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.

Hypersonic vehicles generate shocks that can heat the air sufficiently to partially ionize the air and create an electrically conducting plasma that can be studied using the equations of single fluid magnetohydrodynamics (MHD). Introducing strong applied magnetic and electric fields into the flow could have beneficial effects such as reducing heat damage, providing a sort of MHD parachute, and generating electric power or thrust in the vehicle. The Low Diffusion E-CUSP (LDE) scheme with a fifth order WENO scheme has recently been developed by Zha et al. [1, 2]. The purpose of this work is to incorporate the low magnetic Reynolds number MHD model and the thermodynamics of high temperature air to the above CFD algorithm so that it can be used to simulate hypersonic flows with MHD effects. In this work we compare results treating air as chemically frozen, neglecting all high temperature real gas effects with results obtained treating the air as a real gas in thermodynamic equilibrium, whose thermodynamic properties are changed by the high temperature. The hypersonic flows at high altitudes considered in this study have low Reynolds numbers. The Reynolds numbers range from about 2000 to 5000 for Mach 6 flows and reach up to 1200000 for Mach 15 flows. Thus, the flows are treated as laminar for the former cases and as turbulent for the latter using the Baldwin-Lomax turbulence model.

This thesis considers the application of the type II third order WENO finite volume reconstruction for unstructured tetrahedral meshes proposed by Zhang and Shu in (CCP, 2009) and the third order multirate Runge-Kutta time-stepping to the solution of Maxwell's equations. The dependance of accuracy of the third order WENO scheme on the small parameter in the definition of non-linear weights is studied in detail for one-dimensional uniform meshes and numerical results confirming the theoretical analysis are presented for the linear advection equation. This analysis is found to be crucial in the design of the efficient three-dimensional WENO scheme, full details of which are presented. Several multirate Runge-Kutta (MRK) schemes which advance the solution with local time-steps assigned to different multirate groups are studied. Analysis of accuracy of three different MRK approaches for linear problems based on classic order-conditions is presented. The most flexible and efficient multirate schemes based on works by Tang and Warnecke (JCM, 2006) and Liu, Li and Hu (JCP, 2010) are implemented in three-dimensional finite volume time-domain (FVTD) method. The main characteristics of chosen MRK schemes are flexibility in defining the time-step ratios between multirate groups and consistency of the scheme. Various approaches to partition the three-dimensional computational domain into multirate groups to maximize the achievable speedup are discussed. Numerical experiments with three-dimensional electromagnetic problems are presented to validate the performance of the proposed FVTD method. Three-dimensional results agree with theoretical and numerical accuracy analysis performed for the one-dimensional case. The proposed implementation of multirate schemes demonstrates greater speedup than previously reported in literature. / February 2016

La miniaturisation de plus en plus poussée (micro et nano) des systèmes mécanique connaît un important développement depuis une dizaine d'années. Leur conception et réalisation nécessite une connaissance approfondie des écoulements micro-fluidiques. Dans le domaine énergétique, le rendement d'un moteur thermique se dégrade sérieusement lors d'une réduction d'échelle. En effet, les pertes de chaleur pariétales peuvent devenir aussi importantes que l'énergie libérée. Une voie prometteuse consiste à utiliser les ondes de choc / détonation pour accélérer la libération d'énergie. Dans ce cas, la détonation peut être assimilée à une onde de choc inerte, couplée à une zone de réaction, caractérisée par la présence d'instabilités longitudinales et transverses, soumettant ainsi le front de choc à de violentes accélérations / décélérations. L'objectif de la thèse est de mieux appréhender la structure moyenne de la zone de réaction qui s'étend du choc jusqu'à la surface sonique. Sur le plan de la modélisation numérique, les équations de Navier-Stokes compressibles, multi-espèces, réactives sont résolues au sein du solveur CHOC-WAVES développé au CORIA, avec une thermodynamique variables et des coefficients de transport dépendant des espèces. La condition de Chapman-Jouguet généralisée a été élaborée et confirmée par les résultats de simulations numériques dans le cas d'une détonation multidimensionnelle stable. En particulier, il a été montré que les instabilités transverses s'atténuaient avec la réduction d'échelle. A cet effet, un scénario a été proposé pour expliquer le déficit de la vitesse du front de détonation, en se basant sur la structure de la poche subsonique aval, en corrélation avec l'épanouissement de la couche limite. Ce schéma partage de fortes similitudes avec la macro-détonation, tout en gardant des différences. En particulier, il a été montré que la forte vorticité, produite au niveau de la singularité de Prandtl-Meyer, souvent négligée dans les modèles de macro-détonation, diffusait au sein de la poche subsonique. Ces résultats tout à fait originaux ont permis une avancée significative dans la compréhension du mécanisme de propagation des fronts de détonation stables et confinées. / Progress towards the miniaturization of increasingly advanced micro- and nano-electromechanical systems has highlighted the need for a better knowledge of the design of such devices. knowledge of micro-nano pipe flows is still mandatory. In field of energy power generation, as the systems are scaled down, the thermal efficiency of conventional propellant devices is seriously degraded due to significant heat losses which can cause the combustion extinction. A promising approach is to use shock or detonation waves in gazeous media to enhance chemical reaction rates. A detonation is a rapid regime of burning in which a strong shock ignites the fuel and the burning proceeds to equlibrium behind the shock, while the energy released continues to drive the shock. It is also characterized by the presence of longitudinal and transverse instabilities, thereby subjecting the shock front to violent deceleration / acceleration. The objective of this thesis is to better understand the mean structure of the reaction zone that extends from the shock to the sonic surface. As for numerical modelling, the compressible multi-species reactive Navier-Stokes equations are solved using an in-house code "CHOC-WAVES", including variable thermodynamic and transport coefficients depending on the species. The Generalized Chapman-Jouguet condition was developed and corroborated by the numerical results in the case of stable multidimensionnal detonation. More specially, it was shown that the transverse instabilities are attenuated with the scale reduction.To this end, a scenarion, based on the structure of downstream subsonic pocket, which is correlated to the development of the boundary layer, has been proposed to explain the deificit of the detonation from velocity. This scheme shares many similarities with the macro-detonation, while keeping some differences. In particular, it was shown that the strong vorticity, generated at the Prandlt-Meyersingularity and often neglected in macro-detonation models, diffuses in the subsonic pocket. The present contribution enables us to shade more physical insight for the propagation of stable and confined detonation fronts.