The gas transfer process across the air-water interface in a buoyant-convective environment has been investigated by Direct Numerical Simulation (DNS) to gain improved understanding of the mechanisms that control the process. The process is controlled by a combination of molecular diffusion and turbulent transport by natural convection. The convection when a water surface is cooled is combination of the Rayleigh-B´enard convection and the Rayleigh-Taylor instability. It is therefore necessary to accurately resolve the flow field as well as the molecular diffusion and the turbulent transport which contribute to the total flux. One of the challenges from a numerical point of view is to handle the very different levels of diffusion when solving the convection-diffusion equation. The temperature diffusion in water is relatively high whereas the molecular diffusion for most environmentally important gases is very low. This low molecular diffusion leads to steep gradients in the gas concentration, especially near the interface. Resolving the steep gradients is the limiting factor for an accurate resolution of the gas concentration field. Therefore a detailed study has been carried out to find the limits of an accurate resolution of the transport for a low diffusivity scalar. This problem of diffusive scalar transport was studied in numerous 1D, 2D and 3D numerical simulations. A fifth-order weighted non-oscillatory scheme (WENO) was deployed to solve the convection of the scalars, in this case gas concentration and temperature. The WENO-scheme was modified and tested in 1D scalar transport to work on non-uniform meshes. To solve the 2D and 3D velocity field the incompressible Navier-Stokes equations were solved on a staggered mesh. The convective terms were solved using a fourth-order accurate kinetic energy conserving discretization while the diffusive terms were solved using a fourth-order central method. The diffusive terms were discretized using a fourth-order central finite difference method for the second derivative. For the time-integration of the velocity field a second-order Adams-Bashworth method was employed. The Boussinesq approximation was employed to model the buoyancy due to temperature differences in the water. A linear relationship between temperature and density was assumed. A mesh sensitivity study found that the velocity field is fully resolved on a relatively coarse mesh as the level of turbulence is relatively low. However a finer mesh for the gas concentration field is required to fully capture the steep gradients that occur because of its low diffusivity. A combined dual meshing approach was used where the velocity field was solved on a coarser mesh and the scalar field (gas concentration and temperature) was solved on an overlaying finer submesh. The velocities were interpolated by a second-order method onto the finer sub-mesh. A mesh sensitivity study identified a minimum mesh size required for an accurate solution of the scalar field for a range of Schmidt numbers from Sc = 20 to Sc = 500. Initially the Rayleigh-B´enard convection leads to very fine plumes of cold liquid of high gas concentration that penetrate the deeper regions. High concentration areas remain in fine tubes that are fed from the surface. The temperature however diffuses much stronger and faster over time and the results show that temperature alone is not a good identifier for detailed high concentration areas when the gas transfer is investigated experimentally. For large timescales the temperature field becomes much more homogeneous whereas the concentration field stays more heterogeneous. However, the temperature can be used to estimate the overall transfer velocity KL. If the temperature behaves like a passive scalar a relation between Schmidt or Prandtl number and KL is evident. A qualitative comparison of the numerical results from this work to existing experiments was also carried out. Laser Induced Fluorescence (LIF) images of the oxygen concentration field and Schlieren photography has been compared to the results from the 3D simulations, which were found to be in good agreement. A detailed quantitative analysis of the process was carried out. A study of the horizontally averaged convective and diffusive mass flux enabled the calculation of transfer velocity KL at the interface. With KL known the renewal rate r for the so called surface renewal model could be determined. It was found that the renewal rates are higher than in experiments in a grid stirred tank. The horizontally averaged mean and fluctuating concentration profiles were analysed and from that the boundary layer thickness could be accurately monitored over time. A lot of this new DNS data obtained in this research might be inaccessible in experiments and reveal previously unknown details of the gas transfer at the air water interface.

This dissertation investigates characteristics of the vertical distributions of mass flux observed in field and laboratory experiments. Thirty vertical mass flux profiles were measured during a field experiment in Jericoacoara, Brazil from October to November, 2008. These data were supplemented with 621 profiles gathered from an extensive review of the aeolian literature. From the field experiment, the analysis of the grain-size statistics for the flux caught in each trap shows that a reverse in grain-size trends occurs at an inflection zone located 0.05 ? 0.15 m above the bed. Below this inflection, mean grain-size decreases steeply with elevation in the near bed region dominated by reptation and saltation modes of transport. Above the inflection there is a coarsening of grain size with elevation; as saltation becomes the dominant transport mode. These results indicate that the coarsest grains are found close to and farthest from the bed. Using a data set comprising 274 vertical flux profiles, the performance of the exponential, power and logarithmic functions were tested to see which provided the best fit to the vertical flux distributions. The exponential function performed best 88% of the time. The average r2 value for the grouped exponential, logarithmic, and power function fits are 0.98, 0.85 and 0.91, respectively. The populations of the exponent coefficients, representing the relative rate of decrease with height above the surface, or slope of the vertical mass flux profiles, are statistically different in wind tunnels and field experiments. The slopes of the vertical flux profiles observed in wind tunnel experiments are steeper compared to field environments, which infers that saltation is suppressed in wind tunnels. These differences are magnified in wind tunnels with small working cross section areas, and in wind tunnel experiments that use extreme environmental conditions, such as very high shear velocities. The Rouse concentration model, widely used in water studies, was tested to see if it could replicate the observed vertical flux distributions and transport rates. A fall velocity (w0) equation for particles falling in air was derived using a grain size (d) dependency: w0 (in m/s) = 4.23d (in mm) + 0.1956 (r^2=0.88). The Rouse model performs poorly when the value of the beta (a form of the Schmidt number in the Rouse number exponent) is assumed to be unity. The values of beta were modeled using a relationship derived from a dependency of beta on the w0/u* ratio: beta = 3.2778(w0/u*) - 0.4133 (r^2=0.65). The values of beta ranged from 6.11 ? 17.83 for all the experiments. The Rouse profiles calculated using this approach predict very similar vertical distributions to the observed data and predicted 86% and 81% of the observed transport rate in field and wind tunnel experiments respectively. The Rouse approach is more physically meaningful than current approaches that use standard curve fitting functions to represent the vertical flux data but do not provide any explanatory power for the shape or magnitude of the profile.

Le flot optique est un outil, prometteur et puissant, pour estimer le mouvement des objets de différentes natures, solides ou fluides. Il permet d’extraire les champs de vitesse à partir d’une séquence d’images. Dans cette étude, nous développons la méthode du flot optique pour récupérer, d’une manière précise, le champ de vitesse des mouvements turbulents incompressibles. L’estimation de turbulence consiste à minimiser une fonction d’énergie composée par un terme d’observation et un terme de régularisation. L’équation de transport d’un scalaire passif est alors employée pour représenter le terme d’observation. Cependant, dans le cas où le nombre de Reynolds est grand, et, à cause des contraintes optiques, l’image n’est pas pleinement résolue pour prendre en compte la physique de toutes les échelles de la turbulence. Pour compléter les informations manquantes liées aux physiques des petites échelles, nous adoptons une démarche similaire à celle de Large Eddy Simulation (LES), et, proposons d’utiliser le modèle mixte afin de tenir compte de l’interaction entre les grandes échelles et celles non-résolues. Quant au terme de régularisation, il se repose sur l’équation de continuité des fluides incompressibles. Les tests à l’aide des images synthétiques et expérimentales de la turbulence bi-dimensionnelle - des données des cas test de la communauté du flot optique -, ont non seulement validé notre démarche, mais montrent une amélioration significative des qualités des champs de vitesses extraites. Le cas du flot optique, en 3D, relève encore du défi dans le cas de l’estimation des champs de vitesse de la turbulence. D’une part, contrairement au 2D où il existe des cas tests bien établis, il n’existe pas, à notre connaissance, des séquences d’images 3D référentielles permettant de tester notre démarche et méthode. D’autre part, l’augmentation du coût d’estimation demande des algorithme adaptés. Ainsi, nous sommes amené à utiliser la simulation numérique directe d’écoulement turbulent en présence d’un scalaire passif, pour générer des données de scalaires afin d’évaluer la performance du flot optique. Nous prêtons également attention à l’effet du nombre de Schmidt qui caractérise la relation entre la diffusion moléculaire scalaire et la dissipation de turbulence. Les tests sont ensuite effectués avec cette base de données numériques. Les résultats montrent que la précision de l’estimation augmente avec des nombres de Schmidt plus élevés. Par ailleurs, l’influence du terme de régularisation est aussi étudié au travers deux équations qui se différencient par l’ordre spatial des dérivées partielles. Les résultats numériques montrent que l’équation avec un terme de régularisation de seconde-ordre est meilleure que celle de premier-ordre. / The method of optical flow is a powerful tool for motion estimation. It is able to extract the dense velocity field from image sequence. In this study, we employ this method to retrieve precisely the incompressible turbulent motions. For 2D turbulence estimation, it consists in minimizing an objective function constituted by an observation term and a regularization one. The observation term is based on the transport equation of a passive scalar field. For non-fully resolved scalar images, we propose to use the mixed model in large eddy simulation (LES) to determine the interaction between large-scale motions and the unresolved ones. The regularization term is based on the continuity equation of 2D incompressible flows. Evaluation of the proposed formulation is done over synthetic and experimental images. In addition, we extend optical flow to three dimensional and multiple scalar databases are generated with direct numerical simulation (DNS) in order to evaluate the performance of optical flow in the 3D context. We propose two formulations differing by the order of the regularizer. Numerical results show that the formulation with second-order regularizer outperforms its first-order counterpart. We also draw special attention to the effect of Schmidt number, which characterizes the ratio between the molecular diffusion of the scalar and the dissipation of the turbulence. Results show that the precision of the estimation increases as the Schmidt number increases. Overall, optical flow has showcased its capability of reconstructing the turbulent flow with excellent accuracy. This method has all the potential and attributes to become an effective flow measurement approach in fluid mechanics community.

This thesis is concerned with the study of parallel mixing of two dissimilar gases under compressible conditions in the confined environment. A number of numerical studies are reported in the literature for the compressible mixing of two streams of gases where (1) both the streams are of similar gases at the same temperatures, (2) both the streams are at different temperatures with similar gases, and (3) dissimilar gases are with nearly equal temperatures. The combination of dissimilar gases at large temperature difference, mixing under compressible conditions, as in the case of scramjet propulsion, has not been adequately addressed numerically. Also many of the earlier studies have used two dimensional numerical simulation and showed good match with the experimental results on mixing layers that are inherently three dimensional in nature. In the present study, both two-dimensional (2-d) and three dimensional (3-d) studies are reported and in particular the effect of side wall on the three dimensionality of the flow field is analyzed, and the reasons of the good match of two dimensional simulations with experimental results have been discussed. Both two dimensional and three dimensional model free simulations have been conducted for a flow configuration on which experimental results are available. In this flow configuration, the mixing duct has a rectangular cross section with height to width ratio of 0.5. In the upper part of the duct hydrogen gas at a temperature of 103 K is injected through a single manifold of two Ludweig tubes and in the lower part of the duct nitrogen gas at a temperature of 2436 K is supplied through an expansion tube, both the gases are at Mach numbers of 3.1 and 4.0 respectively. Measurements in the experiment are limited to wall pressures and heat flux. The choice of this experimental condition gives an opportunity to study the effect of large temperature difference on the mixing of two dissimilar gases with large molecular weights under compressible conditions. Both two dimensional and three dimensional model free simulations are carried out using higher order numerical scheme (4th order spatial and 2nd order temporal) to understand the structure and evolution of supersonic confined mixing layer of similar and dissimilar gases. Two dimensional simulations are carried out by both SPARK (finite difference method) and OpenFOAM (finite volume method based open source software that was specially picked out and put together), while 3D model free simulations are carried out by OpenFOAM. A fine grid structure with higher grid resolution near the walls and shear layer is chosen. The effect of forcing of fluctuations on the inlet velocity shows no appreciable change in the fully developed turbulent region of the flow. The flow variables are averaged after the attainment of statistical steady state established through monitoring the concentration of inert species introduced in the initial guess. The effect of side wall on the flow structure on the mixing layer is studied by comparing the simulation results with and without side wall. Two dimensional simulations show a good match for the growth rate of shear layer and experimental wall pressures. Three dimensional simulations without side wall shows 14% higher growth rate of shear layer than that of two dimensional simulations. The wall pressures predicted by these three dimensional simulations are also lower than that predicted using two dimensional simulations (6%) and experimental (9%) results in the downstream direction of the mixing duct. Three dimensionality of the flow is thought of as a cause for these differences. Simulations with the presence of side wall show that there is no remarkable difference of three dimensionality of the flow in terms of the variables and turbulence statistics compared to the case without side walls. However, the growth rate of shear layer and wall surface pressures matches well with that predicted using two dimensional simulations. It has been argued that this good match in shear layer growth rate occurs due to formation of oblique disturbances in presence of side walls that are considered responsible for the decrease in growth rate in 3-d mixing layers. The wall pressure match is argued to be good because of hindrance from side wall in the distribution of momentum in third direction results in higher wall pressure. The effect of dissimilar gases at large temperature difference on the growth rate reduction in compressible conditions is studied. Taking experimental conditions as baseline case, simulations are carried out for a range of convective Mach numbers. Simulations are also carried out for the same range of convective Mach numbers considering the mixing of similar gases at the same temperature. The normalized growth rates with incompressible counterpart for both the cases show that the dissimilar gas combination with large temperature difference shows higher growth rate. This result confirms earlier stability analysis that predicts increased growth rate for such cases. The growth rate reduction of a compressible mixing layer is argued to occur due to reduced pressure strain term in the Reynolds stress equation. This reduction also requires the pressure and density fluctuation correlation to be very near to unity. This holds good for a mixing layer formed between two similar gases at same temperature. For dissimilar gases at different temperatures this assumption does not hold well, and pressure-density correlation coefficient shows departure from unity. Further analysis of temperature density correlation factor, and temperature fluctuations shows that the changes in density occur predominantly due to temperature effects, than due to pressure effects. The mechanism of density variations is found to be different for similar and dissimilar gases, while for similar gases the density variations are due to pressure variations. For dissimilar gases density variation is also affected by temperature variations in addition to pressure variations. It has been observed that the traditional k-ε turbulence model within the RANS (Reynolds Averaged Navier Stokes) framework fails to capture the growth rate reduction for compressible shear layers. The performance of k-ε turbulence model is tested for the mixing of dissimilar gases at large temperature difference. For the experimental test case the shear layer growth rate and wall pressures show good match with other model free simulations. Simulations are further carried out for a range of convective Mach numbers keeping the mixing gases and their temperatures same. It has been observed that a drop in the growth rate is well predicted by RANS simulations. Further, the compressibility option has been removed and it has been observed that for the density and temperature difference, even for incompressible case, the drop in growth rate exists. This behaviour shows that the decrease in growth rate is mainly due to the interaction of temperature and species mass fraction on density. Also it can be inferred that RANS with k-ε turbulence model is able to capture the compressible shear layer growth rate for dissimilar gases at high temperature difference. The mixing of heat and species is governed by the values of turbulent Prandtl and Schmidt numbers respectively. These numbers have been observed to vary for different flow conditions, while affecting the flow field considerable in the form of temperature and species distribution. Model free simulations are carried out on an incompressible convective Mach number mixing layer, and the results are compared with that of a compressible mixing layer to study the effect of compressibility on the values of turbulent Prandtl / Schmidt numbers. It has been observed that both turbulent Prandtl and Schmidt numbers show an almost constant value in the mixing layer region for incompressible case. While, for a compressible case, both turbulent Prandtl and Schmidt numbers show a continuous variation within the mixing layer. However, the turbulent Lewis number is observed to be near unity for both incompressible and compressible cases. The thesis is composed of 8 chapters. An introduction of the subject with critical and relevant literature survey is presented in chapter 1. Chapter 2 describes the mathematical formulation and assumptions along with solution methodology needed for the simulations. Chapter 3 deals with the two and three dimensional model free simulations of the non reacting mixing layer. The effect of the presence of side wall is studied in chapter 4. Chapter 5 deals with the effect of compressibility on the mixing of two dissimilar gases at largely different temperatures. The performance of k-ε turbulence model is checked for dissimilar gases in Chapter 6. Chapter 7 is concerned with the effect of compressibility on turbulent Prandtl and Schmidt numbers. Finally concluding remarks are presented in chapter 8. The main aim of this thesis is the exploration of parallel mixing of dissimilar gases under compressible conditions for both two and three dimensional cases. The outcome of the thesis is (a) a finding that the presence of sidewall in a mixing duct does not make flow field two dimensional, instead it causes the formation of oblique disturbances and the shear layer growth rate is reduced, (b) that it has been shown that the growth rates of dissimilar gases are affected far more by large temperature difference than by compressibility as in case of similar gases, (c) that the growth rates of compressible shear layers formed between dissimilar gases are better predicted using k-εturbulence model and (d) that for compressible mixing conditions the turbulent Prandtl and Schmidt numbers vary continuously in the mixing layer region necessitating the use of some kind of model instead of assuming constant values.