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

The negative impact of gas turbine emissions on the environment and human health is a growing concern. Recent studies suggest injecting water into the combustion process effectively reduces emissions and increases power output. However, this approach presents new challenges that need to be thoroughly investigated. Siemens Energy (SE) has recently conducted a study on water injection and its effects on gaseous combustion mixtures but encountere challenges the simulation results when adding water. Therefore, the primary objective of this thesis is to evaluate the methodologies available in Star CCM+ for modeling water injection in a simplified combustor model (SCM) using both liquid (diesel) and gas (methane) fuels. In addition, the behavior of the flame, temperature field inside the combustor, and burner outlet temperature, are investigated.The study has compared physical phenomena such as, the flame shape, velocity, and vorticity field of SCMs with the complete combustor model of the SGT-800 gas turbine for gas fuel. Additionally, the thesis has examined the capability of STAR CCM+ for predicting flame temperature at the outlet against in-house calculation data and Cantera software for parametric cases. The methodology involves a parametric study using the Realizable k-ε TwoLayer turbulence model for steady-state RANS simulations. Combustion is modeled using the FGM method, while Lagrangian multiphase approach is used for liquid injection.The employed FGM combustion model, Lagrangian multiphase model, and RANS simulations yielded realistic results. In addition, the convergence of gas fuel cases was smoother compared to liquid fuel cases, which involved multiphase modelling and evaporation, makes it more complex. The physical phenomena were captured by CFD simulations for the SCM. Flame shape, velocity and vorticity field have good agreement with the theory in the field of gas turbine combustion and other literature sources. Disagreements between CFD and in-house calculations were observed, with the greatest differences being 24 ℃ for premixed methane (at WFR (Water Fuel Ratio) of 0) and 28 ℃ for non-premixed diesel (at WFR of 1). On the other hand, Cantera results for Vapor and for methane cases with water addition were in limit of 10 ℃ with CFD results for WFR between 0-0.5. Nevertheless, achieving a simulation accuracy within a 10 ℃ limit proved challenging due to limitations and potential sources of error in the in-house calculation sheet, combustion modelling, RANS simulations, and reaction mechanism.