The increasingly competitive market for cast products has required the development of higher quality and lower cost products. Although conventional process development techniques have improved, the cost and time associated to process development needs to be reduced. A faster and more cost-effective development method is required. Numerical modelling techniques provide a means by which casting design and process parameters can be optimized with minimum use of prototypes. This thesis reviews the current state of the art in solidification modelling. A typical casting problem is modelled, and the numerical results compared against measured temperatures. further work is required to from this investigation it is concluded that obtain, and accurately model the material properties and complex radiation behaviour within the fibrous insulation.

Abstract The steady thermocapillary motion in shallow enclosures is studied. Two different configurations, imposed heat flux and differentially heated side walls, are considered. A numerical simulation of the problem in the imposed heat flux case is made. The Pressure Correction Method is used to treat the pressure velocity coupling, in particular, the SIMPLER approximation. The discretization is made using central differences along with an appropriate non-uniform grid.

Polymer electrolyte fuel cells are regarded as one of the most promising alternatives to the depleting and high pollutant fossil fuel energy sources. High temperature Polymer electrolyte fuel cells are especially suitable for stationary power applications. However, the length scale of a PEM fuel cells main components range from the micro over the meso to the macro level, and the time scales of various transport processes range from milliseconds up to a few hours. This combination of various spatial and temporal scales makes it extremely challenging to conduct in-situ measurements or other observations through experimental means. Thus, numerical simulation becomes a very important tool to help understand the underlying electrochemical dynamics and transient transport phenomena within PEM fuel cells. In this thesis research a comprehensive, three- dimensional mathematical model is developed which accounts for the convective and diffusive gas flow in the gas channel, multi-component diffusion in the porous backing layer, electrochemical reactions in the catalyst layers, as well as flow of charge and heat through the solid media. The governing equations which mathematically describe these transport processes, are discretized and solved using the finite-volume based software, Ansys FLUENT, with its in-built CFD-solvers. To handle the significant non-linearity stemming from these transport phenomena, a set of numerical under-relaxation schemes are developed using the programming language C++. Good convergence is achieved with these schemes, though the model is based on a serpentine single-channel flow approach. The model results are validated against experimental results and good agreement is achieved. The result shows that the activation overpotential is the greatest cause of voltage loss in a high temperature PEM fuel cell. The degree of oxygen depletion in the catalyst layer, under the ribs, is identified and quantified for a given set of input parameters. This factor is followed by membrane resistance to protonic migration. The model can thus be suitable applied as a tool to predict cell performance. The results also show that performance is influenced by not just one, but a combination of inter-related factors, thus temperature increases, and flow rate changes will only be effective if simultaneously, the concentration of inlet oxygen, and the mobility of proton-ions in the membrane is increased. Not only does the model results verify these phenomena, but provide a quantitative output for any given set of input parameters. It can therefore be suitably applied as an optimisation tool in high temperature PEM fuel cell design.

A finite element code has been developed at the University of Sheffield to simulate the structural response of steel and composite framed buildings subjected to fire. The steel skeleton is represented using two-noded line elements, the steel-to-steel connections using spring elements and the flooring system by isotropic flat shell elements. Structures are therefore considered as a complete entity, allowing a more realistic prediction of structural behaviour at elevated temperature. A series of numerical simulations of fire tests carried out on the full-scale, eight-storey composite frame at the BRE laboratory at Cardington in 1995 and 1996 have been conducted. These tests have been subject to a number of significant parametric studies including slab thickness and secondary beam connection strength and stiffness. The concrete floor slab element has also been extended to a layered flat shell element allowing the inclusion of material non-linearities, thermal bowing, thermal degradation, anisotropic properties and a more advanced cracking model. Using the new concrete floor slab element the Cardington fire tests have been simulated in detail, to further understanding of the structural reaction in fire. Another series of parametric studies have been conducted considering again the thickness of the floor slab, the effect of the slab temperature gradient, the compressive strength, tensile strength and load ratios. These have all been compared to results from the Cardington fire tests. Current design methods based on isolated element design are considered by comparing the results of analyses in which the concrete floor is either included as a continuous slab in an extensive subframe, or is treated simply as forming the flanges of composite beams in a three-dimensional skeleton. These examples show clearly the effects of membrane and bridging actions of the continuous floor slab. The implications for future design developments are discussed with particular reference to the parametric studies conducted.

In the study of computational turbulence, the success of Large Eddy Simulation (LES) is largely determined by the quality of the sub-filter scale (SFS) model and the properties of the filter used to introduce resolved and unresolved length scales. Explicit filters are desirable so that better control over the filter may be achieved, and filter operator errors can be then controlled to a desired order of accuracy. One large advantage to using an explicit filter is that the mathematical definition of the filter may be exploited when considering various SFS models or even different LES techniques. Approximate deconvolution is a technique used in LES, which performs an inverse filtering operation to partly restore the original unfiltered solution. The discrete explicit filtering technique will be used to perform the deconvolution, and numerical results will show how the approximate solution may be used to perform LES.

In the study of computational turbulence, the success of Large Eddy Simulation (LES) is largely determined by the quality of the sub-filter scale (SFS) model and the properties of the filter used to introduce resolved and unresolved length scales. Explicit filters are desirable so that better control over the filter may be achieved, and filter operator errors can be then controlled to a desired order of accuracy. One large advantage to using an explicit filter is that the mathematical definition of the filter may be exploited when considering various SFS models or even different LES techniques. Approximate deconvolution is a technique used in LES, which performs an inverse filtering operation to partly restore the original unfiltered solution. The discrete explicit filtering technique will be used to perform the deconvolution, and numerical results will show how the approximate solution may be used to perform LES.

No

This paper explores ways in which civil conflict can be simulated using numerical methods. A general two-party model of conflict is developed by extending an approach proposed by [Christia, F., (2012), Alliance Formation in Civil Wars, Cambridge University Press, New York], which is based on a metric of the 'relative power' that exists between the state and a rebel group. Various definitions of relative power are considered and one of these is chosen to illustrate different types of two-sided armed conflict, namely direct-fire, guerrilla and asymmetric warfare. The additional suggestion of Christia that random or stochastic events can lead to unexpected conflict outcomes is also further extended in this paper. The inclusion in the model of terms describing concurrent rebel recruitment of civilians and state deployment of troops are then described. Examples are presented for various hypothetical cases. It is demonstrated that numerical simulation techniques have great potential for modelling civil war. The Christia approach is shown to provide an excellent basis from which numerical models of civil conflict can be built and from which the progress of a conflict can usefully be visualised graphically.

O solos saproliticos sÃo encontrados no fundo das escavaÃÃes de jazidas que sÃo normalmente usadas na construcao de barragens de terra. NÃo sÃo normalmente utilizados pelo desconhecimentos de suas propriedades adequadas para gerar uma estrutura de vedaÃÃo. Em algumas situaÃÃes por inexistÃncias de solos residuais maduros suficientes para construÃÃo da barragem ou por questÃes de distancia e possÃvel construir a barragem com solos pouco desenvolvidos (solos residuais jovens). Este foi a motivaÃao para realizaÃÃo deste pesquisa. Foram realizados todos os ensaios de caracterizaÃÃo e mecÃnicos em amostras solos jovens (saproliticos) e a partir do conhecimento de suas propriedades foram realizadas simulaÃÃes numÃricas para demonstrar ser possÃvel construir pequenas barragens com solo residual jovem com o atendimento das questoes relativas a seguranÃa e a reduÃÃo provavel de custos. Os resultados experimentais e numÃricos comprovaram essa possibilidade / The saprolite soils are found on the bottom of the excavation of deposits that are commonly used in the construction of earth dams. Are not normally used by the unknowns of their suitable properties to generate a sealing structure. In some situations by inexistÃncias sufficient mature residual soils for construction of the dam or distance issues and possible to build the dam with poorly developed soils (young residual soils). This was the motivation for conducting this research. All mechanical and characterization tests on soil samples young (saprolite) and from knowledge of its properties numerical simulations were performed to demonstrate possible to build small dams with young residual soil with the care of the issues related to safety and reduction were performed probable costs. The experimental and numerical results confirmed this possibility

Low back pain is a major social and economic dilemma in the United States. Despite its high impact, the origins of low back remain unclear. Nonetheless, degenerative changes to the intervertebral discs (IVD) of the spine have been implicated as a possible source leading to pain. Poor nutritional supply to the IVD is believed to play a primary role in the pathophysiology of disc degeneration. Since the disc is avascular, vital nutrients, such as glucose, must be supplied by surrounding blood vessels. However, the transport and metabolic properties of glucose in the IVD have not been fully delineated. This knowledge is necessary in order to elucidate the nutrition-related mechanisms of disc degeneration. Therefore, in this dissertation, experimental and theoretical methods are used to investigate the transport and metabolism of glucose in the intervertebral disc. Strain-dependent and anisotropic (i.e., direction-dependent) transport of glucose in human annulus fibrosus (AF) was investigated using custom apparatuses. Results indicate that diffusivity and partitioning of glucose in human AF decreases with increasing compressive strain. Furthermore, diffusivity of glucose is anisotropic, being lower in the radial direction than the axial or circumferential directions at all strain levels. Transport of glucose in human AF was also found to diminish with increasing disc degeneration. A new method was developed to measure the rate of glucose consumption by IVD cells; this method was then validated with porcine AF and nucleus pulposus (NP) cells at varying levels of oxygen tension. Results show a positive Pasteur effect, with the glucose consumption rate by AF and NP cells increasing at low levels of oxygen. Moreover, results indicate that the rate of consumption of glucose by NP cells is significantly higher than that by AF cells. A new, three-dimensional finite element model of the IVD was developed in order to theoretically predict nutrient distributions in the disc. This model incorporated anatomical disc geometry, nutrient transport coupled to cellular metabolism, and mechanical loading conditions. The model was used to investigate the effects of endplate calcification and in vivo loading conditions on glucose distributions in the disc. Both calcification and compressive loading resulted in diminished glucose concentrations in the tissue. The model was also used to analyze the effects of degeneration and compression on cell viability in IVD by incorporating viability criteria. Our model could predict cell death in degenerated tissue, and compressive loading augmented this effect. The model prediction can be used to supplement experimental results, and may also serve as a useful tool in developing new strategies for the treatment of disc degeneration. The findings of this dissertation greatly enhance the knowledge of glucose transport and metabolism in the intervertebral disc. Given that glucose is a critical nutrient for disc cell survival, this knowledge can provide important insight into nutritional pathways and mechanisms in the IVD, as well as related disc degeneration.