Summary Microfluidic two-phase flows are increasingly being used in many mass transfer applications because of the numerous advantages of operating in the microscale such as stability of the interface and low cost. Such two-phase flows have multiple applications in various fields such as medicine, metal extraction, chemistry, oil and gas, and handling of industrial effluents. It is particularly important in both the transport and extraction of substances from one fluid to another fluid. The main reasons for this are the short diffusion distances and large surface-volume ratios when using multiple chips in parallel.

Among the various flow regimes, parallel flow in the microscale is considered to be advantageous for extraction applications, especially radioisotope transfer. In this regime, the two fluids move parallel to each other in a microfluidic channel. If the fluid-fluid interface remains stable throughout, efficient transfer is possible without necessitating a step to separate the two fluids. This benefit offered by microfluidics is very important for radioisotopes with short half-lives, as the absence of a separation step ensures that radioisotopes can be transferred efficiently in a quick time, thereby maximizing their utility for different applications such as pharmaceuticals.

However, stable parallel flow is hard to achieve as it is contingent on several factors. In a microfluidic channel with two inlets, a rectangular main channel and outlets, the ideal scenario for efficient mass transfer involves a stable fluid-fluid interface to be located exactly in the middle of the rectangular channel, followed by the two fluids flowing to their respective outlets without any fluid leaking to another outlet. Considering the utility of such a regime, it is important to study the underlying flow phenomena which govern the regime and leakage. This thesis, therefore, focuses on using simulations and experiments to study parallel flow in microfluidic channels, followed by an analysis of the mass transfer when using such a regime for radioisotope extraction...@en

Over the next couple of decades, the world will face the challenge of drastically reducing carbon emissions. Innovative Generation-IV nuclear reactor designs can play an important role in driving this energy transition. One of these designs is the Molten Salt Fast Reactor (MSFR), characterized by a fast neutron spectrum and the use of a liquid fuel. Because of the liquid fuel, melting and solidification phenomena need to be considered. To this end, this thesis presents a combined experimental and numerical investigation of melting and solidification phenomena in the MSFR. The experimental part was primarily motivated by the lack of suitable experimental data for the transient development of an ice-layer in internal flow, which is a relevant case for the analysis of accident scenarios in a MSFR where solidification may pose a risk. The main focus of the numerical part was to improve the computational efficiency of current state-of-the-art melting and solidification models.

As part of the experimental investigation, a new experimental facility (ESPRESSO) was designed and built. The ESPRESSO facility consists of a water tunnel capable of reaching both laminar and turbulent flow rates, in which ice is grown from a cold plate at the bottom of a square channel. The ESPRESSO facility was designed to have well-described experimental boundary conditions, through careful consideration of the inflow and cold-plate specifications. Subsequently, experimental data was generated for the transient development of an ice layer in laminar internal flow using particle image velocimetry (PIV), which may be used for numerical validation. The onset of ice formation was found to coincide with a sudden increase of the cold-plate temperature, which was therefore used to identify the zero time instant in our experiments. This was attributed to subcooling effects prior to nucleation, of which evidence was obtained using laser induced fluorescence (LIF) temperature measurements.

In addition, non-intrusive temperature measurements have been performed for the transient development of an ice layer in laminar channel flow using LIF, which is so far only the second application of LIF as a non-intrusive temperature measurement technique in solid-liquid phase change experiments. The LIF method presented in this thesis is a novel approach for solid-liquid phase change experiments because of the use of a two color (instead of a one color) technique, the use of a post-processing algorithm to remove top to bottom striations and reduce other measurement noise, and a detailed analysis of the uncertainty in the temperature fields. Good results were obtained for sufficiently large temperature differences of approximately C with an uncertainty of σ=0.3-0.5 °C, however further improvements are needed to remove artefacts as a result of laser light scattering from the solid-liquid interface, and to obtain a sufficiently high accuracy for numerical validation purposes, especially for smaller temperature differences.

The numerical work performed as part of this thesis aims to address the need for more efficient melting and solidification models, which can accurately capture the solid-liquid interface and resolve the recirculation zones in the fluid region at a lower computational cost. To this end, an energy-conservative DG-FEM approach based on the `linearized enthalpy melting/solidification model' was developed and validated. Although certain solid-liquid phase change problems with strong gradients in the flowfield can benefit from the use of the higher order DG-FEM method, overall a suboptimal O(h) mesh convergence rate was obtained due to an inaccurate numerical solution of the discontinuities at the solid-liquid interface. Therefore, further development of the DG-FEM solid-liquid phase change solver is needed to fully benefit from the arbitrarily high order of accuracy of the hierarchical polynomial basis function set.

Very promising results were obtained with a parallel finite volume adaptive mesh refinement method for solid-liquid phase. Cells were refined based on the maximum difference in the liquid fraction over the cell faces and the estimated numerical discretization error in the flow and temperature fields, using the cell residual method. With this approach, a very good agreement was obtained between the adaptive mesh results and the reference solutions on a uniformly refined grid with significantly less degrees of freedom. This demonstrates the potential of the proposed finite volume adaptive mesh refinement approach as a more computationally efficient numerical method for solid-liquid phase change problems.

The final part of this thesis details a five-stage benchmark for modelling phase change in molten salt reactors, modelled after the MS(F)R freeze-valve design. With each stage, an additional layer of complexity is added, which enabled the identification of potential sources of discrepancy between different numerical modelling approaches. Results were obtained with three different codes: STAR-CCM+, OpenFOAM and DGFlows (inhouse DG-FEM based code for computational fluid dynamics). The results from the benchmark showed an overall good agreement between the three codes, although some discrepancies were observed when adding conjugate heat transfer effects. Therefore, we recommend some caution when coupling different solid-liquid phase change and conjugate heat transfer modelling approaches.

To summarize, this thesis presents new experimental data for the transient ice-growth in laminar internal flow, driven by a general lack hereof. In addition, this thesis illustrates the potential of LIF as a non-intrusive temperature measurement technique for solid-liquid phase change experiments. Two new numerical methods were developed and validated for solid-liquid phase change problems, and especially the finite volume adaptive mesh refinement approach showed promising results in terms of enhanced computational efficiency. On a final note: solid-liquid phase change is a vast and ongoing field of research. We believe this thesis is a substantial addition to the field, yet there are still a lot of opportunities for future work. Some suggestions are given in the concluding chapter.
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The growing amount of plastic pollution in the oceans is worldwide a huge problem. There is an increasing amount of projects that try to clean up this pollution. To remove the pollution efficiently, it is useful to know how plastic litter moves, degrades and sinks. Models are being developed that can describe what happens with plastic in the ocean.

To model the behaviour of plastic in the ocean a lot of parameters need to be taken into account. The transport of plastic particles is largely determined by processes like the wind and the current but their movement also has a random character due to dispersion. Due to this random movement, the future position of a particle can be described by a probability distribution. To find that probability distribution, the Kolmogorov forward equation (or Fokker-Planck equation), in this context the same as the advection-diffusion equation, needs to be solved.

It is also possible that the plastic particles sink and settle on the bottom of the ocean. One goal of this project was to incorporate the settling of particles as an extra term into the advection-diffusion equation.

Forward models are used to predict where particles will go to. It can also be useful to have reverse time models that can describe where particles had their origin. To make reverse time models, it is necessary to solve a reverse time advection-diffusion equation. The main goal of this project was to derive and solve the reverse time advection-diffusion equation that includes the settling of particles. This is done by finding the adjoint of the Kolmogorov forward equation and the settling term.

Fluids above the critical point are widely used in industry. Chemical, pharmaceutical, food industry and energy production are some examples. In the energy production sector they are mainly used as cooling fluids, because they allow to increase the thermal efficiency of the power plants. However, the fundamentals of their heat transfer behavior are still unknown and current heat transfer models fail to predict it. Supercritical (SC) fluids are characterized by strongly varying fluid properties, which are responsible for their particular heat transfer behavior and make them very difficult to model, simulate and experimentally investigate. In past studies, buoyancy was identified as a key cause for the heat transfer deterioration observed in SC fluids. The aim of the research described in this thesis is to investigate the possibility of performing non-intrusive local velocity measurements with the optical technique PIV and to acquire global heat transfer measurements, with strongly changing fluid properties at SC conditions. The experiments were performed in a pure buoyancydriven flow: a Rayleigh-Bénard (RB) flow. The velocity fields of RB convection with strongly varying properties, beyond the so-called Oberbeck-Boussinesq (OB) approximation, were experimentally studied at atmospheric pressure first. An increase of the time-averaged velocity close to the bottom wall of the cell with respect to the top wall of about 13% was found. This finding confirmed experimentally a top-bottom ”broken symmetry” in the velocity field, which was observed in previous numerical and theoretical studies, but it was never experimentally demonstrated before. The heat transfer with strongly variable properties at SC conditions for constant Prandtl and Rayleigh numbers, specifically defined outside the validity range of the OB approximation, was experimentally studied. The measurements were performed at the Max Planck Institute of Dynamics and Self-Organization in Göttingen (Germany), with a European EuHIT project. It was observed that the measured Nusselt number defined for non-OB conditions was different from point to point, showing that merely the Rayleigh and Prandtl numbers are not sufficient to determine the heat transfer through the cell. It was also seen that the measured Nusselt number was 16% larger with respect to the one predicted by the Grossmann-Lohse theory (2000) for the same Rayleigh and Prandtl numbers at OB conditions. A feasibility study of particle image velocimetry (PIV) at SC conditions was done by using the background oriented schlieren technique (BOS). An estimation of the PIV experimental uncertainty at SC conditions was done with the statistical correlation method proposed by Wieneke et al., (2015). PIV was successfully performed at SC conditions. Main difficulties about its applicability were due to blurring and optical distortions in the boundary layer and thermal plumes regions. PIV measurements were performed at three different magnitudes of density difference between top and bottom of the cell. Two of the three experiments were done at similar Rayleigh and Prandtl numbers, defined for non-OB conditions: one towards the liquid phase and the other one towards the gas phase. The former showed a lower large scale circulation (LSC) velocity than the latter. All cases showed the presence of one asymmetric LSC roll, which is different from a typical RB convection flow at OB conditions.
Improvements in the accuracy of PIV measurements and the acquisition of more
heat transfer data at SC conditions, would help the study of the thermal and viscous boundary layer thicknesses and turbulence modifications that are responsible for different heat transfer regimes in SC fluids.@en