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.

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.

Depuis le début du millénaire, la simulation numérique directe est apparue comme un outil précieux capable d'étudier l’atomisation d’une goutte isolée par un écoulement à grande vitesse. L’atomisation peut être divisée en deux phases distinctes : l'éclatement se produit d'abord sous la forme d'aplatissement de la goutte, formant également des filaments, puis il se poursuit via l'obtention d'une multitude de gouttes de tailles réduites ce qui complète le processus d’atomisation. Les principaux objectifs pour le présent travail étaient donc d’établir un modèle et une méthode numérique capables d’étudier au mieux ces phénomènes. L'atomisation d’une goutte isolée est présentée et est accompagnée d’une comparaison avec l’expérience qui confirme les capacités du modèle et de la méthode à simuler numériquement les différents processus physiques mis en jeu. Des informations essentielles quant aux mécanismes d’atomisation, non exploitables avec l’expérience, sont décrites et l’objectif d’obtenir des gouttes de tailles réduites est atteint. / Only at the beginning of the millennium, direct numerical simulation has emerged as a valuable tool capable of studying the atomization of an isolated droplet by a high-speed flow. The atomization can be divided into two distinct phases: the aerobreakup occurs first in the form of flattening of the droplet, also forming filaments, and then it continues via the obtaining of a multitude of reduced sizes droplets what completes the process of atomization. The main objectives of this work were therefore to establish a model and a numerical method able to study these phenomena as well as possible. The atomization of an isolated droplet is presented and is accompanied by a comparison with the experiment which confirms the capacities of the model and the method to numerically simulate the different physical processes involved. Essential information on atomization mechanisms, which cannot be exploited with experiments, is described and the objective of obtaining droplets of reduced sizes is achieved.

Dans le cadre du développement récent des schémas numériques compacts d’ordre élevé, tels que la méthode de Galerkin discontinu (discontinuous Galerkin) ou la méthode des différences spectrales (spectral differences), nous nous intéressons aux difficultés liées à l’utilisation de ces méthodes lors de la simulation de solutions discontinues.L’utilisation par ces schémas numériques d’une représentation polynomiale des champs les prédisposent à fournir des solutions fortement oscillantes aux abords des discontinuités. Ces oscillations pouvant aller jusqu’à l’arrêt du processus de simulation, l’utilisation d’un dispositif numérique de détection et de contrôle de ces oscillations est alors un prérequis nécessaire au bon déroulement du calcul. Les processus de limitation les plus courants tels que les algorithmes WENO ou l’utilisation d’une viscosité artificielle ont d’ores et déjà été adaptés aux différentes méthodes compactes d’ordres élevés et ont permis d’appliquer ces méthodes à la classe des écoulements compressibles. Les différences entre les stencils utilisés par ces processus de limitation et les schémas numériques compacts peuvent néanmoins être une source importante de perte de performances. Dans cette thèse nous détaillons les concepts et le cheminement permettant d’aboutir à la définition d’un processus de limitation compact adapté à la description polynomiale des champs. Suite à une étude de configurations monodimensionnels, différentes projections polynomiales sont introduites et permettent la construction d’un processus de limitation préservant l’ordre élevé. Nous présentons ensuite l’extension de cette méthodologie à la simulation d’écoulements compressibles bidimensionnels et tridimensionnels. Nous avons en effet développé les schémas de discrétisation des différences spectrales dans un code CFD non structuré, massivement parallèle et basé historiquement sur une méthodologie volumes finis. Nous présentons en particulier différents résultats obtenus lors de la simulation de l’interaction entre une onde de choc et une couche limite turbulente. / Following the recent development of high order compact schemes such as the discontinuous Galerkin or the spectraldifferences, this thesis investigates the issues encountered with the simulation of discontinuous flows. High order compactschemes use polynomial representations which tends to introduce spurious oscillations around discontinuities that can lead to computational failure. To prevent the emergence of these numerical issues, it is necessary to improve the schemewith an additional procedure that can detect and control its behaviour in the neighbourhood of the discontinuities,usually referred to as a limiting procedure or a limiter. Most usual limiters include either the WENO procedure, TVB schemes or the use of an artificial viscosity. All of these solutions have already been adapted to high order compact schemes but none of these techniques takes a real advantage of the richness offered by the polynomial structure. What’s more, the original compactness of the scheme is generally deteriorated and losses of scalability can occur. This thesis investigates the concept of a compact limiter based on the polynomial structure of the solution. A monodimensional study allows us to define some algebraic projections that can be used as a high-order tool for the limiting procedure. The extension of this methodology is then evaluated thanks to the simulation of different 2D and 3D test cases. Those results have been obtained thanks to the development of a parallel solver which have been based on a existing unstructured finite volume CFD code. The different exposed studies detailed end up to the numerical simulation of the shock turbulent boundary layer.

Dans les installations nucléaires, les explosions, qu’elles soient d’origine interne ou externe, peuvent entrainer la rupture du confinement et le rejet de matières radioactives dans l’environnement. Il est donc fondamental, dans un cadre de sûreté de modéliser ce phénomène. L’objectif de cette thèse est de contribuer à l’élaboration de schémas numériques performants pour résoudre ces modèles complexes. Les travaux présentés s’articule autour de deux axes majeurs : le développement de schémas volumes finis consistants pour les équations d’Euler compressible qui modélise les ondes de choc et celui de schémas performants pour la propagation d’interfaces comme le front de flamme lors d'une déflagration. La discrétisation spatiale est de type mailles décalées pour tous les schémas développés. Les schémas pour les équations d'Euler se basent sur une formulation en énergie interne qui permet de préserver sa positivité ainsi que celle de la masse volumique. Un bilan d'énergie cinétique discret peut être obtenu et permet de retrouver un bilan d'énergie totale par l'ajout d'un terme de correction dans le bilan d'énergie interne. Le schéma ainsi construit est consistant au sens de Lax avec les solutions faibles entropiques des équations continues. On utilise les propriétés des équations de type Hamilton-Jacobi pour construire une classe de schémas volumes finis performants sur une large variété de maillages modélisant la propagation du front de flamme. Ces schémas garantissent un principe du maximum et possèdent des propriétés importantes de monotonie et consistance qui permettent d'obtenir un résultat de convergence. / In nuclear facilities, internal or external explosions can cause confinement breaches and radioactive materials release in the environment. Hence, modeling such phenomena is crucial for safety matters. The purpose of this thesis is to contribute to the creation of efficient numerical schemes to solve these complex models. The work presented here focuses on two major aspects: first, the development of consistent schemes for the Euler equations which model the blast waves, then the buildup of reliable schemes for the front propagation, like the flame front during the deflagration phenomenon. Staggered discretization is used in space for all the schemes. It is based on the internal energy formulation of the Euler system, which insures its positivity and the positivity of the density. A discrete kinetic energy balance is derived from the scheme and a source term is added in the discrete internal energy balance equation to preserve the exact total energy balance. High order, MUSCL-like interpolators are used in the discrete momentum operators. The resulting scheme is consistent (in the sense of Lax) with the weak entropic solutions of the continuous problem. We use the properties of Hamilton-Jacobi equations to build a class of finite volume schemes compatible with a large number of meshes to model the flame front propagation. These schemes satisfy a maximum principle and have important consistency and monotonicity properties. These latters allows to derive a convergence result for the schemes based on Cartesian grids.

Minimizing numerical dissipation without compromising the robust shock-capturing attributes remains an outstanding challenge in the design of numerical methods for high-speed compressible flows. The conflicting requirements of low and high numerical dissipation for accurate resolution of discontinuous and smooth flow features, respectively, are the principal reason behind this challenge. In this work we pursue a recently proposed novel strategy of combining adaptive mesh redistribution with conservative high-order shock-capturing finite-volume discretization methodology to overcome this challenge. In essence, we perform high-order finite-volume WENO (weighted essentially non oscillatory) reconstruction on a continuously moving grid the nodes of which are repositioned adaptively in such a way that maximum spatial resolution is achieved in regions associated with sharpest flow gradients. Moreover, to reduce computational expense, the finite-volume WENO discretization strategy is combined with the midpoint quadrature so that only one reconstruction along each intercool location is necessary. To estimate a monotone upwind flux, a rotated HLLC (Harten-Lax-vanLeer-contact resolving) Riemann solver is employed at each intercool location with the state variables estimated from the high-order WENO reconstruction procedure. The effectiveness of this adaptive high-order discretization methodology is assessed on the well-known double Mach reflection test case for reconstruction orders ranging from five to eleven. We find that the resolution of the intricate flow features such as the wall-jet improves progressively with the reconstruction order, which is indicative of the reduced dissipation level of the adaptive high-order WENO discretization. The adaptive discretization methodology is applied to simulate a flow configuration consisting of a Mach 3 supersonic jet injected in a Mach 2 supersonic crossflow of similar ideal gas. It is found that the flow characteristics and especially features that are formed as a result of the Kelvin-Helmholtz instability are strongly influenced by the reconstruction order. The influence of the jet inclination angle on the overall flow features is analyzed.

<div>Shock-wave/turbulent boundary-layer interactions (SWTBLIs) are characterized by low-frequency unsteadiness, amplified aerothermal loads, and a complex three-dimensional flowfield. Presence of a broad range of length and time-scales associated with compressible turbulence generates additional gasdynamic features that interact with different parts of the flowfield via feedback mechanisms. Determining the physics of such flows is of practical importance as they occur frequently in different components of a supersonic/hypersonic aircraft such as inlets operating in both on- and off-design conditions, exhaust nozzles, and control surfaces. SWTBLIs can cause massive flow separation which may trigger unstart by choking the flow in an inlet. On control surfaces, fatigue loading caused by low-frequency shock unsteadiness, coupled with high skin-friction and heat transfer at the surface, can result in failure of the structure.</div><div><br></div><div>The objective of this study is twofold. The first aspect involves examining the causes of unsteadiness in SWTBLIs associated with two geometries – a backward facing step flow reattaching on to a ramp, and a highly confined duct flow. Signal processing and statistical techniques are performed on the results obtained from Delayed Detached-Eddy Simulations (DDES) and Implicit Large-Eddy Simulations (ILES). Dynamic Mode Decomposition (DMD) is used as a complement to this analysis, by obtaining a low-dimensional approximation of the flowfield and associating a discrete frequency value to individual modes. </div><div><br></div><div>In case of the backward facing step, Fourier analysis of wall-pressure data brought out several energy dominant frequency bands such as separation bubble breathing, oscillations of the reattachment shock, shear-layer flapping, and shedding of vortices from the recirculation zone. The spectra of reattachment shock motion suggested a broadband nature of the oscillations, wherein separation bubble breathing affected the low-frequency motion and shear-layer flapping, and vortex shedding correlated well at higher frequencies. A similar exercise was carried out on the highly confined duct flow which featured separation on the floor and sidewalls. In addition to the low-frequency shock motions, the entire interaction exhibited a cohesive back-and-forth in the streamwise direction as well as a left-right motion along the span. Mode reconstruction using DMD was used in this case to recover complex secondary flows induced by the presence of sidewalls.</div><div><br></div><div>For the final aspect of this study, a flow-control actuator was computationally modeled as a sinusoidally varying body-force function. Effects of high-frequency forcing at F⁺ =1.6 on the flowfield corresponding to a backward facing step flow reattaching on to a ramp were examined. Conditionally averaged profile of streamwise velocity fluctuations, based on reattachment shock position, was used for the formulation of spatial distribution of the actuator. The forcing did not change the mean and RMS profiles significantly, but affected the unsteadiness of the interaction significantly. The effects of forcing were localized to the recirculation zone and did not affect the evolution of the shear-layer. The acoustic disturbances propagating through the freestream and recirculation zone drove the motion of the reattachment shock, and did not alter the low-frequency dynamics of the interaction.</div>

Current-to-pressure (I/P) converters are pneumatic devices which provide precise control of pressure in various industries – for example these devices are often used in valve positioner systems (typically found in the oil and gas industry) and tensioning systems (typically used in the packaging industry). With an increasing demand for such devices to operate in harsh environments all by delivering acceptable performance means that Current-to-pressure converters need to be carefully designed such that environmental factors have no or minimal effects on its performance. This work presents an investigation of the principles of operation of an existing I/P converter through mathematical modelling. A simulation model has been created and which allows prediction of performance of the I/P converter. This tool has been used to identify areas of poor performances through theoretical analysis and consequently led to optimisation of certain areas of the I/P converter through a design change to deliver improved performances, for instance the average percentage shift in gain at 1mA input signal (over the temperature range of -40°C to 85°C) on the new I/P converter is 2.13% compared to the average gain of 4.24% on the existing I/P converter, which represents an improvement of almost two fold. Experimental tests on prototypes have been carried out and tests results showed that improved linearity and temperature sensitivity can be expected from the new design.

Made available in DSpace on 2014-06-11T19:23:39Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-07Bitstream added on 2014-06-13T20:11:13Z : No. of bitstreams: 1 lourenco_mas_me_ilha.pdf: 1600140 bytes, checksum: b00979a5a599fe5b08838113e8ca6489 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho apresenta resultados da simulação numérica de escoamentos hipersônicos de fluidos, por meio de pySolver - um aplicativo computacional desenvolvido pelo autor. No aplicativo, as Equações de Euler foram discretizadas pelo método de elementos finitos de Galerkin (GFEM- Galerkin Finite Element Method) juntamente com a técnica CBS (Characteristic Based Split). O aplicativo pySolver, que foi construído baseado nas ferramentas de códigos fontes abertos Python, Blender e Visit, além da linguagem C, possui interface gráfica para o usuário, é multiplataforma e com orientação a objetos, além de contar com um framework especialmente projetado para a realização de todo o pré processamento, visando o modelamento geométrico bi ou tridimensional de problemas. O autor implementou um método para o refinamento de malha, modificando os programas abertos Triangle e TetGen, de tal forma a permitir o refinamento dinâmico e local de malhas até que determinadas tolerâncias sejam alcançadas nos resultados. Isto contribuiu para uma considerável robustez do aplicativo. Para verificação do aplicativo, foram simulados alguns casos-teste de escoamentos supersônicos e hipersônicos ao redor de corpo de diferentes configurações geométricas, principalmente aqueles encontrados na indústria aeronáutica e aeroespacial. Os dados obtidos são comparados com alguns resultados experimentais disponíveis na literatura, quando possível, e também com outros resultados numéricos obtidos da literatura. / This work presents some results for the numerical simulation of hypersonic fluid flows, utilizing pySolver – a software developed by the author. In this application, the Euler equations have been discretized by means of the Galerkin Finite Element Method (GFEM) using the CBS (Characteristic Based Split) scheme. pySolver, a multiplatform object-oriented software, built around the set of open source tools Python, Blender and Visit, besides C language, exhibits a proper graphical user interface and a framework specially developed to deal with data pre-processing and capable of geometrical modeling of either two or three-dimensional problems. The author has also implemented a scheme for the mesh refinement, by adapting the open-source softwares Triangle and TetGen, obtaining local and dynamic mesh refinement until reaching a determined tolerance in the results. That refinement scheme has contributed to considerable application robustness. In order to compare the software, some test cases composed of supersonic and hypersonic flows over di erent geometrical configuration bodies, mostly encountered in the aerospace and aeronautic industry data, have been simulated. The results compared very well with experimental data from the literature and, when possible, with other numerical results also obtained in the literature.

Resumo: Este trabalho apresenta resultados da simulação numérica de escoamentos hipersônicos de fluidos, por meio de pySolver - um aplicativo computacional desenvolvido pelo autor. No aplicativo, as Equações de Euler foram discretizadas pelo método de elementos finitos de Galerkin (GFEM- Galerkin Finite Element Method) juntamente com a técnica CBS (Characteristic Based Split). O aplicativo pySolver, que foi construído baseado nas ferramentas de códigos fontes abertos Python, Blender e Visit, além da linguagem C, possui interface gráfica para o usuário, é multiplataforma e com orientação a objetos, além de contar com um framework especialmente projetado para a realização de todo o pré processamento, visando o modelamento geométrico bi ou tridimensional de problemas. O autor implementou um método para o refinamento de malha, modificando os programas abertos Triangle e TetGen, de tal forma a permitir o refinamento dinâmico e local de malhas até que determinadas tolerâncias sejam alcançadas nos resultados. Isto contribuiu para uma considerável robustez do aplicativo. Para verificação do aplicativo, foram simulados alguns casos-teste de escoamentos supersônicos e hipersônicos ao redor de corpo de diferentes configurações geométricas, principalmente aqueles encontrados na indústria aeronáutica e aeroespacial. Os dados obtidos são comparados com alguns resultados experimentais disponíveis na literatura, quando possível, e também com outros resultados numéricos obtidos da literatura. / Abstract: This work presents some results for the numerical simulation of hypersonic fluid flows, utilizing pySolver - a software developed by the author. In this application, the Euler equations have been discretized by means of the Galerkin Finite Element Method (GFEM) using the CBS (Characteristic Based Split) scheme. pySolver, a multiplatform object-oriented software, built around the set of open source tools Python, Blender and Visit, besides C language, exhibits a proper graphical user interface and a framework specially developed to deal with data pre-processing and capable of geometrical modeling of either two or three-dimensional problems. The author has also implemented a scheme for the mesh refinement, by adapting the open-source softwares Triangle and TetGen, obtaining local and dynamic mesh refinement until reaching a determined tolerance in the results. That refinement scheme has contributed to considerable application robustness. In order to compare the software, some test cases composed of supersonic and hypersonic flows over di erent geometrical configuration bodies, mostly encountered in the aerospace and aeronautic industry data, have been simulated. The results compared very well with experimental data from the literature and, when possible, with other numerical results also obtained in the literature. / Orientador: João Batista Campos Silva / Coorientador: Emanuel Rocha Woiski / Banca: João Batista Aparecido / Banca: Paulo Gilberto de Paula Toro / Mestre