Browsing by Author "Laurie, Henri"

Now showing 1 - 7 of 7
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    An analysis of frictional effects in non-stationary contact problems for metal forming simulations
    (2021) Colville, Kevin; Laurie, Henri; Ronda; Jacek
    The finite element method (FEM) is widely used for the simulation of metal forming processes and has been successfully used in contact problems which arise in processes such as deep-drawing, punching, extrusion and rolling. All these processes involve friction between the contact surfaces: the sheet-metal workpiece and the toolpieces. The model of friction is thus an important part of any simulation of metal forming processes. Most FEM codes use a friction model that assumes that the contact surface is a plane. Attempts to address this problem have focused on the convective description of deformation, which has the advantage of being naturally extended to numerical methods like the FEM at the expense of additional computation and numerical complexity. The convective description is used in this work, which focuses on the numerical implementation of the objective measure. The effects of the rotation of the material contact point is taken into account by including objective time derivatives of the slipping (tangential) direction function. The objective rate of the direction function includes the surface spin induced by the rigid motion of a contact point sliding over the tool surface, and the material spin occurring during the elastic-plastic deformation of the blank. This is introduced by adapting the incremental relations of the friction slip. This thesis presents the results of numerical experiment to determine the influence that the rotation and convection of contact points has on the frictional stresses and slipping energy. Four different friction models are implemented within the finite element program ABAQUS and applied to simulations of standardmetal forming benchmark processes: the square-cup and s-rail deep drawing benchmarks of the Numisheet conferences, for which several experimental and numerical results are available to compare with the solution of a finite element simulation. The results for each metal-forming simulation are calculated for different friction models, and are compared and a choice made as to which is the “best” friction model for the process. Further, the reverse problem of determining the values of friction parameters by comparison of simulation and experimental results is performed for these benchmark problems. As there is yet no ideal friction model for all processes that are modelled, finding the most appropriate friction model by numerical means is proposed to improve the quality of a simulation.
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    Computer construction of species richness maps: Testing a new type of multifractal algorithm
    (2008) Perrier, Edith; Laurie, Henri
    We show how a new theoretical multifractal model provides means to generate virtual maps of highly variable spatial distributions of species richness. It should allow for various computer experiments in landscape ecology and the study of biodiversity. In this paper, the explicit distribution of species-representative individuals over a large range of scale leads to an original algorithm for the estimation of the Renyi dimensions of a multifractal measure. The method is successfully tested for simulated (S, A) data sets, where the variable S is simply the number of species found in a given domain of area A. This easy tool will help to characterize the spatial variability of multiscale density distributions in many fields, requiring only randomly sampled data at different locations and scales.
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    Mathematical modelling of agglomerate scale phenomena in heap bioleaching
    (2006) Ogbonna, Nneoma; Petersen, Jochen; Laurie, Henri
    Bioleaching is a naturally occurring process that has been harnessed in metal recovery from low grade ores. The heap bioleaching technique involves complex interactions between chemical reactions, microbial processes and transport processes. The need for efficient heap operations has led to the scientific investigation of heap bioleaching and the development of mathematical models for the process. Over time, the focus of heap leach modelling has moved from models that emphasize particle scale processes to models that emph8size bulk scale processes. In many cases however, the particle scale effects in these bulk scale models are quite simplified. This thesis aims to provide a means for the systematic integration of particle (or micro-) scale processes into bulk (or macro-) scale models for heap bioleaching, by the development of an intermediate (or meso-) scale "agglomerate" model. The agglomerate is defined as a unit volume of a heap that comprises a solid phase (a size distribution of ore particles), a liquid phase (stagnant and flowing leaching solution, which contains dissolved solutes, attached and planktonic microbes) and a gas phase (flowing air and air pockets). The processes incorporated into the proposed model include reagent diffusion and ree1ction in a s.ze distribution of ore particles, microbial attachment, detachment and oxidation processes, and the transport of chemical and microbial species to and from the agglomerate. Isothermal agglomerate conditions, and a uniform distribution of reagents in the stagnant liquid phase, are among the modelling assumptions made. The agglomerate model is applied to investigate the meso-scale bioleaching of a theoretical case study ore that contains mainly chalcocite and pyrite, in the presence of iron oxidizing microbes. The numerical implementation of the model is done in the Python programming language. The integrity of the numerical results is confirmed by performing mass balance checks at the end of each simulation.
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    Modelling credit spreads in an illiquid South African corporate debt market
    (2019) Jones, Samantha; Laurie, Henri; Fredericks, Ebrahim; Becker, Ronald; Dugmore, Brett
    The South African debt market suffers from severe illiquidity, as is common in most emerging markets. Infrequent trading leads to out-of-date market prices and stale, unreliable credit spreads. Since the coverage of the South African debt market by credit ratings agencies is poor, meaningful credit spreads become even more important in gauging credit worth. The illiquidity of corporate vanilla bonds traded on the Johannesburg Stock Exchange and the ensuing adverse effects on their credit spreads are rigourously illustrated. Lack of data poses a serious problem when modelling any system and this analysis provides motivation for the necessity of a framework that addresses the statistical complications that incomplete data sets present. A new model, which is a distinctive modification of the well-known mean-reverting Ornstein-Uhlenbeck or Vasicek process, is introduced. This innovative approach creates a mathematically and intuitively sound relationship between the credit spread process and that of the stock price of the bond issuer. This key feature is used in a Bayesian methodology to impute missing credit spread data for calibration, for more meaningful inference. On sparse simulated data and market observed credit spread time series, the model proves to deliver an improved quality of the estimations, with probabilities that are now statistically founded. Even on complete credit spread time series, the model is shown to have some merit over the traditional model in terms of goodness of fit, giving further credence to its validity and explanatory power.
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    Three-dimensional mathematical model of a high temperature polymer electrolyte membrane fuel cell
    (2016) Hess, Victor George; Laurie, Henri
    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.
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    Two-patch herbivore/vegetation models with density-dependent migration
    (2013) Bakheet, Mohamed Abdalaziz Abdalla; Laurie, Henri
    In this thesis we constructed two mathematical models for herbivore/vegetation interactions in environment of two patches, using the metaphysiological approach and a density-dependent migrations. In the first model we considered the case when the environment is constant, and we constructed a system of four perturbed ordinary differential equations describing the dynamics when only herbivores allowed to move between the two patches searching for food. The model contain two different timescales, fast for migrations and slow for the other demographic changes in the system. We used the geometric singular perturbation theory in order to reduce the dimension of the system. Using the continuation software AUTO we provided bifurcation diagrams for the reduced systems and we also provided some numerical illustrations to show the dynamics of the system for different migrations propensities. We analyzed the bifurcation diagrams using Morse decompositions and Conley index theory, to confirm their correctness. We constructed a second mathematical model, by considering that the vegetation growth depends on seasonal rainfall and the soil moisture. We provided some numerical simulations to illustrate several variates of dynamics for different migration speed and, when the migration propensities and the vegetation quality are change.