Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: In the present study, two-phase natural circulation flow in a multi-parallel channel system was investigated using experimental and numerical modelling. The investigation was carried out under different power excitations and various system operations (open system, closed system and heat pipe mode). The multichannel system was equipped at the upper end with a condenser enclosed within a steam drum, while the lower portion of each channel was heated to heat the system. For the numerical modelling, transient one-dimensional conservation equations were derived from first principle for both single- and two-phase fluids and used to computer program the system’s discretised simulation model. Temperatures and mass flow rates of the fluid responses as a result of different power excitations and operations were obtained for both the experimental and numerical modelling. It was observed from the results that the fluid experiences a start-up transient before accomplishing steady-state conditions. It was further noted that the transient duration varies with power excitations and system operation modes and hence with the stability of the system. A rise in power proved not to necessarily increase the fluid mass flow rate, but invited oscillations with higher amplitudes, depending on the system’s mode of operation. Type I instability and low-quality steam oscillations were witnessed at low power and open system operation mode (system open to the atmosphere). Type II instabilities and flashing instability were observed to be associated with medium and high-power excitations for the open system mode of operation. The fluid flow became more stable and less oscillatory at all power excitations for the closed system operation mode (system not open to the atmosphere). However, a sub-cooling effect was evident at higher power, where the two-phase fluid temperatures oscillated in a sinusoidal manner. However, the mass flow rates oscillated with high amplitudes in the forward direction in some channels and assumed a unidirectional flow in other channels. In general, steady-state conditions were obtained earlier when the system was operated as a closed system. For the heat pipe mode of operation, the system transient response in all channels exhibited a geysering instability followed by flashing-induced boiling. In-phase (flow in channels exhibiting the same behaviour) and out-of-phase (flow in channels exhibiting contradictory conduct) behaviour between adjacent channels were observed at all power excitations and system operation modes. Flow reversal in heated channels of a natural circulation system were proven to exists even under equal power excitations. / AFRIKAANSE OPSOMMING: In hierdie studie is tweefasige natuurlike sirkulasievloei in ’n parallelle multikanaalstelsel ondersoek deur middel van eksperimentele en numeriese modellering. Die ondersoek is onder verskillende kragopwekkings en verskeie stelselwerkings (oop stelsel, toe stelsel en hittepypmodus). Die multikanaalstelsel is aan die bopunt met ’n kondensor binne ’n stoomdrom toegerus, terwyl die laer gedeelte van elke kanaal verhit is om die stelsel te verhit. Vir die numeriese modellering, is oorgangseendimensionele behoundsvergelykings vanaf die eerste beginsel vir beide een- en tweefasige vloeistowwe afgelei en dit is gebruik om die stelsel se gediskretiseerde simulasiemodel vir ’n rekenaar te programmeer. Temperature en massavloeitempo’s van die vloeistofrespons as gevolg van verskillende kragopwekkings en -werkings is vir beide die eksperimentele en die numeriese modellering verkry. Dit is in die resultate waargeneem dat die vloeistof ’n aansitoorgang ervaar voor dit vloeiewewigstoestande bereik. Daar is verder waargeneem dat die duur van die oorgang wissel volgens kragopwekkings en stelselwerkingsmodusse en dus op grond van die stabiliteit van die stelsel. ’n Toename in krag het nie noodwendig die vloeitempo van die vloeistofmassa verhoog nie, maar het aanleiding gegee tot ossillasies met groter amplitudes, afhangende van die stelsel se metode van werking. Tipe I-onstabiliteit en stoom-ossillasies van ’n lae intensiteit is teen lae krag en oop stelselwerkingsmodus waargeneem (stelsel oop aan die atmosfeer). Tipe II-onstabiliteit en flitsingsonstabiliteit (flashing instability) is met medium- en hoë kragopwekkings vir die oop stelsel modus van werking waargeneem. Die vloeistofvloei het meer stabiel en minder ossillerend geraak by alle kragopwekkings in die geslote stelsel van werking (stelsel nie oop na die atmosfeer nie). ’n Subverkoelingseffek was egter teen hoër krag duidelik, waar die tweefasige vloeistof se temperature sinusvormig geossilleer het. Die massavloeitempo’s het egter met hoë amplitudes in die vorentoe rigting in sommige kanale gevloei en eenrigtingvloei in ander kanale vertoon. Oor die algemeen is vloei-ewewigstoestande vroeër verkry toe die stelsel as ’n geslote stelsel bedryf is. Vir die hittepypmodus van werking het die stelsel se oorgangsweergawe in alle kanale ’n geysering onstabiliteit getoon, gevolg deur flitsinggeïnduseerde (flashing induced) kook. Gelykfasige gedrag (vloei in kanale vertoon dieselfde gedrag) en ongelykfasige gedrag (vloei in kanale vertoon teenstrydige gedrag) tussen langsliggende kanale is met al die kragopwekkings en stelselwerkingsmodusse waargeneem. Vloei-omkering in die verhitte kanale van ’n natuurlike sirkulasiestelsel is bewys om selfs onder gelyke kragopwekkings te bestaan.

A consequence of high speed rail transportation is the generation of elevated ground borne vibrations. This thesis presents several original contributions towards the prediction of these vibrations. Firstly, a new three dimensional finite element model capable of vibration prediction was developed. Its main feature was its ability to model complex track geometries while doing so through a fully coupled vehicle-tracksoil system. Model output was compared to experimental results obtained during this thesis and also to independent data sets. It was shown to predict velocity time histories, vibration frequency spectrums and international vibration descriptors with high accuracy. An appraisal of the suitability of a finite difference time domain modelling approach for railway vibration prediction was also undertaken. This resulted in the development of a new ‘higher order’ perfectly matched layers absorbing boundary condition. This condition was found to offer higher performance in comparison to current alternative absorbing boundary conditions. Field work was then undertaken on high speed lines with varying embankment conditions in Belgium and England. Vibration data was recorded up to 100m from each track and geophysical investigations were performed to determine the underlying soil properties. The results were used for numerical model validation and also to provide new insights into the effect of various embankment conditions on vibration propagation. It was found that embankments generate higher frequency excitation in comparison to nonembankment cases and that cuttings generate higher vibration levels than noncuttings. Once validated the finite element model was used to provide new insights into the effect of train speed, embankment constituent materials and railway track type on vibration levels. It was found that the shape and magnitude of ground vibration increased rapidly as the train’s speed approached the Rayleigh wave speed of the underlying soil. It was also found that ballast, slab and metal tracks produced similar levels of vibration and that stiffer embankments reduced vibration levels at distances near and far from the track. Two vibration mitigation techniques were also explored through numerical simulation. Firstly, an analysis was undertaken to determine the ability of a new modified ballast material to actively isolate vibration within the track structure. Secondly, wave barrier geometries were investigated to optimise their performance whilst minimising cost. It was found that barrier depth was the most influential parameter, whereas width had little effect. Additionally, geometry optimisation was found to result in a 95% cost saving in comparison to a base case. Using a vast array of results generated using the previously developed finite element model, a new empirical prediction model was also developed, capable of quickly assessing vibration levels across large sections of track. Unlike currently available empirical models, it was able to account for soil properties in its calculation and could predict a variety of international vibration metrics. It was shown to offer increased prediction performance in comparison to an alternative empirical model.

It is crucial for a building to maintain structural stability when subjected to multiple and sequential extreme loads. Safety and economic considerations dictate that structures are built to resist extreme events, such as a earthquakes, impacts, blasts or fires, without collapse and to provide adequate time for evacuation of the occupants. However, during such events, some structural damage may be permissible. Design codes do not account for the scenario where two extreme events occur consecutively on a structure nor do they address the situation of the structure having some initial damage prior to being subjected to a fire load. This work begins by detailing the major inconsistancies between designing reinforced concrete structures for extreme mechanical loads and designing for fire. The material behaviour and traits of the constitutive parts (i.e. the concrete and the steel), including post yielding behaviour, thermal relationships and their interaction with each other are all explored in detail. Comprehensive experimental and numerical investigations are undertaken to determine whether, and to what extent, phenomena such as tensile cracking and loss of the concrete cover affect the local and global fire resistance of a member or structure. The thermal propagation through tensile cracks in reinforced concrete beams is examined experimentally. A comparison is made between the rate of thermal propagation through beams that are undamaged and beams that have significant tensile cracking. The results show that, although small differences occur, there is no significant change in the rate of thermal propagation through the specimens. Consequently, it is concluded that the effects of tensile cracking on the thermal propagation through concrete can be ignored in structural analyses. Significantly this means that analyses of heated concrete structures which are cracked can be carried out with heat-transfer and mechanical analyses being conducted sequentially, as is currently normal and fully-coupled thermo-mechanical analyses are not required. The loss of concrete cover and the impact on the thermal performance is examined numerically. A comparison is made of the thermal propagation, beam deflections and column rotations between structures that are undamaged and structures that have partial cover loss in a variety of locations and magnitudes. Results show that any loss of cover can lead to unsymmetrical heating, causing larger deflections in both vertical and horizontal directions, which can result in a more critical scenario. It is concluded that the effect of cover loss on the thermal performance of the structure is extremely significant. A new approach to numerically simulating the loss of cover by mechanical means from a member is developed. This new approach provides the user with an extremely flexible yet robust method for simulating this loss of cover. The application of this method is then carried out to show its effectiveness. A large experimental study carried out at the Indian Institute of Technology, Roorkee and separately numerically modelled at the University of Edinburgh. Unfortunately, due to unforseen circumstances, the experimental data available is limited at this time and as a result the validation of the numerical simulation is limited. Through these investigations it is clear that it is necessary to develop a method in enhance the stability and integrity of the concrete when subjected to the scenario of a fire following another mechanically extreme event. Therefore, finally a method is proposed and experimentally investigated into the use of fibres to increase the post crushing cohesiveness of the concrete when subjected to thermal loads. Results show that the fibrous members display an increased thermal resistance by retaining their concrete cover through an enhanced post crushing cohesion. From this investigation, it is concluded that the use of fibrous concrete is extremely beneficial for the application of enhancing the performance under extreme sequential mechanical and thermal loading.

The company Rio Deserto is currently mining the famous Barro Branco coal seam in the state of Santa Catarina located in the south of Brazil. One of their coal mines, #101, is experiencing problems related to the pillars in one panel. The coal seam is slightly inclined and several pillars have developed damages on the down-slope side with focus in the top corner. Damage inspections revealed a thin clay layer located between the coal pillar and the overlying siltstone. The clay layer is believed to affect the pillar strength and possibly be a source for the observed damages. Aim of this report has been to evaluate different theories behind the damages, focusing on the clay interface using numerical modelling with FLAC. Using convergence data, a calibration of the model is initially done before evaluating the combination of different interface and coal strength while observing the pillar. In addition is an evaluation of influence from structures such as cleats/joints. The results clearly show that with a small shear displacement (1-4 mm) the pillar damages are almost symmetrical on the up-slope and down-slope side of the pillar. Structures can influence and contribute to non-symmetrical pillar damages although not perfectly matching the field observations. Furthermore, the results show that a forced shear movement (8-25 mm) best reproduce the observed damages. A shear movement along the interface is therefore believed to be source mechanism behind the pillar damages. The forced shearing can potentially be explained by factors not considered in the model such as horizontal stresses, disturbances by mining and presence of water within the clay.

Sandwich panels using fibre-reinforced composite skins and low-density cores are being increasingly used in the aerospace industry due to their superior specific strength and stiffness, and increased design flexibility over traditional metallic and composite structures. However, it is well-known that sandwich panels are highly vulnerable to the effects of impact damage, with even low-energy impacts potentially causing very severe reductions in the in-plane compressive strength of these structures. The objective of this project was to produce a faithful and reliable numerical model for the simulation of the compression-after-impact strength of composite sandwich panels. An in-depth literature review revealed that delamination within the skins of a sandwich panel is a damage mechanism that has gone almost entirely neglected in previous efforts at modelling this problem, despite the proven significance of this mechanism in the failure of impact damaged sandwich panels in compression. Consequently, the use of the cohesive zone model for delamination initiation and propagation is the key unique feature of this model, with Hashin s criteria being used for intra-laminar damage formation, and a simple plasticity response capturing core crushing. An experimental study is performed to produce a thorough dataset for model validation, featuring differing levels of damage induced via quasi-static indentation, and novel asymmetric panels with skins of unequal thickness (the thinner skin being on the unimpacted side). The experimental study revealed that the use of a thinner distal (undamaged) skin could improve the strength of mildly damaged sandwich panels over undamaged sandwich panels using the same asymmetric configuration. It is believed that this effect is due to the movement of the neutral plane of the sandwich panel caused by the reduction in the stability of the damaged skin through stiffness reduction and geometric imperfections. This removes the eccentricity of the compressive loading that exists in the undamaged asymmetric panels, which has mismatched axial stiffness between the indented skin and the thinner distal skin, and thus a noticeably lower ultimate strength than the undamaged symmetric panels. The sandwich model is developed using pre-existing experimental and material data, and trialled for a variety of different skin lay-ups, core thicknesses and indenter sizes. The numerical model generally agreed well with the ultimate stress found in the experiments for these different configurations, but is quite poor at estimating the magnitude of the damage induced by the indentation. When used to model the experimental study, the model gave generally good, conservative estimates for the residual compressive strength of both the symmetric and asymmetric panels. The tendency of the asymmetric panels to become stronger with mild damage was not captured by the model per se, with the numerical results instead showing an insensitivity to damage in the asymmetric panels, which was not shared by the symmetric panels. However, the numerical model did exhibit erroneous strain-stress responses for both panel configurations, particularly for the undamaged and mildly damaged cases. Investigations revealed that this erroneous behaviour was caused by inconsistency in the material data, which had been collected partially via experimentation and partly from literature sources. Overall, the model developed here represents a promising advancement over previous efforts, but further development is required to provide accurate damage states.

The effects of lime treatment on the mechanical properties of soils are usually not accounted for in the design of geotechnical structures. As a result the potential of lime treatment has not been fully exploited. In this thesis, a comprehensive experimental program has been carried out to identity the key features of the mechanical behaviour of structured materials. The chemical modifications arising from lime treatment were quantified using thermal analysis methods. From these results a non-linear chemo-mechanical coupling was established between the concentration of cementitious compounds and the yield stress. Using these results, a new formulation to model the degradation of the structure at yield has been developed and implemented in a constitutive model for structured materials. This new model, developed in the framework of the Modified Cam Clay model, requires a limited number of additional parameters that all have a physical meaning and can all be determined from a single isotropic compression test. The model has proven to be successful in reproducing the key features of structured materials and for the modelling of the mechanical behaviour of lime treated specimens under various stress paths. Due to similarities in behaviour, it is shown that the formulation is also suitable for naturally structured soils. To account for a structured material in the design of geotechnical structures, a fully functional finite element program for elasto-plastic problems was developed including the pre- and post-processing of the results. A thorough validation has confirmed the good implementation of the finite element method and its suitability for the modelling of complex geometries involving structured materials.

Oceans cover two thirds of the Earth’s surface and the energy potential of ocean waves as a renewable energy source is huge. It would therefore be a tremendous achievement if the vast mechanical energy in waves was converted into a form of energy that could be used successfully by society. For years, scientists and engineers have endeavored to exploit this renewable energy by inventing various generators designed to transform wave energy into electrical energy. Generally, this sort of generator is called a Wave Energy Converter (WEC). In this thesis, the research is based on the WEC developed in the Lysekil Project. The Lysekil Project is led by a research group at Uppsala University and has a test site located on the west coast of Sweden. The project started in 2002. So far, more than ten prototypes of the WEC have been deployed and relevant experiments have been carried out at the test site. The WEC developed at Uppsala University can be categorized as a point absorber. It consists of a direct-drive linear generator connected to a floating buoy. The linear generator is deployed on the seabed and driven by a floating buoy to extract wave energy. The absorbed energy is converted to electricity and transmitted to a measuring station on land. The work presented in this thesis focuses on building a linear generator model which is able to predict the performance of the Lysekil WEC. Studies are also carried out on the damping behavior of the WEC under the impact of different sea climates. The purpose is to optimize the energy absorption with a specific optimal damping coefficient. The obtained results indicate an optimal damping for the Lysekil WEC which can be used for optimizing the damping control. Additionally, the impact two central engineering design features (the translator weight and the stroke length) are investigated. The aim is to find a reasonable structural design for the generator which balances the cost and the energy production.

This doctoral dissertation presents a study of the glacial history of the North American Cordillera using numerical ice sheet modelling calibrated against field evidence. This area, characterized by the steep topography of several mountain ranges separated by large inter-montane depressions, was once covered by a large-scale ice mass: the former Cordilleran ice sheet. Because of the irregular topography on which the ice sheet formed, geological studies have often had only local or regional relevance, thus leaving the Cordilleran ice sheet least understood among Pleistocene ice sheets in terms of its extent, volume, and dynamics. Here, I present numerical simulations that allow quantitative reconstructions of the former ice sheet evolution based on approximated physics of glacier flow. These simulations show that the geometry of the Last Glacial Maximum Cordilleran ice sheet was largely controlled by sharp contrasts in regional temperature, precipitation, and daily temperature variability associated with the presence of mountain ranges. However, this maximum stage appears short-lived and out of balance with contemporaneous climate. During most of the simulated last glacial cycle, the North American Cordillera is characterized by an intermediate state of glaciation including isolated glaciers and ice caps covering major mountain ranges, the largest of which is located over the Skeena Mountains. The numerically modelled Cordilleran ice sheet appears in constant imbalance with evolving climate conditions, while the complexity of this transient response transcends that encapsulated in two-dimensional, conceptual models of ice sheet growth and decay. This thesis demonstrates the potential of numerical ice sheet modelling to inform on ice sheet history and former climate conditions over a glacial cycle, given that ice sheet models can be calibrated against field constraints. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Mansucript.</p>

Metamaterials offer the freedom to tune the rich electromagnetic coupling between the constituent meta-atoms to tailor their collective electromagnetic response. Therefore, a comprehensive understanding of the nature of electromagnetic interactions between meta-atoms is necessary for novel metamaterial design, which is provided in the first part of this thesis. The subsequent work in the thesis applies the understanding from the first part to design and demonstrate novel one-dimensional metamaterials that overcome the limitations of metamaterials proposed in literature or exhibit electromagnetic responses not previously observed. Split-ring Resonators (SRRs) are a fundamental building block of many electromagnetic metamaterials. In the first part of the work in this thesis, it is shown that bianisotropic SRRs (with magneto-electric cross-polarisation) when in close proximity to each other, exhibit a rich coupling that involves both electric and magnetic interactions. The strength and nature of the coupling between two identical SRRs are studied experimentally and computationally as a function of their separation and relative orientation. The electric and magnetic couplings are characterised and it is found that, when SRRs are close enough to be in each other's near-field, the electric and magnetic couplings may either reinforce each other or act in opposition. At larger separations retardation effects become important. The findings on the electromagnetic interactions between bianisotropic resonators are next applied to developing a one-dimensional ultra-wideband backward-wave metamaterial waveguide. The key concept on which the metamaterial waveguide is built is electro-inductive wave propagation, which has emerged as an attractive solution for designing backward-wave supporting metamaterials. Stacked metasurfaces etched with complementary SRRs (CSRRs) have also been shown to exhibit a broadband negative dispersion. It is demonstrated through experiment and numerical modeling, that the operational bandwidth of a CSRR metamaterial waveguide can be improved by restricting the cross-polarisation effects in the constituent meta-atoms. The metamaterial waveguide constructed using the modified non-bianisotropic CSRRs are found to have a fractional bandwidth of 56.3\% which, based on a thorough search of relevant literature, is the broadest reported value for an electro-inductive metamaterial. A traditional coupled-dipole toy-model is presented as a tool to understand the field interactions in CSRR based metamaterials, and to explain the origin of their negative dispersion response. This metamaterial waveguide should be of assistance in the design of broadband backward-wave metamaterial devices, with enhanced electro-inductive waveguiding effects. In the final part of the thesis, a one-dimensional metamaterial prototype that permits simultaneous forward- and backward-wave propagation is designed. Such a metamaterial waveguide could act as a microwave analogue of nanoparticle chains that support electromagnetic energy transfer with a positive or a negative dispersion due to the excitation of their longitudinal or transverse dipole modes. The symmetry of the designed hybrid meta-atom permits the co-existence of two non-interfering resonances closely separated in frequency. It is experimentally and computationally shown that the metamaterial waveguide supports simultaneous non-interacting forward- and backward-wave propagation in an overlapping frequency band. The proposed metamaterial design should be suitable for realising bidirectional wireless power transfer applications.

Carbonate sediments are often highly heterogeneous due to the numerous factors that control deposition. Understanding the processes and controls that are responsible for such complexity has, however, proved problematic. In addition, several of these processes are non-linear, so that depositional stratigraphies may consequently form complicated, perhaps even chaotic, geometries. Forward modelling can help us to understand the interactions between the various processes involved. Here a new three-dimensional forward model of carbonate production and deposition is presented, Carbonate GPM, which is specifically designed to test the interactions between the three main carbonate production controls: light intensity, wave power and carbonate supersaturation, the latter of which is unique to this model. The model also includes transport processes specific to the reef sediment only. The effect of supersaturation and reef transport is demonstrated by comparing the output of three, otherwise, identical runs. From these simulations the need to accurately model the flow of water around a reef system and to correctly take into the account the binding nature of reefal sediments can be seen. Analysis of the stratigraphy generated by changing the antecedent topography by 1m in one locality over a 50km square platform suggest that it may be impossible to predict in detail the stratigraphy of carbonate deposits due to its sensitivity to initial conditions or controlling parameters. This reinforces the conclusions reached using previous process models. However, unlike previous models, our model does not explicitly include nonlinear biological interactions as a control. Instead it shows that similar sensitive behaviour may originate from physicochemical processes alone. External factors, such as sea-level changes, will also influence the complex stratigraphy generated by the model. The effect of several different relative sea-level curves was assessed, each corresponding to a combination of three different hierarchies of sea-level oscillations. Large-scale external processes dominate internal processes, dampening their effect on stratigraphy. However, small-scale, high frequency external processes coupled with autocyclic processes do not show any discernable stratigraphic differences from autocyclcic processes alone. The model also produces an exponential cycle thickness distributions that are similar to those found in ancient deposits.