Dissertations / Theses on the topic 'Fundamental and theoretical fluid dynamics'

The work presented in this thesis concerns computer simulations of lubrication processes, and the main part deals with simulations in the elastohydrodynamic lubrication (EHL) regime. The thesis summarises the work performed in the five papers referred to as Paper A, B, C, D and E. The aim is to give the reader a more explanatory description of the investigations performed in the papers and of the physical processes present in EHL. Lubrication is a sub-area of tribology, which is the science of interacting bodies in relative motion, two other sub-areas being wear and friction. Lubrication is commonly referred to as a way of reducing friction and protecting the surfaces from wear. Typical devices where EHL is present are machine components. Examples of these are bearings, cams and gears. The lubricant can in such an application have many different tasks. The ultimate goal is that the surfaces in motion should be separated by a fluid film, thus reducing the friction and wear. That leads to low frictional losses and long operating life for the machine components. This goal is, however, not always fulfilled, and to protect the surfaces from wear when the lubricating film collapses, there are additives added to the lubricant. Commonly, lubricants contain of a number of additives, but these are not in focus in this thesis. Common to many EHL-applications, especially machine components, are thin lubricating films and high fluid pressures. The high pressures result in elastic deformation of the contacting bodies. The lubricating films in such applications are very thin, often in the range 0.1-1 10^-6m with pressures ranging from 0.5-3 GPa. The contact diameter is approximately 1 mm and the time a fluid element needs to pass through the contact is approximately 0.1 ms. The altering geometrical scales and rapid changes in the physical variables, such as pressure, viscosity and temperature etc., make numerical simulations to a challenging task. The variables of primary interest in the numerical simulations are: film thickness, pressure, temperature and friction. The film thickness is an important variable that gives information as to whether the surfaces are separated by the lubricating film. It is the lifting force generated by the hydrodynamic pressure that governs the separation of the surfaces in motion. However, even if a lubricating film is present, EHL machine components deteriorate when they have been in service for a long time. It is then that the cycling in pressure and temperature leads to fatigue of the surfaces, so that the level of these variables is also of importance. The friction that has developed in the EHL-contacts leads to a loss of energy, which increases the temperature in the conjunctions. Friction is therefore important not only for the efficiency, but also when thermal aspects have to be considered. The physical processes present in EHL are inter-disciplinary, closely related to other fields of science such as fluid mechanics, solid mechanics, and rheology. In almost all numerical simulations of lubrication performed today, the hydrodynamics are modelled by an equation referred to as the Reynolds equation. This equation is derived from a simplified form of the momentum equations, which are combined with the continuity equation; and the result is a Poisson equation for the fluid pressure. The assumptions made when deriving this equation limit the size of the computational or spatial domain, and the equation cannot predict pressure variations across the lubricating fluid film. In the work presented in this thesis, an extended approach, where the technique is based on CFD (computational fluid dynamics), is used to simulate the lubricant flow. The extended approach is here based on more complete forms of the equations of momentum, continuity and energy and the above degeneracy will be removed. That implies, if such an approach works, that it should now be possible to simulate the lubricant flow under conditions where the Reynolds equation is not valid. So far, only few attempts have been made to use the CFD-technique. From the preceding discussion of rapid changes in accordance with elastic deformation of the contacting surfaces, a great deal of work has been carried out to modify the numerical algorithm in the CFD-software to fit EHL-problems. The CFD- software used throughout the work in this thesis is CFX4 (2003).
Godkänd; 2004; 20061030 (haneit)

The objective of this thesis is the development of a unifying framework for the integration and upscaling of the fluid mechanical, ecological and biomechanical processes occurring in aquatic flows. Particular focus is on the interactions of the fluid motion with aquatic plants and sediments in aquatic systems. Appropriately formulated coupled conservation equations are developed for fluid, sediment, and plant motions. The starting points for their derivation are the continuity and momentum equations written for instantaneous local field variables, for fluid, sediment and aquatic plants. The equations of motion for fluid, sediment and plants (at the stem scale) are averaged over time and space to cope with the temporal and spatial heterogeneity of the flow field near the interfacial boundary and couple the fluid and non-fluid equations of motion. To deal with the possible discontinuity of the time-averaged fields within the averaging time, appropriate definitions and theorems for time-averaging are proposed. Time-averaging is then applied on the equations of motion for each phase to obtain the respective time-averaged equations. Time-averaged equations for the second-order velocity moments are also proposed for mobile-boundary flows. The application of consecutive time-space averaging on the continuum equations led to the development of the double-averaged equations of motion for each phase. Double-averaged continuity and momentum equations have been recently proposed for mobile-boundary flows. In this thesis, the coupled double-averaged continuity and momentum equations are proposed for the sediment material and aquatic plants at the reach scale. Double-averaged equations for the second-order velocity moments have been derived for the case of fluid and sediments. By applying the double-averaging methodology (i) the governing equations are upscaled to the scales relevant to applications, (ii) the fluid motion is rigorously coupled with the non-fluid (plants or sediments) motions, and (iii) the effect of the moving interfacial boundary is introduced explicitly in the governing averaged equations. The derived second-order hydrodynamic double-averaged equations are applied to the analysis of extensive data from Direct Numerical Simulations of turbulent open-channel flows over mobile granular beds (the simulations were performed in the Dresden Technical University by Professor J. Fröhlich's Group). The use of the double-averaged equations provides significant data reduction and assists in the data interpretation. The key physical mechanisms involved in the energy transfers between the fluid mean, form-induced and turbulent fields as well as sediment motions are identified based on the assessment of the terms in the double-averaged balances of kinetic energy.

Thesis (M.S.)--West Virginia University, 2009.
Title from document title page. Document formatted into pages; contains x, 83 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 79-83).

In recent years, Polymer Electrolyte Membrane Fuel Cells (PEMFC) have attracted much attention due to their potential as a clean power source for many applications, including automotive, portable and stationary devices. This resulted in a tremendous technological progress, such as the development of new membranes and electro-catalysts or the improvement of electrode structures. However, in order to compete within the most attractive markets, the PEMFC technologies did not reach all the required characteristics yet, in particular in terms of cost and durability.Because of the strong coupling between different physicochemical phenomena, the interpretation of experimental observations is difficult, and analysis through modeling becomes crucial to elucidate the degradation and failure mechanisms, andto help improving both PEMFC electrochemical performance and durability.The development of a theoretical tool is essential for industrials and the scientific community to evaluate the PEMFC degradation and to predict itsperformance and durability in function of the materials properties and in a diversity of operating conditions. This manuscript summarizes my scientific research efforts in this exciting topic during the last 9 years in France, including my invention of the MEMEPhys multiscale simulation package,developed on the basis of my childhood passion for the New Technologies for Energyin Argentina. My perspectives of adapting this approach to other electrochemical systems such as water electrolyzers and batteries are also discussed.

Cette thèse décrit diverses situations liées au transport fluidique aux nano-échelles. Le premier chapitre est une introduction à la nanofluidique qui contient une revue des longueurs caractéristiques, des forces et des phénomènes présents aux nano-échelles. Le deuxième chapitre est une étude de l'impact de la géométrie sur la perméabilité hydrodynamique d'un nanopore. Inspirée par la forme des aquaporines, cette étude suggère une optimisation possible pour des canaux biconiques. Le troisième chapitre est une étude du remplissage capillaire dans des canaux sub-nanométriques en carbone. Cette étude montre l'importance de la pression de disjonction induite par la structure du fluide sur le remplissage. Le quatrième chapitre est une étude d'une diode nanofluidique, un composant connu pour imiter le comportement d'une diode à semi-conducteur. On montre qu'un fort couplage entre l'eau et la dynamique des ions entraîne une rectification du flux d'eau à l'intérieur de la diode. Le cinquième et dernier chapitre est une étude de l'origine du bruit rose (1=f) communément observé lors des mesures de courant ionique dans les nanopores
This thesis discusses various situations linked to transport at the nanoscale. The first chapter is an introduction to nanofluidics, containing a review of characteristic lengths, forces, or phenomena existing at the nanoscale. The second chapter is a study of the impact of geometry on the hydrodynamic permeability of a nanopore. This study, inspired by the shape of aquaporins, suggests a possible optimisation of permeability for bi-conical channels. The third chapter is a study of capillary filing inside subnanometric carbon channels which highlights the importance of the disjoining pressure induced by the fluid structuring inside the nanochannel. The fourth chapter is a study of nanofluidic diode, a component known to mimic the behaviour of semiconductor diode. The study highlights a strong coupling between water and ion dynamics which leads to a water flow rectification inside the diode. The fifth and last chapter is a study of the origin of commonly observed pink noise (1=f) in ionic current measurements through nanopores

In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M. For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.

Millions of years of evolution have led to a wealth of highly adapted functional surfaces in nature. Among the most fascinating are superhydrophobic surfaces which are highly water-repellent and shed drops very easily owing to their chemical hydrophobicity combined with micropatterning. Superhydrophobic materials have attracted a lot of attention due to their practical applications as ultra-low friction surfaces for ships and pipes, water harvesters, de-humidifiers and cooling systems. At small length scales, where surface tension dominates over gravity, these surfaces show a wealth of phenomena interesting to physicists, such as directional flow, rolling, and drop bouncing. This thesis focuses on two examples of dynamic drop interactions with micropatterned surfaces and studies them by means of a lattice Boltzmann simulation approach. Inspired by recent experiments, we investigate the phenomenon of the self-propelled bouncing of coalescing droplets. On highly hydrophobic patterned surfaces drop coalescence can lead to an out-of-plane jump of the composite drop. We discuss the importance of energy dissipation to the jumping process and identify an anisotropy of the jumping ability with respect to surface features. We show that Gibbs' pinning is the source of this anisotropy and explain how it leads to the inhibition of coalescence-induced jumping. The second example we study is the novel phenomenon of pancake bouncing. Conventionally, a drop falling onto a superhydrophobic surface spreads due to its inertia, retracts due to its surface tension, and bounces off the surface. Here we explain a different pathway to bouncing that has been observed in recent experiments: A drop may spread upon impact, but leave the surface whilst still in an elongated shape. This new behaviour, which occurs transiently for certain impact and surface parameters, is due to reversible liquid imbibition into the superhydrophobic substrate. We develop a theoretical model and test it on data from experiments and simulations. The theoretical model is used to explain pancake bouncing in detail.

Convergence acceleration techniques for the iterative solution of system of equations arising in the discretisations of compressible flow problems governed by the steady state Euler or Navier-Stokes equations is considered. The system of PDE is discretised using a finite difference or finite volume method yielding a large sparse system of equations. A solution is computed by integrating the corresponding time dependent problem in time until steady state is reached. A convergence acceleration technique based on semicirculant approximations is applied. For scalar model problems, it is proved that the preconditioned coefficient matrix has a bounded spectrum well separated from the origin. A very simple time marching scheme such as the forward Euler method can be used, and the time step is not limited by a CFL-type criterion. Instead, the time step can asymptotically be chosen as a constant, independent of the number of grid points and the Reynolds number. Numerical experiments show that grid and parameter independent convergence is achieved also in more complicated problem settings. A comparison with a multigrid method shows that the semicirculant convergence acceleration technique is more efficient in terms of arithmetic complexity. Another convergence acceleration technique based on fundamental solutions is proposed. An algorithm based on Fourier technique is provided for the fast application. Scalar model problems are considered and a theory, where the preconditioner is represented as an integral operator is derived. Theory and numerical experiments show that for first order partial differential equations, grid independent convergence is achieved.

Dans les réacteurs industriels ou dans la nature, l'écoulement de fluides peut être couplé à des réactions chimiques. Dans de nombreux cas, il en résulte l'apparition de structures complexes dont les propriétés dépendent entre autres de la géométrie du système.

Dans ce contexte, le but de notre thèse a été d'étudier de manière théorique et sur des modèles réaction-diffusion-convection simples les propriétés de dynamiques spatio-temporelles résultant du couplage chimie-hydrodynamique.

Nous nous sommes focalisés sur les instabilités hydrodynamiques de digitation visqueuse et de densité qui apparaissent respectivement lorsqu'un fluide dense est placé au-dessus d'un fluide moins dense dans le champ de gravité et lorsqu'un fluide visqueux est déplacé par un fluide moins visqueux dans un milieu poreux.

En particulier, nous avons étudié les problèmes suivants:

- L'influence d'une réaction chimique de type A + B → C sur la digitation visqueuse. Nous avons montré que les structures formées lors de cette instabilité varient selon que le réactif A est injecté dans le réactif B ou vice-versa si ces réactifs n'ont pas un coefficient de diffusion ou une concentration initiale identiques.

- Le rôle de pertes de chaleur par les parois du réacteur dans le cadre de la digitation de densité de fronts autocatalytiques exothermiques. Nous avons caractérisé les conditions de stabilité de fronts en fonction des pertes de chaleur et expliqué l'apparition de zones anormalement chaudes lors de cette instabilité.

- L'influence de l'inhomogénéité du milieu sur la digitation de densité de solutions réactives ou non. Nous avons montré que les variations spatiales de perméabilité d'un milieu poreux peuvent figer ou faire osciller la structure de digitation dans certaines conditions.

- L'influence d'un champ électrique transverse sur l'instabilité diffusive et la digitation de densité de fronts autocatalytiques. Il a été montré que cette interaction peut donner lieu à des nouvelles structures et changer les propriétés du front.

En conclusion, nous avons montré que le couplage entre réactions chimiques et mouvements hydrodynamiques est capable de générer de nouvelles structures spatio-temporelles dont les propriétés dépendent entre autres des conditions imposées au système.

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In industrial reactors or in nature, fluid flows can be coupled to chemical reactions. In many cases, the result is the emergence of complex structures whose properties depend among others on the geometry of the system.

In this context, the purpose of our thesis was to study theoretically using simple models of reaction-diffusion-convection, the properties of dynamics resulting from the coupling between chemistry and hydrodynamics.

We focused on the hydrodynamic instabilities of viscous and density fingering that occur respectively when a dense fluid is placed above a less dense one in the gravity field and when a viscous fluid is displaced by a less viscous fluid in a porous medium.

In particular, we studied the following issues:

- The influence of a chemical reaction type A + B → C on viscous fingering. We have shown that the fingering patterns observed during this instability depends on whether the reactant A is injected into the reactant B or vice versa if they do not have identical diffusion coefficients or initial concentrations.

- The role of heat losses through the reactor walls on the density fingering of exothermic autocatalytic fronts. We have characterized the conditions of stability of fronts depending on heat losses and explained the appearance of unusually hot areas during this instability.

- The influence of the inhomogeneity of the medium on the density fingering of reactive solutions or not. We have shown that spatial variations of permeability of a porous medium may freeze or generate oscillating fingering pattern under certain conditions.

- The influence of a transverse electric field on the Rayleigh-Taylor and diffusive instabilities of autocatalytic fronts. It was shown that this interaction may lead to new structures and may change the properties of the front.

In conclusion, we showed that the coupling between chemical reactions and hydrodynamic motions can generate new space-time structures whose properties depend among others, on the conditions imposed on the system.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

Liquid fragmentation phenomenon is explored from both a fundamental (fully resolved) and an engineering (modeled) perspective. The dual objectives compliment each other by providing an avenue to gain further understanding into fundamental processes of atomization as well as to use the newly acquired knowledge to address practical concerns. A compressible five-equation interface model based on a Roe-type scheme for the simulation of material boundaries between immiscible fluids with arbitrary equation of state is developed and validated. The detailed simulation model accounts for surface-tension, viscous, and body-force effects, in addition to acoustic and convective transport. The material interfaces are considered as diffused zones and a mixture model is given for this transition region. The simulation methodology combines a high-resolution discontinuity capturing method with a low-dissipation central scheme resulting in a hybrid approach for the solution of time- and space-accurate interface problems. Several multi-dimensional test cases are considered over a wide range of physical situations involving capillary, viscosity, and gravity effects with simultaneous presence of large viscosity and density ratios. The model is shown to accurately capture interface dynamics as well as to deal with dynamic appearance and disappearance of material boundaries. Simulation of atomization processes and its interaction with the flow field in practical devices is the secondary objective of this study. Three modeling requirements are identified to perform Large-Eddy Simulation (LES) of spray combustion in engineering devices. In concurrence with these requirements, LES of an experimental liquid-fueled Lean Direct Injection (LDI) combustor is performed using a subgrid mixing and combustion model. This approach has no adjustable parameters and the entire flow-path through the inlet swirl vanes is resolved. The inclusion of the atomization aspects within LES eliminates the need to specify dispersed-phase size-velocity correlations at the inflow boundary. Kelvin-Helmholtz (or aerodynamic) breakup model by Reitz is adopted for the combustor simulation. Two simulations (with and without breakup) are performed and compared with measurements of Cai et al. Time-averaged velocity prediction comparison for both gas- and liquid-phase with available data show reasonable agreement. The major impact of breakup is on the fuel evaporation in the vicinity of the injector. Further downstream, a wide range of drop sizes are recovered by the breakup simulation and produces similar spray quality as in the no-breakup case.

This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space.
Physics

Ce manuscrit présente une description théorique des propriétés de transport exceptionnelles des liquides dans les nanotubes de carbone (CNT). La perméabilité de ces canaux dépasse largement ce qui est prévu par les équations de l'hydrodynamique et la condition limite de non-glissement. Au cours des dernières années, plusieurs groupes ont effectué des expériences d'écoulement de liquides dans des membranes de CNT. Une perméabilité très supérieure à l'attente classique a été observée. Dans ce contexte, nous avons mené une étude exhaustive du frottement liquide/solide qui apparaît pendant l'écoulement d'un fluide dans un CNT, à l'aide de simulations de dynamique moléculaire. Le coefficient de frottement a été mesuré pour différents systèmes en utilisant plusieurs méthodes indépendantes. Les simulations ont montré que le coefficient de frottement était indépendant du confinement, mais qu'il dépendait considérablement de la courbure de la paroi. Pour l'eau dans un CNT, le coefficient de frottement diminue avec le rayon du tube. Nous avons ensuite établi une expression approchée du coefficient de frottement, qui le relie à des propriétés microscopiques de l'interface entre le liquide et la paroi. Cette expression reproduit la dépendance du coefficient de frottement avec la courbure, et permet de l'expliquer à partir des trois paramètres statiques suivants : la densité surfacique de l'eau, la rugosité de la paroi et la commensurabilité entre les structures de la paroi et de la première couche d'eau à l'interface. En résumé, notre étude a permis une compréhension détaillée du frottement de l'eau dans les CNT, qui explique l'origine de sa valeur extrêmement basse
Within the scope of this thesis, a theoretical study of liquid flow in graphitic nanopores was performed. More precisely, a combination of numerical simulations and analytic approach was used to establish the special properties of carbon nanotubes for fluid transport: Molecular dynamics flow simulations of different liquids in carbon nanotubes exhibited flow velocities that are 1-3 orders of magnitude higher than predicted from the continuum hydrodynamics framework and the no-slip boundary condition. These results support previous experiments performed by several groups reporting exceptionally high flow rates for water in carbon nanotube membranes. The reason for this important flow enhancement with respect to the expectation was so far unclear. In this work, a careful investigation of the water/graphite friction coefficient which we identified as the crucial parameter for fast liquid transport in the considered systems was carried out. In simulations, the friction coefficient was found to be very sensitive to wall curvature: friction is independent of confinement for water between at graphene walls with zero curvature, while it increases with increasing negative curvature (water at the outside of the tube), and it decreases with increasing positive curvature (water inside the tube), eventually leading to quasi frictionless flow for water in a single file configuration in the smallest tubes. A similar behaviour was moreover found with several other liquids, such as alcohol, alcane and OMCTS. urthermore, a theoretical approximate expression for the friction coefficient is presented which predicts qualitatively and semi-quantitatively its curvature dependent behavior. Moreover, a deeper analysis of the simulations according to the proposed theoretical description shed light on the physical mechanisms at the origin of the ultra low liquid/solid friction in carbon nanotubes. In fine, it is due to their perfectly ordered molecular structure and their atomically smooth surface that carbon nanotubes are quasi-perfect liquid conductors compared to other membrane pores like, for example, nanochannels in amorphous silica. The newly gained understanding constitutes an important validation that carbon nanotubes operate as fast transporters of various liquids which makes them a promising option for different applications like energy conversion or filtration on the molecular level

Within the scope of this thesis, a theoretical study of liquid flow in graphitic nanopores was performed. More precisely, a combination of numerical simulations and analytic approach was used to establish the special properties of carbon nanotubes for fluid transport: Molecular dynamics flow simulations of different liquids in carbon nanotubes exhibited flow velocities that are 1-3 orders of magnitude higher than predicted from the continuum hydrodynamics framework and the no-slip boundary condition. These results support previous experiments performed by several groups reporting exceptionally high flow rates for water in carbon nanotube membranes. The reason for this important flow enhancement with respect to the expectation was so far unclear. In this work, a careful investigation of the water/graphite friction coefficient which we identified as the crucial parameter for fast liquid transport in the considered systems, was carried out. In simulations, the friction coefficient was found to be very sensitive to wall curvature: friction is independent of confinement for water between flat graphene walls with zero curvature, while it increases with increasing negative curvature (water at the outside of the tube), and it decreases with increasing positive curvature (water inside the tube), eventually leading to quasi frictionless flow for water in a single file configuration in the smallest tubes. A similar behavior was moreover found with several other liquids, such as alcohol, alcane and OMCTS. Furthermore, a theoretical approximate expression for the friction coefficient is presented which predicts qualitatively and semi-quantitatively its curvature dependent behavior. Moreover, a deeper analysis of the simulations according to the proposed theoretical description shed light on the physical mechanisms at the origin of the ultra low liquid/solid friction in carbon nanotubes. In fine, it is due to their perfectly ordered molecular structure and their atomically smooth surface that carbon nanotubes are quasi-perfect liquid conductors compared to other membrane pores like, for example, nanochannels in amorphous silica. The newly gained understanding constitutes an important validation that carbon nanotubes operate as fast transporters of various liquids which makes them a promising option for different applications like energy conversion or filtration on the molecular level.

Studying the coupling between buoyancy-driven instabilities and chemical reactions is not only relevant to fundamental research, but has also recently gained increased interest because of its relevance to CO$_2$ sequestration in subsurface geological zones. This technique aims to limit the emissions of CO$_2$ to the atmosphere, with a view to mitigating climate change. When injected in e.g. a saline aquifer, CO$_2$ dissolves into the brine occupying the geological formation, thereby increasing the density of the aqueous phase. This increase of density upon dissolution leads to a denser fluid boundary layer rich in CO$_2$ on top of less dense fluid in the gravity field, which drives dissolution-driven convection. This process, also called convective dissolution, accelerates the transport of dissolved CO$_2$ to the host phase and thus improves the safety of CO$_2$ sequestration. The same kind of instability can develop in other contexts involving the dissolution of a phase A into a host phase, such as solid dissolution or transfer between partially miscible liquids. In this context, the goal of our thesis is to understand how chemical reactions coupled to dissolution-driven convection affect the dynamics of the dissolving species A in the host solution. To do so, we introduce a general reaction of the type A + B $rightarrow$ C where A, B and C affect the density of the aqueous solution. We theoretically analyze the influence of the relative physical properties of A, B and C on the convective dynamics. Our theoretical analysis uses a reaction-diffusion-convection model for the evolution of solute concentration in a host fluid solvent occupying a porous medium. First, we quantify the characteristic growth rate of the perturbations by using a linear stability analysis. Thereby we show that a chemical reaction can either accelerate or slow down the development of convection, depending on how it modifies the density profile that develops in the reactive solution. In addition, new dynamics are made possible by differential diffusion effects. Then, by analyzing the full nonlinear dynamics with the help of direct numerical simulations, we calculate the dissolution flux into the host phase. In particular, the dissolution flux can be amplified when convection develops earlier, as CO$_2$ is then transported faster away from the interface. Finally, we compare these theoretical and numerical predictions with results of laboratory experiments and discuss the possible implications of this study for CO$_2$ sequestration.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

In this dissertation, various VAT parameters are investigated to determine the effect of the overall efficiency of the turbine at a high Reynolds number. To increase the efficiency of the vertical axis turbines, 2D CFD simulations are completed in an effort to better understand the physics behind the operation of these turbines. Specifically, the effect of advance ratio, solidity, and wake interactions were investigated. Simulations were completed in OpenFOAM using the k-ω SST turbulence model at a nominal Reynolds number of 500,000 using a NACA 0015 airfoil. To simulate the motion of the turbine, Arbitrary Mesh Interfacing (AMI) was used. For all of the parameters tested, it was found that the geometric effective angle of attack seen by the turbine blades had a significant impact on the power extracted from the flow. The range of effective angles of attack was found to decrease as the advance ratio increased. In spite of this, a severe loss in the power coefficient occurred at an advance ratio of 2.5 during which the blade experienced dynamic stall. This effect was also seen when the number of turbine blades was changed to four, at a solidity of 1.08. This negative impact on performance was found to be due to the increase in the drag component of the tangential force when dynamic stall occurs. Results indicate that wake interactions between subsequent blades have a large impact on performance especially when the wake interaction alters the flow direction sufficiently to create conditions for dynamic stall. To improve the performance of the VAT in the presence of dynamic stall, calculations were completed of a static twisted blade profile using GenIDLEST and OpenFOAM. There was found to be no improvement in the lift coefficient when comparing the twisted blade profile with a 2D blade at the same median angle of attack as the twisted blade. To further see the effects of the twisted blade, an effective VAT pitching motion was given to the blade and again compared to a 2D blade with the same motion. In this case there was significant improvement seen in the performance of the twisted blade.
Master of Science

In this study, the effects of design parameters on the fan noise level are investigated both theoretically and experimentally. For the theoretical study, a computational aero- acoustic method is used to predict the flow induced noise of a fan. This method involves the coupling of a flow solver and a wave equation solver. Unsteady flow analysis is performed with URANS using FLUENT. Then the time dependent data are processed with LMS Sysnoise to compute the acoustic radiation. Experimental studies are performed to verify the theoretical results and additionally to investigate the effects of different design alternatives on noise level of the fan. The sound pressure and intensity level measurements are performed in the full anechoic room of Arç
elik A.S. Research and Development Laboratories. The validation experiments indicate that there is a good agreement between numerical and experimental results. The experimental study with different fan designs gives information about the noise reduction possibilities.

Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xii, 200 p.; also includes graphics (some col.). Includes abstract and vita. Advisor: Frederick C. Michel, Jr., Dept. of Food, Agricultural, and Biological Engineering. Includes bibliographical references (p. 173-181).

Several types of instability can affect the interface between two fluids. For instance, a Rayleigh-Taylor instability (or density fingering) is encountered when a heavier fluid is placed upon a lighter one in the gravity field and double diffusive instabilities can be triggered by differential diffusivity of the different species present in the fluid.

In this context our work aims to understand theoretically in which way a chemical reaction can induce and influence such instabilities in a fluid initially at rest.

To understand the dynamics resulting from the coupling between chemical reactions and hydrodynamical instabilities we use chemical fronts as model systems. These fronts result from the coupling between autocatalytical chemical reactions and diffusion and they allow to create a self-organized interface between the products and the reactants. As during a chemical reaction the density may vary due to solutal and thermal effects, the products and the reactants can have different densities which may trigger convection movements leading to the destabilization of the fronts.

We have in particular studied the influence of the exothermicity of the reaction on the fingering of chemical fronts, focusing first on the influence of heat losses through the walls of the set-up.

These leaks have a marked influence on the dynamics because they affect the temperature profiles and hence the density profiles too. We have also classified the various types of instabilities that may appear dues to solutal and thermal effects. We have found a new type of hydrodynamic instability of statically stable fronts induced by the chemical reaction.

We have furthermore analyzed an isothermal model with two chemical species. If they diffuse at different rates the front can be subject to diffusive instabilities as well. We have shown that the coupling between such a diffusive instability and fingering can trigger complex dynamics. We have eventually studied the influence of an external electric field on the diffusive instabilities and on fingering underlying the possibility to destabilize otherwise stable fronts./

Différents types d'instabilités hydrodynamiques peuvent affecter les interfaces entre deux fluides comme par exemple, une instabilité de Rayleigh-Taylor (ou digitation de densité) quand un fluide plus dense se trouve placé au-dessus d'un fluide moins dense dans le champ de gravité ou des instabilités de double diffusion induites par des différences entre les diffusivités d'un soluté et de la chaleur contenus dans les fluides. Dans ce contexte, notre thèse s'attache à comprendre de manière théorique comment une réaction chimique peut influencer ces instabilités voire les générer dans un fluide initialement au repos. Pour étudier les dynamiques résultant du couplage entre réactions chimiques et instabilités hydrodynamiques, nous utilisons des systèmes modèles: les fronts chimiques de conversion résultant de la compétition entre réactions chimiques autocatalytiques et diffusion créant une interface auto-organisée entre les réactifs et les produits. Comme au cours d'une réaction chimique la densité peut varier par des effets solutaux et thermiques, les produits et les réactifs de densités différentes peuvent générer des mouvements de convection qui conduisent à la déstabilisation des fronts.

Nous avons en particulier étudié l'influence de l'exothermicité de la réaction sur les instabilités de digitation de fronts chimiques, en nous focalisant dans un premier temps sur l'influence des pertes de chaleur par les parois du réacteur.

Ces fuites ont un effet marqué sur les instabilitités car elles affectent les profils de température et donc les profils de densité dans le système. Nous avons également classifié les différentes instabilités qui peuvent apparaître via des changements de densité dûs à des effets thermiques et solutaux et mis en évidence un nouveau type de déstabilisation hydrodynamique de fronts statiquement stables induit par une réaction chimique.

Nous avons ensuite analysé un modèle isotherme impliquant deux espèces chimiques. Si ces dernières diffusent a des vitesses différentes le front peut être sujet à une instabilité diffusive. Nous avons montré qu'un couplage entre une telle instabilité diffusive et de la digitation peut être à l'origine de dynamiques complexes. Nous avons ensuite considéré l'influence d'un champ électrique sur les instabilité diffusives et de digitation en soulignant la possibilié de déstabiliser via ce champ des fronts initialement stables.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

L'objectif de cette thèse est de développer des méthodes numériques dans un code de simulation numérique direct contenant une méthode de suivi Lagrangien de phase disperse. Ces méthodes numériques ont permis d'optimiser le suivi Lagrangien parallèle des gouttes afin de pouvoir simuler de très grands domaines. Un algorithme de gestion des collisions entre les gouttes a aussi été développé et mis en place ainsi qu'une procédure permettant d'intégrer des corps immergés de formes quelconques. Ces méthodes numériques ont permis d'effectuer des simulations de référence et d'obtenir des statistiques détaillées de diverses configurations telles que le croisement de jets de gouttes qui se collisionnent ou bien la propagation d'un front de flamme dans un spray évaporant. La comparaison de ces caractéristiques avec les mêmes simulations où la prise en charge du spray était effectuée par une méthode Eulérienne multi-fluide ont été faites. Les très bonnes concordances qualitatives et quantitatives entre les prises en charge Lagrangiennes et Eulériennes ont permis de montrer les capacités du modèle Eulérien à rendre compte de phénomènes physiques complexes. Ce modèle Eulérien permettra de bien meilleurs scaling lors de son portage sur des architectures massivement parallèles.

Unsteady shock wave propagation through ducts has many applications, ranging from blast wave shelter design to advanced high-speed propulsion systems. The research objective of this study was improved fundamental understanding of the transient flow structures during unsteady shock wave propagation through rectangular ducts with varying cross-sectional area. This research focused on the fluid dynamics of the unsteady shock-induced flow fields, with an emphasis placed on understanding and characterizing the mechanisms behind flow compression (wave structures), flow induction (via shock waves), and enhanced mixing (via shock-induced viscous shear layers). A theoretical and numerical (CFD) parametric study was performed, in which the effects of these parameters on the unsteady flow fields were examined: incident shock strength, area ratio, and viscous mode (inviscid, laminar, and turbulent). Two geometries were considered: the backward-facing step (BFS) geometry, which provided a benchmark and conceptual framework, and the splitter plate (SP) geometry, which was a canonical representation of the engine flow path. The theoretical analysis was inviscid, quasi-1D and quasi-steady; and the computational analysis was fully 2D, time-accurate, and viscous. The theory provided the wave patterns and primary wave strengths for the BFS geometry, and the simulations verified the wave patterns and quantified the effects of geometry and viscosity. It was shown that the theoretical wave patterns on the BFS geometry can be used to systematically analyze the transient, 2D, viscous flows on the SP geometry. This work also highlighted the importance and the role of oscillating shock and expansion waves in the development of these unsteady flows. The potential for both upstream and downstream flow induction was addressed. Positive upstream flow induction was not found in this study due to the persistent formation of an upstream-moving shock wave. Enhanced mixing was addressed by examining the evolution of the unsteady shear layer, its instability, and their effects on the flow field. The instability always appeared after the reflected shock interaction, and was exacerbated in the laminar cases and damped out in the turbulent cases. This research provided new understanding of the long-term evolution of these confined flows. Lastly, the turbulent work is one of the few turbulent studies on these flows.

This dissertation presents a theoretical study of a variety of charged polymer systems: Critical conditions are determined for adsorption of a charged polymer chain in an electrolyte solution by a curved, charged surface; the scaling behavior and density profiles of a polyelectrolyte brush is examined; the stretch-colapse transition of a charged, grafted polymer layers in a poor solvent is analyzed; and, the sequence dependence of heteropolymer configurations is calculated. These problems are studied theoretically using standard techniques of statistical mechanics.

The thermodynamic and structural effects of highly anisotropic, short-ranged attraction are investigated for single- and four-site interaction models using Wertheim's multi-density graph theory of chemical association. Both models consist of associating hard spheres, where the saturable attraction sites are described by conical wells centered in the hard core and evaluated in the "sticky-spot" limit. The resulting fluids then mimic many of the directional and steric-constrained properties of hydrogen-bonded fluids. The single-site model is used to explore the effects of dimerization upon the well-known properties of a planar liquid-vapor interface. Apart from hard sphere repulsion and sticky-spot attraction, a van der Waals-like dispersion interaction is incorporated to generate the critical point. Association is treated within Wertheim's thermodynamic perturbation theory, along with classical density functional methods to determine the interfacial density profile. The direct correlation functions which carry all bonding information are derived by means of the associative Ornstein-Zernike equations with a Percus-Yevick-like closure relation. The primary effects of dimerization are manifest in system thermodynamics. Critical temperatures and densities are shifted from their non-associating values and small, non-monotonic shifts in the correlation length and surface tension are also observed. While these effects are accompanied by interface compositional changes, any influence upon the density profile seems to be subsumed by use of the proper T/T[subscript c]. The four-site, network-forming model is investigated as a prototype for the thermodynamics and structural properties of water. Bonding interactions occur between "hydrogen" and electron "lone pair" sites described in the sticky-spot limit. System properties are derived under the ideal network approximation using the same methods as for the one-site model and are found to qualitatively reproduce some thermodynamic and connectivity features characteristic of real water. Partial densities are calculated self-consistently within the theory, and most thermodynamic quantities can be written in terms of the average number of hydrogen bonds per molecule. An analytical structure factor is also derived for this model.
Graduation date: 2003

1a. Two model porous media and a precise drying protocol are employed in numerical simulation of fluid configurations in partially saturated porous media. Over a substantial range of partial saturation $N\sb{L},$ the liquid-vapor configurations are inhomogeneous on a length scale that is a sensitive function of $N\sb{L}.$ Several measures of the characteristics of fluid configurations are developed. Details of the fluid configurations are found in the study of $p(x;\ell,N\sb{L}),$ the probability density for a porous medium of partial saturation $N\sb{L}$ to contain a piece of material of size $\ell\sp{d}$ having partial saturation x. This probability density is a gauge of inhomogeneity and appears importantly in NMR studies of porous media. 1b. The equations governing magnetization evolution in fluid filled pore systems are developed. In pore systems with a range of pore sizes (and/or decay rates) the magnetization evolution is described exactly by a spectrum of decay rates, leading to multiple exponential decay. We study this spectrum of decay rates as a function of coupling strength between pores using perturbation theory, effective medium theory, and matrix diagonalization. The spectrum of decay rates evolves from the individual pore decay rate distribution, at zero coupling, to a delta function distribution, at infinite coupling. The effect of coupling between pores is important in NMR studies of temperature dependence of characteristic decay rates in porous media. 2. The equation of motion describing a borehole elastic system (BES) is studied in the form of a perturbation problem, i.e. as the sum of terms describing a model elastic system (MES) and terms describing the departure of the BES being studied from the MES. The MES is chosen such that the departure terms in the BES equation of motion are small. The Green tensor for an infinite, azimuthally symmetric borehole is developed. As an illustration of the perturbation technique, the consequences of a mudcake layer on the borehole wall are explored. Comparison of first order perturbation calculations confirms the perturbation method is a valid technique for probing small changes to a model elastic system.

The standard contemporary approaches to modelling non-equilibrium, many-body phenomena are to use detailed computational models or to analyse large datasets. Here we explore an alternative approach: the use of simple idealized models based on the novel application of statistical mechanics in a non-equilibrium, many-body setting. This thesis has two main elements. The first element is the development of idealized statistical mechanics models to address particular topics in physics and biology. The particular topics to be addressed are as follows: (i) we show using a statistical mechanics approach that global patterns of tree/grass co-existence in savanna ecology can be interpreted as primarily the result of the different water use of trees and grasses subject to considerable fluctuation due to other factors such as disturbances; (ii) we discuss the unification of stochastic and mechanistic approaches in community ecology using a statistical mechanics framework, and develop a statistical mechanical model of a plant ecosystem to predict species abundance patterns, stability-diversity relationships and a phase transition between vegetated and non-vegetated community states, aspects of ecosystem behaviour which have so far been studied largely in isolation from one another; (iii) we clarify aspects of Malkus's variational approach to anisotropic, inhomogeneous fluid turbulence and revisit his statistical stability argument for maximising flow quantities, discussing possible connections to statistical mechanical justifications for flow quantity maximisation. The second main element of this thesis is the discussion of some of the broader methodological concerns surrounding the use of statistical mechanics in a generalised non-equilibrium setting. A central theme of this discussion is emphasizing the distinction between statistical mechanics and statistical inference.

This dissertation is concerned with the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors. After discussing the historical development and major contributions to the understanding of wall injected flows, we present an inviscid rotational model for solid and hybrid rockets with arbitrary headwall injection. Then, we address the problem of pressure integration and find that for a given divergence free velocity field, unless the vorticity transport equation is identically satisfied, one cannot find an analytic expression for the pressure by direct integration of the Navier-Stokes equations. This is followed by the application of a variational procedure to seek novel solutions with varying levels of kinetic energies. These are found to cover a wide spectrum of admissible motions ranging from purely irrotational to highly rotational fields. Subsequently, a second law analysis as well as an extension of Kelvin's energy theorem to open boundaries are presented to verify and corroborate the variational model. Finally, the focus is shifted to address the problem of laminar viscous flow in a porous cylinder with regressing walls. This is tackled using two different analytical techniques, namely, perturbation and decomposition. Comparisons with numerical Runge--Kutta solutions are also provided for a variety of wall Reynolds numbers and wall regression speeds.

In this thesis we study a variety of problems in superfluid turbulence, princi-pally in two dimensions. A summary of the main results of our studies is given below; we indicate the Chapters in which we present these. In Chapter 1, we provide an overview of several problems in superfluid turbulence with special emphasis on background material for the problems we study in this thesis. In particular, we give: (a) a brief introduction of fluid turbulence; (b) an overview of superfluidity and the phenomenological two-fluid model; (c) a brief overview of experiments on superfluid turbulence; (d) an introductory accounts of the phenomenological models used in the study of superfluid turbulence. We end with a summary of the problems we study in subsequent Chapters of this thesis. In Chapter 2, we present a systematic, direct numerical simulation of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power- law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power laws and the extents of the scaling regions change with time and depend on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers k > kc and partial thermalization takes place for modes with k < kc ; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t. Finally, in the fourth regime, complete thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms. Our work is a natural generalization of recent studies of thermalization in the Euler and other hydrodynamical equations; it combines ideas from fluid dynamics and turbulence, on the one hand, and equilibrium and nonequilibrium statistical mechanics on the other. In Chapter 3, we present the first calculation of the mutual-friction coefficients α and α (which are parameters in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model that we study in chapter 5) as a function of temperature in a homogeneous Bose gas in two-dimensions by using the Galerkin-truncated Gross-Pitaevskii equation, with very special initial conditions, which we obtain by using the advective, real, Ginzburg-Landau equation (ARGLE) and an equilibration procedure that uses a stochastic Ginzburg-Landau equation (SGLE). We also calculate the normal-fluid density as a function of temperature. In Chapter 4, we elucidate the interplay of particles and fields in superfluids, in both simple and turbulent flows. We carry out extensive direct numerical simulations (DNSs) of this interplay for the two-dimensional (2D) Gross-Pitaevskii (GP) equation. We obtain the following results: (1) the motion of a particle can be chaotic even if the superfluid shows no sign of turbulence; (2) vortex motion depends sensitively on particle charateristics; (3) there is an effective, superfluid-mediated, attractive interaction between particles; (4) we introduce a short-range repulsion between particles, with range rSR, and study two- and many-particle collisions; in the case of two-particle, head-on collisions, we find that, at low values of rSR, the particle collisions are inelastic with coefficient of restitution e = 0; and, as we in-crease rSR, e becomes nonzero at a critical point, and finally attains values close to 1; (5) assemblies of particles and vortices show rich, turbulent, spatio-temporal evolution. In Chapter 5, we present results from our direct numerical simulations (DNSs) of the Hall-Vinen-Bekharevich-Khalatnikov (HVBK) two-fluid model in two dimensions. We have designed these DNSs to study the statistical properties of inverse and forward cascades in the HVBK model. We obtain several interesting results that have not been anticipated hitherto: (1) Both normal-fluid and superfluid energy spectra, En(k) and Es(k), respectively, show inverse- and forward-cascade regimes; the former is characterized by a power law Es(k) En(k) kα whose exponent is consistent with α 5/3. (2) The forward-cascade power law depends on (a) the friction coefficient, as in 2D fluid turbulence, and, in addition, on (b) the coefficient B of mutual friction, which couples normal and superfluid compo-nents. (3) As B increases, the normal and superfluid velocities, un and us, re-spectively, get locked to each other, and, therefore, Es(k) En(k), especially in the inverse-cascade regime. (4) We quantify this locking tendency by calculating the probability distribution functions (PDFs) P(cos(θ)) and P(γ), where the angle θ ≡ (un • us)/( |un||us|) and the amplitude ratio γ = |un|/|us |; the former has a peak at cos(θ) = 1; and the latter exhibits a peak at γ = 1 and power-law tails on both sides of this peak. (4) This locking increases as we increase B, but the power-law exponents for the tails of P(γ) are universal, in so far as they do not depend on B, ρn/ρ, and the details of the energy-injection method. (5) We characterize the energy and enstrophy cascades by computing the energy and enstrophy fluxes and the mutual-friction transfer functions for all wave-number scales k. In Chapter 6, we examine the multiscaling of structure functions in three-dimensional superfluid turbulence by using a shell-model for the three-dimensional HVBK equations. Our HVBK shell model is based on the GOY shell model. In particular, we examine the dependence of multiscaling on the normal-fluid fraction and the mutual-friction coefficients. We hope our in silico studies of 2D and 3D superfluid turbulence will stimulate new experimental, numerical, and theoretical studies.

Fractional calculus is the integration and differentiation to an arbitrary or fractional order. The techniques of fractional calculus are not commonly taught in engineering curricula since physical laws are expressed in integer order notation. Dr. Richard Magin (2006) notes how engineers occasionally encounter dynamic systems in which the integer order methods do not properly model the physical characteristics and lead to numerous mathematical operations. In the following study, the application of fractional order calculus to approximate the angular position of the disk oscillating in a Newtonian fluid was experimentally validated. The proposed experimental study was conducted to model the nonlinear response of an oscillating system using fractional order calculus. The integer and fractional order mathematical models solved the differential equation of motion specific to the experiment. The experimental results were compared to the integer order and the fractional order analytical solutions. The fractional order mathematical model in this study approximated the nonlinear response of the designed system by using the Bagley and Torvik fractional derivative. The analytical results of the experiment indicate that either the integer or fractional order methods can be used to approximate the angular position of the disk oscillating in the homogeneous solution. The following research was in collaboration with Dr. Richard Mark French, Dr. Garcia Bravo, and Rajarshi Choudhuri, and the experimental design was derived from the previous experiments conducted in 2018.