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.