Turbulent swirling flows are important in many applications including gas turbines, furnaces and cyclone dust separators among others. Although the mean flow fields have been relatively well studied, a complete understanding of the flow field including its dynamics has not been achieved. The work contained in this dissertation attempts to shed further light on the behavior of turbulent swirling flows, especially focused on the dynamic behavior of a turbulent swirling flow encountering a sudden expansion. Experiments were performed in a new isothermal turbulent swirling flow test facility. Two geometrical nozzle configurations were studied. The \cb\ nozzle configuration exhibits a cylindrical \cb\ in the center of the nozzle. The free vortex nozzle configuration is obtained when the cylindrical \cb\ is removed. Detailed laser velocimeter measurements were performed to map out the flow field near the sudden expansion of the 2.9" (ID) nozzle leading to the 7.4" (ID) downstream section. In addition to presenting detailed flow profiles for both nozzle and downstream flow fields, representative frequency spectra of the flow dynamics are presented. Along with the flow time histories and histograms, the wide variety of dynamic behavior was thus described in great detail. The dynamics observed in the experiment can be classified into three main categories: coherent and large scale motion, intermittent motion and coherent periodic motion. Free vortex geometry flows, in the parameter space of the experiments (Swirl number = 0 - 0.21), exhibited mostly coherent and large scale motion. The spectra in these cases were broadband with very light concentration of spectral energy observed in some specific cases. Center--body geometry flows exhibited all three categories of flows as swirl strength was increased from zero. Flows with little or no swirl exhibited broad--band spectra similar to those for the free vortex geometry. Intermediate swirl levels resulted in a large amount of low frequency energy which, with the aid of the time histories, was identified as a large scale intermittence associated with radial movement of the annular jet as it enters the sudden expansion. Large swirl levels resulted in high magnitude coherent oscillations concentrated largely just downstream of the sudden expansion. Linear stability analysis was used to help in the interpretation of the observed dynamics. Although, as implemented here (using the parallel flow assumption), the analysis was not successful in quantitatively matching the experimentally observed dynamics, significant insight into the physical mechanisms of the observed dynamics was obtained from the analysis. Specifically, the coherent oscillations observed for larger swirl levels were able to be described in terms of the interaction between the inner and outer shear layers of the flow field. / Ph. D.

We develop a physics-based reduced-order model of the aero-acoustic sound sources in reacting mixing layers as a method for fast and accurate predictions of the radiated sound. Instabilities in low-speed mixing layers are known to be dominated by the traditional Kelvin–Helmholtz (K–H)-type “central” mode, which is expected to be superseded by the “outer” modes as the chemical-reaction-based heat-release modifies the mean density, yielding new peaks in the density-weighted vorticity profiles. Although, these outer modes are known to be of lesser importance in the near-field mixing, how these radiate to the far-field is uncertain, on which we focus primarily, when the mixing layer is supersonic, but also report subsonic cases. On keeping the flow compressibility fixed, the outer modes are realized via biasing the respective mean density of the fast (oxidizer) or slow (fuel) side. In the linearized model that we use, the mean flow are laminar solutions of two-dimensional compressible boundary layers with an imposed composite turbulent spread rate, which we show to correctly predict the growth of instability waves by saturating them earlier, similar to in non-linear calculations, but obtained here via solving the linear parabolized stability equations (PSE). The chemical reaction is modeled via a single-step, single-product overall process which introduces a heat release term in the mean temperature equation. As the flow parameters are varied, modes that are unstable on the slow side are shown to be more sensitive to heat release, potentially exceeding equivalent central modes, as these modes yield relatively compact sound sources with lesser spreading of the mixing layer, when compared to the corresponding fast modes. In contrast, the radiated sound, obtained directly from the PSE solutions, seems to be relatively unaffected by a variation of mixture equivalence ratio, except for a lean mixture which is shown to yield a pronounced effect on the slow mode radiation by reducing its modal growth. For subsonic mixing layers, the sensitivity of central mode is explored, which in addition requires an acoustic analogy based method (e.g. the Lilley–Goldstein equations) to predict the sound from the linearized PSE sources, as used here, unlike in supersonic cases.

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. I describe initial experiments with two independent but complementary strategies for attacking this "time barrier". First I describe computational experiments exploring the performance improvements from overlapping computation and communication on hybrid parallel computers. My test case is explicit time integration of linear advection with constant uniform velocity in a three-dimensional periodic domain. I present results for Fortran implementations using various combinations of MPI, OpenMP, and CUDA, with and without overlap of computation and communication. Second I describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, along with a parallel implementation discretized on the cubed sphere. It shows optimal accuracy at Courant numbers of 10-20, more than an order of magnitude higher than explicit methods. Finally I describe the development and stability analyses of the time integrators and advection methods I used for my experiments. I develop explicit single-step methods with stability up to Courant numbers of one in each dimension, hybrid explicit-implict methods with stability for arbitrary Courant numbers, and interpolation operators that enable the arbitrary stability of semi-Lagrangian methods.

We investigate the linear stability and perform the bifurcation analysis for Hopfield neural networks with a general distribution of delays, where the neurons are identical. We start by analyzing the scalar model and show what kind of information can be gained with only minimal information about the exact distribution of delays. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are. We compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that, in general, the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments. Further, we extend these results to a network of n identical neurons, where we examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. Finally, for the scalar model, we show under what conditions a Hopf bifurcation occurs and we use the centre manifold technique to determine the criticality of the bifurcation. When the kernel represents the gamma distribution with p=1 and p=2, we transform the delay differential equation into a system of ordinary differential equations and we compare the centre manifold computation to the one we obtain in the ordinary differential case.

The materials that exhibit martensite transformation have very important applications in engineering, and the microstructures of the materials play a key role foraffecting their mechanical behavior in macroscope. Therefore many attentions havebeen drawn for studying the related problems. This work focuses on the motion oftwin boundaries. Three questions are being asked: how is a twin boundary is nucleated in a homogenous (untwinned) material? After the twin boundary is nucleated,how is its motion initiated? How fast does it move? This study provides an atomisticunderstanding for these three questions. Linear stability analysis is firstly applied to capture the initiation of motion of atwin boundary. When a twin boundary is about to move, the lowest eigenvalue of thesystem Hessian drops to zero. And the corresponding eigenvector predicts accuratelythe way in which the twin boundary is going to move. The same idea is applied toinvestigate how motion of an irrational twin boundary is initiated. Atomic modelsof irrational twin boundaries are constructed by employment of continuum models,provided that the point group of rotations which relate two variants is extended toany rotations in plane. The zero eigenvectors reveal the complicated behavior ofmotion of irrational twin boundaries. The problem of nonuniqueness of kinetic relations proposed by Schwetlick andZimmer is solved in a thermoelasticity framework. By calculating the net heat fluxcrossing the phase boundary which is carried by the phonons, a unique kinetic relationcan be determined. Finally, a nonlocal criterion for nucleation of twin boundariesis proposed. By checking the stiffness of each unit cell evaluated with respect to asingle variable that represents the displacement along the unit cell diagonal direction,locations and the orientations of nucleated twin boundaries can be predicted.

Density stratification is one of the essential underlying physical mechanisms for atmospheric and oceanic flow. As a first step to investigating the mechanisms of stratified turbulence, linear stability plays a critical role in determining under what conditions a flow remains stable or unstable. In the study of transition to stratified turbulence, a common vortex model, known as the Lamb-Chaplygin dipole, is used to investigate the conditions under which stratified flow transitions to turbulence. Numerous investigations have determined that a critical length scale, known as the buoyancy length, plays a key role in the breakdown and transition to stratified turbulence. At this buoyancy length scale, an instability unique to stratified flow, the zigzag instability, emerges. However investigations into sub-buoyancy length scales have remained unexplored. In this thesis we discover and investigate a new instability of the Lamb-Chaplyin dipole that exists at the sub-buoyancy scale. Through numerical linear stability analysis we show that this short-wave instability exhibits growth rates similar to that of the zigzag instability. We conclude with nonlinear studies of this short-wave instability and demonstrate this new instability saturates at a level proportional to the cube of the aspect ratio.

We investigate the linear stability and perform the bifurcation analysis for Hopfield neural networks with a general distribution of delays, where the neurons are identical. We start by analyzing the scalar model and show what kind of information can be gained with only minimal information about the exact distribution of delays. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are. We compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that, in general, the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments. Further, we extend these results to a network of n identical neurons, where we examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. Finally, for the scalar model, we show under what conditions a Hopf bifurcation occurs and we use the centre manifold technique to determine the criticality of the bifurcation. When the kernel represents the gamma distribution with p=1 and p=2, we transform the delay differential equation into a system of ordinary differential equations and we compare the centre manifold computation to the one we obtain in the ordinary differential case.

Alors qu'il est bien connu que le phénomène d'instabilité de Faraday est une manifestation d'ondes de gravité capillaire, son comportement lorsque les effets capillaires et gravitationnels disparaissent reste inexploré théoriquement et expérimentalement. Une étude expérimentale et théorique détaillée est réalisée pour comprendre la physique de ce phénomène dans une petite cavité rectangulaire où la proximité des murs entraîne des contraintes considérables sur les parois latérales. Un couple de liquides binaires est utilisé avec une faible tension interfaciale pour une interface presque plate. Le contrôle thermique de ce système de fluide est utilisé pour diminuer la force capillaire et d’étudier ainsi les instabilités de Faraday dans les fluides miscibles où la tension interfaciale s’annule. Afin de prendre en compte les effets gravitationnels, l'expérience a été réalisée dans des campagnes de vols paraboliques. Pour l'approche théorique, une analyse de stabilité linéaire est effectuée à l'aide d'équations de Navier-Stokes dans un système de fluide visqueux incompressible et newtonien. Ceci est réalisé grâce à une méthode de Fourier-Floquet résultant en un problème aux valeurs propres. Les comparaisons montrent des différences non négligeables. Les équations sont ensuite résolues en incluant des effets d'amortissement visqueux pour compenser les contraintes des parois latérales. Les fluides binaires ont fourni une option commode pourchanger le coefficient de tension interfaciale en augmentant la température jusqu’à la température critique, ce qui a permis de passer d’un système de fluides non miscibles à celui des fluides miscibles tout en restant au-dessous de la température d’ébullition. Le taux d'amortissement visqueux linéaire est mesuré expérimentalement. La correction des calculs théoriques en prenant en compte le taux d'amortissement visqueux a permis une amélioration nette des résultats et donc de mieux comprendre la prédiction de l'amplitude critique expérimentale pour les modes sous-harmonique et harmonique. / While it is well known that the phenomenon of Faraday instability is a manifestation of vibrational acceleration, its behaviour when both the capillary and gravitational effects vanish, remains unexplored theoretically and experimentally. A detailed experimental and theoretical study is performed to understand the physics of this phenomenon in small rectangular geometry where the proximity of wall results in considerable sidewall stresses. A novel binary liquids system is utilized with low interfacial tension for a near flat interface. Thermal control of fluid system is utilized for achieving reduction in capillary force with study of miscible fluids where interfacial tension reduces to almost zero. In order to discriminate between gravity and capillarity effects, experiments were performed in parabolic flight campaigns. . For the theoretical approach a linear stability analysis is performed through Navier-Stokes equations in a Newtonian incompressible viscous fluid system. This is achieved through a Fourier Floquet method resulting into an eigenvalue problem. Equations are solved by including viscous damping effects for compensating sidewall stresses. Experimentally binary fluids provided a convenient option of changing the coefficient of interfacial tension by temperature control and going through immiscible to miscible system without change of liquid charge. Viscous damping rate is determined experimentally by measuring the linear damping rate. The correction in the theoretical calculations with the viscous damping rate helped in achieving a better understanding of the prediction of the experimental critical amplitude for sub-harmonic and harmonic modes.

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

The aim of this theses is to create application, which is able to calculate buckling load of structure made from 1D bar elements, using finite element method. introduction is devoted to basic principles of buckling and derivation of necessary formulas. Then are described all operations and numerical methods needed for the application. At the and is in detail analyzed few structures and results are compared with known solutions or with other applications.