Dynamic interactions between solids and viscous liquids with free surface = Interacciones dinámicas entre sólidos y líquidos viscosos con superficie libre

En esta tesis se investiga la interacción entre un fluido viscoso y un cuerpo sólido en presencia de una superficie libre. El problema se expresa teóricamente poniendo especial atención a los aspectos de conservación de energía y de la interacción del fluido con el cuerpo. El problema se considera 2D y monofásico, y un desarrollo matemático permite una descomposición de los términos disipativos en términos relacionados con la superficie libre y términos relacionados con la enstrofía. El modelo numérico utilizado en la tesis se basa en el método sin malla Smoothed Particle Hydrodynamics (SPH). De manera análoga a lo que se hace a nivel continuo, las propiedades de conservación se estudian en la tesis con el sistema discreto de partículas. Se tratan también las condiciones de contorno de un cuerpo que se mueve en un flujo viscoso, implementadas con el método ghost-fluid. Se ha desarrollado un algoritmo explícito de interacción fluido / cuerpo. Se han documentado algunos casos de modo detallado con el objetivo de comprobar la capacidad del modelo para reproducir correctamente la disipación de energía y el movimiento del cuerpo. En particular se ha investigado la atenuación de una onda estacionaria, comparando la simulación numérica con predicciones teóricas. Se han realizado otras pruebas para monitorizar la disipación de energía para flujos más violentos que implican la fragmentación de la superficie libre. La cantidad de energía disipada con los diferentes términos se ha evaluado en los casos estudiados con el modelo numérico. Se han realizado otras pruebas numéricas para verificar la técnica de modelización de la interacción fluido / cuerpo, concretamente las fuerzas ejercidas por las olas en cuerpos con formas simples, y el equilibrio de un cuerpo flotante con una forma compleja. Una vez que el modelo numérico ha sido validado, se han realizado simulaciones numéricas para obtener una comprensión más completa de la física implicada en casos (casi) realistas sobre los había aspectos que no se conocían suficientemente. En primer lugar se ha estudiado el el flujo alrededor de un cilindro bajo la superficie libre. El estudio se ha realizado con un número de Reynolds moderado, para un rango de inmersiones del cilindro y números de Froude. La solución numérica permite una investigación de los patrones complejos que se producen. La estela del cilindro interactúa con la superficie libre. Se han identificado algunos inestabilidades características. El segundo estudio se ha realizado sobre el problema de sloshing, tanto experimentalmente como numéricamente. El análisis se restringe a aguas poco profundas y con oscilación horizontal, pero se ha estudiado un gran número de condiciones, lo que lleva a una comprensión bastante completa de los sistemas de onda involucradas. La última parte de la tesis trata también sobre un problema de sloshing pero esta vez el tanque está oscilando con rotación y hay acoplamiento con un sistema mecánico. El sistema se llama pendulum-TLD (Tuned Liquid Damper - con líquido amortiguador). Este tipo de sistema se utiliza normalmente para la amortiguación de las estructuras civiles. El análisis se ha realizado analíticamente, numéricamente y experimentalmente utilizando líquidos con viscosidades diferentes, centrándose en características no lineales y mecanismos de disipación. ABSTRA C T The subject of the present thesis is the interaction between a viscous fluid and a solid body in the presence of a free surface. The problem is expressed first theoretically with a particular focus on the energy conservation and the fluid-body interaction. The problem is considered 2D and monophasic, and some mathematical development allows for a decomposition of the energy dissipation into terms related to the Free Surface and others related to the enstrophy. The numerical model used on the thesis is based on Smoothed Particle Hydrodynamics (SPH): a computational method that works by dividing the fluid into particles. Analogously to what is done at continuum level, the conservation properties are studied on the discrete system of particles. Additionally the boundary conditions for a moving body in a viscous flow are treated and discussed using the ghost-fluid method. An explicit algorithm for handling fluid-body coupling is also developed. Following these theoretical developments on the numerical model, some test cases are devised in order to test the ability of the model to correctly reproduce the energy dissipation and the motion of the body. The attenuation of a standing wave is used to compare what is numerically simulated to what is theoretically predicted. Further tests are done in order to monitor the energy dissipation in case of more violent flows involving the fragmentation of the free-surface. The amount of energy dissipated with the different terms is assessed with the numerical model. Other numerical tests are performed in order to test the fluid/body interaction method: forces exerted by waves on simple shapes, and equilibrium of a floating body with a complex shape. Once the numerical model has been validated, numerical tests are performed in order to get a more complete understanding of the physics involved in (almost) realistic cases. First a study is performed on the flow passing a cylinder under the free surface. The study is performed at moderate Reynolds numbers, for various cylinder submergences, and various Froude numbers. The capacity of the numerical solver allows for an investigation of the complex patterns which occur. The wake from the cylinder interacts with the free surface, and some characteristical flow mechanisms are identified. The second study is done on the sloshing problem, both experimentally and numerically. The analysis is restrained to shallow water and horizontal excitation, but a large number of conditions are studied, leading to quite a complete understanding of the wave systems involved. The last part of the thesis still involves a sloshing problem but this time the tank is rolling and there is coupling with a mechanical system. The system is named pendulum-TLD (Tuned Liquid Damper). This kind of system is normally used for damping of civil structures. The analysis is then performed analytically, numerically and experimentally for using liquids with different viscosities, focusing on non-linear features and dissipation mechanisms.

Deflection of jets discharged into a reservoir with a free surface

Deflections of jets discharged into a reservoir with a free surface are investigated numerically. The jets are known to deflect towards either side of the free surface or the bottom, whose direction is not determined uniquely in some experimental conditions, i.e. there are multiple stable states realizable in the same condition. The origin of the multiple stable states is explored by utilizing homotopy transformations in which the top boundary of the reservoir is transformed from a rigid to a free boundary and also the location of the outlet throat is continuously moved from mid-height to the top. We depicted bifurcation diagrams of the flow compiling the data of numerical simulations, from which we identified the origin as an imperfect pitchfork bifurcation, and obtained an insight into the mechanism for the direction to be determined. The parameter region where such multiple stable states are possible is also delimited. © 2011 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.

Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Sex-linked genetic markers in the shrews of the Sorex araneus group : from free gene flow to speciation

SUMMARY: The shrews of the Sorex araneus group are morphologically .very similar, but have undergone a spectacular chromosomal evolution. Altogether, the shrews of this group present a complete array of every possible level of chromosomal and genetic differentiation. In South-Western Europe, four species are recognised: S. antiriorii, S. araneus, S. coronatus and S. granarius, which differ essentially by the amount and the composition of Robertsonian metacentric chromosomés. Additionally, several chromosome races of S. araneus are also present in the same region (i.e. Bretolet, Carlit, Cordon, Jura and Vaud). The objective of this thesis was to examine the genetic relationships between populations, races and /or species of the Sorex araneus group with a special emphasis onsex-specific markers (mtDNA and Y chromosome). We first investigate the evolutionary history of the shrews of the Sorex araneus group distributed in the South-Western Europe. The results of. these analyses confirmed the difficulty to draw a single dichotomic tree within this group. Incongruent mtDNA and Y chromosome phylogenies suggest further that genetic and chromosomal evolution are in this group partially independent processes and that the evolutionary history of the south-western European populations of the S. araneus group can only be understood if we consider secondary contacts between taxa, after their divergence (with genetic exchanges by means of hybridization and / or introgression). Using one male-inherited, one female inherited and eight biparentally inherited markers, we investigate the population genetic structure of the Valais shrew (Sorex antinorii). Overall there results suggest that two already well-differentiated genetic lineages colonized the Swiss Alps after the last glacial period and came into contact in the Rhône Valley. After the Valais shrew (Sorex antinorii) reached the Swiss Alps, it came into contact with the common shrew (Sorex araneus). When two species come into contact and hybridize, endogenous counter-selection of hybrids is usually first expressed as a reduced fertility or viability in hybrids of the heterogametic sex, a mechanism know as Haldane's rule (Haldane 1922). We first evaluated the extent of introgression for Y chromosome, mtDNA and autosomal markers in a hybrid zone between S. antinoriii and S. araneus. The overall level of genetic and karyotypic differentiation between the two species must be strong .enough to allow the detection asymmetric introgression. Secondly, we compared the levels of gene flow between chromosome common to both species and chromosome differently rearranged in each of them. We detected a significantly stronger genetic structure in rearranged chromosomes. Over a 10-year period, we even observed a decrease of genetic structure for common chromosomes. These results strongly support the role of chromosomal rearrangements in the reproductive barrier between S. araneus and S. anfinorii. Overall, this thesis underlines the need to use different inherited (paternally, maternally and / or biparentally) and chromosomally located (on common vs. on rearranged chromosomes) markers to obtain more accurate pictures of genetic relationships between populations or species. RÉSUMÉ: Les musaraignes du groupe Sorex araneus sont morphologiquement très proches, mais ont connu une spectaculaire évolution chromosomique. Prises dans leur ensemble, les musaraignes de ce groupe présentent tous les nivaux possibles de différenciation génétique et chromosomique. Dans le sud-ouest de l'Europe, quatre espèces appartenant à ce groupe sont présentes : S. antinorii, S. araneus, S. coronatus et S. granarius. Celles-ci diffèrent essentiellement par leur caryotype dont la variabilité est principalement due à des fusions Robertsoniennes. De plus, plusieurs races chromosomiques appartenant à S. araneus sont aussi présentes dans la même région (i.e. les races Bretolet, Carlit, Cordon, Jura et Vaud). L'objectif de cette thèse était d'examiner les relations génétiques entre populations, races et/ou espèces du groupe S. araneus, en utilisant particulièrement des marqueurs liés aux sexes (ADN mitochondrial et Chromosome Y). Nous avons dans un premier temps retracé l'histoire évolutive des musaraignes de ce groupe dans le sud-ouest de l'Europe. Les résultats dé ces analyses confirment qu'il est difficile de tracer un simple arbre dichotomique au sein de ce groupe. Les arbres phylogénétiques obtenus sur l'ADN mitochondrial et le chromosome Y sont incongruents et suggèrent de plus que l'évolution génétique et chromosomique sont des processus indépendants. L'histoire évolutive -des populations de ce groupe ne peut. être comprise qu'en considérant des contacts secondaires entre taxa postérieure à leur divergence et induisant des échanges génétiques par hybridation et/ou introgression. Par la suite, nous avons examiné la structure génétique des populations de la musaraigne du Valais, S. antinorii, en utilisant un marqueur transmis par les mâles, un marqueur transmis par les femelles et huit marqueurs transmis par les 2 sexes. Nos résultats suggèrent que deux lignées génétiquement bien différenciées aient colonisé les Alpes Suisses, après les dernières glaciations et entrent en contact dans là Vallée du Rhône. Après avoir franchi les Alpes Suisses, la musaraigne du Valais est entrée en contact avec là musaraigne commune (S. araneus). Lorsque deux espèces entrent en contact et s'hybrident, la sélection contre les hybrides implique habituellement une baisse de fertilité ou de viabilité des hybrides du sexe hétérogamétique (i.e. les mâles XY chez les mammifères). Ce mécanisme est connu sous le nom de règle de Haldane (Haldane 1922) et implique une plus forte structuration génétique de marqueurs males - spécifiques que des marqueurs femelles spécifiques. Nous avons donc évalué le degré d'introgression des marqueurs situés sur le chromosome Y, sur l'ADN mitochondrial et sur des autosomes dans une zone hybride entre S. araneus et S. antinorii. Le niveau de différenciation chromosomique et génétique entre les 2 espèces doit être suffisamment fort pour ne pas permettre la détection d'une introgression asymétrique entre les sexes. Dans un second temps, nous avons comparé les niveaux de flux de gênes mesurés à l'échelle du chromosome, pour des chromosomes communs aux deux espèces et pour des chromosomes différemment arrangées dans chacune des deux espèces. Nous avons détecté une structure génétique significativement plus forte sur les chromosomes réarrangés et comme la zone hybride a été étudiée à dix années d'intervalle, nous observons même une diminution de la structure génétique pour les chromosomes communs au cours du temps.. Ces résultats soutiennent fortement l'hypothèse d'un rôle des réarrangements chromosomiques dans l'établissement d'une barrière reproductive entre S. araneus et S. antinorii. Ainsi cette thèse souligne l'utilité d'utiliser des marqueurs génétiques avec différents modes de transmission. (par les mâles, par les femelles et/ou par les 2 sexes) ou localisés au niveau du chromosome (chromosomes communs vs chromosomes réarrangés) afin d'obtenir une image plus juste ou du moins plus complète des relations génétiques entre populations ou espèces.

Streamside management zone (SMZ) efficiency in herbicide retention from simulated surface flow

Plot-scale overland flow experiments were conducted to evaluate the efficiency of streamside management zones (SMZs) in retaining herbicides in runoff generated from silvicultural activities. Herbicide retention was evaluated for five different slopes (2, 5, 10, 15, and 20%), two cover conditions (undisturbed O horizon and raked surface), and two periods under contrasting soil moisture conditions (summer dry and winter wet season) and correlated to O horizon and site conditions. Picloram (highly soluble in water) and atrazine (moderately sorbed into soil particles) at concentrations in the range of 55 and 35 µg L-1 and kaolin clay (approximately 5 g L-1) were mixed with 13.000 liters of water and dispersed over the top of 5 x 10 m forested plots. Surface flow was collected 2, 4, 6, and 10 m below the disperser to evaluate the changes in concentration as it moved through the O horizon and surface soil horizon-mixing zone. Results showed that, on average, a 10 m long forested SMZ removed around 25% of the initial concentration of atrazine and was generally ineffective in reducing the more soluble picloram. Retention of picloram was only 6% of the applied quantity. Percentages of mass reduction by infiltration were 36% for atrazine and 20% for picloram. Stronger relationships existed between O horizon depth and atrazine retention than in any other measured variable, suggesting that better solid-solution contact associated with flow through deeper O horizons is more important than either velocity or soil moisture as a determinant of sorption.

Relaxation of surface tension in the free-surface boundary layers of simple Lennard-Jones liquids

In this paper we use molecular dynamics to answer a classical question: how does the surface tension on a liquid/gas interface appear? After defining surface tension from the first principles and performing several consistency checks, we perform a dynamic experiment with a single simple liquid nanodroplet. At time zero, we remove all molecules of the interfacial layer of molecules, creating a fresh bare interface with the bulk arrangement of molecules. After that the system evolves towards equilibrium, and the expected surface tension is re-established. We found that the system relaxation consists of three distinct stages. First, the mechanical balance is quickly re-established. During this process the notion of surface tension is meaningless. In the second stage, the surface tension equilibrates, and the density profile broadens to a value which we call “intrinsic” interfacial width. During the third stage, the density profile continues to broaden due to capillary wave excitations, which does not however affect the surface tension.We have observed this scenario for monatomic Lennard-Jones (LJ) liquid as well as for binary LJ mixtures at different temperatures, monitoring a wide range of physical observables.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

A marker-and-cell approach to free surface 2-D multiphase flows

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solitary waves on a free surface of a heated Maxwell fluid

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A Numerical Study of the FENE-CR Model Applied to a Jet Flow Problem

The FENE-CR model is investigated through a numerical algorithm to simulate the time-dependent moving free surface flow produced by a jet impinging on a flat surface. The objective is to demonstrate that by increasing the extensibility parameter L, the numerical solutions converge to the solutions obtained with the Oldroyd-B model. The governing equations are solved by an established free surface flow solver based on the finite difference and marker-and-cell methods. Numerical predictions of the extensional viscosity obtained with several values of the parameter L are presented. The results show that if the extensibility parameter L is sufficiently large then the extensional viscosities obtained with the FENE-CR model approximate the corresponding Oldroyd-B viscosity. Moreover, the flow from a jet impinging on a flat surface is simulated with various values of the extensibility parameter L and the fluid flow visualizations display convergence to the Oldroyd-B jet flow results.

A marker-and-cell approach to free surface 2-D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front-tracking method. The velocity field is computed using a finite-difference discretization of a modification of the NavierStokes equations. These equations together with the continuity equation are solved for the two-dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright (c) 2012 John Wiley & Sons, Ltd.