cardiac cycle in a phantom reflecting an IA. To obtain the WSS, TAWSS, OSI and Trans-WSS on the wall of the phantom these images were post-processed using Davis, Tecplot and Python. The hemodynamic quantities are successfully calculated and visualized on 3D models of the aneurysm. An accurate result for these hemodynamic quantities was achieved when using a minimum of 51 images evenly spread out during a cardiac cycle. In cases without time constraints, it is still recommended to use as many images as possible to account for local WSS fluctuations. In further research the data structure in DaVis should be altered to a constant Cartesian coordinate structure for every dataset of the phantom. This will remove the biggest error and will greatly increase the value of this thesis and the analysis of these quantities.

Tata Steel employs physical vapour deposition (PVD) as a novel galvanization technique in their line production to prevent corrosion. In this process, zinc is evaporated in a vapour distribution box (VDB) and directed via nozzles into a vacuum where it is deposited on a steel substrate. In order to reduce stray deposition, achieve high and uniform mass flow rate from the nozzles and avoid condensation, understanding of the flow phenomena in the VDB and nozzles are necessary. Seeing that the PVD process is carried out at high temperatures in vacuum which makes it infeasible to experimentally characterise the flow for optimization purposes, thus, this research utilizes computational fluid dynamics (CFD).

In this study, the flow behaviour of the zinc vapour in the VDB and nozzles are investigated by solving the fluid governing equations numerically using finite volume method (FVM) in openFOAM. This analysis is done using the pressure-based sonicFoam solver to cope with the subsonic flow in the VDB and supersonic flow in the nozzles. The mass flow rate was compared to the ideal isentropic expression and experimental results. Regions in the set-up with high probability of condensation was investigated using a four coefficient Antoine equation.

A uniform pressure build-up in the VDB enabled uniform deposition. Around the corner of the inlet channel, a stable recirculation pattern affected the nozzle flow, however, this effect reduced as the outlet pressure decreased. The simulated total mass flow rate was greater than the experimental data by a factor of four possibly as a result of numerical errors and experimental stray depositions. And the simulated nozzle mass flow rate was less than the analytical isentropic expression by a factor of five due to the nozzle viscous boundary effect, and VDB wall heating. The mass flow rate from the nozzles decreased with increase in distance from the inlet channel. However, the nozzles far away are less likely to form zinc droplets as compared to those close to the inlet stream. For scale-up under the same conditions, it is expected that non-uniformity would be pronounced and the effect of the small eddies would become more significant. Thus, the simulation of the PVD process gives a qualitative description of the flow and a first approximation for the mass flow rate. To further improve the mass flow prediction, the sensitivity of the mass flow rate depending on the melt temperature and inlet velocity boundary condition should be studied in future works.

Synchrony is a phenomenon that pervades all fields of science. The Kuramoto model is a prominent model that describes synchronization in systems (networks). It models each element of the network as an oscillator with an individual phase. Due to global coupling, a phase transition is realized, such that some oscillators of the network synchronize. An example of this model is the synchronization of chemical oscillators. However, this model is sometimes insufficient. It is found that in some parts of the brain, synchronization is required, but that excessive synchronization may lead to epilepsy. This reveals that negative feedback is required in order to avoid excessive synchronization. In this study, the Kuramoto model is extended to an adaptive network by introducing two opposing adaptation rules, such that the strength of coupling can differ per pair of oscillators. The anti-Hebbian rule promotes links between oscillators that are in anti-phase. It is found that networks with this adaptation rule organize themselves in a way that links occur between oscillators whose frequencies are most distant, and that other links are weakened or pruned completely. This suggests that networks with this adaptation rule are able to avoid excessive synchronization. However, the network is still able to sustain explosive synchronization. The second rule, the Hebbian rule, promotes links between oscillators that are in phase. Networks with this rule do not prune links. Again explosive synchronization is revealed in this network. A stability analysis is performed to obtain more fundamental insights in the dynamics of the network. The results of this thesis can help obtaining deeper understanding the dynamics and principles of link pruning and explosive synchronization in complex networks: phenomena that are observed in, among others, the field of neuroscience.

A CFD study is made to get more insight in the flow, temperature and heat distribution in a side heated cavity filled with coarse grained porous media. This was investigated for 105≤Ra≤107 and 0.01≤Ri≤100. The question is how the solid beads influence the heat transfer. It was found that the spheres dampen the flow, influence the local heat transfer rate and affect the ratio of natural to forced convection (expressed with the Ri number). A modification was proposed by multiplying Ri with the square root of Da to take the influence of the spheres into account.

Crowd modelling is essential to the understanding of pedestrian logistics and prevention of crowd disasters. Agent-based approaches can realistically predict crowd behaviour. The social force model as proposed by Helbing and Mólnar in 1995[1] is a widely used agent-based approach. This is a physical model for psychological behaviour that relies strongly on its various parameter values. To investigate the underlying thought of the social force model the physical consequences of the effects and parameters are reviewed in this thesis. Next to this, an adjustment onHelbing andMólnar’s model is made by treating agents as particleswith a hard kernel, requiring a walkover- and ghost-prevention functionality. In addition, it is suggested to set the agent interaction magnitude to U0 ®¯ Æ 21 m2/s2. Subsequently, the adjusted model is validated to empirical research done by Seyfried et al.[2] and to simulations done by Helbing andMólnar[1]. For validation a cluster analysis method is developed to give a quantitative measure of the number of lanes.

Currently, 54% of the general population lives in urban areas. This number is estimated to increase to 66% by 2050. Urbanization is generally linked to several phenomena that are detrimental to the overall quality of life; the urban heat island effect, and the decrease of air quality due to pollutants. The addition of vegetation to urban areas is generally seen as the best measure to combat these phenomena, due to their suggested filtering and cooling capacity. Currently, both phenomena are studied as separate processes, but research suggest that the cooling power of vegetation is linked to the amount of pollution that is present. This calls for a numerical implementation that is able to accurately model both the filtering, and cooling effect such that the interplay between them can be studied in the future. In this work, an existing RANS k− solver is extended with the dry-deposition model to deter-mine the filtering capacity of the vegetation, and the leaf energy balance model to determine the cooling effect of the vegetation. Using the dry deposition model, we were able to accurately reproduce experimental measurements of the filtering capacity of a hawthorn hedge in an open field, obtained by Tiwary et al. [2006]. We assumed that the filtering took place due to both needle-like and broad leaf collectors. The same case was studied byˇS ́ıp and Beneˇs [2016], who obtained similar results, but used a different mixing parameters of the collector types. We concluded that additional studies are needed to determine the importance of the collector mixing parameters for multiple species, before the dry deposition model can be considered as valid. Using the leaf energy balance model, we were able to determine the cooling power of a simple vegetation block, exactly reproducing the results obtained by [Manickathan et al., 2017]. Using the leaf energy balance model, we were not able to reproduce experimental measurements of the leaf temperature of potted impatiens, obtained by [Kichah et al., 2012]. This was caused by the nature of the flow, which proved to be barely turbulent and outside of the scope of our RANSk− solver. We concluded that the leaf energy balance model needs to tested against other experimental measurements, obtained under different flow conditions. As of yet, we cannot determine if the model is able to accurately reproduce experimental measurements.

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.

Vapour Distribution Boxes (VDBs) are used for continuous Physical Vapour Deposition (PVD) coating. The present study shows a Computational Fluid Dynamics (CFD) simulation of Zinc vapour inside a VDB, analyses the lateral Zinc vapour distribution and identifies regions in which phase change is likely to happen.

This MSc thesis reports on an experimental study performed to test the effects of packed beds of relatively large spheres on natural convection inside a cubical enclosure which is heated from the left side and cooled from the right side. With ’relatively large’, a ratio of L/D=5 is meant where L is the length between the hot and cold plate and D is the diameter of each sphere where the packed bed consists of. To gain a better understanding and enhanced knowledge of the effects of coarse-grained porous media on side-heated natural convection, heat transfer experiments were performed as well as flow and temperature distribution measurements using the optical measurement techniques Particle Imaging Velocimetry (PIV) and Liquid Crystal Thermography (LCT). In the optical measurement experiments, hydrogel balls were used which have the same refractive index as that of water.