The existence of multiple hydrodynamic states (MHS) in trickle bed operation has been proved by hysteresis observed in flow loops, as well as variation between different prewetting modes. The most common theory presented as explanation for the existence of MHS, is the film vs. rivulet concept. Based on this concept, it was suspected that in-situ upsets might promote the formations of films, thereby providing a method through which the hydrodynamic states of the Dry and Levec modes can be manipulated to perform like the Kan Liquid and Super modes. Large performance enhancements can be obtained by altering the prewetting procedure, even for systems with a low surface tension. For the water system, the gas liquid mass transfer coefficient of the Kan Liquid and Super modes could be as much as 6 times greater than that of the Dry mode. For the low surface tension system, the gas liquid mass transfer of the Kan Liquid and Super modes could be up to 8 times greater than that of the Dry mode. Through a thorough investigation of various types of transient upsets and manipulation strategies, it was confirmed that prewetting is indeed the only way by which drastic variation in hydrodynamic states may be obtained. None of the investigated upsets (hysteresis, periodic operation or surface tension doping) resulted in changes in the liquid morphology that could compare to the significant variation that was observed by varying the prewetting mode. Two methods were identified by which the hydrodynamic gaps between the less uniform (Dry and Levec) modes and the more uniform modes (Kan Liquid and Super) could be bridged. The first is to reduce the Levec draining time, while the second method may be seen as an in-situ type of Kan Liquid prewetting. This type of prewetting was obtained during doping with a low surface tension liquid, at a flow rate associated with the high interaction regime for the low surface tension system. Though the hysteresis cycles did not drastically alter the predominant flow type, interesting trends were observed, some of which raised doubt about the application of the films vs. rivulet concept. One mode in particular displayed behaviour which contributed to this doubt, namely the Kan Gas mode; • Gas liquid mass transfer on this mode decreased with an increase in liquid flow rate • Relatively low pressure drops on this mode corresponded to relatively high liquid holdup • It was the only mode that exhibited no hysteresis with gas flow variation, on any of the hydrodynamic parameters The various trends and variations observed with the different types of upsets, leads to the conclusion that the concept of films vs. rivulets simply does not provide adequate explanation of the observed results. In general, two flow types may be distinguished. That which is caused by an initial increase in liquid flow rate as opposed to that which is caused by an initial increase in gas flow rate An investigation to determine the behaviour of each of the investigated parameters near the transition boundaries on all the modes, as well as a repetition of this study with non-intrusive visual techniques is recommended. / Dissertation (MEng (Chemical Engineering))--University of Pretoria, 2008. / Chemical Engineering / unrestricted

Le relargage contrôlé est un enjeu industriel auquel l'encapsulation peut répondre. Une méthode prometteuse pour fabriquer des micro-capsules consiste à déposer couche après couche des polymères à la surface de goutte d'huiles ou de bulles d'air. Cette thèse a pour objet ces assemblages en multicouches de polymères aux interfaces liquides. A partir d'expériences menées sur des interfaces modèles entre deux fluides non miscibles et leur modélisation, nous avons étudié l'effet des interactions à l'échelle des chaînes de polymère sur les propriétés rhéologiques de l'interface. Dans un premier temps nous avons utilisé la géométrie modèle qu'est la goutte pendante pour étudier indépendamment les différents phénomènes impliqués dans l'assemblage des multicouches et dans leur déformation. Nous avons revisité différents modèles classique pour décrire l'adsorption de nos polymères à l'interface, puis nous avons mesuré les modules interfaciaux de différents systèmes de polymères. Pour cela, à l'aide de mesures complémentaires, nous avons établi un cadre pour les mesures de modules élastiques en goutte pendante. Dans un second temps, nous avons utilisé la microfluidique pour fabriquer différents types de micro-capsules et pour mesurer leurs propriétés mécaniques. Celles-ci résultent des différents phénomènes étudiés dans la première partie de cette thèse. Nous avons établi un modèle et effectué des simulations numériques qui nous permettent d'extraire les principales propriétés interfaciales de nos capsules à partir de la mesure de leur déformation dans les canaux microfluidiques. / In order to improve control over the delivery of chemicals, industries seek a way to encapsulate them. A promising method to produce artificial micro-capsules consists in assembling several layers of polymer at the interface of an oil droplet or an air bubble. This thesis focuses on these multilayer assemblies of polymers at liquid interfaces. Through experimental observations on model interfaces and modeling, we studied the effect of the molecular interactions of polymer chains at an interface between two immiscible fluids on the rheological behaviour of this interface. In a first part, we used the model macroscopic geometry of the pendant drop to study independently the different phenomena taking place during the assembly and the deformation of the multilayers. We revisited classical models to describe the adsorption dynamics of our polymers, and we measured the interfacial dilational modulus of various systems. To this aim, by performing independent measurements, we delimited the range of validity of the pendant-drop apparatus. In the second part, we used microfluidics to create micro-capsules of different kinds and to probe their mechanical properties resulting from all the phenomena studied in the first part. We developed a model and we performed numerical simulations to extract the main interfacial properties of our capsules from the measurement of their deformation in the channels.

The ageing population has become more active and live longer, these patients require hip replacement surgery at a younger age. Artificial hip implants, consisting of the acetabular cup and femoral head, affect the lives of many people, and the longevity of these implants pose significant concerns (rarely longer than 17 years). To help understand the lubricating performance of such a system, a hip joint model was built based on the Reynolds equation; the model developed simulated hydrodynamic lubrication. A steady-state angular rotation model was built whereby it was concluded that such motion would not support any load due to the anti-symmetric nature of the resultant pressure distribution (anti-symmetric about the axis of rotation). The pressure distribution from the steady-state rotation simulation contained a pressure source and sink which converged to the centre of the cup and whose pressure value increased in magnitude, as the eccentricity ratio increased. Infeasible results were obtained when the intermediary pressure constraint, allowing only positive pressure values, was implemented. The results obtained were not representative of the problem and it is recommended that this constraint not be implemented. The transient walking cycle model showed that a fluid with viscosity of 0.0015Pa.s is not sufficient to support a load in the walking cycle under conditions representative of hydrodynamic lubrication. Increasing the fluid viscosity promoted better results in the hydrodynamic model. Increasing the femoral head radius and decreasing the radial clearance between the components also improves the possibility of hydrodynamic lubrication. It is recommended that the model should be extended to investigate elasto-hydrodynamic lubrication. If possible, the effects of a boundary lubrication model should be investigated, as it is believed to be a major contribution to the lubrication of hip joints. / Dissertation (MEng)--University of Pretoria, 2008. / Chemical Engineering / unrestricted

The remarkable efficacy with which normal surface mass transpiration (blowing and suction) alters a given base flow to achieve a desired predefined objective has motivated several investigations on drag reduction, self-propulsion and suppression of separation and wake unsteadiness in bluff body flows. However, the energetic efficiency, a critical parameter that determines the true efficacy and in particular practical feasibility of this control strategy, has received significantly less attention. In this work, we determine the optimal zero net mass transpiration blowing and suction profiles that minimize net power consumption while reducing drag or enabling self-propulsion in typical bluff body flows. We establish the influence of prescribed blowing and suction profiles on the hydrodynamic loads and net power consumption for a representative bluff body flow involving flow past a stationary two-dimensional circular cylinder. Using analysis based on Oseen’s equations, we find that all the symmetric modes, except the first one, lead to an increase in the net power consumption without affecting hydrodynamic drag. The optimal blowing and suction profile that yields minimum power consumption is such that the normal stress acting on the cylinder surface vanishes identically. Furthermore, we show that a self-propelling state corresponding to zero net drag force is attained when the first mode of blowing and suction profile is such that the flow field be-comes irrigational. Based on these findings we employ direct numerical simulation tools to decipher the Reynolds number dependence of the optimal profiles and the associated power consumption for both drag reduction and self-propulsion. For a typical Reynolds number, the time-averaged drag coefficient first decreases due to vortex shedding suppression, then increases and eventually decreases again after attaining a local maximum as the strength of the first mode is increased. The net power consumption continues to decrease with an increase in the strength of the first mode before reaching a minima after which it rises continuously. For a Reynolds number of 1000 over fifteen fold reduction in drag is achieved for an optimal blowing and suction profile with a maximum radial surface velocity that is nearly 1.97 times the free stream velocity. Next, to establish whether or not higher modes play a role in decreasing net power consumption at finite Reynolds number, we perform theoretical analysis of a configuration similar to the one described above for a spherical body. At zero Reynolds number, as a result of mode independence, we show that surface blow-ing and suction of any form that involves second or higher order axisymmetric or non-axisymmetric modes does not contribute to drag and only leads to an increase in total power consumption. However, at finite Reynolds number, using analysis based on Oseen’s equations, we find that the second and higher modes contribute substantially to the optimal profiles. Finally to understand the effects of a change in shape we consider generalization of the above analysis to axisymmetric prolate and oblate spheroidal bodies. We find that for a general axisymmetric body with non-constant curvature, the optimal drag reducing and self-propelling blowing and suction profiles for minimum power consumption contain second and higher-order modes along with the first mode even when the Reynolds number is zero. The net decrease in power consumption with the use of second and higher order modes exceeds 33% for a disk-like low aspect ratio self-propelling oblate spheroid. Moreover, we perform comparisons between blowing and suction and tangential surface velocity based boundary deformation propulsion mechanisms. Below an aspect ratio of 0.56 we find blowing and suction mechanism to be more efficient for self-propulsion of an oblate spheroid. In contrast, for a self-propelling pro-late spherical micro-swimmer, we show that the tangential surface tread milling consumes less power irrespective of the aspect ratio.

This thesis deals with problems arising in the study of nonlinear partial differential equations arising from many-body problems. It is divided into two parts: The first part concerns the derivation of a nonlinear diffusion equation from a microscopic stochastic process. We give a new method to show that in the hydrodynamic limit, the particle densities of a one-dimensional zero range process on a periodic lattice converge to the solution of a nonlinear diffusion equation. This method allows for the first time an explicit uniform-in-time bound on the rate of convergence in the hydrodynamic limit. We also discuss how to extend this method to the multi-dimensional case. Furthermore we present an argument, which seems to be new in the context of hydrodynamic limits, how to deduce the convergence of the microscopic entropy and Fisher information towards the corresponding macroscopic quantities from the validity of the hydrodynamic limit and the initial convergence of the entropy. The second part deals with problems arising in the analysis of nonlinear Schrödinger equations of Gross-Pitaevskii type. First, we consider the Cauchy problem for (energy-subcritical) nonlinear Schrödinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum gases in rotating traps. We prove global existence (in the energy space) for defocusing nonlinearities without any restriction on the rotation frequency, generalizing earlier results given in the literature. Moreover, we find that the rotation term has a considerable influence in proving finite time blow-up in the focusing case. Finally, a mathematical framework for optimal bilinear control of nonlinear Schrödinger equations arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects. In particular, the cost induced by the physical work load over the control process is taken into account rather then often used L^2- or H^1-norms for the cost of the control action. We prove well-posedness of the problem and existence of an optimal control. In addition, the first order optimality system is rigorously derived. Also a numerical solution method is proposed, which is based on a Newton type iteration, and used to solve several coherent quantum control problems.

Large-scale unsteady flow structures play an influential role in the dynamics of many practical flows, such as those found in gas turbine combustion chambers. This thesis is concerned primarily with large-scale unsteady structures that arise due to self-sustained hydrodynamic oscillations, also known as global hydrodynamic instability. Direct numerical simulation (DNS) of the Navier--Stokes equations in the low Mach number limit is used to obtain a steady base flow, and the most unstable direct and adjoint global modes. These are combined, using a structural sensitivity framework, to identify the region of the flow and the feedback mechanisms that are responsible for causing the global instability. Using a Lagrangian framework, the direct and adjoint global modes are also used to identify the regions of the flow where steady and unsteady control, such as a drag force or heat input, can suppress or promote the global instability. These tools are used to study a variety of reacting and non-reacting flows to build an understanding of the physical mechanisms that are responsible for global hydrodynamic instability in swirling diffusion flames. In a non-swirling lifted jet diffusion flame, two modes of global instability are found. The first mode is a high-frequency mode caused by the instability of the low-density jet shear layer in the premixing zone. The second mode is a low-frequency mode caused by an instability of the outer shear layer of the flame. Two types of swirling diffusion flames with vortex breakdown bubbles are considered. They show qualitatively similar behaviour to the lifted jet diffusion flames. The first type of flame is unstable to a low-frequency mode, with wavemaker located at the flame base. The second type of flame is unstable to a high-frequency mode, with wavemaker located at the upstream edge of the vortex breakdown bubble. Feedback from density perturbations is found to have a strong influence on the unstable modes in the reacting flows. The wavemaker of the high-frequency mode in the reacting flows is very similar to its non-reacting counterpart. The low-frequency mode, however, is only observed in the reacting flows. The presence of reaction increases the influence of changes in the base flow mixture fraction profiles on the eigenmode. This increased influence acts through the heat release term. These results emphasize the possibility that non-reacting simulations and experiments may not always capture the important instability mechanisms of reacting flows, and highlight the importance of including heat release terms in stability analyses of reacting flows.

No description available.

In the case of cold accretion disk, coupling between charge neutral gas and magnetic field is too weak such that the magneto-rotational instability will be less effective or even stop working. In such a situation it is of prime interest to investigate the pure hydrodynamic turbulence and transport phenomenon. As the Reynolds number increases, the relative importance of the non-linear term in the hydrodynamic equation increases and in the case of accretion disk where molecular viscosity is too small the Reynolds number is large enough for the non-linear term to bring new effects. We investigate a scenario, the ‘weakly non-linear’ evolution of amplitude of linear mode when the flow is bounded by two parallel walls. The unperturbed flow is similar to plane Couette flow but with Coriolis force included in the hydrodynamic equation. Although there is no exponentially growing eigenmode, due to self-interaction the least stable eigenmode will grow in an intermediate phase. Later on this will lead to higher order non-linearity and plausible turbulence. Although the non-linear term in the hydrodynamic equation is energy conserving, within the weakly non-linear analysis it is possible to define a lower bound of the energy needed for flow to transform to turbulent phase. Such an unstable phase is possible only if the Reynolds number ≥ 103−4. In Chapter-2 we set up equation of amplitude for the hydrodynamic perturbation and study the effect of weak non-linear evolution of linear mode for general angular momentum distribution, where Keplerian disk is obtained as a special case. As we know that to explain observed hard X-rays the choice of Keplerian angular momentum profile is not adequate, we consider the sub-Keplerian regime of the disk. In Chapter-3 we assume that the cooling mechanism is dominated by bremsstrahlung process (without any strict knowledge of the magnetic field structure).We show that in a range of Shakura-Sunyaev viscosity 0.2 ≥ α ≥ 0.0005, flow behavior varies widely, particularly by means of the size of disk, efficiency of cooling and corresponding temperatures of ions and electrons. We also show that the disk around a rotating black hole is hotter compared to that around a Schwarzschild black hole, rendering a larger difference between ion and electron temperatures in the former case. We finally reproduce the observed luminosities(L) of two extreme cases—the under-fed AGNs and quasars and ultra-luminous X-ray sources at different combinations of mass accretion rate, ratio of specific heats, Shakura-Sunyaev viscosity parameter and Kerr parameter. In Chapter-4 we investigate the viscous two temperature accretion disk flows around rotating blackholes. We describe the global solution of accretion flows, unlike that in Chapter-3, with a sub-Keplerian angular momentum profile, by solving the underlying conservation equations including explicit cooling processes self-consistently. Bremsstrahlung, synchrotron and inverse comptonization of soft photons are considered as possible cooling mechanisms. We focus on the set of solutions for sub-Eddington, Eddington and super-Eddington mass accretion rates around Schwarzschild and Kerr black holes with a Kerr parameter 0.998. We analyse various phases of advection–general advective paradigm to radiatively inefficient paradigm. The solution may potentially explain the hard X-rays and γ-rays emitted from AGNs and X-ray binaries. We also compare the solutions for two different regimes of viscosity. We finally reproduce the observed luminosities of the under-fed AGNs and quasars, ultra-luminous X-ray sources at different combinations of input parameters such as mass accretion rate and ratio of specific heats.

Among sources of renewable energy, development of tidal energy has traditionally been plagued by relatively high costs and limited availability of sites with sufficiently high tidal amplitudes or flow velocities. However, many recent technology developments and improvements, both in design (e.g. dynamic tidal power, tidal lagoons) and turbine technology (e.g. new axial turbines, crossflow turbines), showed that the economic and environmental costs may be brought down to competitive levels comparing to other conventional energy sources. It has long been identified that the Bay of Fundy is one of the world’s premier locations for the development of tidal power generating systems, since it has some of the world’s largest tidal ranges. Consequently, several proposals have been made in the recent years to find economical ways to harness the power of tides. Presently, there is considerable interest in installing tidal lagoons in the Bay of Fundy. The lagoon concept involves temporarily storing seawater behind an impoundment dike and generating power by gradually releasing the impounded seawater through conventional low-head hydroelectric turbines. A tidal lagoon will inherently modify the tides and tidal currents regime in the vicinity of the lagoon, and possibly induce effects that may be felt throughout the entire Bay of Fundy. The nature of these hydrodynamic impacts will likely depend on the size of the tidal lagoon, its location, and its method of operation. Any changes in the tidal hydrodynamics caused by a tidal lagoon may also impact on the transport of sediments throughout the region and upset ecosystems that are well adapted to existing conditions. The scale and character of the potential hydrodynamic impacts due to tidal lagoons operating in the Bay of Fundy have not been previously investigated. The present study endeavours to investigate these potential impacts to help the development of sustainable, science-based policies for the management and development of clean energy for future generations. After outlining fundamental aspects of tidal power projects taken in consideration in the Bay of Fundy, an analysis of present knowledge on tidal lagoons was conducted in order to provide a focus for subsequent investigations. Hydrodynamic modeling was used to quantify any of the potential hydrodynamic changes induced in the Bay of Fundy due to the presence of tidal lagoons. In the last part of the thesis, new relationships were derived in order to describe the amount of energy removed from tidal lagoons associated with its hydrodynamic impacts.

Tsunamis are among the most terrifying and complex physical phenomena potentially affecting almost all coastal regions of the Earth. Tsunami waves propagate in the ocean over thousands of kilometres away from their generating source at considerable speeds. Among several other tsunamis that occurred during the past decade, the 2004 Indian Ocean Tsunami and the 2011 Tohoku Tsunami in Japan, considered to be the deadliest and costliest natural disasters in the history of mankind, respectively, have hit wide stretches of densely populated coastal areas. During these major events, severe destruction of inland structures resulted from the action of extreme hydrodynamic forces induced by tsunami flooding. Subsequent field surveys in which researchers from the University of Ottawa participated ultimately revealed that, in contrast to seismic forces, such hydrodynamic forces are not taken into proper consideration when designing buildings for tsunami prone areas. In view of these limitations, a novel interdisciplinary hydraulic-structural engineering research program was initiated at the University of Ottawa, in cooperation with the Canadian Hydraulic Centre of the National Research Council, to help develop guidelines for the sound design of nearshore structures located in such areas. The present study aims to simulate the physical laboratory experiments performed within the aforementioned research program using a single-phase three-dimensional weakly compressible Smoothed Particle Hydrodynamics (SPH) numerical model. These experiments consist in the violent impact of rapidly advancing tsunami-like hydraulic bores with individual slender structural elements. Such bores are emulated based on the classic dam-break problem. The quantitatively compared measurements include the time-history of the net base horizontal force and of the pressure distribution acting on columns of square and circular cross-sections, as well as flow characteristics such as bore-front velocity and water surface elevation. Good agreement was obtained. Results show that the magnitude and duration of the impulsive force at initial bore impact depend on the degree of entrapped air in the bore-front. The latter was found to increase considerably if the bed of the experimental flume is covered with a thin water layer of even just a few millimetres. In order to avoid large fluctuations in the pressure field and to obtain accurate simulations of the hydrodynamic forces, a Riemann solver-based formulation of the SPH method is utilized. However, this formulation induces excessive numerical diffusion, as sudden and large water surface deformations, such as splashing at initial bore impact, are less accurately reproduced. To investigate this particular issue, the small-scale physical experiment of Kleefsman et al. (2005) is also considered and modeled. Lastly, taking full advantage of the validated numerical model to better understand the underlying flow dynamics, the influence of the experimental test geometry and of the bed condition (i.e. dry vs. wet) is investigated. Numerical results show that when a bore propagates over a wet bed, its front is both deeper and steeper and it also has a lower velocity compared to when it propagates over a dry bed. These differences significantly affect the pressure distributions and resulting hydrodynamic forces acting on impacted structures.