Liquid waste discharged from industrial outfalls is categorized into two major classes based on their density. One type is the effluent that has a higher density than that of the ambient water body. In this case, the discharged effluent has a tendency to sink as a negatively buoyant jet. The second type is the effluent that has a lower density than that of the ambient water body and is hence defined as a (positively) buoyant jet that causes the effluent to rise. Negatively/Positively buoyant jets are found in various civil and environmental engineering projects: discharges of desalination plants, discharges of cooling water from nuclear power plants turbines, mixing chambers, etc. This thesis investigated the mixing and dispersion characteristics of such jets numerically. In this thesis, mixing behavior of these jets is studied using a finite volume model (OpenFOAM). Various turbulence models have been applied in the numerical model to assess the accuracy of turbulence models in predicting the effluent discharges in submerged outfalls. Four Linear Eddy Viscosity Models (LEVMs) are used in the positively buoyant wall jet model for discharging of heated waste including: standard k-ε, RNG k-ε, realizable k-ε and SST k-ω turbulence models. It was found that RNG k-ε, and realizable k-ε turbulence models performed better among the four models chosen. Then, in the next step, numerical simulations of 30˚ and 45˚ inclined dense turbulent jets in stationary ambient water have been conducted. These two angles are examined in this study due to lower terminal rise height for 30˚ and 45˚, which is very important for discharges of effluent in shallow waters compared to higher angles. Five Reynolds-Averaged Navier-Stokes (RANS) turbulence models are applied to evaluate the accuracy of CFD predictions. These models include two LEVMs: RNG k-ε, and realizable k-ε; one Nonlinear Eddy Viscosity Model (NLEVM): Nonlinear k-ε; and two Reynolds Stress Models (RSMs): LRR and Launder-Gibson. It has been observed that the LRR turbulence model as well as the realizable k-ε model predict the flow more accurately among the various turbulence models studied herein.

The Gaseous state of hydrogen at ambient temperature, combined with the fact that hydrogen is highly flammable, results in the requirement of more robust, high pressure storage systems that can meet modern safety standards. To develop these new safety standards and to properly predict the phenomena of hydrogen dispersion, a better understanding of the resulting flow structures and flammable regions from controlled and uncontrolled releases of hydrogen gas must be achieved. In this study the subsonic release of hydrogen was emulated using helium as a substitute working fluid. A sharp-edged orifice round turbulent jet is used to emulate releases in which leak geometry is circular. Effects of buoyancy, crossflow and adjacent surfaces were studied over a wide range of Froude numbers. The velocity fields of turbulent jets were characterized using particle image velocimetry (PIV). The mean and fluctuation velocity components were well quantified to show the effect of buoyancy due to the density difference between helium and the surrounding air. In the range of Froude numbers investigated, increasing effects of buoyancy were seen to be proportional to the reduction of the Fr number. The obtained results will serve as control reference values for further concentration measurement study and for computational fluid dynamics (CFD) validation. / Graduate

Nous présentons dans cette étude le développement de la convection à partir de différentes perturbations de l'état conductif d'une couche fluide confinée dans une cavité cylindrique, chauffée par le bas et avec une surface supérieure libre. La discrétisation spatiale du domaine repose sur la méthode des éléments spectraux et les itérations temporelles sont assurées par une méthode splitting.Au déclenchement de la convection, les structures convectives correspondent à des modes de Fourier, et les seuils critiques dépendent du rapport de forme de la cavité, et des nombres de Biotet de Marangoni qui caractérisent la surface libre. Les transitions d'écoulements au-delà du seuil primaire sont caractérisées quantitativement en fonction du nombre de Rayleigh pour différentes valeurs du nombre de Biot et Ma = 0. Les résultats présentés sont obtenus en résolvant l'ensemble des équations non-linéaires de conservation à travers une méthode de continuation. Lorsque la convection se déclenche sous la forme d'un mode axisymétrique m = 0, l'évolution non-linéaire montre la coexistence de différentes structures convectives, des structures axisymétriques avec écoulement montant ou descendant au centre de la cavité et des structures correspondant à des combinaisons de modes qui apparaissent sur des branches secondaires sous-critiques.L'action d'un champ magnétique constant est ensuite étudiée pour des fluides conducteurs dans une même configuration comprenant une surface supérieure libre. Nous montrons l'effet stabilisateur du champ magnétique sur les seuils primaires ainsi que son action sélective sur les différents modes de convection. Nous analysons l'évolution des structures convectives au delà de ces seuils et montrons comment le champ magnétique modifie les transitions entre ces structures.En soumettant le bain fondu à un champ magnétique tournant, le mouvement de rotation du fluide se superpose aux mouvements de convection thermique et on observe une diminution des fluctuations de température et un retard du déclenchement de l'instabilité de Rayleigh-Bénard(lorsque les deux parois haut/bas du bain sont rigides). La rotation influe sur ce déclenchement qui de stationnaire devient oscillatoire, à l'exception du mode m = 0 de Fourier, pour qui la transition reste stationnaire jusqu'à une certaine valeur critique du nombre de Taylor magnétique.La dynamique de l'écoulement axisymétrique de part et d'autre de cette valeur critique sera étudiée en détail. / The growth of thermal convection out of different perturbations of the conductive base state is investigated using a spectral element time-stepping code. The fluid is subject to a vertical heat transfer in a cylindrical cavity with an upper free surface corresponding to the so-called Rayleigh-Bénard-Marangoni situation and the heat exchange through the free surface is evaluated via the Biot number. The results of the stability diagrams show that the evolution of the primary thresholds are largely influenced by the Biot number, the Marangoni number, and the aspect ratio of the cavity. Flow transitions are elucidated in quantitative detail as a function of the Rayleigh number for different Biot numbers in the tension free limit Ma = 0. The results shown are obtained by solving the full nonlinear field equations numerically among a continuation method. When an axisymmetric m = 0 Fourier mode is obtained at onset, the non-linear evolution shows the coexistence of different convective structures, the axisymmetric structures with up-ow or down-ow at the center and mixed-mode structures which appear on secondary subcritical branches. The action of a constant magnetic field is then considered for melts in the same type of configuration with an upper free surface. We show the global stabilizing effect of the magnetic field on the primary bifurcation thresholds and the selective effect on the different instability modes. We also analyze the evolution of the convective structures above the thresholds and show how the magnetic field modifies the transitions between these structures. When applying a magnetic body forcing in the azimuthal direction (RMF), one can damp the unavoidable thermal fluctuations inside the melt and delay the transition to the Rayleigh-Bénard instability (for rigid-rigid circular plates at top and bottom). The rotation effect also changes the transitions from steady to oscillatory, except for the m = 0 Fourier mode where the transitionis first steady until a critical Taylor number and then becomes oscillatory. The dynamics of the transitions to the axisymmetric flow, below and above this value of critical magnetic Taylor number, is particularly interesting and will be described.

Discharge of brine wastewater produced from industrial plants into adjacent coastal water bodies is considered as a preferable and common method currently used in many offshore industrial plants. Therefore, it is important to carefully study the behavior of jets and their environmental impacts on water bodies close to the discharge points, especially when the density is different between the jets and the receiving water. The main goal of this study is to improve the understanding of the mixing behaviour of jet trajectories for positively (offset) and negatively (inclined) buoyant jets when density is considered a significant factor, and also to examine the accuracy of some RANS turbulence models and one type of artificial neural network in predicting jet trajectory behaviours. In the first part of this study, experiments using a PIV system for offset buoyant jets were conducted in order to study the effect of the density differences (due to salinity [nonthermal] or temperature [thermal]) between the discharge and the receiving water body on the jet behavior, and the results showed that the nonthermal jets behaved differently as compared to the thermal jets, even though the densimetric Froude numbers (Frd) and density differences (∆ρ) were similar. In addition, a Reynolds-averaged Navier-Stokes (RANS) numerical model was performed using open-source CFD code (OpenFOAM) with a developed solver (modified form of the pisoFoam solver). The realizable k-ε model showed the best prediction among the models. Secondly, an extensive experimental study of an inclined dense jet for two angles (15°and 52°) was conducted to study the effect of these angles on the jets’ geometrical characteristics in the presence of a wide range of densimetric Froude numbers as well as with different discharge densities. More experimental data were obtained for these angles to be added to the previous data for the purpose of calibrating, validating, and comparing the various numerical models for future studies. The results of these experiments are used to evaluate the performance of a type of artificial neural network method called the group method of data handling (GMDH), and the GMDH results are then compared with existing analytical solutions in order to prove the accuracy of the GMDH method in simulating mixing behaviors in water bodies. Thirdly, a comprehensive study on predicting the geometrical characteristics of inclined negatively-buoyant jests using GMDH approach was conducted. The superiority of this model was demonstrated statistically by comparing to several previous analytical models. The results obtained from this study confirm that the GMDH model was highly accurate and was the best among others for predicting the geometrical characteristics of inclined negatively-buoyant jests.

The purpose of this study was to examine the conceptual understandings of 55 elementary preservice teachers for the concept of buoyancy. This study used Ausubel’s Assimilation Theory (Ausubel, 1963) as a framework for a 15-week intervention that used pre/post concept maps (Cmaps), pre/post face-to-face semi-structured interviews, and drawings as evidences for change of formation of cognitive structures. Using a convergent parallel design and mixed methods approach, preservice teachers’ conceptions were analyzed using these evidences. Results of the study show that preservice teachers held both scientific conceptions and misconceptions about buoyancy as a force before and after an instructional intervention. Of importance were the existence of robust misconceptions about buoyancy that included inaccurate scientific knowledge about the foundational concepts of gravity, weight, mass, and density. The largest gains in scientific knowledge included the concepts of gravity, surface area, opposing forces, and the buoyant force. These concepts were consistently supported with evidence from post-concept maps, post, semi-structured interviews, and drawings. However, high frequencies of misconceptions were associated with these same aforementioned concepts as well as additional misconceptions about buoyancy-related concepts (i.e., weight, density, displacement, and sinking/floating). A paired t test showed a statistically significant difference (t = -3.504, p = .001) in the total number of scientifically correct concepts for the pre-concept maps (M = 0.51, SD = .879) and post-concept maps (M = 1.25, SD = 1.542). The Cohen’s d effect size was small, .47. Even through gains for the pre/post concept maps were noted, a qualitative analysis of the results indicated that not only were there serious gaps in the participant’s scientific understanding of buoyancy, after the instructional intervention an increased number of misconceptions were presented alongside the newly learned concepts. A paired t test examining misconceptions showed that there was a statistically significant difference (t = -3.160, p = .003) in the total number of misconceptions for the pre-concept maps (M = 2.709, SD = 1.449) and post-concept maps (M = 3.363, SD = 2.094) after the intervention. The Cohen’s d effect size was small, .43. Taken together, these results revealed that, in general, the preservice teachers had understandings of buoyancy that align with children in preschool and elementary school (Biddulph and Osborne, 1983; Grimellini-Tomasini et al., 1990; Halford, Brown & Thompson, 1986; Hsin and Wu, 2011; Kohn, 1993; Rappolt-Schlichtmann et al., 2007; Yin et al., 2008). Based on these findings, implications for this study suggest that elementary preservice teacher candidates should be carefully screened to ensure they have mastered foundational scientific knowledge that they are expected to teach to children. As such knowledge is a prerequisite to the development of pedagogical content knowledge, it is unlikely that large numbers of robust misconceptions will be significantly reduced or eliminated during a science methods course that is designed to focus on pedagogical content knowledge.

Liquid waste discharged from industrial outfalls is categorized into two major classes based on their density. One type is the effluent that has a higher density than that of the ambient water body. In this case, the discharged effluent has a tendency to sink as a negatively buoyant jet. The second type is the effluent that has a lower density than that of the ambient water body and is hence defined as a (positively) buoyant jet that causes the effluent to rise. Negatively/Positively buoyant jets are found in various civil and environmental engineering projects: discharges of desalination plants, discharges of cooling water from nuclear power plants turbines, mixing chambers, etc. This thesis investigated the mixing and dispersion characteristics of such jets numerically. In this thesis, mixing behavior of these jets is studied using a finite volume model (OpenFOAM). Various turbulence models have been applied in the numerical model to assess the accuracy of turbulence models in predicting the effluent discharges in submerged outfalls. Four Linear Eddy Viscosity Models (LEVMs) are used in the positively buoyant wall jet model for discharging of heated waste including: standard k-ε, RNG k-ε, realizable k-ε and SST k-ω turbulence models. It was found that RNG k-ε, and realizable k-ε turbulence models performed better among the four models chosen. Then, in the next step, numerical simulations of 30˚ and 45˚ inclined dense turbulent jets in stationary ambient water have been conducted. These two angles are examined in this study due to lower terminal rise height for 30˚ and 45˚, which is very important for discharges of effluent in shallow waters compared to higher angles. Five Reynolds-Averaged Navier-Stokes (RANS) turbulence models are applied to evaluate the accuracy of CFD predictions. These models include two LEVMs: RNG k-ε, and realizable k-ε; one Nonlinear Eddy Viscosity Model (NLEVM): Nonlinear k-ε; and two Reynolds Stress Models (RSMs): LRR and Launder-Gibson. It has been observed that the LRR turbulence model as well as the realizable k-ε model predict the flow more accurately among the various turbulence models studied herein.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 1982 / Includes bibliographical references. / by Paul Douglas Symolon. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Mechanical Engineering

Le but de cette étude expérimentale est de caractériser la dynamique de particules solides, à flottabilité nulle, incluse dans un écoulement turbulent isotrope en décroissance libre. Les particules utilisées sont de forme sphérique et ont un diamètre de 4 à 5 fois plus grand que l'échelle spatial de Kolmogorov de l'écoulement. De part leur taille, les particules ont également un nombre de Stokes proche de l'unité. On s'attend alors à ce que ces particules aient une dynamique différente de celle du fluide environnant. Dans cette étude, ont se propose de quantifier les différences de vitesses entre les deux phases à l'aide d'une technique de vélocimétrie simultanée / In this experimental study, the focus is made on the characterization of the dynamics of solid neutrally buoyant particles embedded in a freely decaying, nearly isotropic turbulence, with a weak mean flow. The particles are spherical with diameters several times larger than the Kolmogorov scale. The study of this flow configuration is still challenging both theoretically and numerically. Due to large particle sizes, the local flow around particles can not be considered as uniform and due to fluid-particle density ratio of around unity, the history and Basset forces cannot be neglected in comparison with the viscous drag force. Particle equation of motion is then fully non-linear, in contrast to the equation for heavy particles with diameters smaller then the Kolmogorov scale, for which only the Stokes drag is considered. In several experimental and numerical studies, the effect of particle size on velocity and acceleration statistics has been investigated (Homann and Bec 2010 ; Qureshi et al. 2008 ; Ouellette et al. 2008 ; Xu and Bodenschatz 2008). In the case of isotropic turbulence, Homann and Bec (2010) show that while the PDF of the particle velocity normalized by the square root of its variance does not vary with particle size, the variance itself is size dependent. A scaling relation for particle velocity variance has been proposed by using the Faxen correction (Gatignol 1983) which takes into account the non uniformity of the fluid flow at the scale of the particle. The aim of our research is to further study the dependence of particle dynamics on particle size. To that purpose, a turbulence generator has been set-up and the resulting turbulence is characterized. Then the flow was seeded with millimeter sized, neutrally-buoyant particles and the velocity of the two phases have been measured simultaneously. Simultaneous measurements of particle and surrounding fluid velocities show that although the global velocity statistics of the two phases have comparable values, the particles may have different local velocity from the velocity of the neighboring fluid

Nous cherchons à modéliser numériquement un jet flottant air-hélium dans une cavité avec deux ouvertures à partir de simulations aux grandes échelles (LES) et de simulations numériques directes (DNS). La configuration considérée est basée sur une étude expérimentale menée au CEA de Saclay reproduisant une fuite d'hydrogène en environnement confiné. La dimension de la cavité a été choisie pour permettre une transition laminaire-turbulent intervenant environ à la mi-hauteur de la cavité. Cette étude porte principalement sur trois points majeurs : l'influence des conditions aux limites sur le développement du jet et son interaction avec l'environnement extérieur, la validité du modèle numérique qui est analysée en comparant la distribution de vitesse obtenue numériquement aux mesures expérimentales (PIV) et, enfin, la compréhension de la distribution air-hélium et le phénomène de stratification qui s'établit à l'intérieur de la cavité. Nous observons dans un premier temps que des conditions limites de pression constante appliquées directement au ras des évents conduisent à une sous-estimation du débit volumique d'air entrant dans la cavité et donc à une surestimation de la masse de l'hélium à l'intérieur de la cavité, ce qui n'est pas acceptable dans un contexte d'évaluation du risque hydrogène. En revanche, la prise en compte, dans le domaine de calcul, d'une région extérieure à la cavité prédit correctement le flux d'air entrant. Les résultats numériques sont alors en bon accord avec les données PIV. Il a été montré que les prédictions de la DNS, par rapport à la LES, concordent mieux avec les mesures de vitesse par PIV. Le champ de concentration prédit numériquement présente une couche homogène en haut de la cavité, dont la concentration est en accord avec le modèle théorique de Linden et al. 1990. Cependant, sa position et son épaisseur ne correspondent pas au modèle. Ceci est principalement dû aux interactions directes entre le jet flottant et, d'une part, avec les limites solides de la cavité et d'autre part, avec l'environnement extérieur. L'analyse statistique concernant la production de la flottabilité de l'énergie cinétique turbulente (TKE) a permis d'identifier les limites du jet flottant. / We present numerical results from large eddy simulations (LES) and coarse direct numerical simulations (DNS) of an air-helium buoyant jet rising in a two vented cavity. The geometrical configuration mimics the helium release experimental set-up studied at CEA Saclay in the framework of security assessment of hydrogen-based systems with an indoor usage. The dimension of the enclosure was chosen to ensure a laminar-turbulent transition occurring at about the middle height of the cavity. This study focuses mainly on three key points : the influence of the boundary conditions on the jet development and its interaction with the exterior environment, the validity of the numerical model which is analyzed by comparing the numerical velocity distribution versus the measured particle image velocimetry (PIV) ones, and finally understanding the distribution of air-helium and the stratification phenomenon that takes place inside the cavity. We observe at first that applying constant pressure outlet boundary conditions directly at the vent surfaces underestimates the volumetric flow rate of air entering the enclosure and thus overestimate the helium mass inside the cavity. On the contrary, modelling an exterior region in the computational domain better predicts the air flow-rate entrance and numerical results matches better with the experimental PIV data. It has been figured out that the coarse DNS predictions match better with the velocities PIV measurements, compared to the LES. Numerical prediction of the helium field depicts a homogeneous layer formed at the top of the cavity, with a concentration in good agreement with the theoretical model of Linden et al. 1990. However, the position and the thickness of the layer do not correspond to the theory. This is mainly due to the direct interactions between the buoyant jet and both the solid boundaries of the cavity and the exterior environment. Statistical analysis regarding the buoyancy production of the turbulent kinetic energy (TKE) served to identify the limits of the buoyant jet.

Le but de ce travail de recherche est de contribuer à une meilleure compréhension de la dynamique de propagation et de la miscibilité de jets gravitaires au-dessous d’un liquide ambiant. Des expériences ont été réalisées en laboratoire à l’aide d’une plateforme expérimentale constituée d’un bassin parallélépipédique contenant de l’eau douce et d’un canal d’injection de section rectangulaire de jets gravitaires de concentration constante initiale fixée. Les calculs mathématiques et numériques sont basés sur les modèles RANS (Reynolds-Averaged Navier Stokes equations), k-ε (K-epsilon) et DCE (Diffusion-Convective Equation) de la fraction volumique de l’eau salée pour décrire la propagation et le mélange du jet gravitaire. L’évolution du front du jet obtenue expérimentalement est utilisée pour valider le modèle numérique. Par ailleurs, la comparaison des résultats obtenus sur l’écoulement moyen (z⁄z0.5 =U/Umax) avec ceux des études 2D expérimentales et numériques antérieures ont montré des similarités. La simulation numérique des champs hydrodynamiques montre que la vitesse maximale est atteinte à la position 0.18 z0.5, où z0.5 est la hauteur d’eau pour laquelle la vitesse moyenne u est égale à la moitié de la vitesse maximale Umax. / The aim of this investigation is to contribute to a better understanding of the propagation dynamics and the mixing process of dense gravity currents. The Laboratory experiments proceeded with a fixed initial gravity current concentration in one experimental set-up. The gravity currents are injected using a rectangular injection channel into a rectangular basin containing the ambient lighter liquid. The injection studied is said in unsteady state volume, as the Reynolds number lies in the range 1111 - 3889. The experiments provided the evolution of the boundary interface of the jet, and it is used to validate the numerical model. The numerical model depends on the Reynolds-Averaged Navier Stokes equations (RANS). The k-ε (K-epsilon) and the Diffusion-Convective Equation (DCE) of the saline water volume fraction were used to model the mixing and the propagation of the gravity current jet. On the other hand, comparison of the mean flow (z⁄z0.5 =U/Umax) with previous two-dimensional numerical simulations and experimental measurements have shown similarities. The numerical simulations of the hydrodynamic fields indicate that the velocity maximum at 0.18 z0.5, where z0.5 is the height at which the mean velocity u is the half of the maximum velocity Umax.