The production of long, thin polymeric fibers is a main objective of the textile industry. Melt-spinning is a particularly simple and effective technique. In this work, we shall discuss the equations of melt-spinning in viscous and viscoelastic flow. These quasilinear hyperbolic equations model the uniaxial extension of a fluid thread before its solidification. We will address the following topics: first we shall prove existence, uniqueness, and regularity of solutions. Our solution strategy will be developed in detail for the viscous case. For non-Newtonian and isothermal flows, we shall outline the general ideas. Our solution technique consists of energy estimates and fixed-point arguments in appropriate Banach spaces. The existence result for a simple transport equation is the key to understanding the quasilinear case. The second issue of this exposition will be the stability of the unforced frost line formation. We will give a rigorous justification that, in the viscous regime, the linearized equations obey the ``Principle of Linear Stability''. As a consequence, we are allowed to relate the stability of the associated strongly continuous semigroup to the numerical resolution of the spectrum of its generator. By using a spectral collocation method, we shall derive numerical results on the eigenvalue distribution, thereby confirming prior results on the stability of the steady-state solution. / Ph. D.

Ce manuscrit présente une étude couplée, numérique et théorique, portant sur les écoulements tournants transitionnels et turbulents. L'accent y est mis sur la formation de structures macroscopiques cohérentes au sein de l'écoulement, générées par des procédés rendus fortement tri-dimensionnels par la présence des couches limites sur les disques et le long des parois cylindriques extérieure (carter) et/ou intérieure (moyeu). La complexité de ces écoulements pose de véritables difficultés en recherche fondamentale mais les résultats de ces travaux ont aussi une importance non négligeable pour les machines industrielles tournantes, depuis les disque-durs jusqu'aux turbopompes spatiales, la conception de ces dernières étant la motivation première pour ces travaux de thèse. Ce travail peut être divisé en deux sous-parties. Dans un premier temps, les cavités industrielles sont modélisées par de simples cavités rotor/stator lisses pour y étudier la dynamique de l'écoulement. Comme les campagnes expérimentales sur les machines industrielles ont révélé de dangereux phénomènes instationnaires en leur sein, l'accent est mis sur l'obtention et l'étude des fluctuations de pression dans les écoulements modèles. Ensuite, les SGE de trois configurations de turbine industrielle réelle sont réalisées pour étudier les fluctuations de pression in situ et appliquer les diagnostiques éprouvés sur les géométries modèles. / This thesis provides a numerical and theoretical investigation of transitional and turbulent enclosed rotating flows, with a focus on the formation of macroscopic coherent flow structures. The underlying processes are strongly threedimensional due to the presence of boundary layers on the discs and on the walls of the outer (resp. inner) cylindrical shroud (resp. shaft). The complexity of these flows poses a great challenge in fundamental research however the present work is also of importance for industrial rotating machinery, from hard-drives to space engines turbopumps - the design issues of the latter being behind the motivation for this thesis. The present work consists of two major investigations. First, industrial cavities are modeled by smooth rotor/stator cavities and therein the dominant flow dynamics is investigated. For the experimental campaigns on industrial machinery revealed dangerous unsteady phenomena within the cavities, the emphasis is put on the reproduction and monitoring of unsteady pressure fluctuations within the smooth cavities. Then, the LES of three configurations of real industrial turbines are conducted to study in situ the pressure fluctuations and apply the diagnostics already vetted on academic problems.

La fragmentation d’enveloppes métalliques en expansion dynamique intéresse tant l’industrie civile que celle de la défense. Pour les deux domaines d’application, il s’agit de pouvoir prédire la taille et la vitesse des fragments, résultant de la destruction des enveloppes, afin de mesurer les conséquences que ceux-ci peuvent avoir sur des structures de sécurité. Les modèles de prédiction existants étudient le développement d’un défaut au sein du matériau et arrivent à déterminer une taille caractéristique des fragments. Néanmoins, ces modèles nécessitent une hypothèse dont la validité est remise en cause lorsque la vitesse de déformation est importante. Dans ce travail, nous proposons un nouveau modèle analytique pour des cylindres (sollicitation en traction plane) permettant de s’affranchir de cette hypothèse et d’étudier l’influence du défaut initial en suivant son évolution. Le modèle développé est comparé avec succès à des résultats issus de simulations numériques par éléments finis. Nos travaux permettent notamment de préciser les cadres d’application et de validité des approches classiques. Comme résultats majeurs, la nouvelle approche permet d’analyser les évolutions des perturbations aux faibles déformations mais aussi d’estimer le temps d’apparition des premières décharges élastiques, synonymes de strictions localisées. / This work deals with the fragmentation of dynamically expanding metal shells and covers a problem of interest for both civil and military industries. For both fields of application, it is crucial to predict the size and the speed of fragments, resulting from the destruction of shells in order to measure the consequences that it could have on structures. Current models study the growth of a defect within the material and are able to determine a characteristic size of fragments. Nevertheless, these models require a hypothesis whose validity is questionable when the rate of deformation is important. In this work, we propose a new analytical model for cylinders (equivalent to the dynamic extension of a plate) to overcome this hypothesis and study the influence of the initial defect by following its time evolution. The model is compared successfully with results performed with a finite element method. Our work notably expands the framework of classical linear stability analyses. As a major outcome, the proposed approach is able to track the evolution of a perturbation even for small plastic strain, when the flow may be stable. In addition it is shown that the present approach can predict accurately the time where the elastic unloading is observed in finite element simulations.

No description available.

Control of bulk melt crystal growth techniques is desirable for producing semiconductors with the highest purity and ternary alloys with tunable electrical properties. Because these molten materials are electrically conducting, external magnetic fields are often employed to regulate the flow in the melt. However, complicated by the coupled flow, thermal, electromagnetic and chemical physics, such magnetic control is typically empirical or even an educated guess. Two magnetic flow control mechanisms: flow damping by steady magnetic fields, and flow stirring by alternating magnetic fields, are investigated numerically. Magnetic damping during optically-heated float-zone crystal growth is modeled using a spectral collocation method. The Marangoni convection at the free melt-gas interface is suppressed by applying a steady magnetic field, measured by the Hartmann number Ha. Using normal mode linear stability analyses, suppression of detrimental flow instabilities is quantitatively determined in a range applicable to experiments (up to Ha = 300 for Pr = 0.02, and up to Ha = 500 for Pr = 0.001). The hydrodynamic flow instability for small Prandtl number P r float-zone is confirmed by energy analyses. Rotating magnetic field stirring during confined crystal growth in an ampoule is also modeled. Decoupled from the flow field at small magnetic Reynolds number, the electromagnetic field is solved in a finite element solver. At low AC frequencies, the force is only in the azimuthal direction but penetrates deep into the melt. In contrast, the magnetic shielding effect is observed at high alternating current (AC) frequencies, where the external magnetic field penetrates only by a skin depth into the electrically conducting media within the short AC cycle. As a result, the electromagnetic body force is primarily confined to the ampoule surface. At these high AC frequencies the magnetic flux lines are drastically distorted within the melt. The body force is fully three-dimensional and is much stronger than at low AC frequencies, but is confined to near the ampoule surface due to the magnetic shielding effect. These models promote fundamental understanding of flow dynamics regulated by electromagnetic body forces. They provide quantitative guidance for crystal growth to minimize trial and error experimentation that is slow and expensive.

In this thesis, development process of de-icing and anti-icing solutions and their flow instability characteristics are presented. In the beginning, the chemical additives in the solutions and their effects on the most critical physical properties of the solutions were investigated. Firstly, chemical additives were added to glycol and water mixtures at different weight ratios one by one in order to see their individual effects. Then, the changes in physical properties were observed when the chemicals were added to water-glycol mixture together. After that, study was focused on effect of polymer which makes the solution pseudoplastic. Further investigations on viscosity behavior of the solution at different pH values, glycol and water mixtures and surfactant weight ratios, which is used for surface tension reduction, were performed. For the investigation of flow instability characteristics of the solutions&rsquo / flows, linear stability analysis for two-layer flows is a basic tool. Firstly, the effects of main parameters on the stability of two-layer flows were observed with a parametric study. Then, the commercially available and developed de-icing and anti-icing solutions were compared according to the characteristics of unstable waves. According to the results, unstable waves on developed de-icing fluids are observed at a lower critical wind speed compared to the commercially available de-icing solution. Moreover, it flows off the wing faster due to a higher value of critical wave speed. Developed anti-icing solution has similar wave characteristics compared to commercially available anti-icing solution, except critical wave speed, which is significantly lower. However, this problem can be overcome by decreasing the viscosity of developed anti-icing solution at very low shear rates.

In this thesis a model involving two coupled nonlinear PDEs is developed to study instability of a two-component metal film due to horizontal electric field and in a high-temperature environment similar to operational conditions of integrated circuits. The proposed model assumes the anisotropies of the diffusional mobilities for two atomic species, and negligible stresses in the film. The purpose of the modeling is to describe and understand the time-evolution of the shape of the film surface. Toward this end, the linear stability analysis (LSA) of the initially planar film surface with respect to small shape perturbations is performed. Such characteristics of the instability as the perturbation growth rate omega and the cut-off wave number are studied as functions of key physical parameters.

A mixing layer is generally considered as a prototype of free shear flows whichoccur in a very broad spectrum of applications from natural phenomena to the engineeringscience. The increasing development of the aeroacoustics, more particularly thanks to theprogress in numerical simulations, has allowed to identify the coherent structures which evolvein the flow as the main sound sources. Furthermore, the emergence of the instability wavestaking the form of the coherent structures can be characterized by the stability analysis. In thiscontext, we propose through this work to perform a global stability analysis, in order tounderstand the emergence of fundamental frequencies, as well as a modal decompositionwithin both a linear and nonlinear framework, to characterize the coherent structures primarilyresponsible for the sound generation. In particular, we propose to develop the methods of theglobal stability with respect to the compressible flows as well as a technique of calculation ofcoherent structures applied to the nonlinear regimes based on the DMD method. Such analysistools are validated and illustrated on an academic configuration of a co-flowing mixing layer, atypical noise amplifier, from a simple case where a single source is implicated in the acousticradiation to a more complex case where two sources are present. Both the temporal and spatialDMD are shown capable of describing the characteristics of the coherent structures in the nearfield and the behaviour of the acoustic waves in the far field. Finally, the methods of the modaldecomposition have proven themselves as a relevant model reduction aiming at designing anefficient control strategy.

In this study, numerical investigations of stability and transition problems were performed for 2D compressible boundary layers over a flat plate in adiabatic wall condition. Emphasis was placed on linear stability theory. The mathematical formulation for 3D boundary layers with oblique waves including detailed theoretical information was followed by use of the numerical techniques for the solution of resulting differential system of the instability problem, consequently an eigenvalue problem. First, two-dimensional sinusoidal disturbances were analyzed at various Mach numbers including the subsonic, transonic, supersonic and even hypersonic flow speeds. In this case, the second mode (acoustic mode), namely the Mack mode, and its behavior with the increasing Mach number were visualized. The results were then compared with the available data in literature concluding with good agreements. Secondly, similar analysis was carried out for oblique waves. Here, not only the effect of flow speed but also the effect of wave orientation was demonstrated. For this purpose, instability problem was solved for several wave angles at each Mach number in the range of M=0 and M=5. In this respect, the angle at which the waves were most unstable was also obtained at each investigated flow speed. The resultant stability diagrams corresponding to M=4 and higher Mach numbers for which both first and the second modes appear revealed that plane waves were more stable than oblique waves for the Tollmien-Schlichting mode, however, this was the opposite for the acoustic mode where oblique waves were observed to be more stable. As a final step, estimation of the transition location was handled for the most unstable wave condition. Smith-Van Ingen transition method was applied as the prediction device. The results representing the influence of Mach number on transition Reynolds number were then compared with the experimental data as well as the numerical ones in literature ending up with very good agreements.

Ce manuscrit est consacré au développement et à la validation d'un nouveau modèle de collision destiné à améliorer la stabilité des modèles lattice Boltzmann (LB) d'ordre élevés lors de la simulation d'écoulements : (1) isothermes et faiblement compressibles à nombre de Reynolds élevés, ou (2) compressibles et comprenant des discontinuités telles que des ondes de choc. Ce modèle de collision s'appuie sur une étape de régularisation améliorée. Cette dernière inclut désormais un calcul par récurrence des coefficients hors-équilibre du développement en polynômes d'Hermite. Ces formules de récurrence sont directement issues du développement de Chapman-Enskog, et permettent de correctement filtrer les contributions non-hydrodynamiques émergeant lors de l'utilisation de maillages sous-résolus. Cette approche est d'autant plus intéressante quelle est compatible avec un grand nombre de réseaux de vitesses discrètes. Ce modèle LB d'ordre élevé est validé tout d'abord pour des écoulements isothermes à nombre de Reynolds élevé. Un couplage avec une technique de capture de choc permet ensuite d'étendre son domaine de validité aux écoulements compressibles incluant des ondes de choc. Ce travail se conclut avec une étude de stabilité linéaire des modèles considérés, le tout dans le cas d'écoulements isothermes. Ceci permet de quantifier de manière distincte l'impact des discrétisations en vitesse et numérique, sur le comportement spéctrale du jeu d'équations associé. Cette étude permet au final de confirmer le gain en stabilité induit par le nouveau modèle de collision. / This thesis is dedicated to the derivation and the validation of a new collision model as a stabilization technique for high-order lattice Boltzmann methods (LBM). More specifically, it intends to stabilize simulations of: (1) isothermal and weakly compressible flows at high Reynolds numbers, and (2) fully compressible flows including discontinuities such as shock waves. The new collision model relies on an enhanced regularization step. The latter includes a recursive computation of nonequilibrium Hermite polynomial coefficients. These recursive formulas directly derive from the Chapman-Enskog expansion, and allow to properly filter out second- (and higher-) order nonhydrodynamic contributions in underresolved conditions. This approach is even more interesting since it is compatible with a very large number of velocity sets. This high-order LBM is first validated in the isothermal case, and for high-Reynolds number flows. The coupling with a shock-capturing technique allows to further extend its validity domain to the simulation of fully compressible flows including shockwaves. The present work ends with the linear stability analysis(LSA) of the new approach, in the isothermal case. This leads to a proper quantification of the impact induced by each discretization (velocity and numerical) on the spectral properties of the related set of equations. The LSA of the recursive regularized LBM finally confirms the drastic stability gain obtained with this new approach.