Flame-holding in a recessed cavity is investigated experimentally in a Mach 2.5 preheated cross-flow for both stable and unstable combustion, with a relatively low preheating. Self-sustained combustion is investigated for stagnation pressures and temperatures reaching 1.4 MPa and 750 K. In particular, cavity blowout is characterized with respect to cavity aspect ratio (L/D =2.84 - 3.84), injection strategy (floor - ramp), aft ramp angle (90 deg - 22.5 deg) and multi-fuel mixture (CH₄-H₂ or CH₄-C₂H₄ blends). The results show that small hydrogen addition to methane leads to significant increase in flame stability, whereas ethylene addition has a more gradual effect. Since the multi-fuels used here are composed of a slow and a fast chemistry fuel, the resulting blowout region has a slow (methane dominant) and a fast (hydrogen or ethylene dominant) branch. Regardless of the fuel composition, the pressure at blowout is close to the non-reacting pressure imposed by the cross-flow, suggesting that combustion becomes potentially unsustainable in the cavity at the sub-atmospheric pressures encountered in these supersonic studies. The effect of preheating is also investigated and results show that the stability domain broadens with increasing stagnation temperature. However, smaller cavities appear less sensitive to the cross-flow preheating, and stable combustion is achieved over a smaller range of fuel flow rate, which may be the result of limited residence and mixing time. The blowout data point obtained at lower fuel flow rate fairly matches the empirical model developed by Rasmussen et al. for floor injection phi = 0.0028 Da^-.8, where phi is the equivalence ratio and Da the Damkohler number. An alternate model is proposed here that takes into account the ignition to scale the blowout data. Since the mass of air entrained into the cavity cannot be accurately estimated and the cavity temperature is only approximated from the wall temperature, the proposed scaling has some uncertainty. Nevertheless the new phi-Da scaling is shown to preserve the subtleties of the blowout trends as seen in the current experimental data.

Gradient-based aerodynamic shape optimization, based on Computational Fluid Dynamics analysis of the flow, is a method that can automatically improve designs of aircraft components. The prospect is to reduce a cost function that reflects aerodynamic performances. When the shape is described by a large number of parameters, the calculation of one gradient of the cost function is only feasible by recourse to techniques that are derived from the theory of optimal control. In order to obtain the best computational efficiency, the so called adjoint method is applied here on the complete mapping, from the parameters of design to the values of the cost function. The mapping considered here includes the Euler equations for compressible flow discretized on unstructured meshes by a median-dual finite-volume scheme, the primal-to-dual mesh transformation, the mesh deformation, and the parameterization. The results of the present research concern the detailed derivations of expressions, equations, and algorithms that are necessary to calculate the gradient of the cost function. The discrete adjoint of the Euler equations and the exact dual-to-primal transformation of the gradient have been implemented for 2D and 3D applications in the code Edge, a program of Computational Fluid Dynamics used by Swedish industries. Moreover, techniques are proposed here in the aim to further reduce the computational cost of aerodynamic shape optimization. For instance, an interpolation scheme is derived based on Radial Basis Functions that can execute the deformation of unstructured meshes faster than methods based on an elliptic equation. In order to improve the accuracy of the shape, obtained by numerical optimization, a moving mesh adaptation scheme is realized based on a variable diffusivity equation of Winslow type. This adaptation has been successfully applied on a simple case of shape optimization involving a supersonic flow. An interpolation technique has been derived based on a mollifier in order to improve the convergence of the coupled mesh-flow equations entering the adaptive scheme. The method of adjoint derived here has also been applied successfully when coupling the Euler equations with the boundary-layer and parabolized stability equations, with the aim to delay the laminar-to-turbulent transition of the flow. The delay of transition is an efficient way to reduce the drag due to viscosity at high Reynolds numbers.

The construction of compact high-order Residual Distribution schemes for the discretizationof steady multidimensional advection-diffusion problems on unstructuredgrids is presented. Linear and non-linear scheme are considered. A piecewise continuouspolynomial approximation of the solution is adopted and a gradient reconstructionprocedure is used in order to have a continuous representation of both thenumerical solution and its gradient. It is shown that the gradient must be reconstructedwith the same accuracy of the solution, otherwise the formal accuracy ofthe numerical scheme is lost in applications in which diffusive effects prevail overthe advective ones, and when advection and diffusion are equally important. Thenthe method is extended to systems of equations, with particular emphasis on theNavier-Stokes and RANS equations. The accuracy, efficiency, and robustness of theimplicit RD solver is demonstrated using a variety of challenging aerodynamic testproblems.

Cette thèse est consacrée à l'analyse mathématique de trois problèmes d'écoulements de fluides viscoélastiques de type Oldroyd. Tout d'abord, nous étudions des écoulements stationnaires faiblement compressibles dans un domaine borné avec des conditions au bord de type "rentrante-sortante". Nous étudions aussi le problème d'écoulements stationnaires faiblement compressibles dans un coin convexe. En utilisant une méthode de point fixe (premier et deuxième problèmes) et une décomposition de Helmoltz (deuxième problème), nous montrons des résultats d'existence et d'unicité des solutions. Nous étudions également le cas d'un écoulement non stationnaire. Nous montrons un résultat d'existence locale et un résultat d'existence globale, avec des conditions initiales suffisamment petites, pour des fluides compressibles. Nous démontrons aussi la convergence du modèle d'écoulement viscoélastique compressible à faible nombre de Mach vers le modèle incompressible lorsque les données initiales sont "bien préparées"

This work aims at the numerical simulation of compressible fluid/deformable structure interactions. In particular, we have developed a partitioned coupling algorithm between a Finite Volume method for the compressible fluid and a Discrete Element method capable of taking into account fractures in the solid. A survey of existing fictitious domain methods and partitioned algorithms has led to choose an Embedded Boundary method and an explicit coupling scheme. We first showed that the Discrete Element method used for the solid yielded the correct macroscopic behaviour and that the symplectic time-integration scheme ensured the preservation of energy. We then developed an explicit coupling algorithm between a compressible inviscid fluid and an undeformable solid. Mass, momentum and energy conservation and consistency properties were proved for the coupling scheme. The algorithm was then extended to the coupling with a deformable solid, in the form of a semi-implicit scheme. Finally, we applied this method to unsteady inviscid flows around moving structures: comparisons with existing numerical and experimental results demonstrate the excellent accuracy of our method

In this work, the mathematical implications of merging two different turbulence modeling approaches are addressed by deriving the exact hybrid RANS/LES Navier-Stokes equations. These equations are derived by introducing an additive-filter, which linearly combines the RANS and LES operators with a blending function. The equations derived predict additional hybrid terms, which represent the interactions between RANS and LES formulations. Theoretically, the prediction of the hybrid terms demonstrates that the hybridization of the two approaches cannot be accomplished only by the turbulence model equations, as it is claimed in current hybrid RANS/LES models. The importance of the exact hybrid RANS/LES equations is demonstrated by conducting numerical calculations on a turbulent flat-plate boundary layer. Results indicate that the hybrid terms help to maintain an equilibrated model transition when the hybrid formulation switches from RANS to LES. Results also indicate, that when the hybrid terms are not included, the accuracy of the calculations strongly relies on the blending function implemented in the additive-filter. On the other hand, if the exact equations are resolved, results are only weakly affected by the characteristics of the blending function. Unfortunately, for practical applications the hybrid terms cannot be exactly computed. Consequently, a reconstruction procedure is proposed to approximate these terms. Results show, that the model proposed is able to mimic the exact hybrid terms, enhancing the accuracy of current hybrid RANS/LES approaches. In a second effort, the Two Level Simulation (TLS) approach is proposed as a near-wall model for LES. Here, TLS is first extended to compressible flows by deriving the small-scale equations required by the model. The full compressible TLS formulation and the hybrid TLS/LES approach is validated simulating the flow over a flat-plate turbulent boundary layer. Overall, results are found in reasonable agreement with experimental data and LES calculations.

A dual-axis fluidic thrust vectoring (FTV) system is proposed where the supersonic propulsive jet of an aircraft is exhausted over a scarfed (swept), curved surface to produce flight control moments in both the pitch and yaw axes. This work contributes towards practical dual-axis FTV through expansion of fundamental curved-wall jet (CWJ) understanding, development of the novel Superimposed Characteristics technique for supersonic nozzle design, and performance evaluation of an experimental scarfed curved wall FTV configuration. Previous work has suggested that the use of a sheared exhaust velocity profile improves the attachment of supersonic jets to curved surfaces; however, evidence to support this is limited. To address this, an inviscid numerical CWJ model was developed using the two-dimensional method of characteristics. A major outcome is improved understanding of the effect of exhaust velocity profile on CWJ wave structure and subsequent jet attachment. A sheared velocity exhaust is shown to generate a wave structure that diminishes adverse streamwise pressure gradients within a supersonic curved-wall jet. This reduces the likelihood of boundary layer separation and as a result, a sheared exhaust velocity CWJ is expected to be less readily separated compared to other exhaust velocity profiles. A novel method termed Superimposed Characteristics was developed for the low-order design of supersonic nozzles with rectangular exits. The technique is capable of generating 3D nozzle geometries based on independent exit plane orientation and exhaust velocity distribution requirements. The Superimposed Characteristics method was used to design scarfed rectangular exit nozzles with sheared velocity exhaust profiles. These nozzles were then evaluated using finite volume computational methods and experimental methods. From the analysis, the Superimposed Characteristics method is shown to be valid for preliminary nozzle design. Experimental methods were used to study the on- and off-design attachment qualities of uniform and sheared velocity exhaust jets for a FTV configuration with an external curved wall termination angle of 90 degrees and scarf angle of 30 degrees. Experiments at the on-design nozzle pressure ratio (NPR) of 3.3 demonstrated pitch and yaw jet deflection angles of 78 degrees and 23 degrees respectively for the uniform exhaust velocity CWJ. The sheared exhaust velocity CWJ achieved lower pitch and yaw deflection angles of 34 degrees and 14 degrees respectively at the same on-design NPR. The lower jet deflection angles observed for sheared exhaust velocity jets is inconsistent with the CWJ model prediction of reduced adverse streamwise pressure gradients; however, there was insufficient experimental instrumentation to identify the cause. In the off-design experiments, the uniform exhaust velocity CWJ was observed to detach at an NPR of 3.6, whilst the sheared exhaust velocity CWJ remained attached at NPRs in excess of 4. The capability of sheared exhaust velocity CWJs to remain attached at higher NPRs is consistent with the analytical theory and the CWJ model predictions. An actuation study was carried out to achieve controlled jet detachment using secondary blowing injected normal to the curved wall. Full separation of the wall jets was achieved downstream of the injection point. This provided vectoring angles of more than 20 degrees in pitch and 10 degrees in yaw, exceeding expected vectoring requirements for practical aircraft control. At the on-design NPR, the uniform and sheared exhaust velocity jets required secondary blowing mass flow rates of 2.1% and 3.8% of the primary mass flow respectively to achieve full separation.

Title: Mathematical analysis of equations describing the flow of compressible heat conducting fluids Author: Šimon Axmann Department: Mathematical Institute of Charles University Supervisor: doc. Mgr. Milan Pokorný, Ph.D., Mathematical Institute of Charles University Abstract: The present thesis is devoted to the mathematical analysis of equa- tions describing the flow of viscous compressible newtonian fluid in various time regimes. In particular, we present existence results for three problems arising as special cases of a general model derived in the introductory part. The first chap- ter deals with time-periodic solutions to the full Navier-Stokes-Fourier system for heat-conducting fluid. The second chapter contains the proof of existence of steady solutions to a system arising from phase field model for two-phase com- pressible fluid. Finally, in the last section we study steady strong solutions to the Navier-Stokes equations under the additional assumption that the fluid is suffi- ciently dense. For each problem a different concept of the solution is considered, on the other hand in all cases an essential role is played by the crucial quantity effective viscous flux. Keywords: compressible Navier-Stokes system; weak solution; entropy variational solution; large data

Recent technological advances are based on effectively using complex multiphysics concepts. Therefore, there is an ever increasing need for accurate numerical al-gorithms of reduced complexity for solving multiphysics problems. Traditional mesh-based simulation methods depend on a neighbor connectivity information for formulation of operators like derivatives. In large deformation problems, de-pendence on a mesh could prove a limitation in terms of accuracy and cost of preprocessing. Meshless methods obviate the need to construct meshes thus al-lowing simulations involving severe geometric deformations such as breakup of a contiguous domain into multiple fragments. Smoothed Particle Hydrodynamics (SPH) is a meshless particle based Lagrangian numerical method that has the longest continuous history of development ever since it was introduced in 1977. Commensurate with the significant growth in computational power, SPH has been increasingly applied to solve problems of greater complexity in fluid mechanics, solid mechanics, interfacial flows and astrophysics to name a few. The SPH approximation of the continuity and momentum equations govern-ing fluid flow traditionally involves a stiff equation of state relating pressure and density, when applied to incompressible flow problems. Incompressible Smoothed Particle Hydrodynamics (ISPH) is a variant of SPH that replaces this weak com-pressibility approach with a pressure equation that gives a hydrostatic pressure field which ensures a divergence-free (or density invariant) velocity field. The present study explains the development of an ISPH algorithm and its implementa-tion with focus on application to free surface flows, interaction of fluid with rigid bodies and coupling of incompressible fluids with a compressible second phase. Several improvements to the exiting ISPH algorithm are proposed in this study. A semi-analytic free surface model which is more accurate and robust compared to existing algorithms used in ISPH methods is introduced, validated against experi-ments and grid based CFD results. A surface tension model with specific applica-bility to free surfaces is presented and tested using 2D and 3D simulations. Using theoretical arguments, a volume conservation error in existing particle methods in general is demonstrated. A deformation gradient based approach is used to derive a new pressure equation which reduces these errors. The method is ap-plied to both free surface and internal flow problems and is shown to have better volume conservation and therefore reduced density fluctuations. Also, comments on instabilities arising from particle distributions are made and the role of the smoothing functions in such instabilities is discussed. The challenges in imple-menting the ISPH algorithm in a computer code are discussed and the experience of developing an in-house ISPH code is described. A parametric study on water entry of cylinders of different shapes, angular velocity and density is performed and aspects such as surface profiles, impact pressures and penetration velocities are compared. An analysis on the energy transfer between the solid and the fluid is also performed. Low Froude number water entry of a sphere is studied and the impact pressure is compared with the theoretical estimates. The Incompressible SPH formulation, employing the proposed improvements from the study is then coupled with a compressible SPH formulation to perform two phase flow simulations interacting compressible and incompressible fluids. To gain confidence in its applicability, the simulations are compared against the theoretical predication given by the Rayleigh-Plesset equation for the problem of compressible drop in an incompressible fluid.

Ce travail porte sur l’étude du procédé de projection plasma par voie liquide et en particulier sur l’interaction entre la phase liquide et l’écoulement de plasma. Différents phénomènes physiques ont lieu comme la fragmentation du jet, l’évaporation du liquide et la fusion des particules. La simulation numérique permet de mieux comprendre les phénomènes physiques et vient en appui des expériences qui sont parfois difficiles voire impossibles à réaliser. Un modèle compressible diphasique est développé afin de prendre en compte les effets compressibles du plasma. Des validations sont réalisées sur des cas test académiques et sur un jet d’argon pur. De bons accords sont obtenus entre les simulations et la théorie ou les expériences. Ensuite différents mélanges de gaz plasmagènes, classiquement utilisés en projection plasma, sont étudiés : l’argon/hydrogène et l’argon/hélium.Une analyse du caractère instationnaire et turbulent est ensuite menée et permet de voir l’importance des effets instationnaires dans ces écoulements. Puis des simulations de l’injection de la phase liquide sous forme de gouttes ou de jet continu dans l’écoulement de plasma sont réalisées. L’influence de la nature des gaz plasmagènes et du mode d’injection est démontrée. Les structures observées expérimentalement sont également obtenues parles simulations. / The study of the plasma spraying process is investigated in this work, in particular the interaction between a liquid phase and a plasma flow. Different physical phenomena occureas the jet fragmentation, the liquid vaporization and the particles fusion. The numerical simulation is used to better understand the physical phenomena and is an alternative to experimental measurements, which could be locally difficult to perform because of the measurement techniques limitations and the particular characteristics of the plasma. A compressible two-phase model is developped to take into account the compressible effects of the plasma flow. Validations are realized on academic test cases and on a argonjet. Good agreements are obtained between simulations and theory or experiments. Then different mixtures of plasmagen gas, classically used in plasma spraying, are studied :argon/hydrogen and argon/helium. An analysis of unsteady and turbulent character isled and allows seeing the importance of unsteady effects in these flows. Numerical simulations of the injection of a liquid phase into the plasma flow are realized. The influence of the plasmagen gas nature and the injection type is anlysed. Structures observed by experiments are also obtained by the simulations.