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In this thesis, gas-kinetic methods for inviscid and viscous flow simulations are developed. Initially, the finite volume gas-kinetic methods are investigated for 1-D flows as a preliminary study and are discussed in detail from theoretical and numerical points of view. The preliminary results show that the gas-kinetic methods do not produce any unphysical flow phenomena. Especially the Gas-Kinetic BGK method, which takes into account the particle collisions, predicts compressible flows accurately. The Gas-Kinetic BGK method is then extended for the solution of 2-D and 3-D inviscid and viscous flows on unstructured/hybrid grids. The computations are performed in parallel. Various inviscid and viscous test cases are considered and it is shown that the Gas-Kinetic BGK method predicts both inviscid and viscous flow fields accurately. The implementation of hybrid grids for viscous flows reduces the overall number of grid cells while enabling the resolution of boundary layers. The parallel computations significantly improve the computation time of the Gas-Kinetic BGK method which, in turn, enable the method for the computation of practical aerodynamic flow problems.

Ce travail de thèse est consacré à l’étude des écoulements thermogravitaires et thermocapillaires induits par chauffage laser dans des couches liquides. Le chauffage d’un système à deux liquides donne naissance à deux effets thermiques. Le premier est dû à la variation de la masse volumique avec la température et le second à la variation de la tension interfaciale avec la température. Nous avons dans un premier temps étudié ces deux contributions séparément. En confrontant expériences, théorie et simulations numériques nous avons démontré que la morphologie des écoulements thermogravitaires dépend de l’épaisseur de la couche liquide ainsi que de la largeur du champ de température. Ensuite nous nous sommes intéressés à l’étude théorique et numérique de l’effet thermocapillaire. Cette étude a révélé qu’il est possible d’étudier les écoulements à partir des déformations d’interface induites par ces mêmes écoulements. Nous avons montré qu’il existe deux régimes de déformations en fonction du rapport de hauteurs et du signe de la variation de la tension interfaciale avec la température. Enfin, nous nous sommes intéressés à la compétition entre ces deux mécanismes. L’analyse des déformations d’interface et la comparaison avec un modèle à une dimension a montré qu’en fonction du rapport de hauteurs des couches liquides nous avons une transition d’un régime d’écoulements thermocapillaires vers une régime d’écoulements thermogravitaires. De plus, nous avons montré expérimentalement et numériquement qu’il est possible d’induire une instabilité d’origine thermogravitaire conduisant à la formation d’un pont liquide. / This thesis work is dedicated to thermocapillary and thermogravitary flows induced bylaser-heating in liquid layers. The laser-heating of a two fluids system induces two thermaleffects. The first effect come from the variation of the density with temperature andthe second one is due to the variation of the interfacial tension with the temperature.In a first part, we study separately these two mechanism. With a comparison betweenexperiments, theory and numerical simulations we demonstrated that the morphology ofthe flows depends on the thickness of the layer and the width of the temperature field.Then, we studied numerically and theoretically the thermocapillary effect. That revealedit is possible to understand the flows from the interface deformations. We highligth theseare two deformation regimes depending the thickness ratio and the sign of the interfacialtension gradient. Finally, we studied the competition between the two mechanism and theexperiments revealed a transition between two flow regimes. The comparison of these resultsand a theoritical model showed there is a transition from a thermocapillary regime to athermogravitary regime. In addition, we showed the possibility to induce an instibility bythermogravitary effect which can lead to the formation of a liquid bridge.

In this thesis study, a least-squares finite element method (LSFEM) based conjugate heat transfer solver was developed. In the mentioned solver, fluid flow and heat transfer computations were performed separately. This means that the calculated velocity values in the flow calculation part were exported to the heat transfer part to be used in the convective part of the energy equation. Incompressible Navier-Stokes equations were used in the flow simulations. In conjugate heat transfer computations, it is required to calculate the heat transfer in both flow field and solid region. In this study, conjugate behavior was accomplished in a fully coupled manner, i.e., energy equation for fluid and solid regions was solved simultaneously and no boundary conditions were defined on the fluid-solid interface. To assure that the developed solver works properly, lid driven cavity flow, backward facing step flow and thermally driven cavity flow problems were simulated in three dimensions and the findings compared well with the available data from the literature. Couette flow and thermally driven cavity flow with conjugate heat transfer in two dimensions were modeled to further validate the solver. Finally, a microchannel conjugate heat transfer problem was simulated. In the flow solution part of the microchannel problem, conservation of mass was not achieved. This problem was expected since the LSFEM has problems related to mass conservation especially in high aspect ratio channels. In order to overcome the mentioned problem, weight of continuity equation was increased by multiplying it with a constant. Weighting worked for the microchannel problem and the mass conservation issue was resolved. Obtained results for microchannel heat transfer problem were in good agreement in general with the previous experimental and numerical works. In the first computations with the solver / quadrilateral and triangular elements for two dimensional problems, hexagonal and tetrahedron elements for three dimensional problems were tried. However, since only the quadrilateral and hexagonal elements gave satisfactory results, they were used in all the above mentioned simulations.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

A combined experimental and numerical study of multidimensional viscous flows at speeds exceeding 8 km/s is reported. Experiments were performed in the X3 superorbital expansion tube with air and nitrogen test flows at a Mach number and total enthalpy of 10 and 40 MJ/kg, respectively. Laminar skin friction, heat flux and pressure measurements were obtained at regular intervals along one wall of a rectangular duct. The spatial resolution of the transducers was chosen to capture the multidimensional flow phenomena within the duct. Quasi-steady flow periods were established along the entire length of the duct in the test times offered by the expansion tube. Direct skin friction measurements were accomplished through the use of ‘in house’ acceleration compensated transducers. The successful operation of these skin friction transducers in a high performance expansion tube was demonstrated. Furthermore, the systematic uncertainty in measured shear stress was significantly reduced with the development of a new pressure calibration technique. For the conditions tested, Reynolds analogy was shown to be valid to within experimental uncertainty. The experimental data was in excellent agreement with numerical estimates. Three-dimensional numerical simulations of the diverging duct revealed that the flowfield structure in the vicinity of the corners differs from that of an unbounded corner or a constant area duct. Real gas effects other than those present in the residual nonequilibrium levels of freestream dissociation were negligible for the conditions tested. A computational study of two waverider configurations recently tested in the X3 superorbital expansion tube was conducted to assist in the interpretation of past results. The off-design aerodynamic performance was also analyzed and showed that blunting the leading edges dramatically degraded the performance by increasing drag and decreasing lift for the conditions considered.

Ce travail de thèse est consacré à l’étude des déformations d’interfaces liquides par l’action d’une onde laser continue. Nous démontrons que la diffusion élastique d'une onde laser dans un milieu turbide induit une force diffusive en volume qui donne naissance à des écoulements permanents au sein du fluide. Les contraintes visqueuses associées à ces écoulements, à l’approche d’une interface liquide molle, peuvent engendrer la déformation de celle-ci jusqu’à la déstabiliser et former un jet. Dans ce manuscrit, nous présentons une étude expérimentale de ce nouveau couplage lumière-fluide complétée par des simulations numériques. Nous présentons également une étude des déformations et instabilité d'interfaces par la pression de radiation optique, due au contraste d’indice de réfraction entre les deux phases liquides en coexistence, dans des milieux transparents. Nous avons enfin analysé la combinaison de ces deux couplages dans les milieux turbides, force diffusive et pression de radiation participant différemment à la déformation d’interfaces liquides. Pour ce faire, nous avons eu recours à différents systèmes fluides turbides et transparents, ayant pour particularité principale de présenter une tension interfaciale extrêmement faible. / This thesis work is dedicated to liquid interface deformations from a continuous laser wave. We demonstrate that elastic scattering of the incident wave in turbid medium induces a scattering force density giving birth to permanent bulk flows in the fluid. Near a soft interface, viscous stresses associated to these flows can deform the interface up to instability and produce a liquid jet. In this manuscript, we report an experimental study dedicated to this new light-fluid coupling in combination with numerical simulations. We also study interface deformations and instability induced by radiation pressure, due to refractive index contrast between the two liquid phases in coexistence, in transparent fluids. We finally analyzed the combination of both couplings in turbid media, scattering force and radiation pressure which differently operate for the interface deformation. To do this, we used different turbid and transparent fluids systems, which have the main particularity to present very low interfacial tension.

This work deals with discretizing viscous fluxes in the context of unstructured data based finite volume and meshless solvers, two competing methodologies for simulating viscous flows past complex industrial geometries. The two important requirements of a viscous discretization procedure are consistency and positivity. While consistency is a fundamental requirement, positivity is linked to the robustness of the solution methodology. The following advancements are made through this work within the finite volume and meshless frameworks. Finite Volume Method: Several viscous discretization procedures available in the literature are reviewed for: 1. ability to handle general grid elements 2. efficiency, particularly for 3D computations 3. consistency 4. positivity as applied to a model equation 5. global error behavior as applied to a model equation. While some of the popular procedures result in inconsistent formulation, the consistent procedures are observed to be computationally expensive and also have problems associated with robustness. From a systematic global error study, we have observed that even a formally inconsistent scheme exhibits consistency in terms of global error i.e., the global error decreases with grid refinement. This observation is important and also encouraging from the view point of devising a suitable discretization scheme for viscous fluxes. This study suggests that, one can relax the consistency requirement in order to gain in terms of robustness and computational cost, two key ingredients for any industrial flow solver. Some of the procedures are analysed for positivity as applied to a Laplacian and it is found that the two requirements of a viscous discretization procedure, consistency(accuracy) and positivity are essentially conflicting. Based on the review, four representative schemes are selected and used in HIFUN-2D(High resolution Flow Solver on UNstructured Meshes), an unstructured data based cell center finite volume flow solver, to simulate standard laminar and turbulent flow test cases. From the analysis, we can advocate the use of Green Gauss theorem based diamond path procedure which can render high level of robustness to the flow solver for industrial computations. Meshless Method: An Upwind-Least Squares Finite Difference(LSFD-U) meshless solver is developed for simulating viscous flows. Different viscous discretization procedures are proposed and analysed for positivity and the procedure which is found to be more positive is employed. Obtaining suitable point distribution, particularly for viscous flow computations happens to be one of the important components for the success of the meshless solvers. In principle, the meshless solvers can operate on any point distribution obtained using structured, unstructured and Cartesian meshes. But, the Cartesian meshing happens to be the most natural candidate for obtaining the point distribution. Therefore, the performance of LSFD-U for simulating viscous flows using point distribution obtained from Cartesian like grids is evaluated. While we have successfully computed laminar viscous flows, there are difficulties in terms of solving turbulent flows. In this context, we have evolved a strategy to generate suitable point distribution for simulating turbulent flows using meshless solver. The strategy involves a hybrid Cartesian point distribution wherein the region of boundary layer is filled with high aspect ratio body-fitted structured mesh and the potential flow region with unit aspect ratio Cartesian mesh. The main advantage of our solver is in terms of handling the structured and Cartesian grid interface. The interface algorithm is considerably simplified compared to the hybrid Cartesian mesh based finite volume methodology by exploiting the advantage accrue out of the use of meshless solver. Cheap, simple and robust discretization procedures are evolved for both inviscid and viscous fluxes, exploiting the basic features exhibited by the hybrid point distribution. These procedures are also subjected to positivity analysis and a systematic global error study. It should be remarked that the viscous discretization procedure employed in structured grid block is positive and in fact, this feature imparts the required robustness to the solver for computing turbulent flows. We have demonstrated the capability of the meshless solver LSFDU to solve turbulent flow past complex aerodynamic configurations by solving flow past a multi element airfoil configuration. In our view, the success shown by this work in computing turbulent flows can be considered as a landmark development in the area of meshless solvers and has great potential in industrial applications.