Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008. / The furnace at Polokwane is designed to treat high chromium containing concentrates which requires higher smelting temperatures to prevent or limit the undesirable precipitation of chromium spinels. The furnace has therefore been designed to allow for deep electrode immersion with copper coolers around the furnace to permit the operation with the resulting higher heat fluxes. Deep electrode immersion has been noted to result in dangerously high matte temperatures. Matte temperatures however can be influenced by a number of furnace factors which emphasize the need to understand the energy distribution inside the furnace. Computational fluid dynamics (CFD) has therefore been identified to analyze the flow and heat profiles inside the furnace. The commercial CFD software code Fluent is used for the simulations. Attention has been given only to a slice of the six-in-line submerged arc furnace containing two electrodes or one pair while focusing on the current density profiles, slag and matte flow profiles and temperature distribution throughout the bath to ensure the model reflects reality. Boundary conditions were chosen and calculated from actual plant data and material specifications were derived from previous studies on slag and matte. Three dimensional results for the current, voltage and energy distributions have been developed. These results compare very well with the profiles developed by Sheng, Irons and Tisdale in their CFD modelling of a six-in-line furnace. It was found the current flow mainly takes place through the matte, even with an electrode depth of only 20% immersion in the slag, but the voltage drop and energy distribution still only take place in the slag. Temperature profiles through-out the entire modelling domain were established. The vertical temperature profile similar to Sheng et al. 1998b was obtained which shows a specifically good comparison to the measured temperature data from the Falconbridge operated six-in-line furnace. The temperature in the matte and the slag was found to be uniform, especially in the vertical direction. It has been found that similar results with Sheng et al. (1998b) are obtained for the slag and matte velocity vectors. Different results are, however, obtained with different boundary conditions for the slag/matte interface and matte region; these results are still under investigation to obtain an explanation for this behaviour. The impact of the bubble formation on the slag flow was investigated and found to be a significant contributor to the flow. With the bubble formation, it is shown that possible ‘dead zones’ in the flow with a distinctive V-shape can develop at the sidewalls of the furnace with the V pointing towards the centre of the electrode. This behaviour can have a significant impact on the point of feed to the furnace and indirectly affect the feed rate as well as the settling of the slag and matte. These results are not validated though. Different electrode immersions were modelled with a constant electrical current input to the different models and it was found that the electrode immersion depth greatly affects the stirring of the slag in the immediate vicinity of the electrode, but temperature (which determines the natural buoyancy) has a bigger influence on the stirring of the slag towards the middle and sidewall of the slag bath. The sensitivity of the model to a different electrode tip shape with current flow concentrated at the tip of the electrode was also modelled and it was found that the electrode shape and electrical current boundary conditions are very important factors which greatly affect the voltage, current density and temperature profiles through the matte and the slag. A detailed investigation to determine the electrode tip shape at different immersions, as well as the boundary conditions of the current density on the tip of the electrode is necessary as it was proven that the model is quite sensitive to these conditions. Several recommendations arose from this modelling work carried out in this investigation. Time constraints, however, did not allow for the additional work to be carried out and although valuable results were obtained, it is deemed to be a necessity if a more in-depth understanding of furnace behaviour is to be obtained. Future work will include the validation of the results, understanding the liquid matte model, investigating the MHD effects and modelling different furnace operating conditions.

Thesis (MScEng (Process Engineering))--Stellenbosch University, 2008. / The electric smelting furnace is found at the heart of the platinum recovery process where the power input from the electrodes produces a complex interplay between heat transfer and fluid flow. A fundamental knowledge of the dynamic system hosted by the electric furnace is valuable for maintaining stable and optimum operation. However, describing the character of the system hosted by the electric furnace poses great difficulty due to its aggressive environment. A full-scale threedimensional Computational Fluid Dynamics (CFD) model was therefore developed for the circular, three-electrode Lonmin smelting furnace. The model was solved as time dependent to incorporate the effect of the three-phase AC current, which was supplied by means of volume sources representing the electrodes. The slag and matte layers were both modelled as fluid continuums in contact with each other through a dynamic interface made possible by the Volume of Fluid (VOF) multi-phase model. CO-gas bubbles forming at electrode surfaces and interacting with the surrounding fluid slag were modelled through the Discrete Phase Model (DPM). To account for the effect of concentrate melting, distinctive smelting zones were identified within the concentrate as assigned a portion of the melting heat based on the assumption of a radially decreasing smelting rate from the centre of the furnace. The tapping of slag and matte was neglected in the current modelling approach but compensation was made for the heating-up of descending material by means of an energy sink based on enthalpy differences. Model cases with and without CO-gas bubbles were investigated as well as the incorporation of a third phase between the slag and matte for representing the ‘mushy’ chromite/highly viscous slag commonly found in this region. These models were allowed to iterate until steady state conditions has been achieved, which for most of the cases involved several weeks of simulation time. The results that were obtained provided good insight into the electrical, heat and flow behaviour present within the molten bath. The current density profiles showed a large portion of the current to flow via the matte layer between the electrodes. Distributions for the electric potential and Joule heat within the melt was also developed and showed the highest power to be generated within the immediate vicinity of the electrodes and 98% of the resistive heat to be generated within the slag. Heat was found to be uniformly distributed due the slag layer being well mixed. The CO-gas bubbles was shown to be an important contributor to flow within the slag, resulting in a order of magnitude difference in average flow magnitude compared to the case where only natural buoyancy is at play. The highest flow activity was observed halfway between electrodes where the flow streams from the electrodes meet. Consequently, the highest temperatures are also observed in these regions. The temperature distribution within the matte and concentrate layers can be characterized as stratified. Low flow regions were identified within the matte and bottom slag layer which is where chromite and magnitite deposits are prone to accumulate. The model results were partially validated through good agreement to published results where actual measurements were done while also falling within the typical operating range for the actual furnace. The modelling of the electric furnace has been valuably furthered, however for complete confidence in the model results, further validation is strongly recommended.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: A Computational Fluid Dynamics (CFD) model was developed for the prediction of flotation rate constants in a stirred flotation tank and validated against experimental data. The model incorporated local, time-varying values of the turbulent flow field into an existing kinetic flotation model based on the Generalised Sutherland Equation to predict the overall flotation rate constant. Simulations were performed for the flotation of various minerals at different operational conditions and the predictions were compared with experimental data. It was found that the CFD-based model yielded improvements in the prediction of flotation rate constant for a range of hydrophobicities, agitation speeds and gas flow rates compared with existing methodologies, which use volume-averaged empirical expressions for flow variables. Moreover, comparing to the available CFD alternatives for the flotation modelling this approach eliminates the need for solving an extra partial differential equation resulting in a more computationally economic model. The model was developed in three stages. In the first, a single-phase model was used to establish the requirements for successful modelling of the velocity components and turbulent properties of water inside flotation tanks. Also, a novel use of the Grid Convergence Index for this application was carried out, which allowed determination of the maximum achievable reduction in numerical uncertainties through systematic grid refinement and adaptation. All subsequent simulations were performed at the optimal discretization level determined in this manner. It was found that the Moving Reference Frames (MRF) method was adequate for representation of the impeller movement when the rotational zone was located close to the impeller, using a time step advance of between 10◦ and 15◦ of impeller rotation. Comparison of the different turbulence models for the single-phase modelling revealed that the standard k-e and Large Eddy Simulation turbulence models both performed equally well and that the computational requirement was lower for the standard k-e model, making it the method of choice. Validation of the methodology was done by comparison with experimental data for two different stirred tanks including an unbaffled mixer and a fully baffled standard Rushton turbine tank. The validation against experimental data showed that the model was capable of predicting the flow pattern, turbulent properties and the generation of trailing vortices. The second stage of modelling used an Eulerian-Eulerian formulation for gasliquid modelling of gas-sparged fully baffled vessels (2.25 l, 10 l and 50 l) using a Rushton turbine. It was determined that the minimum model uncertainty resulting from simulation of the sparger was achieved using a disk sparger with a diameter equal to 40% of the impeller diameter. The only significant interfacial force was found to be the drag force, and this was included in the multiphase methodology. A parametric study on the available formulations for the drag coefficient was performed which showed that the effect of turbulence on the air bubbles can accurately be represented using the proposed model of Lane (Lane, 2006). Validation of the methodology was conducted by comparison of the available experimental gas holdup measurements with the numerical predictions for three different scales of Rushton turbine tanks. The results verified that the application of the designed sparger in conjunction with Lane drag coefficient can yield accurate predictions of the gas-liquid flow inside the flotation tank with the error percentage less than 6%, 13%, and 23% for laboratory, pilot and industrial scale Rushton turbine tanks, respectively. The last stage of this study broadened the Eulerian-Eulerian framework to predict the flotation rate constant. The spatially and temporally varying flow variables were incorporated into an established fundamental flotation model due to Pyke (Pyke, 2004) based on the Generalized Sutherland equation for the flotation rate constant. The computation of the efficiency of the flotation sub-processes also incorporated the turbulent fluctuating flow characteristics. Values of the flotation rate constants were computed and volume-weight averaged for validation against available experimental data. The numerical predictions of the flotation rate constants for quartz particles for a range of particle diameters showed improvements in the predictions when compared with values determined from existing methodologies which use spatially uniform values for the important hydrodynamic variables as obtained from empirical correlations. Further validations of the developed CFD-kinetic model were carried out for the prediction of the flotation rate constants of quartz and galena floating under different hydrophobicities, agitation speeds and gas flow rates. The good agreement between the numerical predictions and experimental data (less than 12% error) confirmed that the new model can be used for the flotation modelling, design and optimization. Considering the limited number of CFD studies for flotation modelling, the main contribution of this work is that it provides a validated and optimised numerical methodology that predicts the flotation macro response (i.e., flotation rate constant) by integrating the significance of the hydrodynamic flow features into the flotation micro-processes. This approach also provides a more economical model when it is compared to the available CFD models for the flotation process. Such an approach opens the possibility of extracting maximum advantage from the computed parameters of the flow field in developing more effective flotation devices. / AFRIKAANSE OPSOMMING: 'n Wye verskeidenheid van industriële toepassings gebruik meganies geroerde tenks vir doeleindes soos die meng van verskillende vloeistowwe, verspreiding van 'n afsonderlike fase in 'n deurlopende vloeistoffase en die skeiding van verskillende komponente in ‘n tenk. Die hoofdoel van die tesis is om ‘n numeriese model te ontwikkel vir ʼn flotteringstenk. Die kompleksiteit van die vloei (drie-dimensioneel, veelvuldige fases en volledig turbulent) maak die voorspelling van die werksverrigting van die flottasieproses moeilik. Konvensioneel word empiriese korrelasies gebruik vir modellering, ontwerp en die optimalisering van die flotteringstenks. In die huidige studie word ‘Computational Fluid Dynamics’ (CFD) egter gebruik vir die modellerings doel, aangesien dit ‘n alternatief bied vir empiriese vergelykings deurdat dit volledig inligting verskaf aangaande die gedrag van vloei in die tenk. Die model is ontwikkel in drie agtereenvolgende stadiums. Dit begin met ‘n strategie vir enkelfase modellering in die tenk, vorder dan na ‘n gas-vloeistof CFD model en brei dan die tweede stap uit om ‘n CFD model te skep vir die skeidingsproses deur flottering. ‘n Enkelfase model, gebaseer op die kontinuïteits- en momentumvergelykings, dien as basis vir die flottasie model. Die ‘Multiple Reference Frames’ (MRF) metode word gebruik om die rotasie van die stuwer na te boots, terwyl die dimensies van die rotasie-sone gekies is om die gepaardgaande onsekerhede, insluitend die model- en numeriese foute veroorsaak deur die dimensies van die roterende sones, te verminder. Die turbulensie model studie het getoon dat die standaard k-e turbulensie model redelike akkuraatheid kon lewer in die numeriese voorspellings en die resultate verskil in gemiddeld net minder as 15% van die eksperimentele lesings, terwyl die rekenaartyd min genoeg was om die simulasies op 'n persoonlike rekenaar uit te voer. Verder het die ‘Grid Convergence Index’ (GCI) metode die inherente onsekerhede in die numeriese voorspellings gerapporteer en gewys dat die onderskatting van die turbulensie wat algemeen plaasvind reggestel kan word deur van ‘Large Eddie’ (LES) of ‘Direct Numerical Simulations’ (DNS) gebruik te maak. Die metode wat ontwikkel is, is op twee tipes geroerde tenks getoets, naamlik 'n onafgeskorte menger en 'n standaard Rushton turbine tenk. Die numeriese resultate is teen eksperimentele data gevalideer en het gewys dat die model in staat is om die vloeipatrone, turbulensie einskappe en die vorming van agterblywende vortekse te voorspel. Die CFD resultate het getoon dat die vloeipatroon twee simmetriese rotasies siklusse bo en onder die roterende sone vorm, terwyl die vlak van die ooreenkoms tussen die numeriese voorspellings van die turbulente eienskappe en die eksperimentele lesings met minder as 25% verskil. As die tweede stap van hierdie navorsing is 'n Eulerian-Eulerian struktuur ontwikkel vir die gas-vloeistof modellering binne 'n standaard Rushton turbine flotteringstenk. Soos vir die enkelfase modellering is die Reynolds spanningstensor opgelos deur die standaard k-e turbulensie model, terwyl die lugborrels ingevoer/versamel is in/van die tenk deurmiddel van bron/sink terme. Verskeie ‘sparger’ rangskikkings is in die tenk geïmplementeer om die onsekerheid in die model weens die metode van luginspuiting te verminder. Verder is verskillende korrelasies vir die sleursyfer vergelyk vir laminêre en turbulente vloei in die tenk. Daar is gevind dat die skyf ‘sparger’, met 'n deursnee gelykstaande aan 40% van die stuwer deursnee, in samewerking met die voorgestelde model van Lane (Lane, 2006) vir die bepaalde sleursyfer die naaste ooreenkoms met die eksperimentele metings lewer (met 'n gemiddelde verskil van minder as 25%). 'n Vergelykende studie is ook uitgevoer om die gevolge van die gas vloeitempo en roerspoed vir drie verskillende geroerde tenks met volumes van 2.5 l, 10 l en 50 l te ondersoek. Die resultate van hierdie afdeling bevestig dat die CFD metode in staat was om die gas-vloeistof vloei in die flotteringstenk korrek te voorspel. Die veelvuldigefase model wat ontwikkel is, is uitgebrei vir flottasie modellering. Dit behels die integrasie van die CFD resultate met die fundamentele flottasie model van Pyke (Pyke, 2004) vir die flotteringstempo konstant. Die CFD model is toegerus met Pyke se model deur aanvullende gebruiker gedefinieerde funksies. Die CFD-kinetiese model is geëvalueer vir die flottering van kwartsdeeltjies en die resultate het die geloofwaardigheid van die model bevestig, aangesien die gemiddelde verskil tussen die numeriese voorspellings vir die flotteringstempo konstante en die eksperimentele data minder as 5% was. Die resultate is ook vergelyk met die analitiese berekeninge van Newell en daar is bevind dat die model vergelykbare voorspellings van die flotteringtempo konstantes lewer, met die ‘root mean square deviations’ (RMSD) gelyk of minder as die RMSD waardes vir die analitiese berekeninge. Verdere ondersoeke van die CFD-kinetiese model bestaan uit 'n parametriese studie wat die gevolge van die roertempo, gas vloeitempo en die oppervlak hidrofobisiteit op die flottering van kwarts- en galenietdeeltjies bestudeer. Die aanvaarbare ooreenkoms tussen die numeriese voorspellings en eksperimentele data (oor die algemeen minder as 12% fout) bewys dat die nuwe model gebruik kan word vir flotterings modellering en optimalisering.

Computational Fluid Dynamics (CFD) has been applied to many areas. As one of the most important fluids, the atmosphere is closely related to people’s life. Studying the atmospheres on other planets can help people understand the Earth’s atmosphere and the climate and weather phenomena in it. Because of the complexity of a planetary atmosphere and the limitation of observations, applying CFD to the study of planetary atmospheres is becoming more and more popular. This kind of CFD simulations will also help people design the mission to the extra planets. In this dissertation, through CFD simulations, we studied the three important phenomena in a planetary atmosphere: vortices, zonal winds and clouds. The CFD model Explicit Planetary Isentropic Coordinate (EPIC) Global Circulation Model (GCM) was applied in these simulations. Dynamic simulations of the Great Dark Spots (GDS) on Neptune and the Uranian Dark Spot (UDS) were performed. In this work, constructed zonal wind profiles and vertical pressure-temperature profile were constructed based on the observational data. Then, we imported a two-flux radiation model with two-band absorption coefficients into EPIC to study the seasonal changes on Uranus. Finally, a methane cloud model was imported to study the cloud formation around a great vortex and its effects on the vortex. In the process of the dynamic simulations of Neptune’s atmosphere and its vortices in it, the parameters about the background and the vortex itself were investigated to try to fit the observational results. We found that a small gradient of background absolute vorticity near a GDS is needed to sustain a great vortex in the atmosphere. The drift rate and oscillations of a GDS are closely related to the zonal wind profile and the vortex characteristics. The dynamic simulations of the UDS suggested why it is hard to observe a great vortex on Uranus and indicated that a region of near constant absolute vorticity appearing at ∼28◦N in the zonal wind profile is possibly recommended to the sustainability of the UDS.With the two-flux radiation model, we simulated the seasonal change of the zonal wind profile on Uranus. The observational temperature distribution and global convection were also achieved. With the methane cloud model, we simulated the poleward cloud above great vortices on both Neptune and Uranus. The results suggested that the cloud model can help the GDS on Neptune to keep its shape and moderate its oscillations. Similarly, it can also help the UDS to keep its form.

A new approach to large-eddy simulation (LES) based on the use of explicit spatial filtering combined with backscatter forcing is presented. The forcing uses a discrete dynamical system (DDS) called the compressible ``poor man's'' Navier--Stokes (CPMNS) equations. This DDS is derived from the governing equations and is shown to exhibit good spectral and dynamical properties for use in a turbulence model. An overview and critique of existing turbulence theory and turbulence models is given. A comprehensive theoretical case is presented arguing that traditional LES equations contain unresolved scales in terms generally thought to be resolved, and that this can only be solved with explicit filtering. The CPMNS equations are then incorporated into a simple forcing in the OVERFLOW compressible flow code, and tests are done on homogeneous, isotropic, decaying turbulence, a Mach 3 compression ramp, and a Mach 0.8 open cavity. The numerical results validate the general filter-forcing approach, although they also reveal inadequacies in OVERFLOW and that the current approach is likely too simple to be universally applicable. Two new proposals for constructing better forcing models are presented at the end of the work.

In this thesis, an approach is presented for the generation of grids suitable for the simulation of high Reynolds number viscous flows in complex three-dimensional geometries. The automatic and reliable generation of such grids is today on the biggest bottlenecks in the industrial CFD simulation environment. In the proposed approach, unstructured tetrahedral grids are employed for the regions far from the viscous boundaries of the domain, while semi-structured layers of high aspect ratio prismatic and hexahedral elements are used to provide the necessary grid resolution inside the boundary layers and normal to the viscous walls. The definition of the domain model is based on the STEP ISO standard and the topological information contained in the model is used for applying the hierarchical grid generation parameters defined by the user. An efficient, high-quality and robust algorithm is presented for the generation of the unstructured simplicial (triangular of tetrahedral) part of the grid. The algorithm is based on the Delaunay triangulation and the internal grid points are created following a centroid or frontal approach. For the surface grid generation, a hybrid approach is also proposed similar to the volume. Semi-structured grids are generated on the surface grid (both on the edges and faces of the domain) to improve the grid resolution around convex and concave ridges and corners, by aligning the grid elements in the directions of high solution gradients along the surface. A method is also developed for automatically setting the grid generation parameters related to the surface grid generation based on the curvature of the surface in order to obtain an accurate and smooth surface grid. Finally, a semi-structured prismatic/hexahedral grid generation algorithm is presented for the generation of the part of grid close to the viscous walls of the domain. The algorithm is further extended with improvements meant to increase the grid quality around concave and convex ridges of the domain, where the semi-structured grids are known to be inadequate. The combined methodology is demonstrated on a variety of complex examples mainly from the automotive and aeronautical industry.

No description available.

Numerical models for the simulation of longitudinal and transverse Stokes flow in cylindrical periodic porous media are presented. The models, which are based on a finite-volume formulation in primitive variables, utilize digital image representations of the geometries to simulate, making them particularly well-suited for the rapid automated analysis of creeping flow in porous media with complex morphologies. Complete details of the model formulations are given, including extensive treatment of the pressure boundary conditions at the solid-liquid interface needed to guarantee convergence with all possible geometries. The convergence behavior of both models is tested, and the models are shown to be second-order accurate.The models are used to simulate flow over the whole range of volume fractions of liquid in several regular geometries. The longitudinal model is used to simulate flow in square arrays of circular and square ducts, and both models are used to simulate flow in square and hexagonal arrays of circular cylinders and square arrays of square cylinders rotated by varying amounts. For each of the geometries, accurate empirical expressions for the Darcy permeability as a function of volume fraction solid are presented. Where applicable, model predictions of permeability are compared to existing analytical results.Subsequently, the models are used to simulate Stokes flow in random domains over a wide range of fractions liquid. The sequential random packing algorithm is used to generate 1,000 random packings of circular cylinders at each of 14 fractions of liquid, and longitudinal and transverse flow simulations are performed for each geometry. Histograms and summary statistics are computed for the permeability for each fraction liquid, and empirical expressions for mean permeability as a function of fraction liquid are given. The autocorrelation structure of the geometry and of the fluid velocity is analyzed, and an analysis of the scaling of longitudinal permeability variance is presented. In transverse flow at high packing densities, it is found that lightning-like patterns emerge in the fluid velocity. It is also found that the details of flows in such geometries are strongly sensitive to the placement of individual solid obstacles.

Tidal currents can be used as a predictable source of sustainable energy, and have the potential to make a useful contribution to the energy needs of the UK and other countries with such a resource. One of the technologies which may be used to transform tidal power into mechanical power is a vertical axis turbine, the hydrodynamic analysis of which this thesis is concerned with. The aim of this analysis is to gain a better understanding of the power transformation process, from which position there is the possibility of improving the conversion efficiency. A second aim is to compare the results from different modelling approaches. Two types of mathematical modelling are used: a basic blade element momentum model and a more complex Reynolds-averaged Navier Stokes (RANS) model. The former model has been programmed in Matlab by the present author while the latter model uses a commercial computational fluid dynamics (CFD) code, ANSYS CFX. This RANS model uses the SST k-! turbulence model. The CFD analysis of hydrofoils (equally airfoils), for both fixed and oscillating pitch conditions, is a significant proportion of the present work. Such analysis is used as part of the verification and validation of the CFD model of the turbine. It is also used as input to the blade element momentum model, thereby permitting a novel comparison between the blade element momentum model and the CFD model of the turbine. Both types of turbine model were used to explore the variation in turbine efficiency (and other factors) with tip speed ratio and with and without an angle of attack limiting variable pitch strategy. It is shown that the use of such a variable pitch strategy both increases the peak efficiency and broadens the peak. The comparison of the results from the two different turbine modelling approaches shows that when the present CFD hydrofoil results are used as input to the blade element model, and when dynamic effects are small and the turbine induction factor is low, there is generally good agreement between the two models.

Interface tracking methods for segregated flows such as breaking ocean waves are an important tool in marine engineering. With the development in marine renewable devices increasing and a multitude of other marine flow problems that benefit from the possibility of simulation on computer, the need for accurate free surface solvers capable of solving wave simulations has never been greater. An important component of successfully simulating segregated flow of any type is accurately tracking the position of the separating interface between fluids. It is desirable to represent the interface as a sharp, smooth, continuous entity in simulations. Popular Eulerian interface tracking methods appropriate for segregated flows such as the Marker and Cell Method (MAC) and the Volume of Fluid (VOF) were considered. However these methods have drawbacks with smearing of the interface and high computational costs in 3D simulations being among the most prevalent. This PhD project uses a level set method to implicitly represent an interface. The level set method is a signed distance function capable of both sharp and smooth representations of a free surface. It was found, over time, that the level set function ceases to represent a signed distance due to interaction of local velocity fields. This affects the accuracy to which the level set can represent a fluid interface, leading to mass loss. An advection solver, the Cubic Interpolated Polynomial (CIP) method, is presented and tested for its ability to transport a level set interface around a numerical domain in 2D. An advection problem of the level set function demonstrates the mass loss that can befall the method. To combat this, a process known as reinitialisation can be used to re-distance the level set function between time-steps, maintaining better accuracy. The goal of this PhD project is to present a new numerical gradient approximation that allows for the extension of the reinitialisation method to unstructured numerical grids. A particular focus is the Cartesian cut cell grid method. It allows geometric boundaries of arbitrary complexity to be cut from a regular Cartesian grid, allowing for flexible high quality grid generation with low computational cost. A reinitialisation routine using 1st order gradient approximation is implemented and demonstrated with 1D and 2D test problems. An additional area-conserving constraint is introduced to improve accuracy further. From the results, 1st order gradient approximation is shown to be inadequate for improving the accuracy of the level set method. To obtain higher accuracy and the potential for use on unstructured grids a novel gradient approximation based on a slope limited least squares method, suitable for level set reinitialisation, is developed. The new gradient scheme shows a significant improvement in accuracy when compared with level set reinitialisation methods using a lower order gradient approximation on a structured grid. A short study is conducted to find the optimal parameters for running 2D level set interface tracking and the new reinitialisation method. The details of the steps required to implement the current method on a Cartesian cut cell grid are discussed. Finally, suggestions for future work using the methods demonstrated in the thesis are presented.