Dissertations / Theses on the topic 'Inhomogeneous fluids'

In this thesis, we use nonequilibrium molecular dynamics (NEMD) methods to investigate the structural and dynamic properties of highly confined atomic and polymeric fluids undergoing planar Poiseuille flow. We derive 'method of planes' expressions for pressure tensor and heat flux vector for confined inhomogeneous atomic fluids under the influence of three-body forces. Our derivation is validated against NEMD simulations of a confined atomic fluid acted upon by a two-body Barker-Fisher-Watts force coupled with the Axilrod-Teller three-body force. Our method of planes calculations are in excellent agreement with the equivalent mesoscopic route of integrating the momentum and energy continuity equations directly from the simulation data. Our calculations reveal that three-body forces have an important consequence for the isotropic pressure, but have negligible in�uence on the shear stress and heat flux vector for a confined simple fluid. We use the non-local linear hydrodynamic constitutive model, proposed by Evans and Morriss [1] for computing a viscosity kernel, a function of compact support, for inhomogeneous nonequilibrium fluids. Our results show that the viscosity kernel, �(y), has a peak at y = 0, and gets smaller and decays to zero as y increases. Physically, it means that the strain rate at the location where we want to know the stress contributes most to the stress, and the contribution of the strain rate becomes less significant as the relative distance y increases. We demonstrate that there is a limitation in the model when it is applied to our confined fluids due to the effect of domain restriction on inverse convolution. We study the nanorheology of simple polymeric fluids. Our NEMD simulation results show that sufficiently far from the walls, the radius of gyration for molecules under shear in the middle of the channel follows the power law, Rg / N�, where N is the number of bonds and the exponent has a value � = 0:60�0:04, which is larger than the melt value of 0:5 for a homogeneous equilibrium �uid. Under the conditions simulated, we find that viscous forces dominate the flow, resulting in the onset of plug-like flow velocity pro�les with some wall slippage. An examination of the streaming angular velocity displays a strong correlation with the radius of gyration, being maximum in those regions where Rg is minimum and vice-versa. The angular velocity is shown to be proportional to half the strain rate su�ciently far from the walls, consistent with the behaviour for homogeneous fluids in the linear regime. Finally, we make some concluding remarks and suggestions for future work in the final chapter.

Investigations have been carried out via Monte Carlo simulation of simple, inhomogeneous fluids into two important quantities of colloidal systems; the depletion force and the disjoin'': ing pressure. Simulations of a hard-sphere solvent confined to the annular wedge formed between a spherical hard colloid and a planar hard wall were performed in order to shed light on the recently discovered disagreement of several results for the depletion force in the nanD-colloidal regime at solvent density pa3 > 0.6. Emphasis is placed on attempting to understand the limits of validity in terms of colloid size for the Derjaguin approximation applied to depletion forces and fundamental-measures-theory density functional theory (FMT-DFT), and the manner in which the depletion force scales between these two results at intermediate colloid sizes. The depletion force was evaluated via an exact statistical mechanical sum rule requiring only knowledge of the integral of the one-body density of solvent at the planar hard wall from the apex of the wedge to a large distance from the colloid. Simulations were performed for a colloid/solvent size ratio of 8 = 20 for several colloid-wall separations, h, between physical contact and the hard-sphere solvent diameter, a, at pa3 = 0.764, the results for the depletion force appearing to be consistent with a recently proposed theoretic model suggesting a (curiously non-analytic) 8-1/ 2 correction to the linear scaling behaviour of the depletion force with colloid size between the FMT-DFT and Derjaguin results, with the Derjaguin result valid in the large colloidal limit 8 --t 00 and FMT-DFT only as colloid size approaches solvent size. Further simulations, restricted to h = a for 8 = 10, 30, 50 and 100 though reveal that at least for this special separation 8-1/ 2 scaling does not hold, suggesting that to confirm scaling behaviour requires simulations over the entire range 0 ~ h ~ a for several values of 8. The disjoining pressure profile has been simulated through the three-phase contact line formed between the liquid-vapour interface of a square-well fluid at bulk liquid-vapour coexistence and a planar, square-well wall for three different depths of the wall-fluid potential. The disjoining pressure is found to follow a smooth, downward curve across the contact line that is well fit by a Gaussian. The simulation method used to make these disjoining pressure measurements has been validated using a statistical mechanical sum rule linking the integral of the disjoining pres- . . sure across the contact line to the liquid-vapour surface tension and macroscopic Young's contact angle, both measured from the interface far from three-phase contact.

A liquid crystal (LC) is a substance that exhibits phases intermediate between a crystal and a disordered liquid state. LCs have attracted longstanding research interest because of their potential commercial applications in opto-electronics, pharmaceuticals and surfactants but also because ordered soft matter is prevalent in bio-molecular systems such as DNA and lipid cell membranes. In liquid-crystalline systems, both molecular shape and asymmetric attractive interactions contribute to the formation and ultimate stability of anisotropic phases. The research outlined in this thesis provides a fundamental understanding of these systems by developing theoretical models and undertaking detailed molecular simulation studies. In the first part of this thesis, prototype oblate models for LCs are studied: cut spheres and cylindrical discs. Coupled with a scaled Onsager approach, a general equation of state (EoS) for hard-core discotic LCs is developed that allows for an accurate description of the isotropic and nematic phases of oblate discs by introducing a correction to incorporate the negative contributions from high-order virial coefficients. Combining the above mentioned approach with an extended cell approach, the isotropic-nematic-columnar phase diagram of cut spheres is determined. The accuracy of the EoS is assessed by comparison with the more traditional Parsons-Lee description and existing simulation data. Although the anisotropic athermal hard-body fluid is a reasonable representation of lyotropic or colloidal LCs, for thermotropic LC systems temperature plays a key role. In the second part of this thesis a model of hard-core particles incorporating additional anisotropic attractive interactions is proposed to describe thermotropic LCs. Based on a perturbation theory and the Onsager-Parsons-Lee approach, a van der Waals-type (meanfield level) theory of attractive hard-core particles is formulated in a compact algebraic form. The phase diagrams of model attractive prolate (spherocylinder) and oblate (cylindrical disc) molecules are calculated in order to examine the separate effects of molecular shape and anisotropic attractive interactions. As a practical example, a coarse-grained model comprising an attractive spherocylinder is employed to describe phase behaviour of solutions of the polypeptide poly-(γ-benzyl-L-glutamate) (PBLG) in dimethylformamide (DMF). Quantitative agreement between the results obtained from the EoS and experimental data is obtained. In the final part of the thesis, a detailed Monte Carlo (MC) simulation study of athermal mixtures of hard spherocylinders and hard spheres between two well separated parallel hard walls is performed. A combination of constant volume (canonical ensemble) and constant (normal) pressure (isobaric-isothermal ensemble) simulations are carried out. With these simulations, the bulk phase behaviour as well as surface-induced LC ordering are explored. The phase diagram of binary mixtures of hard spherocylinders and hard spheres is presented and is compared with the predictions of the one-fluid Parsons-Lee and many-fluid theories. Rich phase behaviour is exhibited on the surface of the walls: drying (de-wetting), isotropic wetting, and nematic wetting are all observed. A previously unreported entropy-driven transition from a bulk nematic state to a homeotropic smectic surface ordering (with particles arranged in a perpendicular orientation relative to the surface plane) is seen in for both the pure hard rod system and the mixture of hard rods and hard spheres as the density is increased (high pressure states).

Ce travail vise à étudier les propriétés de transport et le comportement poromécaniquede fluides simples confinés dans des nanopores lamellaires par le biais de simulationsmoléculaires. Pour ce faire, nous avons proposé différents schémas de simulations de ladynamique moléculaire dans des ensembles adaptés aux propriétés étudiées (diffusion demasse, viscosité, force de friction, gonflement …). Il a été note que les propriétés de transportde fluides fortement inhomogènes variaient fortement dans la direction perpendiculaire auxmurs solides. Nous avons alors proposé une approche non-locale permettant de déterminerquantitativement la viscosité locale de fluides inhomogènes à partir du profil de densité etapplicable pour des sphères dures, molles et le fluide de Lennard-Jones. Il a été égalementmontré qu’un fluide de Lennard-Jones fortement confiné pouvait avoir un comportementviscoplastique (et rhéofluidifiant) si un ordre structurel était induit dans le fluide par laposition relative des murs solides. Enfin, nous avons montré qu’une modification importantede la pression de solvatation du fluide confiné peut être induite par cisaillement ce qui peutinduire un gonflement « dynamique » d’un nanopore lamellaire
This work aims at investigating the transport properties and the poromechanics of simple spherical fluids confined in slit nanopores through molecular simulations. To do so, we have proposed different schemes to perform molecular dynamics simulations in ensembles adequate to deal with the properties we were looking after (mass diffusion, shear viscosity,friction force, swelling …). The transport properties of strongly inhomogeneous fluids were found to be varying with space perpendicularly to the solid walls. We have then proposed a non-local approach to determine quantitatively the local shear viscosity of such inhomogeneous fluids from the density profile applicable from the Hard-Sphere to the Lennard-Jones fluids. In addition, it has been shown that highly confined Lennard-Jones fluid may exhibit a visco-plastic (+ shear thinning) behavior when a strong structural order is induced in the whole confined fluid because of the relative position of the solid walls. Finally, it was demonstrated that shear induced modifications of the solvation pressure of a confined fluid may exist that leads to a “dynamic” swelling when a slit micropore is sheared

The dynamics of fractured media flows is relevant in many processes of interest that range from the micrometre to the kilometre lengthscales. Flow in disordered media has been proven to be an interesting system to study fundamental physics problems also. The goal of this Thesis is to study the spatio-temporal dynamics of the oil-air interface between displaced air and invading oil, in imbibition displacements through a model open fracture. The research combines exhaustive experimental work with accurate data analysis based on methods of nonlinear statistical physics. Imbibition is a process of fluid transport in a medium in which an invading fluid that preferentially wets the medium displaces the previously resident, immiscible fluid. According to the driving protocols we define spontaneous imbibition, in which the interface is driven at constant pressure difference between the inlet and the outlet of the medium and the flow rate is free to change in time, and forced-flow imbibition in which a constant flow rate of fluid is imposed at the inlet and the pressure difference may change in time. Our model open fracture consists of a Hele-Shaw (HS) cell, i.e. two parallel plates separated by a narrow gap spacing. Two configurations that mimic an open fracture have been explored: a flat HS cell, with constant aperture, and a HS cell with a dichotomic gap spacing randomly distributed in space (disordered cell). Silicone oils of different viscosities have been used as invading fluid. The advancement of the fluid front is recorded by using either CCD or CMOS cameras. An edge-tracking algorithm is applied to the binarized images to obtain front positions. We first study the evolution in time of the mean position of the interface in spontaneous imbibition experiments (capillary rise) through our two model open fractures. Experiments are performed with and without the presence of an effective gravity, achieved systematically tilting the cell against the advancement of the front or keeping it horizontal. Different pressure differences between the inlet and the outlet are systematically explored as well. We propose a new analytical solution for the spatially-averaged position of the imbibing front, based on a pressure balance equation, that reproduces experimental results at all times. In invasion of the disordered cell, capillary pressure and permeability variations distort imbibition fronts due to medium heterogeneities, while viscous pressure and surface tension tend to restore their flatness. As a result, the oil-air interface develops long-range correlations, with a lateral correlation length that depends on the capillary number Ca, tuned experimentally. Consequently, fronts advancing through the disordered cell are not flat during the whole experiment but get rough as the fluid penetrates the medium from an initially-flat interface to a final, statistically-invariant rough front. The kinetic roughening process, that occurs as a consequence of the competition of forces acting on the interface at different lengthscales, has been characterized in low-viscosity, forced-flow imbibition displacements obtaining a super-rough scaling scenario. The complex spatio-temporal dynamics of the front is studied at the statistically-stationary state of saturated front roughness in forced-flow experiments. We have analysed the spatial and temporal correlations of velocities of the front from the local scale, much smaller than the lateral correlation length and the characteristic length of the disorder, to the system size. Imbibition fronts exhibit burst-like dynamics, advancing by spatially-localized avalanches. These avalanches are power-law distributed in sizes and durations with exponential cutoffs. Power-law exponents are independent of the experimental conditions while the cutoffs diverge as Ca is reduced. We study also the intermittent character of these displacements by analysing different moments of the statistical distributions of velocity increments as a function of the time lag. We show that intermittency is controlled by two parameters only. The ensemble of results presented in this Thesis supports a very general picture of the nonequilibrium dynamics of slowly-driven fronts in open fractures. The lateral propagation of interfacial fluctuations is controlled by local mass conservation, through the lateral correlation length. The advancement of the interface in the direction of propagation is controlled by the characteristic extent of the disorder and by the mean front velocity.
L'objectiu de la tesi és l'estudi de la dinàmica espacio-temporal de la interfície entre aire desplaçat i oli invasor, en desplaçaments d'imbibició a través d'un model de fractura oberta. La recerca presentada combina un extens i exhaustiu treball experimental amb una anàlisi de dades acurada, basada en mètodes utilitzats en física estadística de no-equilibri. El procés d'imbibició, en que el fluid invasor mulla preferentment el medi envaït, és rellevant en diverses situacions d'interès, des de fluxos fisiològics a la irrigació del sòl i l'extracció de petroli. També és un sistema model interessant per a l'estudi de problemes de física fonamental degut a les correlacions de llarg abast que es desenvolupen al front, que indueixen una dinàmica complexa. Primer s'estudia l'avançament de la posició mitjana del front de fluid en condicions d'imbibició espontània (ascens capil•lar). Hem proposat una nova solució analítica que reprodueix els resultats experimentals tant amb presència de gravetat efectiva oposant-se a l'avançament del fluid com sense. En experiments d'imbibició forçada s'ha caracteritzat el procés d'arrugament dinàmic (kineticroughening) del front oli-aire a baixa viscositat. L'escenari d'escalament observat és super-rugós. Finalment s'ha estudiat la dinàmica del sistema en el règim estadísticament estacionari. S'han analitzat les correlacions temporals i espacials de les velocitats des de l'escala local, per sota la mida de les heterogeneïtats del desordre, fins a la mida del sistema. El front mostra una dinàmica a batzegades caracteritzada en termes d'allaus. Les mides i durades d'aquestes allaus estan distribuïdes estadísticament en llei de potències, amb exponents independents de les condicions experimentals, amb un truncament exponencial, que divergeix en reduir el nombre de capil•laritat. La intermitència del senyal s'ha quantificat i se n'ha extret els dos paràmetres que la controlen. El conjunt de resultats presentats en aquesta tesi dóna suport a una descripció molt general de la dinàmica de propagació lenta de fronts d'imbibició fora de l'equilibri en fractura oberta. La conservació local de massa controla la correlació lateral de les fluctuacions de la interfície. La longitud característica de les illes de desordre i la velocitat mitjana del front, per la seva banda, controlen l'avançament del front en la direcció de propagació.

Les expériences de laboratoire montrent que, même dans des solutions très diluées, l’interaction des polymères avec des écoulements fluides peut modifier considérablement les propriétés des écoulements turbulents ou, si l’écoulement est laminaire, peut déclencher un nouveau type de mouvement irrégulier appelé «turbulence élastique». Les écoulements dans un tel régime dynamique sont prometteurs pour améliorer l'efficacité du mélange dans les applications microfluidiques, qui impliquent souvent la présence d'impuretés de taille finie en suspension, telles que des particules solides petites et lourdes. La compréhension de la dispersion des particules dans les écoulements à grand nombre de Reynolds des fluides newtoniens et non newtoniens a déjà été abordée dans des études antérieures, qui ont mis en évidence des effets à la fois à grande et à petite échelle et est un sujet d'intérêt à la fois fondamental et pour des applications environnementales ou industrielles par exemple. Cependant, la dynamique des particules dans les écoulements élastiques et turbulents reste encore peu explorée. L’étude ici vise à étudier les propriétés d’agrégation de particules matérielles ponctuelles (plus lourdes que le fluide porteur) dans les fluides viscoélastiques dans des conditions de turbulence élastique (c’est-à-dire dans le cas de faible inertie du fluide et de grande élasticité). Nous effectuons des simulations numériques directes bi-dimensionelles d’écoulements périodiques avec cisaillement moyen de Kolmogorov avec des solutions de polymères dilués décrites par le modèle Oldroyd-B. Les caractéristiques à petite et grande échelle de la distribution résultante inhomogène de particules sont examinées, en se concentrant sur leur connexion avec la structure sous-jacente de l’écoulement . Notre analyse révèle que les particules sont préférentiellement regroupées dans des régions où les polymères sont instantanément maximalement étirés. L’intensité d’un tel phénomène dépend de l’interaction paramétrée par le nombre de Stokes, entre l’inertie des particules et l’échelle de temps typique associée à l’écoulement de turbulence élastique, et est la plus grande pour des valeurs intermédiaires d’inertie de particules. En particulier, il est montré que la concentration préférentielle de suspensions de particules inertielles dans de tels écoulements ressemblant à la turbulence découle de la nature dissipative de leurs dynamiques. Nous établissons une caractérisation quantitative de ce phénomène (utilisant la corrélation et la dimension de Kaplan-Yorke) qui permet de le relier à l’accumulation de particules dans des régions de l’écoulement filamenteuses fortement déformées produisant des grappes de dimension fractale faiblement supérieure à 1. À plus grande échelle, les particules subissent une ségrégation de type turbophorétique dans la direction non-homogéne de l'écoulement. En effet, nos résultats indiquent que la distribution des particules est fortement liée aux structures moyennes de l’écoulement de type turbulent. En raison de la turbophorèse, les profils de densité moyenne atteignent leur maximum dans les régions où la diffusivité turbulente est la plus faible. L'inhomogénéité à grande échelle de la distribution des particules est interprétée dans le cadre d'un modèle dérivé dans la limite d'inertie des particules, petite mais finie. Les caractéristiques qualitatives de différents observables (telles que L'écart quadratique moyen de la distribution des particules par rapport à la distribution uniforme) sont, dans une large mesure, indépendantes de l'élasticité du l’écoulement. Quand celle-ci est augmentée, on constate cependant que cette dernière diminue légèrement le degré global moyen de mélange turbophorétique
Laboratory experiments show that, even in very dilute solutions, the interaction of polymers with fluid flows can dramatically change the properties of turbulent flows or, if the flow is laminar, can trigger a new sort of irregular motion named “elastic turbulence”. Flows in such a dynamical regime are promising for enhancing mixing efficiency in microfluidic applications, which often involve the presence of suspended finite-size impurities, like small and heavy solid particles. The understanding of particle dispersion in high-Reynolds number flows of Newtonian, as well as non-Newtonian, fluids were addressed by previous investigations, and it is a subject of interest both at a fundamental level and for applications, e.g., environmental or industrial ones. However, the dynamics of particles in elastic turbulent flows are still quite unexplored.The present study aims at investigating the aggregation properties of pointlike material particles (heavier than the carrying fluid) in viscoelastic fluids in elastic turbulence conditions (i.e. in the limit of vanishing fluid inertia and large elasticity). We carry out extensive direct numerical simulations of the periodic Kolmogorov mean shear flow of two-dimensional dilute polymer solutions described by the Oldroyd-B model. Both the small- and large-scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the underlying flow structure. Our analysis reveals that particles are preferentially clustered in regions of instantaneously maximally stretched polymers. The intensity of such a phenomenon depends on the interplay, parametrized by the Stokes number, between the particle inertia and the typical time scale associated with the elastic turbulence flow, and is the largest for intermediate values of particle inertia.In particular, it is shown that the preferential concentration of inertial particle suspensions in such turbulent-like flows follow from the dissipative nature of their dynamics. We provide a quantitative characterization of this phenomenon (using correlation and Kaplan-Yorke dimension) that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of fractal dimension slightly above 1.At larger scales, particles are found to undergo turbophoretic-like segregation along the non-homogeneity direction of the flow. Indeed, our results indicate that the particle distribution is strongly related to the mean turbulent-like structures of the flow. As an effect of turbophoresis, average density profiles peak in the regions of lowest turbulent eddy diffusivity. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables (such as root-mean-square deviation of the particle distribution, relative to the uniform one) are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing

Modem measurement methods ofthe surface turbulent fluxes (STF) of heat, moisture and momentum in the near surface atmospheric layer by the eddy correlation method and their calculation, relay on the validity of the similarity theory of Monin-Obukhov, which requests stationarity and horizontal homogeneity. Experimental data taken at specially selected sites allowed to develop this concept. Recently performed experiments, purposely conducted in non-ideal conditions showed an underestimation ofthe STF values. To systematise this effect it is suggested to parameterize such underestimation as the influence of inhomogeneity and nonstationarity of the landscape and the atmosphere around the point of observation. This scheme might prove to be useful for the design of new validation experiments in non-ideal terrain
Modeme Meßmethoden zur Erfassung der turbulenten Oberflächenflüsse für fühlbare und latente Wärme sowie Impuls mit Hilfe der Eddy-Korrelations-Methode basieren für die bodennahe Grenzschicht auf der Monin-Obukhov-Turbulenztheorie, die stationäre und horizontal homogene Verhältnisse voraussetzt. Über speziell ausgewählten Oberflächen wurde dieses Konzept häufig mit Erfolg überprüft. Experimente jedoch, die gezielt unter inhomogenen Verhältnissen durchgeführt werden, zeigen oft eine Unterschätzung der turbulenten Oberflächenflüsse. Es wird vorgeschlagen, diese Unterschätzungen als einen Einfluß inhomogener Umbegungsbedingungen und instationärer atmosphärischer Prozesse zu interpretieren und zu systematisieren. Dieses Schema kann dazu beitragen, eine neue Art von Validierungsexperimenten unter natürlichen Verhältnissen einer inhomogenen Umgebung zu entwerfen

Le travail engagé dans cette thèse porte sur l'étude numérique des Interactions Fluide-structure en hydrodynamique. Dans une première partie, une analyse détaillée des méthodes de couplage (schémas décalés) a été effectuée sur un cas académique. Il s'agit de la résolution de l'équation non-linéaire de Burgers dans un domaine mobile, dont I'interface mobile est représentée par un système de type masse ressort. Selon la discrétisation en temps et la linéarisation du problème couplé, on distingue quatre schémas de couplages différents : explicite, semi-implicite, implicite-externe et implicite-interne. Une étude comparative des performances en vitesse de convergence et en temps de calcul de ces schémas a été effectuée. Les performances varient suivant le schéma de couplage utilisé. Le schéma explicite permet un calcul rapide en comparaison des autres schémas. En revanche il n'assure pas la conservation de l'énergie mécanique à I'interface fluide-structure. D'où le problème de stabilité du schéma numérique. Ce problème ne se pose pas pour les algorithmes de couplage implicites, car dans ce cas la conservation de l'énergie à I'interface est assurée. Il s'agit en effet d'une condition de convergence du schéma implicite. Ce schéma requière plus de temps de calcul, mais il est nécessaire pour avoir plus de précision dans les résultats. Par ailleurs, I'analyse des déplacements de I'interface fluide-structure montre que l'écart entre la position de I'interface comme étant le bord mobile du fluide et la position de la structure, dépend principalement du schéma d'actualisation du maillage choisi.Dans une deuxième partie une extension de l'étude des algorithmes de couplage à un problème plus concret d'IFS est effectuée. Un hydrofoil en pilonnement et tangage est ainsi étudié. L'équation de la dynamique de I'hydrofoil est écrite en considérant un centre de rotation situé à une distance non nulle du centre de gravité.Ce qui rend l'équation non-linéaire et introduit un couplage des deux modes pilonnement et tangage) ainsi qu'un amortissement du tangage. La dynamique de I'hydrofoil est étudiée pour différentes configurations : en mouvement libre ou forcé, dans un fluide au repos ou en écoulement. On observe que le mouvement de I'hydrofoil est pseudo périodique amorti. L'évolution des charges hydrodynamiques suit également cette tendance et tend vers un point d'équilibre. L'étude vibratoire montre bien une modification des fréquences propres du système, qui varient suivant que le fluide est au repos ou en écoulement. Le problème est également couplé à l'équation de la position du centre de pression, qui dépend de la position de I'hydrofoil et de l'écoulement. Celle-ci présente une singularité lorsque la portance et la traînée s'annulent simultanément.Enfin Les équations prenant en compte la présence d'un fluide non-homogène à I'interface fluide-structure, du type des écoulements cavitants par poche stationnaire ou auto-oscillante, ont été développés. La méthode consiste à séparer les variables du fluide en écoulement autour d'un hydrofoil immobile d'une part et celles de l'écoulement généré par la vibration de I'hydrofoil d'autre part. Il en résulte un opérateur de masse ajoutée non symétrique en milieu non homogène et un opérateur d'amortissement ajouté dû au taux de variations de masse volumique à l’interface dans le cas auto-oscillant. L'ensemble se traduit par une modulation au cours du temps des fréquences propres et des amplitudes du système
A numerical study of Fluid Structure Interaction (FSI) in hydrodynamic case is adressed in this thesis. Thirstly, the analysis of coupling methods (staggered schemes) was established to an academic case. It corresponds to the resolution of non linear Burgers equation in a moving domain where the moving interface is assimilated to a mass spring system. According to the time discretisation and linearization of the coupled problem, four coupling scheme can be defined : explicit, semi-implicit, implicit-outer and implicit-inner. A comparative performance study in convergence and computing time were performed. The performance depends on the coupling scheme used. The explicit scheme requires less time compared to the others schemes. However it does not allow the mechanical energy conservation at the interface, inducing the stability issue of the numerical scheme. This instabilities does not arise for the implicit coupling algorithms because the energy conservation at the interface is fulfilled. lndeed, a convergence condition is added for implicit schemes. Even though these schemes require more computing time, they are necessary to get better precision. Inter alia, the fluid-structure interface analysis shows that the gap between the interface taken as the moving boundary and the structure position mostly depends on the actualization scheme of the chosen mesh.In the second part, the coupling algorithm study is extended to physical problem of FSI. A hydrofoil in heave and pitch immersed in a fluid flow is then studied. The equation of hydrofoil movement takes account the distance between the rotation center and the center of gravity. This causes the equation to be nonlinear and introduces a coupling of the two movements (heave and pitch) and a damping of the heave movement. The hydrofoil dynamic is studied for different configurations : forced movements or not, immersed in a fluid at rest or a flowing one. It shows that the hydrofoil movement is pseudo-periodic followed by a damping movement. The hydrodynamic forces tend to follow the same evolution and converge to an equilibrium point. The vibration study clearly shows a frequency modification of the system that depends on the fluid flow (at rest or with an inflow). The problem is also coupled to center of pressure position's equation which depends on the hydrofoil position and the fluid flow. The trend of the position presents a singularity when the lift and drag coefficients vanishes at the same time.Last part, the equation that take into account the inhomogeneous characteristic of the fluid at the fluid-structure interface as well as sheet cavitation in steady or unsteady case, was developed. The method allows the separation of the fluid variables when flowing around the fixed hydrofoil on one hand and the flow generated by the hydrofoil vibration one the other. This introduces an asymmetric added mass operator and an added damping operation due to the variation of the density of the fluid at the interface in unsteady case.The whole system results in a natural frequencies and amplitudes modulation over time

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of composition in molecular simulations. The CPP method applies a spatially varying external potential to the simulation, causing the composition to depend upon position in the simulation cell. Following equilibration, the homogeneous chemical potential as a function of composition can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. The CPP method allows one to predict chemical potential for a wide range of composition points using a single simulation and works for dense fluids where other prediction methods become inefficient. For pure-component systems, three different methods of approximating the inhomogeneous correction are compared. The first method uses the van der Waals density gradient theory, the second method uses the local pressure tensor, and the third method uses the Triezenberg-Zwanzig definition of surface tension. If desired, the binodal and spinodal densities of a two-phase fluid region can also be predicted by the new method. The CPP method is tested for pure-component systems using a Lennard-Jones (LJ) fluid at supercritical and subcritical conditions. The CPP method is also compared to Widom's method. In particular, the new method works well for dense fluids where Widom's method starts to fail.The CPP method is also extended to an Ewald lattice sum treatment of intermolecular potentials. When computing the inhomogeneous correction term, one can use the Irving-Kirkwood (IK) or Harasima (H) contours of distributing the pressure. We show that the chemical potential can be approximated with the CPP method using either contour, though with the lattice sum method the H contour has much greater computational efficiency. Results are shown for the LJ fluid and extended simple point-charge (SPC/E) water. We also show preliminary results for solid systems and for a new LJ lattice sum method, which is more efficient than a full lattice sum when the average density varies only in one direction. The CPP method is also extended to activity coefficient prediction of multi-component fluids. For multi-component systems, a separate external potential is applied to each species, and constant normal component pressure is maintained by adjusting the external field of one of the species. Preliminary results are presented for five different binary LJ mixtures. Results from the CPP method show the correct trend but some CPP results show a systematic bias, and we discuss a few possible ways to improve the method.

Modem measurement methods ofthe surface turbulent fluxes (STF) of heat, moisture and momentum in the near surface atmospheric layer by the eddy correlation method and their calculation, relay on the validity of the similarity theory of Monin-Obukhov, which requests stationarity and horizontal homogeneity. Experimental data taken at specially selected sites allowed to develop this concept. Recently performed experiments, purposely conducted in non-ideal conditions showed an underestimation ofthe STF values. To systematise this effect it is suggested to parameterize such underestimation as the influence of inhomogeneity and nonstationarity of the landscape and the atmosphere around the point of observation. This scheme might prove to be useful for the design of new validation experiments in non-ideal terrain.
Modeme Meßmethoden zur Erfassung der turbulenten Oberflächenflüsse für fühlbare und latente Wärme sowie Impuls mit Hilfe der Eddy-Korrelations-Methode basieren für die bodennahe Grenzschicht auf der Monin-Obukhov-Turbulenztheorie, die stationäre und horizontal homogene Verhältnisse voraussetzt. Über speziell ausgewählten Oberflächen wurde dieses Konzept häufig mit Erfolg überprüft. Experimente jedoch, die gezielt unter inhomogenen Verhältnissen durchgeführt werden, zeigen oft eine Unterschätzung der turbulenten Oberflächenflüsse. Es wird vorgeschlagen, diese Unterschätzungen als einen Einfluß inhomogener Umbegungsbedingungen und instationärer atmosphärischer Prozesse zu interpretieren und zu systematisieren. Dieses Schema kann dazu beitragen, eine neue Art von Validierungsexperimenten unter natürlichen Verhältnissen einer inhomogenen Umgebung zu entwerfen.

In this work we study vertical, acoustic propagation in a non-homogeneous media for a spatially-compact, time-harmonic source. An analytical, 2-layer model is developed representing the acoustic pressure disturbance propagating in the atmosphere. The validity of the model spans the distance from the Earth's surface to 30,000 meters. This includes the troposphere (adiabatic), ozone layer (isothermal), and part of the stratosphere (isothermal). The results of the model derivation in the adiabatic region yield pressure solutions as Bessel functions of the First (J) and Second (Y) Kind of order $-\frac{7}{2}$ with an argument of $2 \Omega \tau$ (where $\Omega$ represents a dimensionless frequency and $\tau$ is a dimensionless vertical height in z (vertical coordinate)). For an added second layer (isothermal region), the pressure solution is a decaying sinusoidal, exponential function above the first layer. In particular, the vertical, acoustic propagation is examined for various configurations. These are divided into 2 basic classes. The first class consists of examining the pressure response function when the source is located on boundary interfaces, while the second class consists of situations where the source is arbitrarily located within a finite layer. In all instances, a time-harmonic, compact source is implicitly understood. However, each class requires a different method of solution. The first class conforms to a general boundary value problem, while the second requires the use of Green's functions method. In investigating problems of the first class, 3 different scenarios are examined. In the first case, we apply our model to a semi-infinite medium with a time-harmonic source ($e^{-i \omega t}$) located on the ground. In the next 2 cases, a semi-infinite medium is overlain on the previous medium at a height of z=13,000 meters. Thus, there exist two boundaries: the ground and the layer interface between the 2 media. Sources placed at these interfaces represent the 2nd and 3rd scenarios, respectively. The solutions to all 3 cases are of the form $A \frac{J_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}} + B \frac{Y_{-\frac{7}{2}}(2 \Omega \tau)}{{\tau}^{-\frac{7}{2}}}$, where \textit{A} and \textit{B} are constants determined by the boundary conditions. For the 2nd class, we examine the application to a time-harmonic, compact source placed arbitrarily within the 1st layer. The method of Green's functions is used to obtain a particular solution for the model equations. This result is compared with a Fast Field Program (FFP) which was developed to test these solutions. The results show that the response given by the Green's function compares favorably with that of the FFP. Keywords: Linear Acoustics, Inhomogeneous Medium, Layered Atmosphere, Boundary Value Problem, Green's Function Method

Nous avons étudié les phénomènes convectifs et leur interaction dynamique avec la formation des microstructures pendant la solidification dirigée d’alliages étalliquesbinaires.La méthode post-mortem a été utilisée d’abord pour étudier la Transition olonnaire-Equiaxe pendant la solidification dirigée d’échantillons cylindriques d’Al-3,5wt%Ni non affiné sous la Technique de Rotation Accélérée de Creuset. La simulation numérique a été éffectuée et acquérie les résultats en concordance avec les manipulations.La technique in-situ a été appliquée pour comprendre l’évolution en fonction de temps des grains pendant solidification d’Al-4wt%Cu. La caractéstiques tatistiques des grains ont été discutées.La convection d’instabilité déclenchée par la poussée ou la tension superfaciale sous les gradients thermiques verticale et horizontale dans un système de double couches liquide-zone poreuse ont réspectivement étudié par analysis d’instabilité linéaire.L’inhomogénéité de la perméabilité de zone pateuse dendritique a été tenue en compte afin de comprendre son influence sur le début de convection pendant la solidification dirigée d’Al-3,5wt%Li
We studied the convective phenomena and their dynamical interaction with the formation of the microstructurs during directional solidification of binary metallic alloys.The post-mortem method was used first to study the Columnar-Equiaxed-Transition during the directional solidification of unrefined Al-3.5wt%Ni in cylindric samples under the Accelerated Crucible Rotation Technique. The numerical imulation was carried out and achieved the results in agreement with experiments.The in-situ technique was applied to understand the evolution of equiaxed grains during solidification of Al-4wt%Cu in function of time. The statistical characteristics of equiaxed grains were discussed.The buoyancy-driven and surface-tension-driven instability convection under vertical and horizontal thermal gradients in a liquid-porous double-layered system were respectively investigated through linear instability analysis.The inhomogeneity of the dendritic mush permeability was taken into account in order to understand its influence on the triggering of convection during the directional solidification of Al-3.5wt%Li

Am Anfang des Entwicklungsprozesses eines Gussbauteils für die Automobilbranche steht klassischerweise die konstruktive Ausarbeitung und die Auslegung auf Zielgrößen, wie Festigkeit, Steifigkeit bzw. die Erfüllung der Crashlasten. Im nächsten Entwicklungsschritt wird, oftmals in Zusammenarbeit mit externen Lieferanten, das Werkzeugkonzept entwickelt und die Herstellbarkeit mit Hilfe von Gießsimulationen abgesichert. Bei der Fertigung verursachen streuende Prozessgrößen, wie etwa Geschwindigkeits- oder Temperaturniveaus, Schwankungen in der Leistungsfähigkeit des Endprodukts (z. B. lokale Bruchdehnung oder Zugfestigkeit). Maßnahmen zur Erhöhung der Prozessstabilität und zur Reduktion des Verschleißes konzentrieren sich oftmals auf die erfahrungsbasierte Verbesserung des Fertigungsprozesses und Anpassungen des Anguss- und Überlaufsystems. Größere Änderungen der Bauteilgeometrie sind häufig aus zeitlichen Gründen nicht mehr möglich. Das Ziel dieser Arbeit ist es daher, optimierte modularisierte Grundgeometrien, wie Rippen oder Umlenkungen, mit Hilfe von numerischen Formoptimierungen zu entwickeln, um diese schon von Anfang an in der Bauteilentwicklung zu berücksichtigen. Als Zielfunktionen dienen strömungs- und strukturmechanische Kenngrößen, um einerseits verschleißfördernde Mechanismen und füllungsbedingte Defekte zu reduzieren und andererseits die Beanspruchbarkeit zu erhöhen. Bei den Untersuchungen wird zusätzlich die Robustheit des Ergebnisses analysiert, um Verbesserungspotenziale auch bei streuenden Randbedingungen realisieren zu können
The virtual development process of an automotive casting part usually begins with classical design tasks and analyses of material strength, stiffness and crash load cases. In the next step, often in cooperation with external suppliers, the tooling concept is developed and casting simulations are used to ensure manufacturability. During manufacturing there is a scatter in process parameters, such as flow velocity or temperature levels, which in turn cause a scatter in the performance of the final product (e.g. local elongation at fracture or ultimate tensile strength). Means to increase process stability and yield are often limited to knowledge-based improvements of the manufacturing process parameters and adaptations of the gating and overflow system. Major changes to the part geometry are usually no longer possible due to project time constraints. Therefore it is the goal of this thesis to optimize modularized basic geometries, like ribs or bends, by using numerical shape optimizations and employ them right from the beginning of the part development process. For the objective functions of the optimizations the disciplines of fluid dynamic filling and the resulting structural behaviour are considered. In addition, the resulting shape is analyzed with regards to robustness towards scatter in manufacturing operating conditions. By using these new modularized geometries the overall robustness of the final product is expected to be increased

Broadly defined as fluids possessing multiple length scales, complex fluids, typified by polymers, hydrocarbons, surfactants, emulsions etc., exhibit microstructures even when macroscopically homogeneous. This dissertation introduces a classical density functional theory (DFT) that provides structural and thermodynamic information at the molecular level in these fluids near interfaces and in confinement. The microstructure in such systems is a function of both fluid and substrate characteristics, and varies on the order of molecular length scale (sometimes even smaller). The developments presented here can be broken down into two components that separately focus on the fluid and the interface aspects of the system. On the fluid side, the theory provides a very simple method for modeling polymeric mixtures, by treating the polyatomic system as a strongly associating atomic fluid mixture. Derived in terms of segment density, it offers accuracy comparable to the computationally intensive multi-point-density-based theories at a modest expense comparable to those of atomic DFTs. Comparisons with molecular simulations demonstrate its capability to accurately capture the entropic and enthalpic effects dictating the microstructure in inhomogeneous solutions and blends of linear and branched chains. On the interface side, the DFT provides the capability to describe adsorption of associating fluids on functionalized surfaces. These surfaces are activated with polar sites to which fluid molecules can bond, such as water adsorbing on activated carbon, silica, clay minerals, etc. The theory, in excellent agreement with simulations, shows that surface association significantly changes the fluid structure and adsorption behavior. An impressive feature of the theory enables one to estimate the distribution of fluid along the interface, i.e., the three-dimensional (3D) structure, while retaining the one-dimensional (1D) form. This translates into orders of magnitude of savings in computation time. The DFT is based on thermodynamic perturbation theory of the first order (TPT1), which is also the basis of the most widely used theory for bulk polymer solutions and melts---Statistical Associating Fluid Theory (SAFT). This consistency facilitates a seamless integration of the two into a common platform to model combined bulk-interfacial phase behavior and microstructure. This is of critical importance to several applications where interfacial properties need to be predicted based on bulk conditions.

This thesis is a theoretical study of the steady pressure driven channel flow of electrorheological fluids (ERF) under a space dependent electric field generated by finite electrodes. Chapter 1 consists in a general description of ERF and their engineering applications and presents also the motivation, the goal and the borders of this work. Chapter 2 summarizes the governing equations of electrorheology with the corresponding jump conditions. It is assumed that the flow does not affect the electric field and consequently, the electrical problem is decoupled from the mechanical one. Both electrical and mechanical boundary value problems are formulated for various configurations of finite electrodes with different potentials placed along the channel walls. The simple case of two infinite electrodes which generate a homogeneous electric field is solved analytically. In Chapter 3 analytical solutions for different mixed boundary value problems arising from the electrical problem formulated in Chapter 2 are found by use of the Wiener-Hopf method. The solutions are given in terms of infinite series involving Gamma functions. The results can be used to describe the electric field generated between two infinite grounded electrodes by either one long electrode or two long electrodes charged in an anti-symmetric or a non-symmetric way. The electric field in the vicinity of the electrode edges is asymptotically evaluated. Some parametric studies are made with respect to the ratio between the permittivity of the electrorheological fluid and the permittivity of the isolating material outside the channel. We compare the analytical with numerical solutions and find good agreement which is considered as a validation of the numerical method. Chapter 4 treats the mechanical problem in more detail. First a review of the constitutive models used to describe the ER-fluids in the literature is given. Then two-dimensional alternative constitutive laws appropriate for numerical simulations originating from the Casson-like and power law models are introduced using a parameter. In the end we non-dimensionalize the problem in both cases. In the last Chapter, we simulate numerically the flow of the Rheobay TP AI 3565 ER-fluid using the alternative Casson-like model and the EPS 3301 ER-fluid using the alternative power-law model by applying a finite element program. The behaviour of different fields such as velocity, pressure, generalized viscosity and the second invariant of the strain rate tensor near the electrode edges is studied for both fluids. A comparison with the experimental data is performed, validating the simulations. In order to investigate how the numerical solution depends on the constitutive model we perform a parallel analysis of the two rheological models by applying them to the same material (Rheobay). Then we optimize the configuration of the electrodes by using the inhomogeneities caused by the end effects of the electrodes in order to obtain an enhancement of the ER-effect.

Accurate prediction of the thermodynamics and microstructure of complex fluids is contingent upon a model's ability to capture the molecular architecture and the specific intermolecular and intramolecular interactions that govern fluid behavior. This dissertation makes key contributions to improving the understanding and molecular modeling of complex bulk and inhomogeneous fluids, with an emphasis on associating and macromolecular molecules (water, hydrocarbons, polymers, surfactants, and colloids). Such developments apply broadly to fields ranging from biology and medicine, to high performance soft materials and energy. In the bulk, the perturbed-chain statistical associating fluid theory (PC-SAFT), an equation of state based on Wertheim's thermodynamic perturbation theory (TPT1), is extended to include a crossover correction that significantly improves the predicted phase behavior in the critical region. In addition, PC-SAFT is used to investigate the vapor-liquid equilibrium of sour gas mixtures, to improve the understanding of mercaptan/sulfide removal via gas treating. For inhomogeneous fluids, a density functional theory (DFT) based on TPT1 is extended to problems that exhibit radially symmetric inhomogeneities. First, the influence of model solutes on the structure and interfacial properties of water are investigated. The DFT successfully describes the hydrophobic phenomena on microscopic and macroscopic length scales, capturing structural changes as a function of solute size and temperature. The DFT is used to investigate the structure and effective forces in nonadsorbing polymer-colloid mixtures. A comprehensive study is conducted characterizing the role of polymer concentration and particle/polymer size ratio on the structure, polymer induced depletion forces, and tendency towards colloidal aggregation. The inhomogeneous form of the association functional is used, for the first time, to extend the DFT to associating polymer systems, applicable to any association scheme. Theoretical results elucidate how reversible bonding governs the structure of a fluid near a surface and in confined environments, the molecular connectivity (formation of supramolecules, star polymers, etc.) and the phase behavior of the system. Finally, the DFT is extended to predict the inter- and intramolecular correlation functions of polymeric fluids. A theory capable of providing such local structure is important to understanding how local chemistry, branching, and bond flexibility affect the thermodynamic properties of polymers.

In this paper, the complete double layer boundary integral equation formulation for Stokes flows is extended to viscoelastic fluids to solve the mobility problem for a system of particles, where the non-linearity is handled by particular solutions of the Stokes inhomogeneous equation. Some techniques of the meshless method are employed and a point-wise solver is used to solve the viscoelastic constitutive equation. Hence volume meshing is avoided. The method is tested against the numerical solution for a sphere settling in the Odroyd-B fluid and some results on a prolate motion in shear flow of the Oldroyd-B fluid are reported and compared with some theoretical and experimental results.
Singapore-MIT Alliance (SMA)

Am Anfang des Entwicklungsprozesses eines Gussbauteils für die Automobilbranche steht klassischerweise die konstruktive Ausarbeitung und die Auslegung auf Zielgrößen, wie Festigkeit, Steifigkeit bzw. die Erfüllung der Crashlasten. Im nächsten Entwicklungsschritt wird, oftmals in Zusammenarbeit mit externen Lieferanten, das Werkzeugkonzept entwickelt und die Herstellbarkeit mit Hilfe von Gießsimulationen abgesichert. Bei der Fertigung verursachen streuende Prozessgrößen, wie etwa Geschwindigkeits- oder Temperaturniveaus, Schwankungen in der Leistungsfähigkeit des Endprodukts (z. B. lokale Bruchdehnung oder Zugfestigkeit). Maßnahmen zur Erhöhung der Prozessstabilität und zur Reduktion des Verschleißes konzentrieren sich oftmals auf die erfahrungsbasierte Verbesserung des Fertigungsprozesses und Anpassungen des Anguss- und Überlaufsystems. Größere Änderungen der Bauteilgeometrie sind häufig aus zeitlichen Gründen nicht mehr möglich. Das Ziel dieser Arbeit ist es daher, optimierte modularisierte Grundgeometrien, wie Rippen oder Umlenkungen, mit Hilfe von numerischen Formoptimierungen zu entwickeln, um diese schon von Anfang an in der Bauteilentwicklung zu berücksichtigen. Als Zielfunktionen dienen strömungs- und strukturmechanische Kenngrößen, um einerseits verschleißfördernde Mechanismen und füllungsbedingte Defekte zu reduzieren und andererseits die Beanspruchbarkeit zu erhöhen. Bei den Untersuchungen wird zusätzlich die Robustheit des Ergebnisses analysiert, um Verbesserungspotenziale auch bei streuenden Randbedingungen realisieren zu können.:1 Einleitung 1.1 Motivation und Problemstellung 1.2 Zielsetzung und Vorgehensweise 1.3 Stand von Wissenschaft und Technik 2 Grundlagen 2.1 Leichtmetallgussbauteile im Automobil 2.2 Geometrische Gestaltung von Gussbauteilen 2.3 Modellierung gießtechnischer Fertigungsverfahren 2.4 Strukturmechanische Modellierung von Gussbauteilen 2.5 Numerische Optimierung 3 Modellaufbau und -analyse 3.1 Geometrische Entwurfsmodelle 3.2 Strömungsmodellbildung zur Abbildung der Fertigungseinflüsse 3.3 Strukturberechnungsmodell unter Berücksichtigung materieller Defekte 4 Optimierung der Umlenkung 4.1 Optimierungsstrategie und -prozesskette 4.2 Zielfunktionen 4.3 Optimierung mit Entwurfsmodell I 4.4 Optimierung mit Entwurfsmodell II 4.5 Diskussion der Ergebnisse 5 Optimierung der Rippe 5.1 Optimierungsstrategie und -prozesskette 5.2 Ziel- und Restriktionsfunktionen 5.3 Multidisziplinäre Optimierung 5.4 Diskussion der Ergebnisse 6 Zusammenfassung 7 Ausblick Anhang Abkürzungs- und Symbolverzeichnis Literatur- und Quellenverzeichnis
The virtual development process of an automotive casting part usually begins with classical design tasks and analyses of material strength, stiffness and crash load cases. In the next step, often in cooperation with external suppliers, the tooling concept is developed and casting simulations are used to ensure manufacturability. During manufacturing there is a scatter in process parameters, such as flow velocity or temperature levels, which in turn cause a scatter in the performance of the final product (e.g. local elongation at fracture or ultimate tensile strength). Means to increase process stability and yield are often limited to knowledge-based improvements of the manufacturing process parameters and adaptations of the gating and overflow system. Major changes to the part geometry are usually no longer possible due to project time constraints. Therefore it is the goal of this thesis to optimize modularized basic geometries, like ribs or bends, by using numerical shape optimizations and employ them right from the beginning of the part development process. For the objective functions of the optimizations the disciplines of fluid dynamic filling and the resulting structural behaviour are considered. In addition, the resulting shape is analyzed with regards to robustness towards scatter in manufacturing operating conditions. By using these new modularized geometries the overall robustness of the final product is expected to be increased.:1 Einleitung 1.1 Motivation und Problemstellung 1.2 Zielsetzung und Vorgehensweise 1.3 Stand von Wissenschaft und Technik 2 Grundlagen 2.1 Leichtmetallgussbauteile im Automobil 2.2 Geometrische Gestaltung von Gussbauteilen 2.3 Modellierung gießtechnischer Fertigungsverfahren 2.4 Strukturmechanische Modellierung von Gussbauteilen 2.5 Numerische Optimierung 3 Modellaufbau und -analyse 3.1 Geometrische Entwurfsmodelle 3.2 Strömungsmodellbildung zur Abbildung der Fertigungseinflüsse 3.3 Strukturberechnungsmodell unter Berücksichtigung materieller Defekte 4 Optimierung der Umlenkung 4.1 Optimierungsstrategie und -prozesskette 4.2 Zielfunktionen 4.3 Optimierung mit Entwurfsmodell I 4.4 Optimierung mit Entwurfsmodell II 4.5 Diskussion der Ergebnisse 5 Optimierung der Rippe 5.1 Optimierungsstrategie und -prozesskette 5.2 Ziel- und Restriktionsfunktionen 5.3 Multidisziplinäre Optimierung 5.4 Diskussion der Ergebnisse 6 Zusammenfassung 7 Ausblick Anhang Abkürzungs- und Symbolverzeichnis Literatur- und Quellenverzeichnis