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No description available.

Reynolds average Navier-Stokes (RANS) modeling has established itself as a critical design tool in many engineering applications, thanks to its superior computational efficiency. The drawbacks of RANS models are well known, but not necessarily well understood: poor prediction of transition, non-equilibrium flows, mixing and heat transfer, to name the ones relevant to our study. In the present study, we use a direct numerical simulation (DNS) of a reciprocating channel flow driven by an oscillating pressure gradient to test several low- and high-Reynolds' RANS models. Temperature is introduced as a passive scalar to study heat transfer modeling. Low-Reynolds' models manage to capture the overall physics of wall shear and heat flux well, yet with some phase discrepancies, whereas high-Reynolds' models fail. We have derived an integral method for wall shear and wall heat flux analysis, which reveals the contributing terms for both metrics. This method shows that the qualitative agreement appears more serendipitous than driven by the ability of the models to capture the correct physics. The integral method is shown to be more insightful in the benchmarking of RANS models than the typical comparisons of statistical quantities. This method enables the identification of the sources of discrepancies in energy budget equations. For instance, in the wall heat flux, one model is shown to have an out of phase dynamic behavior when compared to the benchmark results, demonstrating a significant issue in the physics predicted by this model. Our study demonstrates that the integral method applied to RANS modeling yields information not previously available that should guide the derivation of physically more accurate models.

Le contrôle non destructif (CND) de pièces pour des applications dans l'industrie a mené au besoin de modèles rapides et précises. Tels modèles servent au développement des méthodes d'inspection, à l'optimisation des capteurs utilisés aux essais, à l'évaluation des courbes de Probabilité de Detection (POD) ainsi qu'à la caractérisation de défauts. Cette thèse se focalise au CND par Courants de Foucault (CF) de pièces cylindriques avec des discontinuités selon z et contenant un défaut fin. Un modèle pour l'inspection de telles pièces a été développé afin de traiter des applications comme l'inspection des pièces alésées trouvées en aéronautique et des tubes des générateurs de vapeur utilisés dans l'industrie nucléaire. Ce modèle est basé sur une formulation d'équation intégrale. Plus précisément, la variation de l'impédance du capteur, dit signal CF, est calculée à partir d'une équation intégrale sur la surface du défaut. La formulation suivie est basée sur la méthode d'intégration surfacique (SIM). Cette formulation nécessite, d'un côté, le calcul du champ électrique en absence du défaut et, de l'autre côté, l'expression d'une fonction de Green qui correspond à la géométrie de la pièce sans défaut. Les deux problèmes électromagnétiques sont résolus en utilisant la méthode Truncation Region Eigenfunction Expansion (TREE). La méthode TREE est un outil performant pour la résolution des problèmes électromagnétiques qui prend en compte la décroissance rapide de l'intensité du champ afin de tronquer le domaine d'intérêt à une distance, où le champ est négligeable.Le modèle est validé en comparant le signal CF calculé avec des résultats obtenues par une approche combinant la méthode d'intégration volumique (VIM) et SIM, dite l'approche VIM-SIM (implémentée dans la plateforme CIVA) ainsi qu'avec le modèle d'éléments finis (FEM). Nous avons traité trois configurations différentes : un demi-espace conducteur alésé avec un défaut fin, une plaque conductrice avec un alésage et un défaut, et un tube semi-infini avec un défaut fin à la proximité de son bord. La comparaison des résultats montre un très bon accord entre les trois modèles. Le temps de calcul avec le modèle SIM est considérablement inférieur aux temps de calcul des autres modèles. En outre, le modèle SIM donne la possibilité d'effectuer le balayage du capteur dans le tube ou l'alésage dans le cas des pièces alésées. / Nondestructive Testing (NDT) of parts for industrial applications such as in nuclear and aeronautical industry has led to the need for fast and precise models. Such models are useful for the development of the inspection methods, the optimisation of probes, the evaluation of the Probability of Detection (POD) curves or for the flaw characterisation.This PhD thesis focuses on the eddy-current NDT of layered cylindrical pieces with discontinuities in the z direction and containing a narrow crack. A model for the inspection of such pieces is developed in order to be applied on the inspection of fastener holes met in aeronautics and of steam generator tubes in nuclear sector.The model is based on an integral equation formalism. More precisely, for the calculation of the impedance change one needs to solve an integral equation over the surface of the narrow crack, which is represented by a surface electric dipole distribution. This is the method known as surface integration method (SIM). This formulation requires, on the one hand, the calculation of the electric field in the absence of the flaw, the so-called primary field, and, on the other hand, the Green's function expression corresponding to the geometry of the flawless piece. Both electromagnetic problems are solved by means of the Truncation Region Eigenfunction Expansion (TREE) method. The TREE method is a powerful tool for the solution of electromagnetic problems which uses the rapid decrease of the field in order to truncate the region of interest at a distance where the field is negligible.The model is validated by comparing the results of the coil impedance variation with those obtained by an approach that combines the volume integral method (VIM) with SIM, known as VIM-SIM method, implemented in the commercial software CIVA and the finite element method (FEM) implementation in COMSOL software. Three different configurations have treated. The more general geometry of a conducting half-space with a borehole, a conducting plate with a borehole and a crack and a conducting semi-infinite tube with a crack near the edge. The results of the three models show good agreement between them. The computational time of the SIM model is significantly lower compared to previous models. Furthermore, another advantage of the SIM model is that it provides the possibility of a scan inside the borehole.

The uranium price decline has negatively impacted on the uranium mining industry. This decline in price requires that uranium metallurgical processes be made to operate more efficiently. Some key parameters that influence the dissolution and kinetics of leaching uraninite (one of the main minerals from which uranium can be extracted) are pH, oxidationreduction potential and iron concentration. A good understanding of the effect these parameters have on the leach kinetics would lead to an efficient operation of metallurgical processes. The objective of this work was therefore to investigate the effects of these key drivers on leach kinetics of Rӧssing Uranium ore. Added to this, was an attempt to come up with a mathematical model which can successfully replicate the leach kinetics. A series of laboratory leach experiments were performed on Rӧssing ore where the pH, oxidationreduction potential and total iron were varied, one at a time, to establish the effects they have on the leach kinetics and on the uranium extraction. Analysis of the data collected from this study showed that the leach kinetics are more dependent on the oxidation-reduction potential, followed by the iron concentration and least affected by the pH. It was further shown that oxidation-reduction potential is a function of total iron. An integral method was used to analyse the kinetic data. A literature study reveals that uraninite dissolution follows first order kinetics, but of interest in these results was that the uranium dissolution was found to closely follow the second order. Further research is recommended to look at ascertaining these results. Two models were developed, one using regression and the other by curve fitting method. Both models could fit the experimental data well enough. / Dissertation (MSc)--University of Pretoria, 2016. / Materials Science and Metallurgical Engineering / MSc / Unrestricted

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The forced water entry and exit of two-dimensional bodies through a free surface is computed for various 2D bodies (symmetric wedges, asymmetric wedges, truncated wedges and boxes). These bodies enter or exit water with constant velocity or constant acceleration. The calculations are based on the fully non-linear timestepping complex-variable method of Vinje and Brevig. The model was formulated as an initial boundary-value problem with boundary conditions specified on the boundaries (dynamic and kinematic free-surface boundary conditions) and initial conditions at time zero (initial velocity and position of the body and free-surface particles). The formulated problem was solved by means of a boundary-element method using collocation points on the boundary of the domain and solutions at each time were calculated using time stepping (Runge-Kutta and Hamming predictor corrector) methods. Numerical results for the deformed free-surface profile, the speed of the point at the intersection of the body and free surface, the pressure along the wetted region of the bodies and force experienced by the bodies, are given for the entry and exit. To verify the results, various tests such as convergence checks, self-similarity for entry (gravity-free solutions) and Froude number effect for constant velocity entry and exit (half-wedge angles 5 up to 55 degrees) are investigated. The numerical results are compared with Mackie's analytical theory for water entry and exit with constant velocities, and the analytical added mass force computed for water entry and exit of symmetric wedges and boxes with constant acceleration and velocity using conformal mapping. Finally, numerical results showing the effect of finite depth are investigated for entry and exit.

Une technique numérique basée sur le couplage d’une approximation par éléments finis et d’une méthode intégrale a été développée pour le calcul du signal induit dans les antennes I.R.M. Ce signal est issu du mouvement de précession libre de l’aimantation transversale du corps à explorer pendant la relaxation. Dans notre modélisation, l’aimantation transversale représente le champ magnétique source. Celui-ci induit dans l’antenne un courant d’une durée très brève (quelques millisecondes) ; il représente le signal contenant toutes les informations de l’échantillon. Notre modélisation des antennes d’I.R.M de type circuit imprimé a été validée par comparaison avec des mesures expérimentales ainsi qu’avec une méthode analytique. Nous l’avons développée en tenant compte de leurs géométries et de leurs caractéristiques électromagnétiques afin d’avoir un meilleur rapport Signal/Bruit. Nous avons pris en considération des principaux facteurs tels que la distance entre l’antenne et l’échantillon à explorer ainsi que les caractéristiques électromagnétiques de l’antenne. / A numerical technique, based on the combination of a finite element method and a boundary integral method, has been developed to compute the induced signal in MRI antennas. This signal rises from a free movement of precession of the transverse magnetization of the sample to explore. In our modeling, the transverse magnetization represents the magnetic source field. Its flux embraces the antenna to give rise to a sinusoidal current which is very quickly attenuated in time (a few ms); it represents the signal containing all the information of the sample. We here want to find the geometrical and electromagnetic characteristics of the antennas which permit to have a signal to noise ratio as great as possible. In our computation, we have taken into account leading factors such as the distance between the probe and the organ to be explored and also the geometrical and electromagnetic characteristics of the probe. Our modeling of printed circuits MRI antenna has been validated by comparing with experimental measurements and also with an anlytical method. We have developped it by taking into account their geometries and their electromagnetical characteristics in order to have a better signal/noise ratio. We have considered principal factors such as the distance between the antenna and the organ to explore and also the electromagnetic characteristics of the antenna.

he focus of this research has been devoted to study the interaction between two or more self-propelled toroidal swimmers in Stokes flow by applying the method of regularized Stokeslets and also study the effect of a nearby wall to the movement of a helical ring by using the method of regurlarized Stokeslets with images. In the study of the interaction between two or more toroidal swimmers, we interpret these as three-dimensional, zero Reynolds number analogues of finite vortex dipoles in an ideal fluid. Then, we examine the stability of relative equilibria that can form for these swimmers when they are initially placed in tandem or abreast. In addition, we examine the dynamics of the torus when a spherical cell body is placed at its center. This gives us an insight into the mechanical role of the transverse flagellum of dinoflagellates. Moreover, we show that the torus with a sphere moves more efficiently than one without. Lastly, we model the transverse flagellum of a dinoflagellate as a helical ring and study the effect of a nearby wall on its movement. The numerical results show that the wall baffles the movement of the helical ring, which is consistent with the phenomenon of sperm accumulation near surfaces. / acase@tulane.edu

Modeling of wave scattering from grating couplers has become increasingly important due to extensive recent research interest in the problem of plasmonic resonance. Computational algorithms which are specially used to model the problem of scattering from the grating surfaces suffer from several drawbacks such as accuracy, computational efficiency, and generality. To address the challenges of the previous methods, this work presents a novel hybrid Finite Element-Boundary Integral Method (FE-BIM) solution to the problem of scattering from grating surfaces consisting of finite or infinite array of two-dimensional cavities and holes in an infinite metallic walls covered with a stratified dielectric layer. To solve the scattering problem from finite number of cavities or holes engraved in a perfectly conducting screen (PEC), the solution region is divided into interior regions containing the cavities or holes and the region exterior to them. The finite element formulation is applied inside the interior region to derive a linear system of equations associated with nodal field values. Using two-boundary formulation, the surface integral equation employing free-space Green's function is then applied at \emph{only} the opening of the cavities or holes to truncate the computational domain and to connect the matrix subsystem generated from each cavity or hole. The hybrid FE-BIM method is extended to solve the scattering problem from an infinite array of cavities or holes in a PEC screen by deriving the quasi-periodic Green's function. In the scattering problem from an infinite array of cavities, the finite element formulation is first used inside a single cavity in the unit-cell. Next, the surface integral equation employing the quasi-periodic Green's function is applied at the opening of \emph{only} a single cavity as a boundary constraint to truncate the computational domain. Effect of the infinite array of cavities is incorporated into the system of the nodal equations by the quasi-periodic Green's function. Finally, the method based on the hybrid FE-BIM is developed to solve the scattering problem from grating surfaces covered with a stratified dielectric layer. In this method, the surface integral equation employing grounded dielectric slab Green's function is applied at the opening of the cavities or holes inside the dielectric coating to truncate the solution region efficiently. An accurate algorithm is presented to derive the grounded dielectric slab Green's function in spatial domain incorporating the effects of the surface-waves and leaky-waves excited and propagated inside the dielectric slab. Numerical examples of near and far field calculations for finite or infinite array of cavities or holes are presented to validate accuracy, versatility, and efficiency of the algorithm presented in this thesis.