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.

Numerical simulation of mold filling in low pressure die casting is considered in this study. The physical model includes modeling of free surface flow, heat transfer with phase change, surface tension, natural convection together with effect of trapped air in the mold. The governing equations are discretized by control volume finite difference method. The pressure field is computed by two-step projection method and the free surface is tracked by PLIC-VOF method. Water analog model is used for the validation purpose. Good agreement between numerical and experimental results is observed which supports the feasibility of the presented method.

The main focus of this thesis is on fast numerical methods, where adaptivity is an important mechanism to lowering the methods' complexity. The application of the methods are in the areas of wireless communication, antenna design, radar signature computation, noise prediction, medical ultrasonography, crystal growth, flame propagation, wave propagation, seismology, geometrical optics and image processing.   We first consider high frequency wave propagation problems with a variable speed function in one dimension, modeled by the Helmholtz equation. One significant difficulty of standard numerical methods for such problems is that the wave length is very short compared to the computational domain and many discretization points are needed to resolve the solution. The computational cost, thus grows algebraically with the frequency w. For scattering problems with impenetrable scatterer in homogeneous media, new methods have recently been derived with a provably lower cost in terms of w. In this thesis, we suggest and analyze a fast numerical method for the one dimensional Helmholtz equation with variable speed function (variable media) that is based on wave-splitting. The Helmholtz equation is split into two one-way wave equations which are then solved iteratively for a given tolerance. We show rigorously that the algorithm is convergent, and that the computational cost depends only weakly on the frequency for fixed accuracy.  We next consider interface tracking problems where the interface moves by a velocity field that does not depend on the interface itself. We derive fast adaptive  numerical methods for such problems. Adaptivity makes methods robust in the sense that they can handle a large class of problems, including problems with expanding interface and problems where the interface has corners. They are based on a multiresolution representation of the interface, i.e. the interface is represented hierarchically by wavelet vectors corresponding to increasingly detailed meshes. The complexity of standard numerical methods for interface tracking, where the interface is described by marker points, is O(N/dt), where N is the number of marker points on the interface and dt is the time step. The methods that we develop in this thesis have O(dt^(-1)log N) computational cost for the same order of accuracy in dt. In the adaptive version, the cost is O(tol^(-1/p)log N), where tol is some given tolerance and p is the order of the numerical method for ordinary differential equations that is used for time advection of the interface.   Finally, we consider time-dependent Hamilton-Jacobi equations with convex Hamiltonians. We suggest a numerical method that is computationally efficient and accurate. It is based on a reformulation of the equation as a front tracking problem, which is solved with the fast interface tracking methods together with a post-processing step.  The complexity of standard numerical methods for such problems is O(dt^(-(d+1))) in d dimensions, where dt is the time step. The complexity of our method is reduced to O(dt^(-d)|log dt|) or even to O(dt^(-d)). / <p>QC 20121116</p>

abstract: The Volume-of-Fluid method is a popular method for interface tracking in Multiphase applications within Computational Fluid Dynamics. To date there exists several algorithms for reconstruction of a geometric interface surface. Of these are the Finite Difference algorithm, Least Squares Volume-of-Fluid Interface Reconstruction Algorithm, LVIRA, and the Efficient Least Squares Volume-of-Fluid Interface Reconstruction Algorithm, ELVIRA. Along with these geometric interface reconstruction algorithms, there exist several volume-of-fluid transportation algorithms. This paper will discuss two operator-splitting advection algorithms and an unsplit advection algorithm. Using these three interface reconstruction algorithms, and three advection algorithms, a comparison will be drawn to see how different combinations of these algorithms perform with respect to accuracy as well as computational expense. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2015

Worldwide demand for energy is increasing rapidly, partly driven by dramatic economic growth in developing countries. This growth has sparked concerns over the finite availability of fossil fuels and the impact of their combustion on climate change. Consequently, many recent research efforts have been devoted to the development of renewable fuels and sustainable energy systems. Interest in liquid biofuels, such as ethanol, has been particularly high because these fuels fit into the conventional infrastructure for the transportation sector. Ethanol is a renewable fuel produced through the anaerobic fermentation of sugars obtained from biomass. However, the relatively high energy demand of its production process is a major factor limiting the usefulness of ethanol as a fuel. Due to the dilute nature of the fermentation product stream and the presence of the ethanol-water azeotrope, the separation processes currently used to recover anhydrous ethanol are particularly inefficient. In fact, the ethanol separation processes account for a large fraction of the total process energy demand. In the conventional ethanol separation process, ethanol is recovered using several distillation steps combined with a dehydration process. In this dissertation, a new hybrid pervaporation-distillation system, named Membrane Dephlegmation, was proposed and investigated for use in ethanol recovery. In this process, countercurrent vapour-liquid contacting is carried out on the surface of a pervaporation membrane, leading to a combination of distillation and pervaporation effects. It was intended that this new process would lead to improved economics and energy efficiency for the entire ethanol production process. The Membrane Dephlegmation process was investigated using both numerical and experimental techniques. Multiphase Computational Fluid Dynamics (CFD) was used to study vapour-liquid contacting behaviour in narrow channels and to estimate heat and mass transfer rates. Results from the CFD studies were incorporated into a simplified design model and the Membrane Dephlegmation process was studied numerically. The results indicated that the Membrane Dephlegmation process was more efficient than simple distillation and that the ethanol-water azeotrope could be broken. Subsequently, a pilot-scale experimental system was constructed using commercially available, hydrophilic NaA zeolite membranes. Results obtained from the experimental system confirmed the accuracy of the simulations.

Worldwide demand for energy is increasing rapidly, partly driven by dramatic economic growth in developing countries. This growth has sparked concerns over the finite availability of fossil fuels and the impact of their combustion on climate change. Consequently, many recent research efforts have been devoted to the development of renewable fuels and sustainable energy systems. Interest in liquid biofuels, such as ethanol, has been particularly high because these fuels fit into the conventional infrastructure for the transportation sector. Ethanol is a renewable fuel produced through the anaerobic fermentation of sugars obtained from biomass. However, the relatively high energy demand of its production process is a major factor limiting the usefulness of ethanol as a fuel. Due to the dilute nature of the fermentation product stream and the presence of the ethanol-water azeotrope, the separation processes currently used to recover anhydrous ethanol are particularly inefficient. In fact, the ethanol separation processes account for a large fraction of the total process energy demand. In the conventional ethanol separation process, ethanol is recovered using several distillation steps combined with a dehydration process. In this dissertation, a new hybrid pervaporation-distillation system, named Membrane Dephlegmation, was proposed and investigated for use in ethanol recovery. In this process, countercurrent vapour-liquid contacting is carried out on the surface of a pervaporation membrane, leading to a combination of distillation and pervaporation effects. It was intended that this new process would lead to improved economics and energy efficiency for the entire ethanol production process. The Membrane Dephlegmation process was investigated using both numerical and experimental techniques. Multiphase Computational Fluid Dynamics (CFD) was used to study vapour-liquid contacting behaviour in narrow channels and to estimate heat and mass transfer rates. Results from the CFD studies were incorporated into a simplified design model and the Membrane Dephlegmation process was studied numerically. The results indicated that the Membrane Dephlegmation process was more efficient than simple distillation and that the ethanol-water azeotrope could be broken. Subsequently, a pilot-scale experimental system was constructed using commercially available, hydrophilic NaA zeolite membranes. Results obtained from the experimental system confirmed the accuracy of the simulations.

Worldwide demand for energy is increasing rapidly, partly driven by dramatic economic growth in developing countries. This growth has sparked concerns over the finite availability of fossil fuels and the impact of their combustion on climate change. Consequently, many recent research efforts have been devoted to the development of renewable fuels and sustainable energy systems. Interest in liquid biofuels, such as ethanol, has been particularly high because these fuels fit into the conventional infrastructure for the transportation sector. Ethanol is a renewable fuel produced through the anaerobic fermentation of sugars obtained from biomass. However, the relatively high energy demand of its production process is a major factor limiting the usefulness of ethanol as a fuel. Due to the dilute nature of the fermentation product stream and the presence of the ethanol-water azeotrope, the separation processes currently used to recover anhydrous ethanol are particularly inefficient. In fact, the ethanol separation processes account for a large fraction of the total process energy demand. In the conventional ethanol separation process, ethanol is recovered using several distillation steps combined with a dehydration process. In this dissertation, a new hybrid pervaporation-distillation system, named Membrane Dephlegmation, was proposed and investigated for use in ethanol recovery. In this process, countercurrent vapour-liquid contacting is carried out on the surface of a pervaporation membrane, leading to a combination of distillation and pervaporation effects. It was intended that this new process would lead to improved economics and energy efficiency for the entire ethanol production process. The Membrane Dephlegmation process was investigated using both numerical and experimental techniques. Multiphase Computational Fluid Dynamics (CFD) was used to study vapour-liquid contacting behaviour in narrow channels and to estimate heat and mass transfer rates. Results from the CFD studies were incorporated into a simplified design model and the Membrane Dephlegmation process was studied numerically. The results indicated that the Membrane Dephlegmation process was more efficient than simple distillation and that the ethanol-water azeotrope could be broken. Subsequently, a pilot-scale experimental system was constructed using commercially available, hydrophilic NaA zeolite membranes. Results obtained from the experimental system confirmed the accuracy of the simulations.

Worldwide demand for energy is increasing rapidly, partly driven by dramatic economic growth in developing countries. This growth has sparked concerns over the finite availability of fossil fuels and the impact of their combustion on climate change. Consequently, many recent research efforts have been devoted to the development of renewable fuels and sustainable energy systems. Interest in liquid biofuels, such as ethanol, has been particularly high because these fuels fit into the conventional infrastructure for the transportation sector. Ethanol is a renewable fuel produced through the anaerobic fermentation of sugars obtained from biomass. However, the relatively high energy demand of its production process is a major factor limiting the usefulness of ethanol as a fuel. Due to the dilute nature of the fermentation product stream and the presence of the ethanol-water azeotrope, the separation processes currently used to recover anhydrous ethanol are particularly inefficient. In fact, the ethanol separation processes account for a large fraction of the total process energy demand. In the conventional ethanol separation process, ethanol is recovered using several distillation steps combined with a dehydration process. In this dissertation, a new hybrid pervaporation-distillation system, named Membrane Dephlegmation, was proposed and investigated for use in ethanol recovery. In this process, countercurrent vapour-liquid contacting is carried out on the surface of a pervaporation membrane, leading to a combination of distillation and pervaporation effects. It was intended that this new process would lead to improved economics and energy efficiency for the entire ethanol production process. The Membrane Dephlegmation process was investigated using both numerical and experimental techniques. Multiphase Computational Fluid Dynamics (CFD) was used to study vapour-liquid contacting behaviour in narrow channels and to estimate heat and mass transfer rates. Results from the CFD studies were incorporated into a simplified design model and the Membrane Dephlegmation process was studied numerically. The results indicated that the Membrane Dephlegmation process was more efficient than simple distillation and that the ethanol-water azeotrope could be broken. Subsequently, a pilot-scale experimental system was constructed using commercially available, hydrophilic NaA zeolite membranes. Results obtained from the experimental system confirmed the accuracy of the simulations.

An adaptive remeshing algorithm has been developed for multiphase flow simulations using the moving-mesh interface tracking (MMIT) technique. The edge-swapping algorithm uses the Delaunay criterion (in 2D) and a dynamic programming technique (in 3D) to maximize the quality of mesh primitives surrounding edges in the mesh, and performs local remeshing to minimize interpolation errors. Edge bisection and contraction operations are also performed to adjust the mesh resolution around important features like fluid-interfaces, driven by a local length scale estimation algorithm that is efficient and easily parallelized. Flow-field interpolation after reconnection is achieved using a conservative, second-order accurate remapping scheme that can be extended to arbitrary mesh pairs. To minimize the number of mesh reconnection operations, vertices in the mesh are also moved in a manner that optimizes the quality of cells at every time step, using a spring-analogy based Laplacian smoother for surface meshes, and an optimization-based smoothing approach for interior points. To facilitate the simulation of large-scale problems, all smoothing and reconnection algorithms in this work have been parallelized for shared- and distributed-memory paradigms. This approach allows meshes to undergo very large deformations which are characteristic of multiphase flows, and the method is versatile enough to extend its applicability to a broad range of problems including error-driven mesh refinement, reciprocating machinery, fluid-structure interation, and wing flapping simulations.

La distillation est un procédé industriel de séparation de phases qui fait typiquement intervenir un écoulement diphasique caractérisé par un film liquide laminaire ou faiblement turbulent s'écoulant par gravité et cisaillé à contre-courant par un courant gazeux turbulent. Afin de comprendre la dynamique de ce genre d'écoulements, nous avons développé un modèle numérique de simulation d'écoulements diphasiques prenant en compte la présence éventuelle des structures turbulentes. Ce modèle s'appuie sur un couplage entre les méthodologies Volume of Fluid sans étape de reconstruction pour le suivi d'interface et la simulation des grandes échelles pour le traitement de la turbulence. Les contraintes de sous-maille sont évaluées par une approche dynamique mixte, ce qui permet au modèle de s'adapter aux caractéristiques locales de la turbulence et de fonctionner même dans des zones laminaires. Le modèle développé est ensuite testé en simulant différentes configuration d'écoulements de films liquides cisaillés ou non par un courant gazeux. / Distillation is an industrial process of phase separation which involves a two-phase flow characterized by a laminar or weakly turbulent gravity- riven liquid film sheared by a countercurrent turbulent gas stream. To understand the dynamics of such flows, we developed a numerical technique aimed at computing incompressible turbulent two-phase flows. A large eddy simulation (LES) approach based on a dynamic mixed model is used to compute turbulence while the two-phase nature of the flow is described through a Volume of Fluid (VOF) approach with no interface reconstruction step. The use of a dynamic mixed approach for modelling the subgrid stresses allows the developed model to self-adapt to local characteristics of turbulence, so that it also works in laminar flows. The whole methodology is then applied to the computation of different configurations of liquid films sheared or not by a gas stream.