There are two coupled objectives for this study of buoyancy-driven turbulence. The first objective is to determine if the development of a Rayleigh-Taylor (RT) mixing layer can be manipulated experimentally by altering the initial condition of the experiment. The second objective is to evaluate the performance of the Besnard, Harlow, and Rauenzahn (BHR) turbulent transport model when initialized with experimentally measured initial conditions. An existing statistically steady water channel facility at Texas A&M University and existing experimental diagnostics developed for this facility have been used to measure the turbulent quantities of buoyancy-driven turbulence. A stationary, bi-planar grid with a high solidity ratio, σ, has been placed immediately downstream of the termination of the splitter plate, perpendicular to the flow direction, to generate a turbulent initial condition. The self-similar growth parameter, α , for the RT mixing layer has been measured using a visualization technique to determine if the initial conditions affect the development of the RT mixing layer. The self-similar growth parameter, α , decreased from a value of 0.072 ± 0.0003 with the fine grid to values of 0.063 ± 0.0003 and 0.060 ± 0.0003 with the medium and coarse grids, respectively. With the results from the first objective, a unique opportunity arose to evaluate the performance of the variable density, RANS-type, BHR turbulent transport model. Measurements of velocity statistics necessary to initialize the model accurately have been obtained using particle image velocimetry (PIV). The performance of the BHR model was evaluated through comparison of the experimentally measured and BHR modeled self-similar growth parameter, α , from the penetration height of the bubbles/spikes and the self-similar growth parameter, K α , of the turbulent kinetic energy at the centerline of the low Atwood RT driven turbulent mixing layer. When initialized with the experimentally measured initial conditions, the BHR model did agree with the experimental measurements of the penetration height growth parameter, α , as well as the centerline turbulent kinetic energy growth parameter, K α , in the self-similar portion of the flow.

An existing water channel facility at Texas A&M University is used to experimentally study a stratified, buoyant wake. A cylindrical obstruction placed at the centerline of a developing Rayleigh-Taylor mixing layer serves to disturb the equilibrium of the Rayleigh-Taylor mixing layer. The development of the near wake in the presence of unstable stratification is examined, in addition to the recovery of the buoyancy driven mixing layer. Planar laser induced fluorescence (PLIF) is used to visualize the mixing layer / wake interactions, and qualitative observations of the behavior have been made. Also, quantitative measurements of velocity fluctuations and density fluctuations in the near wake have been obtained using particle image velocimetry (PIV) and a high resolution thermocouple system. These experimental measurements were used to investigate how the wake and buoyancy driven mixing layer interact. Finally, a mathematical model has been used to describe the decay of vertical velocity fluctuations in the near wake due to the effects of buoyancy.

An existing water channel facility at Texas A&M University is used to experimentally study a stratified, buoyant wake. A cylindrical obstruction placed at the centerline of a developing Rayleigh-Taylor mixing layer serves to disturb the equilibrium of the Rayleigh-Taylor mixing layer. The development of the near wake in the presence of unstable stratification is examined, in addition to the recovery of the buoyancy driven mixing layer. Planar laser induced fluorescence (PLIF) is used to visualize the mixing layer / wake interactions, and qualitative observations of the behavior have been made. Also, quantitative measurements of velocity fluctuations and density fluctuations in the near wake have been obtained using particle image velocimetry (PIV) and a high resolution thermocouple system. These experimental measurements were used to investigate how the wake and buoyancy driven mixing layer interact. Finally, a mathematical model has been used to describe the decay of vertical velocity fluctuations in the near wake due to the effects of buoyancy.

The present work aims at studying the coupling between hydrodynamic fingering instabilities and chemical reactions at the interface between two miscible solutions. Hydrodynamic deformations of interfaces between two reactive fluids as well as flows induced by chemical reactions at the front between two initially steady fluids are encountered frequently in combustion, petroleum, chemical and pharmaceutical engineering. Most of the time, concrete applications imply a very large number of variables so that an understanding of the fundamental processes of chemo-hydrodynamic coupling is out of reach. Our goal is here to analyze a much simpler model system in which only one mechanism of hydrodynamic instability is at play and for which the chemical reactions can be modeled by a one or two-variable model. Buoyantly unstable, autocatalytic chemical fronts, are one such model system, which can be used as prototype to study the effects of the coupling between chemical reactions and hydrodynamic fingering instabilities. Fingering processes occur whenever a fluid of high mobility displaces a less mobile one in a porous medium. The initially planar interface looses then stability and a cellular fingering deformation of the interface is observed. Such an instability has been observed, for instance, in the iodate-arsenous acid and chlorite-tetrathionate reactions, autocatalytic redox reactions known to produce a change of density across a traveling front. Fingering happens there when the heavier solution lies on top of the lighter one in the gravity field. Our theoretical contribution to the analysis of fingering of chemical fronts focuses on different points which we detail in this thesis along the following outline. In chapter 2, we introduce fingering phenomena occurring in porous media and distinguish the situation of viscous and density fingering of pure non reactive fluids. Chapter 3 reviews the literature on coupling between fingering and chemical reactions before studying the linear stability conditions as well as nonlinear dynamics of density fingering of isothermal iodate-arsenous acid fronts. This prototype nonlinear redox reaction is the first one on which experimental results on fingering in spatially extended set-ups have been obtained. We next analyze in chapter 4 the density fingering of another front producing autocatalytic system i.e. the chlorite-tetrathionate reaction in order to address the influence of the chemical kinetics on the dynamics observed. The influence of the exothermicity of the reaction is then presented in chapter 5. Eventually, chapter 6 analyzes what happens if the kinetics is now bistable and further compares the situation of both viscous and density fingering of bistable fronts. We then conclude and present suggestions for future work in this subject at the frontier between nonlinear chemistry, hydrodynamics and engineering.

No description available.

Experiments and direct numerical simulations (DNS) have been performed to examine the e¤ects of initial conditions on the dynamics of a Rayleigh-Taylor unsta- ble mixing layer. Experiments were performed on a water channel facility to measure the interfacial and velocity perturbations initially present at the two-fluid interface in a small Atwood number mixing layer. The experimental measurements have been parameterized for use in numerical simulations of the experiment. Two- and three- dimensional DNS of the experiment have been performed using the parameterized initial conditions. It is shown that simulations implemented with initial velocity and density perturbations, rather than density perturbations alone, are required to match experimentally-measured statistics and spectra. Data acquired from both the exper- iment and numerical simulations are used to examine the role of initial conditions on the evolution of integral-scale, turbulence, and mixing statistics. Early-time turbu- lence and mixing statistics are shown to be strongly-dependent upon the early-time transition of the initial perturbation from a weakly-nonlinear to a strongly-nonlinear flow.

The effect of initial conditions in combined shear- and buoyancy- driven mixing was investigated through the use of an implicit large eddy simulation code under active development at Los Alamos National Laboratory and Texas A&M University. Alterations were done over several months both at Los Alamos National Laboratory and at the Texas A&M University campus, and include a transition from tilted rig to convective channel arrangement, introduction of an inertial reference frame, alteration of boundary conditions, etc. This work resulted in the development of a numerical framework with the capability to model various shear and Atwood number arrangements such as those seen in an inertial confinement fusion environment. In order to validate the code, it was compared to three published experiments, one with Atwood number 0.46 (White et al. 2010), one with high Atwood number 0.6 (Banerjee et al. 2010), and one with very low Atwood number 0.032 (Akula et al. 2012). Upon validating the code, pure Rayleigh-Taylor and pure Kelvin-Helmholtz instabilities were modeled along with five intermediate cases of increasing shear and constant density gradient. Plots of mixing width, Richardson number, growth parameter, and molecular mixing were compared in order to determine at what level of shear the minimum amount of mixing occurs. The results of height gradient and Reynolds number were to previous experiments and theory. The least amount of molecular mixing at the centerline was found to be when the system had a low Atwood number (0.032) and a multimode initial interface perturbation. While the increase in modes of the interface perturbation did not result in a significant change in the growth parameter, the level of molecular mixing at the centerline substantially decreased. As shear was increased in the system, the mixing width and molecular mixing subsequently increased. For this reason, the shear in the system should be eliminated, or at least minimized, if at possible so as to prevent any additional amalgamation in the system. Analysis of the Reynolds number revealed that with an increase in velocity difference between the fluid layers, the value consequently increased. This trend matches with theoretical results as the value is a function of the mixing width and velocity, thus further validating the code. Analysis of the transitional Richardson number revealed that it had a smaller value in the computational case over the experiment, but this fact can be attributed the difference in mixing width between the two methods. The development of the numerical framework with the capability to model various shear and Atwood number arrangements offers the platform for future study of hydrodynamic instabilities.

Le développement des instabilités hydrodynamiques lors d'une expérience de fusion par confinement inertiel représente un sévère obstacle à l'obtention des conditions nécessaires à l'allumage et l'auto-entretien des réactions thermonucléaires. Il est ainsi crucial de comprendre, modéliser et éventuellement contrôler ces instabilités. L'instabilité se développant au front d'ablation est particulièrement étudiée dans le cadre du schéma d'attaque directe, à cause notamment du phénomène d'empreinte laser. Cependant le stade fortement non-linéaire de l'instabilité de Rayleigh-Taylor au front d'ablation reste peu explore. Cette étude vise donc à analyser ce régime.Dans un premier temps, une nouvelle plateforme expérimentale est développée sur le laser National Ignition Facility (NIF) permettant l'étude de phénomènes hydrodynamiques avec plusieurs dizaines de nanosecondes d'impulsion laser. Cette plateforme est ensuite calibrée avec l'étude de la croissance d'une perturbation 2D sous l'effet de l'instabilité de Rayleigh-Taylor. Une plateforme de simulations numériques 2D est également développée sur le code hydrodynamique CHIC capable de modéliser les expériences réalisées.L'étude du régime fortement non-linéaire de l'instabilité de Rayleigh-Taylor est réalisée a partir d'une perturbation multimode 3D imprimée par laser.L'impact de la condition initiale est étudiée en utilisant un faisceau d'empreinte lisse d'une part et non lisse d'autre part. L'analyse des données de radiographie dans l'espace de Fourier et dans l'espace réel permet d'évaluer tous les différents paramètres de l'instabilité (taux de croissance linéaire, vitesses de saturation, taux de coalescence de bulles et paramètre de croissance auto-semblable ) et de comparer les mesures aux modèles existants.L'importance de la condition initiale au stade fortement non-linéaire de la perturbation est ainsi démontrée dans les résultats obtenus. / Experimental and numerical study of the non-linear stage of the ablative Rayleigh-Taylor instability in direct drive

The effect of single mode initial conditions at the interface of Rayleigh-Taylor(RT) mixing are experimentally examined utilizing the low Atwood number water channel facility at Texas A&M. The water channel convects two separated stratified flows and unifies them at the end of a splitter plate. The RT instability is attained by convecting a cold stream above a warmer stream. Average density calculations are based on long time average optical measurements. The water channel was modifified with a flapper fin like device at the end of the splitter plate which was actuated by a computer controlled servo motor. Other modifications to the experiment were implemented resulting in reduced uncertainty. The experiment examined five different modes in addition to the baseline: 2 cm, 3 cm, 4 cm, 6 cm, and 8 cm wavelengths. The mixing width growth rates were shown to be dependent on initial conditions. Additionally, it appears that the growth rates commence with terminal velocity and are observed to line up with the baseline case.

Nous avons modélisé numériquement la stabilité d'un système de deux couches d'un même fluide pur supercritique soumis à une différence de température initiale à l'interface. La grande compressibilité et la faible diffusivité thermique des fluides critiques entraînent une instabilité gravitationnelle de type Rayleigh-Taylor de la couche de diffusion. Cette instabilité est similaire à celle que l'on retrouve dans le cas de deux fluides miscibles à condition de remplacer le coefficient de diffusion moléculaire par celui de la diffusion thermique. Nos résultats numériques semblent être consistants, d'un point de vue de la relation de dispersion dans le cas linéaire, avec ceux de Duff et al. [Duf62] considérés dans le cas de deux fluides miscibles. Nous avons aussi montré que, lorsque l'épaisseur de la couche inférieure devient plus petite que l'épaisseur de la couche de diffusion thermique basée sur le taux de croissance maximal alors le système devenait stable. Un diagramme de stabilité a été établi en fonction de trois paramètres: l'épaisseur de la couche inférieure, la différence de densité entre les deux couches et la distance au point critique. Lorsque l'on s'approche du point critique, la stratification devient de plus importante (à cause de la forte compressibilité) et tend à stabiliser la configuration. Par ailleurs, le filtrage acoustique initialement utilisé afin de réduire les coûts de calcul, ne s'est pas avéré nécessaire puisque la méthode des volumes finis est naturellement filtrante (formulation intégrale ou variationnelle des équations).