The thesis is about the arrangement of the last known claim values into the run-off triangle. This diagram is used in non-life insurance, mainly in methods for calculating technical claims reserves. Individual methods will be described in detail and consecutively applied on real data. The real data are a set of data with long tail. We are differentiating between easier deterministic and stochastic methods, which are more demanding for calculation. The results will be compared by basic statistical parameter of the analyzed data and at the end the best method will be chosen for the data.

Le biogaz doit être purifié pour devenir un combustible renouvelable. De nombreux traitements actuels ne sont pas satisfaisants car, pour des raisons de coûts les procédés de séparation privilégiés aboutissent souvent au rejet direct ou indirect du sulfure d'hydrogène (H2S) à l’atmosphère, c’est le cas de la séparation à l’eau sous pression. Les objectifs de la thèse portent d’abord sur l’étude et la modélisation des méthodes connues de séparation de l'hydrogène sulfuré du méthane. Les concentrations typiques varient de 200 à 5000 ppm, et la séparation devra réduire la teneur résiduelle en H2S à moins de 1 ppm. Parallèlement seront étudiées les méthodes de traitement de H2S. Une fois la (ou les) méthode(s) de séparation sélectionnée(s), des essais de validation seront effectués sur un système traitant de l’ordre de 85 Nm3/h de méthane où seront injectées des quantités de H2S variant entre 1 et 100 ppm.Cette thèse requiert des modélisations réalistes sous Aspen Plus® ou sous un code équivalent pour établir a priori des efficacités de séparation selon différentes conditions opératoires et en prenant en compte le paramètre température. L’énergie dépensée pour la séparation effective sera un des critères fort de la comparaison, de même que l’économie de matière.Une approche système est indispensable pour étudier la rétroaction de la méthode de valorisation du H2S sur la ou les méthodes séparatives. A priori c’est aussi l’outil Aspen Plus® ou équivalent qui permettra cette approche système.L’étude du procédé sera menée selon la double approche modélisation et expérimentation, pour l’étude expérimentale des méthodes séparatives, l’échelle du banc sera semi-industrielle et le banc permettra d’étudier les méthodes de séparation jusqu’à -90°C. / Biogas must be purified for becoming a renewable fuel. At now, the most part of the purification techniques are not satisfactory because they imply hydrogen sulfides (H2S) rejection to the atmosphere. One example of these methods is the treatment with high pressure water. The first objective of the thesis is modeling the conventional methods for separating H2S from methane. Typical concentrations of H2S in methane vary from 200 to 5000 pm. Separation methods must decrease the concentration of H2S in methane to less than 1 ppm. At the same time, methods for H2S treatment will be studied.Once the most appropriated separation methods will be selected, some test will be carried out on a pilot plant capable of treating 85 Nm3/h of methane, where quantities of H2S ranging from 1 and 100 ppm will be injected. These tests will allow validating the modeling of the separation process. On the basis of the obtained results, a specific test bench will be conceived and constructed for validating the selected process.The thesis work requires simulating the separation process using the software Aspen Plus® or an equivalent one. The effectiveness of different operative conditions will be tested, varying also the parameter temperature. The energy necessary for the separation will be one of the most important criteria for the comparison, as well as the mass consumption of the different fluids involved in the process.A system approach is fundamental for evaluating the backward effect of the H2S valorization method on the separation techniques. The process simulator (Aspen Plus® or equivalent) will allow the system approach.The study will involve modeling and experimental parts. The experimental part will be carried out taking advantage of a semi-industrial size test bench, allowing studying the separation methods down to -90°C.

This diploma thesis follows my bachelor thesis. The main purpose of the bachelor thesis was to clarify fundamental terms and to explain the sorting of particular parts of a direct flow that involves both the surface saturated flow and the hypodermic flow. This diploma thesis is focusing on the origin of direct flow in a river basin. Specifically, it deals with river sub-basin P6, P52, and P53, which are located in Kopaninský potok river basin. Furthermore, it deals with Jenín I. and II. river basins and the last analysed is Ostřice river basin (SO2). Factors influencing direct flow are researched on all river basins. It is impossible to say that the origin of direct flow is caused solely by a single factor; it is always the result of multiple factors. Among these factors belongs the atmospheric precipitation, type of soil, vegetation, climatic and anthrophogenic conditions, land use, and inclination of the area. The bachelor thesis explains the issues of multiple methods of flow separation, but this diploma thesis is primarily focused on two methods for calculation of ratio between the direct and the total flow. 1) Empirical method GROUND, which is used to separate hydrographs of medium daily river basin flow. 2) Method of digital filter by Lyne Hollick separate fast and slowcomponents from the overall concentrated flow and are based on the theory od signal analysis. Afterwards, the results of flow separation were compared to the factors influencing the origin of the direct flow. The daily total flow rates for every analysed river basin were used as the input data for calculating the flow separation.

The context of this thesis is the numerical simulation of turbulent flows at moderate Reynolds numbers and the improvement of the capabilities of an in-house 3D unsteady and incompressible flow solver called SFELES to simulate such flows.<p>In addition to this abstract, this thesis includes five other chapters.<p><p>The second chapter of this thesis presents the numerical methods implemented in the two CFD solvers used as part of this work, namely SFELES and PHASTA.<p><p>The third chapter concentrates on the implementation of a new library called FlexMG. This library allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods, which require much less memory to solve linear systems than a direct sparse LU solver available in SFELES. Multigrid is an iterative procedure that relies on a series of increasingly coarser approximations of the original 'fine' problem. The underlying concept is the following: low wavenumber errors on fine grids become high wavenumber errors on coarser levels, which can be effectively removed by applying fixed-point methods on coarser levels.<p>Two families of algebraic multigrid preconditioners have been implemented in FlexMG, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES (Generalized Minimal RESidual) method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics (unsteady flow past a circular cylinder at low Reynolds number), their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in this work.<p><p>The fourth chapter is devoted to the study of subgrid scale models for the large eddy simulation (LES) of turbulent flows.<p>It is well known that turbulence features a cascade process by which kinetic energy is transferred from the large turbulent scales to the smaller ones. Below a certain size, the smallest structures are dissipated into heat because of the effect of the viscous term in the Navier-Stokes equations.<p>In the classical formulation of LES models, all the resolved scales are used to model the contribution of the unresolved scales. However, most of the energy exchanges between scales are local, which means that the energy of the unresolved scales derives mainly from the energy of the small resolved scales.<p>In this fourth chapter, constant-coefficient-based Smagorinsky and WALE models are considered under different formulations. This includes a classical version of both the Smagorinsky and WALE models and several scale-separation formulations, where the resolved velocity field is filtered in order to separate the small turbulent scales from the large ones. From this separation of turbulent scales, the strain rate tensor and/or the eddy viscosity of the subgrid scale model is computed from the small resolved scales only. One important advantage of these scale-separation models is that the dissipation they introduce through their subgrid scale stress tensor is better controlled compared to their classical version, where all the scales are taken into account without any filtering. More precisely, the filtering operator (based on a top hat filter in this work) allows the decomposition u' = u - ubar, where u is the resolved velocity field (large and small resolved scales), ubar is the filtered velocity field (large resolved scales) and u' is the small resolved scales field. <p>At last, two variational multiscale (VMS) methods are also considered.<p>The philosophy of the variational multiscale methods differs significantly from the philosophy of the scale-separation models. Concretely, the discrete Navier-Stokes equations have to be projected into two disjoint spaces so that a set of equations characterizes the evolution of the large resolved scales of the flow, whereas another set governs the small resolved scales. <p>Once the Navier-Stokes equations have been projected into these two spaces associated with the large and small scales respectively, the variational multiscale method consists in adding an eddy viscosity model to the small scales equations only, leaving the large scales equations unchanged. This projection is obvious in the case of a full spectral discretization of the Navier-Stokes equations, where the evolution of the large and small scales is governed by the equations associated with the low and high wavenumber modes respectively. This projection is more complex to achieve in the context of a finite element discretization. <p>For that purpose, two variational multiscale concepts are examined in this work.<p>The first projector is based on the construction of aggregates, whereas the second projector relies on the implementation of hierarchical linear basis functions.<p>In order to gain some experience in the field of LES modeling, some of the above-mentioned models were implemented first in another code called PHASTA and presented along with SFELES in the second chapter.<p>Finally, the relevance of our models is assessed with the large eddy simulation of a fully developed turbulent channel flow at a low Reynolds number under statistical equilibrium. In addition to the analysis of the mean eddy viscosity computed for all our LES models, comparisons in terms of shear stress, root mean square velocity fluctuation and mean velocity are performed with a fully resolved direct numerical simulation as a reference.<p><p>The fifth chapter of the thesis focuses on the numerical simulation of the 3D turbulent flow over a re-entry Apollo-type capsule at low speed with SFELES. The Reynolds number based on the heat shield is set to Re=10^4 and the angle of attack is set to 180º, that is the heat shield facing the free stream. Only the final stage of the flight is considered in this work, before the splashdown or the landing, so that the incompressibility hypothesis in SFELES is still valid.<p>Two LES models are considered in this chapter, namely a classical and a scale-separation version of the WALE model. Although the capsule geometry is axisymmetric, the flow field in its wake is not and induces unsteady forces and moments acting on the capsule. The characterization of the phenomena occurring in the wake of the capsule and the determination of their main frequencies are essential to ensure the static and dynamic stability during the final stage of the flight. <p>Visualizations by means of 3D isosurfaces and 2D slices of the Q-criterion and the vorticity field confirm the presence of a large meandering recirculation zone characterized by a low Strouhal number, that is St≈0.15.<p>Due to the detachment of the flow at the shoulder of the capsule, a resulting annular shear layer appears. This shear layer is then affected by some Kelvin-Helmholtz instabilities and ends up rolling up, leading to the formation of vortex rings characterized by a high frequency. This vortex shedding depends on the Reynolds number so that a Strouhal number St≈3 is detected at Re=10^4.<p>Finally, the analysis of the force and moment coefficients reveals the existence of a lateral force perpendicular to the streamwise direction in the case of the scale-separation WALE model, which suggests that the wake of the capsule may have some <p>preferential orientations during the vortex shedding. In the case of the classical version of the WALE model, no lateral force has been observed so far so that the mean flow is thought to be still axisymmetric after 100 units of non-dimensional physical time.<p><p>Finally, the last chapter of this work recalls the main conclusions drawn from the previous chapters. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished