La turbine Pelton est une turbine hydraulique dont le fonctionnement se caractérise par l’interaction d’un jet d’eau avec les augets d’une roue. Cette étude a pour but de comprendre les phénomènes influençant le jet et son interaction avec les augets. Pour cela deux actions différentes ont été menées. Une première a visé à caractériser expérimentalement la fragmentation d’un jet de turbine Pelton. La seconde s’est attachée à développer une méthode numérique pouvant mener`à la simulation précise de jets réels de turbines Pelton. La partie expérimentale a permis de déterminer le mode de fragmentation de ces jets (atomisation turbulente), mais aussi l’influence de la rugosité des parois de l’injecteur sur les performances de la turbine. La participation de ce travail à un projet expérimental a permis de montrer l’influence de l’écoulement en sortie d’injecteur sur la fragmentation du jet. Les phénomènes physiques influençant principalement l’évolution du jet ont ainsi été déterminés. La partie numérique a eu pour but de mettre en place une méthode permettant de simuler l’évolution d’un jet de turbine Pelton (fragmentation) et son interaction avec un auget. Etant donnés les progrès de la méthode SPH-ALE pour la simulation d’impact de jets pour les turbines Pelton, il a été décidé d’adapter cette méthode pour les simulations visées. Ainsi une étude du choix de la vitesse des interfaces de problème de Riemann a permis de réaliser un modèle multiphase stable pour les forts rapports de densité (eau-air). Cette méthode s’est avérée garantir les propriétés de continuité de vitesse normale et de pression à l’interface entre les fluides. L’ajout des phénomènes de tension de surface s’est fait par l’adaptation du modèle CSF (Continuum Surface Force) et le développement d’un second modèle nommé Laplace Law Pressure Correction (LLPC).L’intégration du saut de pression dans le solveur de Riemann a nécessité une étude précise du calcul de la courbure et a permis d’améliorer la simulation de loi de Laplace. La méthode numérique a été ensuite validée sur les cas académiques d’onde gravitaire, de rupture de barrage et d’oscillation de goutte. Les ressources en mémoire et le temps de calcul associé à cette méthode ont nécessité la parallélisation du code de calcul. Le caractère lagrangien de la méthode a très largement influencé la méthode de découpe de domaine pour permettre une bonne répartition de la charge de calcul entre les différents processeurs. En conclusion les phénomènes physiques influençant la fragmentation de jets issus d’injecteurs de turbine Pelton sont désormais mieux connus et ils ont pu être introduits dans la méthode numérique. Les prochains développements porteront sur la simulation de jets dont la condition d’entrée s’attachera à être représentative des caractéristiques d’un écoulement en sortie d’un injecteur de turbine Pelton. / A Pelton turbine is characterized by a water jet which is impacting rotating buckets. The main goal of this study is to understand the phenomena which are impacting the jet and its interaction with the bucket. This study was considering two main works. One is considering experiments which allow determining the jet fragmentation. The second part considers development of a numerical code able to reproduce phenomena linked to Pelton jet fragmentation. The experimental part succeeds to associate Pelton jet behavior with mode of jet fragmentation (turbulent dispersion) and shows the impact of hydraulic roughness on Pelton turbine performances. The access to experimental results from a project involving this PhD work, demonstrates the role of the inlet velocity/turbulence profile on the jet fragmentation. The numerical part used the SPH-ALE (Smoothed Particle Hydrodynamics - Arbitrary Lagrange Euler) method to implement physical models linked with jet fragmentation. This choice was done because of its ability to predict pressure fields resulting of the interaction of a water jet and a rotating bucket. A multiphase model was developed based on a modification of the velocity of the interface of Riemann problem. This model does not diffuse the interface and recovers continuity of normal velocity and pressure at the interface between both fluids. Surface tension effect was implemented through an adaptation of the CSF (Continuum Surface Force) model and through amodel called LLPC for Laplace Law Pressure Correction. A study of the computational methods to determine the interface curvature was performed for the integration of the pressure jump in the Riemann solver. Validation was done on academicals test cases as gravity waves, dam breakor droplet oscillations. The numerical code was parallelized to perform large numerical simulations.To conclude, the numerical code integrates physical phenomena which were shown as important in the experiments. The developments will try to perform jet simulation with inlet condition which will be representative of flow conditions at the outlet of a Pelon turbine injector.

Die chemische Zusammensetzung und die physikalischen Eigenschaften von troposphärischen Gasen, Partikeln und Wolken hängen aufgrund zahlreicher Prozesse stark voneinander ab. Insbesondere chemische Multiphasenprozesse in Wolken können die physiko-chemischen Eigenschaften der Luft und troposphärischer Partikel klein- und großräumig verändern. Diese chemische Prozessierung des troposphärischen Aerosols innerhalb von Wolken beeinflusst die chemischen Umwandlungen in der Atmosphäre, die Bildung von Wolken, deren Ausdehnung und Lebensdauer, sowie die Transmissivität von einfallender und ausgehender Strahlung durch die Atmosphäre. Damit sind wolken-chemische Prozesse relevant für das Klima auf der Erde und für verschiedene Umweltaspekte. Daher ist ein umfassendes Verständnis dieser Prozesse wichtig. Die explizite Behandlung chemischer Reaktionen in der Flüssigphase stellt allerdings eine Herausforderung für atmosphärische Computermodelle dar. Detaillierte Beschreibungen der Flüssigphasenchemie werden deshalb häufig nur für Boxmodelle verwendet. Regionale Chemie-Transport-Modelle und Klimamodelle berücksichtigen diese Prozesse meist nur mit vereinfachten chemischen Mechanismen oder Parametrisierungen. Die vorliegende Arbeit hat zum Ziel, den Einfluss der chemischer Mehrphasenprozesse innerhalb von Wolken auf den Verbleib relevanter Spurengase und Partikelbestandteile mit Hilfe des state‑of‑the‑art 3D-Chemie-Transport-Modells COSMO-MUSCAT zu untersuchen. Zu diesem Zweck wurde das Model um eine detaillierte Beschreibung chemischer Prozesse in der Flüssigphase erweitert. Zusätzlich wurde das bestehende Depositionsschema verbessert, um auch die Deposition von Nebeltropfen zu berücksichtigen. Die durchgeführten Modellerweiterungen ermöglichen eine bessere Beschreibung des troposphärischen Multiphasensystems. Das erweiterte Modellsystem wurde sowohl für künstliche 2D-Bergüberströmungsszenarien als auch für reale 3D-Simulationen angewendet. Mittels Prozess- und Sensitivitätsstudien wurde der Einfluss (i) des Detailgrades der verwendeten Mechanismen zur Beschreibung der Flüssigphasenchemie, (ii) der Größenauflösung des Tropfenspektrums und (iii) der Tropfenanzahl auf die chemischen Modellergebnisse untersucht. Die Studien belegen, dass die Auswirkungen der Wolkenchemie aufgrund ihres signifikanten Einflusses auf die Oxidationskapazität in der Gas- und Flüssigphase, die Bildung von organischer und anorganischer Partikelmasse sowie die Azidität der Wolkentropfen und Partikel in regionalen Chemie-Transport-Modellen berücksichtigt werden sollten. Im Vergleich zu einer vereinfachten Beschreibung der Wolkenchemie führt die Verwendung des detaillierten chemischen Flüssigphasenmechanismus C3.0RED zu verringerten Konzentrationen wichtiger Oxidantien in der Gasphase, einer höheren Nitratmasse in der Nacht, geringeren nächtlichen pH-Werten und einer veränderten Sulfatbildung. Darüber hinaus ermöglicht eine detaillierte Wolkenchemie erst Untersuchungen zur Bildung sekundärer organischer Partikelmasse in der Flüssigphase. Die größenaufgelöste Behandlung der Flüssigphasenchemie hatte nur geringen Einfluss auf die chemischen Modellergebnisse. Schließlich wurde das erweiterte Modell für Fallstudien zur Feldmesskampagne HCCT‑2010 genutzt. Zum ersten Mal wurde dabei ein chemischer Mechanismus mit der Komplexität von C3.0RED verwendet. Die räumlichen Effekte realer Wolken z. B. auf troposphärische Oxidantien oder die Bildung anorganischer Masse wurden untersucht. Der Vergleich der Modellergebnisse mit verfügbaren Messungen hat viele Übereinstimmungen aber auch interessante Unterschiede aufgezeigt, die weiter untersucht werden müssen. / In the troposphere, a vast number of interactions between gases, particles, and clouds affect their physico-chemical properties, which, therefore, highly depend on each other. Particularly, multiphase chemical processes within clouds can alter the physico-chemical properties of the gas and the particle phase from the local to the global scale. This cloud processing of the tropospheric aerosol may, therefore, affect chemical conversions in the atmosphere, the formation, extent, and lifetime of clouds, as well as the interaction of particles and clouds with incoming and outgoing radiation. Considering the relevance of these processes for Earth\''s climate and many environmental issues, a detailed understanding of the chemical processes within clouds is important. However, the treatment of aqueous phase chemical reactions in numerical models in a comprehensive and explicit manner is challenging. Therefore, detailed descriptions of aqueous chemistry are only available in box models, whereas regional chemistry transport and climate models usually treat cloud chemical processes by means of rather simplified chemical mechanisms or parameterizations. The present work aims at characterizing the influence of chemical cloud processing of the tropospheric aerosol on the fate of relevant gaseous and particulate aerosol constituents using the state-of-the-art 3‑D chemistry transport model (CTM) COSMO‑MUSCAT. For this purpose, the model was enhanced by a detailed description of aqueous phase chemical processes. In addition, the deposition schemes were improved in order to account for the deposition of cloud droplets of ground layer clouds and fogs. The conducted model enhancements provide a better insight in the tropospheric multiphase system. The extended model system was applied for an artificial mountain streaming scenario as well as for real 3‑D case studies. Process and sensitivity studies were conducted investigating the influence of (i) the detail of the used aqueous phase chemical representation, (ii) the size-resolution of the cloud droplets, and (iii) the total droplet number on the chemical model output. The studies indicated the requirement to consider chemical cloud effects in regional CTMs because of their key impacts on e.g., oxidation capacity in the gas and aqueous phase, formation of organic and inorganic particulate mass, and droplet acidity. In comparison to rather simplified aqueous phase chemical mechanisms focusing on sulfate formation, the use of the detailed aqueous phase chemistry mechanism C3.0RED leads to decreased gas phase oxidant concentrations, increased nighttime nitrate mass, decreased nighttime pH, and differences in sulfate mass. Moreover, the treatment of detailed aqueous phase chemistry enables the investigation of the formation of aqueous secondary organic aerosol mass. The consideration of size-resolved aqueous phase chemistry shows only slight effects on the chemical model output. Finally, the enhanced model was applied for case studies connected to the field experiment HCCT-2010. For the first time, an aqueous phase mechanism with the complexity of C3.0RED was applied in 3‑D chemistry transport simulations. Interesting spatial effects of real clouds on e.g., tropospheric oxidants and inorganic mass have been studied. The comparison of the model output with available measurements revealed many agreements and also interesting disagreements, which need further investigations.

Dans l’atmosphère, la matière organique est omniprésente et joue un rôle important par son action sur le bilan radiatif de la Terre et par son impact sur la santé publique notamment dans les zones fortement polluées. A ce jour plus de 10000 Composés Organiques Volatils différents ont été identifiés dans l’atmosphère. Leurs propriétés physico-chimiques (solubilité, volatilité, réactivité, …) sont variées et mal documentées. Leur distribution est perturbée par la présence de nuage qui représente un milieu réactif. L’objectif de cette thèse est d’évaluer la contribution des processus physico-chimiques sur la redistribution des COV à partir d'études numériques via le modèle de processus M2C2 (Model of Multiphase Cloud Chemistry). Les résultats sur les processus microphysiques en phase mixte ont montré que la rétention des composés chimiques dans les cristaux de glace qui grossissent principalement par givrage des gouttelettes de nuage, est un processus important dans la redistribution des espèces en phase gazeuse, comme la forme des cristaux (complexe ou sphérique). Par ailleurs, une intensité du givrage plus élevée entraîne un dégazage des composés chimiques dissous dans l’eau liquide nuageuse plus important et réparti sur une gamme de températures plus faibles dans le cas des cristaux complexes. La chimie en phase aqueuse du modèle M2C2 a été confrontée et calibrée avec des mesures effectuées lors d’expériences d’irradiations d’échantillons d’eau synthétique (i.e. de composition chimique connue). Ce travail a mis en évidence la complexité du système HxOy/fer et les incertitudes associées, notamment en présence de matière organique. Ces premières études ont montré la nécessité, dans le cas considéré, de prendre en compte la photolyse du complexe fer/oxalate à un seul ligand Fe(C2O4)+ et d'étudier expérimentalement la formation de complexes fer – acide formique en détail. Cette thèse aborde le développement de la chimie en phase aqueuse dans M2C2 en ajoutant les voies d’oxydation des composés organiques à deux atomes de carbone à partir de données expérimentales et d'analogie mécanistiques. Ce nouveau mécanisme a été testé sur un ensemble de scénarios académiques (urbain, rural et marin). Les résultats montrent, dans le cas d’un scénario urbain, que les COV influent sur l’évolution temporelle du radical hydroxyle en phase aqueuse à travers une modification importante de ses sources et de ses puits ; notamment par la présence de nouveaux complexes organiques avec le fer. Les alcools, transférés en phase aqueuse ne contribuent que très faiblement, par oxydation, aux aldéhydes dissous. Les aldéhydes sont issus principalement de la phase gazeuse. Enfin, les acides carboxyliques en phase aqueuse sont produits par oxydation des aldéhydes à un taux du même ordre de grandeur que celui de leur transfert de masse. / Organic matter is ubiquitous in the atmosphere and plays a key role on both Earth radiative budget and public health particularly in high pollution level areas. Up to now around 10000 different VOCs (Volatil Organic Compounds) were identified. Their physical and chemical properties (solubility, volatility, reactivity …) are highly variables and not fully documented. Their distribution is perturbed by cloud droplet which represents a reactive media. The aim of this thesis is to evaluate the physical and chemical processes contribution on VOCs distribution from numerical studies using the M2C2 (Model of Multiphase Cloud Chemistry) model. A detailed analysis of the microphysical rates and chemical rates linked to retention and burial effects show that for a moderate precipitating mixed-phase-cloud, the effect of the ice phase on gas phase composition is driven by riming of cloud droplets onto graupels, which leads to retention or not of soluble chemical species in the ice phase. Finally, the impact of crystal geometry on the efficiency of collection is studied together with its impact on the riming of cloud droplets on graupels and also on the retention of chemical species in ice phase. Numerical chemical outputs from M2C2 model were compared with experimental data that consisted of a time evolution of the concentrations of the target species. The chemical mechanism in the model describing the "oxidative engine" of the HxOy/iron chemical system was consistent with laboratory measurements. Thus, the degradation of the carboxylic acids evaluated was closely reproduced by the model. However, photolysis of the Fe(C2O4)+ complex needs to be considered in cloud chemistry models for polluted conditions (i.e., acidic pH) to correctly reproduce oxalic acid degradation. We also show that iron and formic acid lead to a stable complex whose photoreactivity has currently not been investigated. This thesis proposes the development of a new cloud chemical mechanism considering oxidative pathways of VOCs with 2-carbon atoms from experimental data and mechanism analogies. This new mechanism is tested using academic scenarios (urban, remote and marine). Results show that VOCs modify the sources and sinks of hydroxyl radical through the formation of new iron organic complexes in the case of urban scenario. In aqueous phase, alcohols concentrations are mainly drive by mass transfer and are not a significant source for aldehydes which are mostly produced in gaseous phase. Carboxylic acids are formed by aldehydes oxidation with a rate as a same order than their mass transfer.

Multiphase flow is the simultaneous flow of two or several phases through a system such as a pipe. This common phenomenon can be found in the petroleum and chemical engineering industrial fields. Transport of sand particles in multiphase production has attracted considerable attention given sand production is a common problem especially to the oil and gas industry. The sand production causes loss of pipe wall thickness which can lead to expensive failures and loss of production time. Build-up of sand in the system can result in blockage and further hamper production. Monitoring of multiphase flow is a process that has been established over several decades. This thesis reports an assessment of the application of Acoustic Emission (AE) technology as an alternative online technique to monitoring of sand particles under multiphase flow conditions in a horizontal pipe. The research was conducted on a purpose built test rig with the purpose of establishing a relation between AE activity and sand concentration under different multiphase flow conditions. The investigation consisted of five experimental tests. The initial experiment was performed to provide a basis for the application of AE technology to detect sand particle impact prior to performing tests in multiphase flow conditions. Further investigations are reported on two phase air-sand, water-sand and air- water-sand three-phase flows in a horizontal pipe for different superficial gas velocities (VSG), superficial liquid velocities (VSL) and sand concentrations (SC). The experimental findings clearly showed a correlation exists between AE energy levels and multiphase flow parameters, such as superficial liquid velocity (VSL), superficial gas velocity (VSG), sand concentration and sand minimum transport condition (MTC).

Gas lift is a means of enhancing oil recovery from hydrocarbon reservoirs. Gas injected at the production riser base reduces the gravity component of the pressure drop and thereby, increases the supply of oil from the reservoir. Also, gas injection at the base of a riser helps to mitigate slugging and thus, improving the performance of the topside facility. In order to improve the efficiency of the gas lifting technique, a good understanding of the characteristics of gas-liquid multiphase flow in vertical pipes is very important. In this study, experiments of gas/liquid (air/water) two-phase flows, liquid/liquid of oil/water two-phase flows and gas/liquid/liquid (air/oil/water) three-phase flows were conducted in a 10.5 m high 52 mm ID vertical riser. These experiments were performed at liquid and gas superficial velocities ranging from 0.25 to 2 m/s and ~0.1 to ~6.30 m/s, respectively. Dielectric oil and tap water were used as test fluids. Instruments such as Coriolis mass flow meter, single beam gamma densitometer and wire-mesh sensor (WMS) were employed for investigating the flow characteristics. For the experiments of gas/liquid (air/water) two-phase flow, flow patterns of Bubbly, slug, churn flow regimes and transition regions were identified under the experimental conditions. Also, for flow pattern identification and void fraction measurements, the capacitance WMS results are consistent with those obtained simultaneously by the gamma densitometer. Generally, the total pressure gradient along the vertical riser has shown a significant decrease as the injected gas superficial velocity increased. In addition, the rate of decrease in total pressure gradient at the lower injected gas superficial velocities was found to be higher than that for higher gas superficial velocities. The frictional pressure gradient was also found to increase as the injected gas superficial velocity increased. For oil-water experiments, mixture density and total pressure gradient across the riser were found to increase with increasing water cut (ranging between 0 - 100%) and/or mixture superficial velocity. Phase slip between the oil and water was calculated and found to be significant at lower throughputs of 0.25 and 0.5 m/s. The phase inversion point always takes place at a point of input water cut of 42% when the experiments started from pure oil to water, and at an input water cut of 45% when the experiment’s route started from water to pure oil. The phase inversion point was accompanied by a peak increase of pressure gradient, particularly at higher oil-water mixture superficial velocities of 1, 1.5 and 2 m/s. The effects of air injection rates on the fluid flow characteristics were studied by emphasizing the total pressure gradient behaviour and identifying the flow pattern by analysing the output signals from gamma and WMS in air/oil/water experiments. Generally, riser base gas injection does not affect the water cut at the phase inversion point. However, a slight shift forward for the identified phase inversion point was found at highest flow rates of injected gas where the flow patterns were indicated as churn to annular flow. In terms of pressure gradient, the gas lifting efficiency (lowering pressure gradient) shows greater improvement after the phase inversion point (higher water cuts) than before and also at the inversion point. Also, it was found that the measured mean void fraction reaches its lowest value at the phase inversion point. These void fraction results were found to be consistent with previously published results.

No description available.

No description available.

The accurate measurement of multiphase flows of oil/water/gas is a critical element of oil exploration and production. Thus, over the last three decades; the development and deployment of in-line multiphase flow metering systems has been a major focus worldwide. Accurate measurement of multiphase flow in the oil and gas industry is difficult because there is a wide range of flow regimes and multiphase meters do not generally perform well under the intermittent slug flow conditions which commonly occur in oil production. This thesis investigates the use of Doppler and cross-correlation ultrasonic measurements made in different high gas void fraction flow, partially separated liquid and gas flows, and homogeneous flow and raw slug flow, to assess the accuracy of measurement in these regimes. This approach has been tested on water/air flows in a 50mm diameter pipe facility. The system employs a partial gas/liquid separation and homogenisation using a T-Y junction configuration. A combination of ultrasonic measurement techniques was used to measure flow velocities and conductivity rings to measure the gas fraction. In the partially separated regime, ultrasonic cross-correlation and conductivity rings are used to measure the liquid flow-rate. In the homogeneous flow, a clamp-on ultrasonic Doppler meter is used to measure the homogeneous velocity and combined with conductivity ring measurements to provide measurement of the liquid and gas flow-rates. The slug flow regime measurements employ the raw Doppler shift data from the ultrasonic Doppler flowmeter, together with the slug flow closure equation and combined with gas fraction obtained by conductivity rings, to determine the liquid and gas flow-rates. Measurements were made with liquid velocities from 1.0m/s to 2.0m/s with gas void fractions up to 60%. Using these techniques the accuracies of the liquid flow-rate measurement in the partially separated, homogeneous and slug regimes were 10%, 10% and 15% respectively. The accuracy of the gas flow-rate in both the homogeneous and raw slug regimes was 10%. The method offers the possibility of further improvement in the accuracy by combining measurement from different regimes.

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