Thesis (PhD)--Stellenbosch University, 2012 / ENGLISH ABSTRACT: This study presents the development and extension of free-surface modelling techniques for the purpose of modelling two-fluid systems accurately and efficiently. The volume-of-fluid (VOF) method is extended in two ways: Firstly, it is extended to account for variations in the gas density through a weakly compressible formulation. Secondly, a compressive free-surface interface capturing formulation that preserves the integrity of the interface shape is detailed. These formulations were implemented and evaluated using the Elemental software. Under certain flow conditions liquid-gas systems may be subjected to large variations in pressure, making it necessary to account for changes in gas density. Modelling this effectively has received relatively little attention in the context of free-surface modelling and remains a challenge to date. To account for the variations in gas density a weakly compressible free-surface modelling formulation is developed for low Mach number flows. The latter is formally substantiated via a non-dimensional analysis. It is proposed that the new formulation advances on existing free-surface modelling formulations by effecting an accurate representation of the dominant physics in an efficient and effective manner. The proposed weakly compressible formulation is discretised using a vertexcentred edge-base finite volume approach, which provides a computationally efficient method of data structuring and memory usage. Furthermore, this implementation is applicable to unstructured spatial discretisation and parallel computing. In this light, the discretisation is formulated to ensure a stable, oscillatory free solution. Furthermore, the governing equations are solved in a fully coupled manner using a combination of dual time-stepping and a Generalised Minimum Residual solver with Lower-Upper Symmetric Gauss-Seidel preconditioning, ensuring a fast and efficient solution. The newly developed VOF interface capturing formulation is proposed to advance on the accuracy and efficiency with which the evolution of the free-surface interface is modelled. This is achieved through a novel combination of a blended higher-resolution scheme, used to interpolate the volume fraction face value, and the addition of an artificial compressive term to the VOF equation. Furthermore, the computational efficiency of the higher-resolution scheme is improved through the reformulation of the normalised variable approach and the implementation of a new higher-resolution blending function. For the purpose of evaluating the newly developed methods, several test cases are considered. It is demonstrated that the new surface capturing formulation offers a significant improvement over existing schemes, particularly at large CFL numbers. It is shown that the proposed method achieves a sharper, better defined interface for a wide range of flow conditions. With the validation of the weakly compressible formulation, it is found that the numerical results correlate well with analytical solutions. Furthermore, the importance of accounting for gas compressibility is demonstrated via an application study. The weakly compressible formulation is also found to result in negligible additional computational cost while resulting in improved convergence rates. / AFRIKAANSE OPSOMMING: Hierdie studie behels die ontwikkeling van numeriese tegnieke met die doel om twee-vloeistof vloei akkuraat en numeries effektief te modelleer. Die volume-vanvloeistof metode word op twee maniere uitgebrei: Eerstens word variasie van die gasdigtheid in ag geneem deur gebruik te maak van ’n swak samedrukbare model. Tweedens saam is ’n hoë-resolusie metode geformuleer vir die voorstelling van die vloeistof-oppervlak. Hierdie uitbreidings is met die behulp van die Elemental programmatuur geïmplementeer en met behulp van die programmatuur geëvalueer. Onder sekere toestande ervaar vloeistof-gas mengsels groot veranderinge in druk. Dit vereis dat die variasie in gasdigtheid in berekening gebring moet word. Die modellering hiervan het egter tot dusver relatief min aandag ontvang. Om hierdie rede word ’n swak samedrukbare model vir lae Mach-getalle voorgestel om die variasie in gasdigtheid in te reken. Die formulering volg uit ’n nie-dimensionele analise. Daar word geargumenteer dat die nuwe formulering die fisika meer akkuraat verteenwoordig. ’n Gesentraliseerde hoekpunt, rant gebaseerde eindige volume metode word gevolg om die differensiaalvergelykings numeries te diskretiseer. Dit bied ’n doeltreffende manier vir datastrukturering en geheuebenutting. Hierdie benadering is verder geskik vir toepassing op ongestruktureerde roosters en parallelverwerking. Die diskretisering is geformuleer om ’n stabiele oplossing sonder numeriese ossillasies te verseker. Die vloeivergelykings word op ’n gekoppelde wyse opgelos deur gebruik te maak van ’n kombinasie van ’n pseudo tyd-stap metode en ’n Veralgemene Minimum Residu berekeningsmetode met Onder-Bo Simmetriese Gauss- Seidel voorafbewerking. Die nuut ontwikkelde skema vir die modellering van die vloeistof-oppervlak is veronderstel om ’n meer akkurate voorstelling te bied en meer doeltreffend te wees vir numeriese berekeninge. Dit word bereik deur die nuwe kombinasie van ’n hoë-resolusie skema, wat gebruik word om die volumefraksie te interpoleer, met die samevoeging van ’n kunsmatige term in die volume-van-vloeistof vergelyking om die resolusie te verfyn. Verder is die doeltreffendheid van die skema verbeter deur die genormaliseerde veranderlikes benadering te herformuleer en deur die ontwikkeling van ’n nuwe hoë-resolusie vermengingsfunksie. Verskeie toetsgevalle is uitgevoer met die doel om die nuwe modelle te evalueer. Daar word aangetoon dat die nuwe skema vir die modellering van die vloeistofoppervlak ’n meetbare verbetering bied, veral by hoër Courant-Friedrichs-Lewy getalle. Die nuwe formulering bied dus hoër akkuraatheid vir ’n wye verskeidenheid van toestande. Vir die swak samedrukbare formulering is daar ’n goeie korrelasie tussen die numeriese resultate en die analitiese oplossing. In ’n toegepassingsgeval word die noodsaaklikheid om die samedrukbaarheid van die gas in ag te neem gedemonstreer. Die addisionele berekening-kostes van die nuwe formulering is weglaatbaar en in sommige gevalle verhoog die tempo waarteen die oplossing konvergeer

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

Ce travail porte sur le développement d'un module microphysique de nuages liquides et glacés dans un modèle de chimie multiphase (Leriche et al., 2001). Le modèle complet a été appliqué afin d'évaluer le rôle de ces nuages sur les teneurs en polluants atmosphériques. Les nuages modulent le transport horizontal et vertical des polluants ainsi que leur lessivage via les précipitations, ils sont aussi le siège de réactions chimiques complexes. En paramétrisant la répartition des polluants entre les différentes phases du nuage via des processus comme le givrage, la croissance des cristaux par dépôt de vapeur, la fonte et la collection des hydrométéores, il est montré l'importance de la phase glace et de la morphologie des cristaux dans l'évolution chimique du nuage. Des scénarios de formation nuageuse sont définis à partir de masses d'air continentale et / ou marine, pour voir l'influence de la capacité du nuage à précipiter sur la composition chimique des hydrométéores. Des tests sur la rétention et l'enfouissement pilotant les échanges avec la phase glacée lors du givrage et de la croissance par dépôt de vapeur respectivement ont été menés pour conclure au rôle majeur joué par la glace dans le bilan des espèces traces

The purpose of the research was to develop a quantitative method which could be used to obtain a clearer understanding of the time-dependent fluid filteration and load-deformation behavior of soft, porous, fluid filled materials (e.g. biological tissues, soil). The focus of the study was on the development of a finite strain theory for multiphasic media and associated computer models capable of predicting the mechanical stresses and the fluid transport processes in porous structures (e.g. across the large blood vessels walls). The finite element (FE) formulation of the nonlinear governing equations of motion was the method of solution for a poroelastic (PE) media. This theory and the FE formulations included the anisotropic, nonlinear material; geometric nonlinearity; compressibility and incompressibility conditions; static and dynamic analysis; and the effect of chemical potential difference across the boundaries (known as swelling effect in biological tissues). The theory takes into account the presence and motion of free water within the biological tissue as the structure undergoes finite straining. Since it is well known that biological tissues are capable of undergoing large deformations, the linear theories are unsatisfactory in describing the mechanical response of these tissues. However, some linear analyses are done in this work to help understand the more involved nonlinear behavior. The PE view allows a quantitative prediction of the mechanical response and specifically the pore pressure fluid flow which may be related to the transport of the macromolecules and other solutes in the biological tissues. A special mechanical analysis was performed on a representative arterial walls in order to investigate the effects of nonlinearity on the fluid flow across the walls. Based on a finite strain poroelastic theory developed in this work; axisymmetric, plane strain FE models were developed to study the quasi-static behavior of large arteries. The accuracy of the FE models was verified by comparison with analytical solutions wherever is possible. These numerical models were used to evaluate variables and parameters, that are difficult or may be impossible to measure experimentally. For instance, pore pressure distribution within the tissue, relative fluid flow; deformation of the wall; and stress distribution across the wall were obtained using the poroelastic FE models. The effect of hypertension on the mechanical response of the arterial wall was studied using the nonlinear finite element models. This study demonstrated that the finite element models are powerful tools for the study of the mechanics of complicated structures such as biological tissue. It is also shown that the nonlinear multiphasic theory, developed in this thesis, is valid for describing the mechanical response of biological tissue structures under mechanical loadings.

The focus of this thesis is the study of turbulent solid-liquid stirred suspensions, which are involved in many common unit operations in the chemical, pharmaceutical and food industries. The studies of two-phase flows present a big challenge to researchers due to the complexity of experiments; hence there is a lack of quantitative solid and liquid hydrodynamic measurements. Therefore, an investigation of turbulence modulation by dispersed particles on the surrounding fluid in stirred vessels has been carried out, via two-phase fluorescent Particle Image Velocimetry (FPIV) and micromixing experiments. The main property of interest has been the local dissipation rate, as well as root-mean-square (rms) velocities and turbulent kinetic energy (TKE) of the fluid. Initially a single-phase PIV study was conducted to investigate the flow field generated by a sawtooth (EkatoMizer) impeller. The purpose of this study was to gain insight into various PIV techniques before moving on to more complex two-phase flows. Subsequently stereo-, highspeed and angle-resolved measurements were obtained. The EkatoMizer formed a good case study as information regarding its hydrodynamics is not readily available in literature, hence knowledge has been extended in this area. An analysis of the mean flow field elucidated the general structure of fluid drawn into the impeller region axially and discharged radially; the latter characterised the impeller stream. The radial rms velocity was considered to represent best the system turbulence, even though the tangential rms velocity was greater close to the blade; however the radial component was more prevalent in the discharge stream. Due to differences in rms velocities, TKE estimates obtained from two and three velocity components deviated, being greater in the latter case. Integral (1-D and 2-D) length scales were overestimated by the quantity W / 2 in the impeller region. Ratios of longitudinal-to-lateral length scales also indicated flow anisotropy (as they deviated from 2:1). The anisotropy tensor showed that the flow was anisotropic close to the blade, and returned to isotropy further away from the impeller. Instantaneous vector plots revealed vortices in the discharge stream, but these were not associated with flow periodicity. Alternatively, the vortex structures were interpreted as low frequency phenomena between 0-200 Hz; macro-instabilities were found to have a high probability of occurrence in the discharge stream. Dissipation is the turbulent property of most interest as it directly influences micromixing processes, and its calculation is also the most difficult to achieve. Its direct determination from definition requires highly resolved data. Alternative methods have been proposed in the literature, namely dimensional analysis, large eddy simulation (LES) analogy and deduction from the TKE balance. All methods were employed using 2-D and 3-D approximations from stereo-PIV data. The LES analogy was deemed to provide the best estimate, since it accounts for three-dimensionality of the flow and models turbulence at the smallest scales using a subgrid scale model. (Continues...).

Understanding how the water produced in an operating polymer electrolyte membrane fuel cell (PEMFC) is transported in cathode catalyst layer (CCL) is crucial to improving performance and efficiency. In this thesis, a multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is employed to simulate the high density ratio, multiphase water transport in in the CCL. The three-dimensional structure of the catalyst layer is reconstructed based on experimental data acquired with a dual beam scanning electron microscope/focused ion beam system and a stochastic method using lower order statistical functions (e.g. porosity and two point correlation functions). Simulations of the water transport dynamics are performed to examine the effect of a range of physical parameters: wettability, viscosity ratio, pressure gradient, and surface tension. The water penetration patterns in the catalyst layers reveal a complex fingering process and transition of the water transport pattern from a capillary fingering regime to a stable displacement regime is observed when the wettability potential of the catalyst layer changes. The second part of the analysis focuses on quantifying the impact of liquid water distribution and accumulation in the catalyst layer on effective transport properties by coupling two numerical methods: the two-phase LBM is used to determine equilibrium liquid water distribution, and then a finite volume-based pore-scale model (FV-PSM) is used to compute transport of reactant and charged species in the CL accounting for the impact of liquid water saturation .The simulated results elucidate and quantify the significant impact of liquid water on the effective oxygen and water vapor diffusivity, and thermal conductivity in CLs. / Graduate

Une modélisation récente, qualifiée de multiphasique, permettant de décrire le comportement des ouvrages en sols renforcés par inclusions a été développée et intégrée dans un code de calcul par éléments finis. Le champ d'application de cette approche a été étendu pour rendre compte du comportement macroscopique de matériaux à fibres tels que le plâtre, le béton de fibres, les ouvrages en sol renforcés par des fibres et les tissus osseux qui présentent une microstructure constituée d'une matrice et d'une distribution de fibres plus ou moins longues orientées dans toutes les directions de l'espace. Cette approche est d'abord mise en œuvre pour déterminer le comportement élastique du composite à fibre, les résultats obtenus sont comparés à ceux fournis par les schémas d'estimation dilué et de Mori Tanaka, basés sur la solution d'Eshelby, la suite de ce travail est consacrée au développement du modèle dans le cadre d'un comportement anélastique des constituants. Des solutions analytiques ont été développées permettant de retrouver le comportement macroscopique des matériaux à fibres sous certaines sollicitations simples dans le cadre d'un comportement élasto-plastique ou élastique-fragile des différents constituants. Le modèle est par la suite mis en œuvre numériquement dans le cadre de la méthode des éléments finis permettant d'accéder à la réponse de structures en matériaux à fibres / A multiphase model has been recently developed and integrated into a finite element based code for the analysis and design of soil structures reinforced with linear inclusions. This approach is extended to account for the macroscopic behavior of fiber reinforced materials such as plaster, concrete fiber, soil reinforced by short fibers and bone tissues, which are constituted of a matrix and a distribution of continuously oriented fibers. The proposed model is performed to evaluate the elastic macroscopic stiffness of the composite material, the obtained results are compared to those deriving from the dilute and Mori-Tanaka estimations. The model is then extended to take into account a nonelastic behavior of the constituents. Starting from the derivation of some analytical solutions to boundary value problems involving fiber reinforced materials in the context of elasto-plastic and brittle behavior of the matrix and fibers, a f.e.m.-based code is developed and applied to simulating the behavior of some typical structures

Ce travail s'est intéressé à l?étude de la formation de gouttelettes en microsystèmes à l'aide d'outils de visualisation tels que des caméras rapides et la microvélocimétrie par image de particules (µPIV). La taille des gouttelettes principales et satellites formées en jonction flow-focusing est déterminée pour des fluides newtoniens et non-newtoniens. Les mêmes paramètres critiques sont mis en évidence pour ces jonctions flow-focusing et des jonctions T, illustrant l'influence du confinement sur la formation des gouttelettes. L'évolution de la taille des gouttelettes satellites dépend quant à elle d'un nombre capillaire critique. Les champs de vitesses ont été mesurés dans les gouttelettes en formation ainsi qu'autour de ces gouttelettes, de même que les trois étapes de la dynamique de rupture du cou des gouttelettes. Les liens entre cette dynamique, les champs de vitesse et la taille des gouttelettes ont été déterminés. L'émulsification a également été étudiée dans deux micromélangeurs industriels : le Caterpillar et le StarLaminator, avec des formulations proches de celles cométiques. Les performances énergétiques sont particulièrement prometteuses pour le Caterpillar / This work is focused on droplet formation in microsystems using visualization tools such as high-speed cameras and microparticle image velocimetry (µPIV). The size of main and satellite droplets formed in flow-focusing junctions was determined for both Newtonian and non-Newtonian fluids. The same critical parameters were highlighted for both flow-focusing and T-junctions, illustrating walls? influence on the droplet formation. The size evolution of satellite droplets depends on a critical capillary number. The flow fields were measured inside and outside the forming droplets, as well as the three steps dynamics for droplet neck rupture. This dynamics was straightforwardly linked to the flow fields and the droplet size. Emulsification was also investigated in two industrial micromixers, Caterpillar and StarLaminator respectively, with formulations close to cosmetic ones. The energetic performances of the Caterpillar are particularly promising

Numerical simulations of coal gasification process inside a generic 2-stage entrainedflow gasifier are carried out using the commercial CFD solver ANSYS/FLUENT. The 3-D Navier-Stokes equations and eight species transport equations are solved with three heterogeneous global reactions, three homogeneous reactions, and one thermal cracking equation of volatiles. Finite rates are used for the heterogeneous solid-gas reactions. Both finite rate and eddy-breakup combustion models are calculated for each homogeneous gas-gas reaction, and the smaller of the two rates is used. Lagrangian-Eulerian method is employed. The Eulerian method calculates the continuous phase while the Lagrangian method tracks each coal particle. Fundamental study is carried out to investigate effects of five turbulence models (standard k-ε, k-ω, RSM, k-ω SST, and k-ε RNG) and four devolatilization models (Kobayashi, single rate, constant rate, and CPD) on gasification simulation. A study is also conducted to investigate the effects of different operation parameters on gasification process including coal mixture (dry vs. slurry), oxidant (oxygen-blown vs. air-blown), and different coal distributions between two stages. Finite-rate model and instantaneous gasification model are compared. It is revealed that the instantaneous gasification approach can provide an overall evaluation of relative changes of gasifier performance in terms of temperature, heating value, and gasification efficiency corresponding to parametric variations, but not adequately capture the local gasification process predicted by the finite rate model in most part of the gasifier. Simulations are performed to help with design modifications of a small industrial demonstration entrained-flow gasifier. It is discovered that the benefit of opening the slag tap on the quench-type gasifier wider by allowing slag to move successfully without clogging is compromised by increased heat losses, reduced gasification performance, downgraded syngas heating value, and increased unburned volatiles. The investigation of heat transfer on fuel injectors shows that blunt tip fuel injector is less likely to fail compared to conical tip fuel injector because the maximum high temperature on the injector is scattered. Two concentric fuel/oxidant injections provide better fuel-oxidant mixing and higher syngas heating value than four separate fuel and oxidant injections.

In 1999, California Air Resources Board (CARB) implemented a regulation that required all gasoline cars sold in California be fitted with an Onboard Refueling Vapor Recovery System (ORVR). The ORVR system is designed to prevent Volatile Organic Compounds (VOCs) from escaping into the atmosphere during refuelling by storing the gas vapours in a carbon canister. Due to the complex nature of the fuel system, making design changes could have large implications on the ORVR performance of the vehicle. It is therefore desirable to develop a CFD model that can predict the effects of design changes, thereby reducing the need to perform physical tests on each design iteration. This master thesis project was performed at the Fuel Systems department at Volvo Cars in order to help reduce project lead times and product development costs by incorporating CFD as a part of the fuel system development cycle. The CFD results obtained were validated through experimental tests that were also performed as part of this project. In this master thesis project, a CFD model was developed to simulate the refuelling of gasoline for a California specification Volvo XC90 with an OPW-11B pump pistol. The model was set up in STAR-CCM+ using the Eulerian Volume of Fluid model for multiphase flow, the RANS realizable k-epsilon turbulence model and the two layer all y+ wall treatment. The effects of the carbon canister were modelled as a porous baffle interface in the simulations where viscous and inertial resistances of the porous media were adjusted to obtain a desired pressure drop across the canister. This method proved to be a suitable simplification for this study. The effects of evaporation as well as a chemical adsorption model for the carbon canister have been excluded from the project due to time limitations. It was found that the CFD simulations were in good agreement with the experimental results, especially with respect to capturing the overall behaviour of the fuel system during refuelling. It was found that resolving the flow spatially (and temporally) in the filler pipe was a crucial part in ensuring solver stability. A pressure difference between experiment and simulation was also observed as a consequence of excluding evaporation from the CFD model. After the CFD model had been verified and validated, changes to different parts of the fuel system were investigated to observe their effects on ORVR performance. These included changing the recirculation line diameter, changing the carbon canister properties and changing the angle of how the pump pistol was inserted into the capless unit. It was found that the recirculation line diameter is a very sensitive design parameter and increasing the diameter would result in fuel vapour leaking back out into the atmosphere. Similarly, increasing the back pressure by swapping to a different carbon canister would result in the leakage of fuel vapour. On the other hand, insignificant changes in system behaviour were observed when the fuel pistol angle was changed.