QC 20100726

Le SPS (Spark plasma sintering) ou frittage flash est une technique innovante de compaction de poudre. Ce procédé fait intervenir le courant électrique pour chauffer l'échantillon en appliquant simultanément une pression. Grâce à la vitesse de chauffage, le procédé SPS apparaît comme étant une technologie prometteuse dans le secteur aéronautique servant à produire des matériaux denses à microstructure fine, composés par des intermétalliques difficiles à fondre, à former et à usiner avec les procédés conventionnels. Cependant, la fabrication de formes complexes est problématique à cause des hétérogénéités en densité qui peuvent apparaître lors de la compaction et qui proviennent de la distribution de la température et des contraintes dans la poudre compactée. La distribution du courant, de la température et des contraintes, ainsi que leurs différents effets, font l'objet d'une large étude, étant responsables de l'homogénéité de la microstructure. Une modélisation numérique 3D du procédé est réalisée, dans le cadre de la librairie CimLib. Elle englobe trois problèmes physiques fortement couplés : électrique, thermique et mécanique. Nous utilisons une approche monolithique qui consiste à résoudre une équation pour chaque problème sur un maillage unique représentant outils et poudre. Tout d'abord le couplage électrique-thermique est modélisé et les simulations numériques sont validées. Une loi de comportement viscoplastique compressible s'appuyant sur un modèle d'Abouaf est utilisée pour modéliser la densification de la poudre de TiAl. Ce modèle est validé par plusieurs cas tests de compaction de poudre dans un contexte lagrangien puis eulérien avant de passer à une simulation complète de couplage électrique-thermique-mécanique. Dans ce contexte monolithique, nous développons un modèle pour prendre en compte les effets du frottement entre la poudre et le moule. Enfin, la loi de comportement utilisée est identifiée pour la poudre intermétallique de TiAl. Le frittage par SPS d'échantillons de différentes tailles est simulé. Les résultats en termes de distribution de densité et déplacement sont validés grâce à une comparaison avec l'expérience.

The objectives in this thesis are to present a model of a variable venturi in an exhaust gas recirculation (EGR) system located in a heavy duty diesel engine. A new legislation called EURO~4 will come into force in 2005 which affects truck development and it will require an On-Board Diagnostic system in the truck. If model based diagnostic systems are to be used, one of the advantages is that the system performance will increase if a model of a variable venturi is used. Three models with different complexity are compared in ten different experiments. The experiments are performed in a steady flow rig at different percentage of EGR gases and venturi areas. The model predicts the mass flow through the venturi. The results show that the first model with fewer simplifications performs better and has fewer errors than the other two models. The simplifications that differ between the models are initial velocity before the venturi and the assumption of incompressible flow. The model that shows the best result is not proposed by known literature in this area of knowledge and technology. This thesis shows that further studies and work on this model, the model with fewer simplifications, can be advantageous.

<p>The objectives in this thesis are to present a model of a variable venturi in an exhaust gas recirculation (EGR) system located in a heavy duty diesel engine. A new legislation called EURO~4 will come into force in 2005 which affects truck development and it will require an On-Board Diagnostic system in the truck. If model based diagnostic systems are to be used, one of the advantages is that the system performance will increase if a model of a variable venturi is used. </p><p>Three models with different complexity are compared in ten different experiments. The experiments are performed in a steady flow rig at different percentage of EGR gases and venturi areas. The model predicts the mass flow through the venturi. The results show that the first model with fewer simplifications performs better and has fewer errors than the other two models. The simplifications that differ between the models are initial velocity before the venturi and the assumption of incompressible flow. </p><p>The model that shows the best result is not proposed by known literature in this area of knowledge and technology. This thesis shows that further studies and work on this model, the model with fewer simplifications, can be advantageous.</p>

Les garnitures mécaniques assurent l'étanchéité d'arbres tournants. L'augmentation des contraintes de fonctionnement a conduit au développement de garnitures à gaz fonctionnant sans contact des faces, séparées par un film fluide de très faible épaisseur. Le frottement entre les anneaux de la garniture, et donc l'usure, est évité.<br />L'étude bibliographique révèle que peu de travaux sur les garnitures pour gaz à hautes pressions ont été réalisés. Les caractéristiques d'un écoulement à haute pression sont examinées et les points-clefs du modèle sont définis : gaz réels, effets d'inertie, effets thermiques, écoulement bloqué. A hautes pressions, le comportement du gaz diffère de celui d'un gaz parfait, un modèle de gaz réel est donc développé. L'équation de Reynolds pour un fluide compressible est modifiée afin de prendre en compte les effets d'inertie. Les effets thermiques dans l'écoulement sont également introduits dans le modèle. L'écoulement bloqué à la sortie du film fluide est résolu grâce à une méthode originale. Les déformations des solides et le couplage thermique sont pris en compte par la méthode des coefficients d'influence. La méthode des éléments finis est utilisée pour la discrétisation des équations et un algorithme itératif permet la détermination des champs de pression et de température. La comparaison avec une solution analytique et des données expérimentales permet de valider le modèle. L'influence du modèle du gaz est présentée. L'étude paramétrique menée avec le modèle numérique permet d'étudier l'influence des effets d'inertie sur l'écoulement par rapport au cas purement visqueux. Finalement, le couplage fluide-solides est étudié. Cette analyse montre que les déformations des faces influencent notablement le comportement des garnitures.

Over the last three decades, CFD simulations have become commonplace as a tool in the engineering and design of high-speed aircraft. Experiments are often complemented by computational simulations, and CFD technologies have proved very useful in both the reduction of aircraft development cycles, and in the simulation of conditions difficult to reproduce experimentally. Great advances have been made in the field since its introduction, especially in areas of meshing, computer architecture, and solution strategies. Despite this, there still exist many computational limitations in existing CFD methods; in particular, reliable higher order and hp-adaptive methods for the Navier-Stokes equations that govern viscous compressible flow. Solutions to the equations of viscous flow can display shocks and boundary layers, which are characterized by localized regions of rapid change and high gradients. The use of adaptive meshes is crucial in such settings -- good resolution for such problems under uniform meshes is computationally prohibitive and impractical for most physical regimes of interest. However, the construction of "good" meshes is a difficult task, usually requiring a-priori knowledge of the form of the solution. An alternative to such is the construction of automatically adaptive schemes; such methods begin with a coarse mesh and refine based on the minimization of error. However, this task is difficult, as the convergence of numerical methods for problems in CFD is notoriously sensitive to mesh quality. Additionally, the use of adaptivity becomes more difficult in the context of higher order and hp methods. Many of the above issues are tied to the notion of robustness, which we define loosely for CFD applications as the degradation of the quality of numerical solutions on a coarse mesh with respect to the Reynolds number, or nondimensional viscosity. For typical physical conditions of interest for the compressible Navier-Stokes equations, the Reynolds number dictates the scale of shock and boundary layer phenomena, and can be extremely high -- on the order of 10⁷ in a unit domain. For an under-resolved mesh, the Galerkin finite element method develops large oscillations which prevent convergence and pollute the solution. The issue of robustness for finite element methods was addressed early on by Brooks and Hughes in the SUPG method, which introduced the idea of residual-based stabilization to combat such oscillations. Residual-based stabilizations can alternatively be viewed as modifying the standard finite element test space, and consequently the norm in which the finite element method converges. Demkowicz and Gopalakrishnan generalized this idea in 2009 by introducing the Discontinous Petrov-Galerkin (DPG) method with optimal test functions, where test functions are determined such that they minimize the discrete linear residual in a dual space. Under the ultra-weak variational formulation, these test functions can be computed locally to yield a symmetric, positive-definite system. The main theoretical thrust of this research is to develop a DPG method that is provably robust for singular perturbation problems in CFD, but does not suffer from discretization error in the approximation of test functions. Such a method is developed for the prototypical singular perturbation problem of convection-diffusion, where it is demonstrated that the method does not suffer from error in the approximation of test functions, and that the L² error is robustly bounded by the energy error in which DPG is optimal -- in other words, as the energy error decreases, the L² error of the solution is guaranteed to decrease as well. The method is then extended to the linearized Navier-Stokes equations, and applied to the solution of the nonlinear compressible Navier-Stokes equations. The numerical work in this dissertation has focused on the development of a 2D compressible flow code under the Camellia library, developed and maintained by Nathan Roberts at ICES. In particular, we have developed a framework allowing for rapid implementation of problems and the easy application of higher order and hp-adaptive schemes based on a natural error representation function that stems from the DPG residual. Finally, the DPG method is applied to several convection diffusion problems which mimic difficult problems in compressible flow simulations, including problems exhibiting both boundary layers and singularities in stresses. A viscous Burgers' equation is solved as an extension of DPG to nonlinear problems, and the effectiveness of DPG as a numerical method for compressible flow is assessed with the application of DPG to two benchmark problems in supersonic flow. In particular, DPG is used to solve the Carter flat plate problem and the Holden compression corner problem over a range of Mach numbers and laminar Reynolds numbers using automatically adaptive schemes, beginning with very under-resolved/coarse initial meshes. / text

We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic system with a heterogeneous coefficient. We consider the equations written in mixed form. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period epsilon, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when epsilon is small. Moreover, we present numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces. On the other hand, we also propose to use multiscale mortars as a coarse component to construct a two-level preconditioner for the saddle point linear system arising from the fine scale discretization of the mixed finite element system. The two-level preconditioners are constructed based on the interfaces. We propose a framework to define the interpolation operators for the face based two-level preconditioners for different combination of coarse and fine scale mortar spaces for matching and nonmatching grids. In this dissertation, we show that for quasi-homogeneous problems and matching grids, the condition number of the preconditioned interface operator is bounded by (log(H/h))², which is the same as the traditional two-level preconditioners, for quasi-homogeneous problems. We show several numerical examples to demonstrate that for the strongly heterogeneous porous media, it is often desirable and even necessary to use a higher dimensional coarse mortar space to construct the coarse preconditioner to achieve convergence. We apply our ideas to study slightly compressible single phase and two-phase flow in a porous medium. We find that for the nonlinear single phase problem, the two-level preconditioners could be successfully applied to the symmetrized linear system. For the two-phase problem, using the fine scale, instead of multiscale, velocity solutions from the flow problem can greatly benefit the transport problem. / text

The main objective of this dissertation is to develop large-eddy simulation (LES) based computational tools for supersonic inlet and combustor design. In the recent past, LES methodology has emerged as a viable tool for modeling turbulent combustion. LES computes the large scale mixing process accurately, thereby providing a better starting point for small-scale models that describe the combustion process. In fact, combustion models developed in the context of Reynolds-averaged Navier Stokes (RANS) equations exhibit better predictive capability when used in the LES framework. The development of a predictive computational tool based on LES will provide a significant boost to the design of scramjet engines. Although LES has been used widely in the simulation of subsonic turbulent flows, its application to high-speed flows has been hampered by a variety of modeling and numerical issues. In this work, we develop a comprehensive LES methodology for supersonic flows, focusing on the simulation of scramjet engine components. This work is divided into three sections. First, a robust compressible flow solver for a generalized high-speed flow configuration is developed. By using carefully designed numerical schemes, dissipative errors associated with discretization methods for high-speed flows are minimized. Multiblock and immersed boundary method are used to handle scramjet-specific geometries. Second, a new combustion model for compressible reactive flows is developed. Subsonic combustion models are not directly applicable in high-speed flows due to the coupling between the energy and velocity fields. Here, a probability density function (PDF) approach is developed for high-speed combustion. This method requires solution to a high dimensional PDF transport equation, which is achieved through a novel direct quadrature method of moments (DQMOM). The combustion model is validated using experiments on supersonic reacting flows. Finally, the LES methodology is used to study the inlet-isolator component of a dual-mode scramjet. The isolator is a critical component that maintains the compression shock structures required for stable combustor operation in ramjet mode. We simulate unsteady dynamics inside an experimental isolator, including the propagation of an unstart event that leads to loss of compression. Using a suite of simulations, the sensitivity of the results to LES models and numerical implementation is studied. / text

Αντικείμενο της Διατριβής αποτελεί η διερεύνηση των δυνατοτήτων του Γεωαφρού Διογκωμένης Πολυστερίνης (ΓΔΠ) για τη χρησιμοποίησή του ως σεισμικό μονωτικό παρέμβλημα σε συμβατικούς τοίχους εδαφικής αντιστήριξης (τύπου βαρύτητας ή προβόλου) καθώς και σε ακρόβαθρα γεφυρών. Η παρούσα έρευνα βασίζεται στην αριθμητική ανάλυση της συμπεριφοράς συμβατικών τοίχων αντιστήριξης κάτω από τη δράση οριζόντιας σεισμικής διέγερσης βάσης. Οι αναλύσεις διεξάγονται τόσο για μη-μονωμένους τοίχους όσο και για τοίχους σεισμικά μονωμένους με παρέμβλημα ΓΔΠ. Το παρέμβλημα έχει τη μορφή κατακόρυφου φύλλου μικρού σχετικά πάχους που τοποθετείται σε επαφή με την πίσω όψη του τοίχου παρεμβαλλόμενο μεταξύ τοίχου και επιχώματος. Οι αναλύσεις διεξάγονται χρησιμοποιώντας τη μέθοδο πεπερασμένων στοιχείων (κώδικας PLAXIS v.8) με την παραδοχή ιξωδοελαστικής συμπεριφοράς εδαφικού επιχώματος και κατακόρυφου ελαστικού τοίχου δεδομένης ευκαμψίας και στροφικής αντίστασης της βάσης. Ως δυναμική διέγερση βάσης χρησιμοποιούνται αρμονικές χρονοϊστορίες επιτάχυνσης μεταβαλλόμενου εύρους και συχνότητας. Κατ’ αρχήν αξιολογείται η αξιοπιστία της χρησιμοποιούμενης μεθόδου ανάλυσης και τα αποτελέσματα των αναλύσεων συγκρίνονται με ανάλογα δημοσιευμένα αποτελέσματα και διαπιστώνεται πολύ καλή συμφωνία όσον αφορά την τιμή της σεισμικής ώθησης και το ύψος εφαρμογής της από τη βάση του τοίχου. Για την περίπτωση των σεισμικά μονωμένων (με παρέμβλημα ΓΔΠ) τοίχων οι εξεταζόμενες παράμετροι περιλαμβάνουν το σχήμα του παρεμβλήματος, την πυκνότητα και το ποσοστιαίο (σε σχέση με το ύψος του τοίχου) πάχος του ΓΔΠ, tr, την ευκαμψία του τοίχου, την καθ’ ύψος μεταβολή του μέτρου ελαστικότητας του ΓΔΠ και τη συχνότητα διέγερσης της βάσης. Η αποτελεσματικότητα της σεισμικής μόνωσης περιγράφεται ποσοτικά με τον συντελεστή Ar που ορίζεται ως το επί τοις εκατό ποσοστό της μείωσης (λόγω μόνωσης) της σεισμικής ώθησης σε σχέση με την τιμή που προκύπτει χωρίς μόνωση. Σχετικά με το σχήμα του παρεμβλήματος (κατά την έννοια του ύψους του τοίχου) διεξήχθησαν αναλύσεις για ορθογωνικό σχήμα και τρία τριγωνικά σχήματα και τα αποτελέσματα υποδεικνύουν ότι η βέλτιστη αποτελεσματικότητα επιτυγχάνεται με χρήση ορθογωνικού σχήματος. Επίσης διαπιστώθηκε ότι είναι δυνατή η επίτευξη τιμών της αποτελεσματικότητας σεισμικής μόνωσης Ar>50% για τιμές πάχους παρεμβλήματος tr 15%. Τα αποτελέσματα υποδεικνύουν επίσης ότι, επειδή η προκύπτουσα σχέση Ar - tr είναι μη γραμμική, απαιτούνται σχετικά μεγάλα πάχη παρεμβλήματος για τη μείωση της σεισμικής ώθησης σε ποσοστό μεγαλύτερο του 50%. Τέλος, για τον αντισεισμικό σχεδιασμό τοίχων αντιστήριξης προτείνεται δοκιμαστικά η εφαρμογή διαδικασίας που βασίζεται στον ΕΑΚ 2000, χρησιμοποιώντας όμως διπλάσια τιμή για το συντελεστή συμπεριφοράς, qw, εφόσον επιδιώκεται η επίτευξη αποτελεσματικότητας Ar=50%. / The objective of the Thesis is the investigation of the possibility to use the Expanded Polystyrene Geofoam (EPS Geofoam) for the seismic isolation of earth retaining walls. The research is based on the results of numerical analyses (using the finite element method) for determining the response of vertical walls supporting horizontal backfill and subjected to horizontal harmonic base excitation. The seismic isolation is realized by placing a column of EPS geofoam (compressible inclusion) between the back-face of the wall and the backfill. The response is calculated by using elastic analysis (with viscous damping for the backfill material). The efficiency of seismic isolation is quantitavely described by the Isolation Efficiency, Ar, defined as the ratio (in percent) of the reduction of earthquake thrust (due to isolation) to the earthquake thrust without isolation. The parameters investigated are the shape of the inclusion, the density and the (percent) thickness, tr, of the EPS geofoam, the wall flexibility, the variation of EPS geofoam modulus of elasticity with depth as well as the amplitude and frequency of excitation. The results of the analyses indicate that the optimum shape of the inclusion is the orthogonal (i.e. constant thickness with depth) whereas the effect of the inhomogeneity of the EPS geofoam along the depth of the wall is negligible, as long as the analysis is conducted using a constant mean value for the Modulus of Elasticity of EPS. The results also indicate that an Isolation Efficiency of about 50% may be achieved by using an inclusion thickness of about 15% of the wall height. Due to the nonlinearity of the relation Ar – tr, further increase of the inclusion thickness has a minor effect on the isolation efficiency of the inclusion. Based on the results of all analyses a tentative procedure is proposed for the earthquake resistant design of earth retaining walls. According to the procedure, the wall is designed following the methodology of the Hellenic Seismic Code (2000) and using qw values twice as those indicated by the Code. The required thickness of the EPS inclusion, tr, is then selected from a diagram relating the tr value to the flexibility of the wall and the density of the inclusion.

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