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La caractérisation et la simulation des écoulements internes au sein des moteurs àpropergol solide, en considérant des mécanismes physiques fortement couplés, constituentl’objectif principal de ce mémoire de thèse. Dans cette optique, la conjonction entrefluide/régression de surface/couplage fluide structure a imposé de déployer une stratégiepropre lors du développement de la modélisation numérique. En effet, le modèle intègre untraitement de frontière immergée couplé avec un suivi de frontière mobile afin de pouvoirrendre compte de la formidable variation géométrique interne subie au cours d’un tir. Côtéfluide, un maillage automatique est nécessaire et la gestion de ce dernier s’appuie sur undéveloppement récursif avec structure hiérarchisée de type 2n tree. Une attention particulièrea été portée sur le solveur lui-même avec une approche explicite en temps et un schémanumérique basé sur l’approche de Roe avec limiteur de flux au second ordre. Des cas testsont été réalisés afin de valider le solveur et les différentes conditions aux limites introduites,notamment des conditions spécifiques développées pour les besoins de simulation. Lespremiers résultats soulignent tout l’intérêt du modèle proposé et sauf erreur de notre part,pour la première fois, l’analyse des sources tourbillonnaires responsables des instabilités ausein de ces moteurs a été étudiée en intégrant les effets du changement continu de géométrie.Finalement, la faisabilité d’une interaction forte entre solveur fluide et solveur solide a étéréalisée sur un modèle simplifié d’un moteur segmenté.L’ensemble des développements permet un accès aux mécanismes couplés complexeset aux fortes interactions au sein des moteurs à propergol solide et offre de nouvellesperspectives dans la caractérisation des mécanismes fortement couplés. / Characterization and simulation of internaI flow within the solid rocket motors, considering the physicalmechanisms strongly coupled, are the main focus of this thesis objective. In this context, the conjunctionbetween fluid/regression surface/fluid coupling structure imposed deploy c1ean during the development ofnumerical modeling strategy. Indeed, the model incorporates treatment coupled with an immersed boundarytracking moving boundary in order to realize the tremendous internai geometric variation experienced during ashot. Fluid side, an automatic mesh is required and the management of the latter is based on a recursivehierarchical structure development with type 2" tree. Particular attention was paid to the solver itself with anexplicit approach to time and a numerical scheme based on the approach of Roe with flow limiter in the secondorder. Tests cases were conducted to validate the sol ver and different boundary conditions introduced, inc1udingspecific conditions developed for the purpose of simulation. The first results emphasize the interest of theproposed and unless our error model, for the first time, the analysis of the sources responsible vortex instabilitiesin these engines has been studied by incorporating the effects of continuous change in geometry. Finally, thefeasibility of a strong interaction between fluid and solid solver was conducted on a simplified model of a multiengine.AlI the developments allows access to complex mechanisms coupled and strong interactions in solidrocket motors and off ers new insights into the characterization of strongly coupled mechanisms.

This master thesis is covering the modeling of the melting process in a tank filled with AdBlue. Due to AdBlue freezing at temperatures below -11 degree there is a need to add heat to be able to secure dosing in all situations. A rig for simulating freezing conditions is created with the possibility to store AdBlue in temperatures down to -40 degree. Temperatures are measured in and around the tank containing AdBlue and in the equipment used for adding heat. Two models are created from physical relations to estimate the mass of AdBlue melted, a static temperature model and a dynamic temperature model. The static model shows good results when calibrated at this specific setup and is very easy to use. The dynamic temperature model is more advanced but describes the real physical system better without external calibration.

In this study, an attempt is made to obtain convergent and stable solutions of the K-E turbulence model equations for non-reacting turbulent flows over an isothermal solid surface in regression. A physics based mathematical model is used to describe the flow and temperature field over the moving surface. The flow is assumed to be two-dimensional, unsteady, incompressible with boundary layer approximations. Parabolized form of the standard K-E equations is adopted to simulate turbulence in the flow. Regression of the solid surface causes the bounds of the solution domain to change with time, therefore a coordinate transformation is used in the vertical direction. The computational domain with fixed boundaries is discretized using an orthogonal grid system where a coordinate stretching is used in the vertical direction. A second order accurate, explicit finite difference technique is used for discretization of the governing equations. The final set of discretized equations is then solved using a solution algorithm specifically developed for this study. The verification of the solution algorithm includes a grid independence study, time increment study, and a comparison of the steady state results for the laminar and the turbulent flow cases. Finally, a parametric study is conducted using the proposed solution algorithm to test the stability of the numerical results for different Reynolds numbers, regression rates, and surface temperatures. It is concluded that the proposed numerical solution algorithm is capable of providing convergent and stable solutions of the two-equation turbulence model.

Ablative materials can sustain very high temperatures in which surface thermochemical processes are significant enough to cause surface recession. Existence of moving boundary over a wide range of temperatures, temperature-dependent thermophysical properties of ablators, and no prior knowledge about the location of the moving surface augment the difficulty for predicting the exposed heat flux at the receding surface of ablators. In this paper, the conjugate gradient method is proposed to estimate the unknown surface recession and time-varying net surface heat flux for these kinds of problems. The first order Tikhonov regularization is employed to stabilize the inverse solution. Considering the complicated phenomena that are taking place, it is shown via simulated experiment that unknown quantities can be obtained with reasonable accuracy using this method despite existing noises in the measurement data.

For simulations of highly complex geometries, frequently encountered in many fields of science and engineering, the process of generating a high-quality, body-fitted grid is very complicated and time-intensive. Thus, one of the principal goals of contemporary CFD is the development of numerical algorithms, which are able to deliver computationally efficient, and highly accurate solutions for a wide range of applications involving multi-physics problems, e.g. Fluid Structure Interaction (FSI). Immersed interface/boundary methods provide considerable advantages over conventional approaches, especially for flow problems containing moving boundaries.In the present work, a novel, robust, highly-accurate, Immersed Interface Method (IIM) is developed, which is based on a local Taylor-series expansion at irregular grid points enforcing numerical stability through a local stability condition. Various immersed methods have been developed in the past; however, these methods only considered the order of the local truncation error. The numerical stability of these schemes was demonstrated (in a global sense) by considering a number of different test-problems. None of these schemes used a concrete local stability condition to derive the irregular stencil coefficients. This work will demonstrate that the local stability constraint is valid as long as the DFL-number does not reach a limiting value. The IIM integrated into a newly developed Incompressible Navier-Stokes (INS) solver is used herein to simulate fully coupled FSI problems. The extension of the novel IIM to a higher-order method, the compressible Navier-Stokes equations and the Maxwell's equations demonstrate the great potential of the novel IIM.In the second part of this dissertation, the newly developed INS solver is employed to study the flow of a stalled airfoil and steady/unsteady stenotic flows. In this context, a new biglobal stability analysis approach based on solving an Initial Value Problem (IVP), instead of the traditionally used EigenValue Problem (EVP), is presented. It is demonstrated that this approach based on an IVP is computationally less expensive compared to EVP approaches while still capturing the relevant physics.

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This work deals with the one-dimensional Stefan problem with a general time- dependent boundary condition at the fixed boundary. The solution will be obtained using a discrete random walk method and the results will be compared qualitatively with analytical- and finite difference method solutions. A critical part has been to model the moving boundary with the random walk method. The results show that the random walk method is competitive in relation to the finite difference method and has its advantages in generality and low effort to implement. The finite difference method has, on the other hand, higher accuracy for the same computational time with the here chosen step lengths. For the random walk method to increase the accuracy, longer execution times are required, but since the method is generally easily adapted for parallel computing, it is possible to speed up. Regarding applications for the Stefan problem, there are a large range of examples such as climate models, the diffusion of lithium-ions in lithium-ion batteries and modelling steam chambers for oil extraction using steam assisted gravity drainage.

O seguinte trabalho procura estudar problemas de fronteira móvel, conhecidos por problemas de Stefan, bem como aproximar suas soluções. Aplicações de problemas de Stefan encontram-se, por exemplo, na física termal de mudança de estados, presente em diversos fenômenos físicos e químicos naturais e na indústria. Devido a não-linearidade, a maior parte destes problemas não possuem solução analítica conhecida e uma técnica comum para se aproximar soluções é o método de balanceamento integral, inicialmente estudado por Goodman (1958). Este método e suas variações propõem perfis de aproximação no domínio da solução e resolvem uma versão integral da equação diferencial. O problema se resume a resolver uma equação diferencial ordinária no tempo envolvendo a profundidade de penetração do calor e o perfil de aproximação proposto. O trabalho estuda tais métodos para problemas termais clássicos em primeiro lugar, de modo que a extensão para problemas de Stefan seja natural. Refinamentos são apresentados, bem como uma técnica de subdivisão do espaço que resulta num esquema numérico. A técnica de imobilização e fronteira é desenvolvida e aplicada em diversos momentos, a fim de simplificar a utilização dos métodos integrais. / The current work aims to study moving boundary problems, known as Stefan problems, and approximate their solutions. Applications of Stefan problems are found in situations where there is change of physical state, present in several natural and industrial physical and chemical phenomena. Due to their inherent nonlinearity, most of these problems have no known analytic solution and a common technique to approximate solutions is the heat balance integral method, originally studied by Goodman (1958). This method and its variations propose an approximating profile and solve an integral version of the differential equation. The problem is reduced to solving an ordinary differential equation in time involving the depth of heat penetration and the proposed profile. This work studies such classic methods to thermal problems first, in a way that the extension to Stefan problems is natural. Refinements are presented, as well as a technique of subdividing the space domain which results in a numerical scheme. The technique of boundary immobilization is developed and applied at different times in order to simplify the use of these methods.

When a water soluble granular fertilizer, such as potash, is wetted and then dried during storage and transportation processes, clumps or cakes often form in the material even when the maximum moisture content is less than 1% by mass. In order to avoid or decrease these occurred cakes, it is essential to characterize cake strength and to explore the process of cake formulation or caking through theoretical/numerical analysis. In this thesis, both experimental measurements of cake strength and theoretical/numerical simulations for recrystallization near a contact point are used to investigate the relationship between the caking process and the cake strength for important factors such as initial moisture content and drying time. <p>In this research, a centrifugal loading method has been developed to determine cake strength in a caked ring specimen of potash fertilizer where internal tensile stresses dominate. Research on fracture mechanics states that brittle materials, such as caked potash, fail at randomly positioned fracture surfaces in tension so the centrifuge test method is well suited to provide good data. A two-dimensional plane stress analysis was used to determine the area-averaged tensile stress at the speed of the centrifuge when each specimen fractures. Repeated tests and uncertainty calculations give data with a narrow range of uncertainty. <p>The centrifuge test facility was used for a series of tests in which the initial moisture content, drying time, particle size and chemical composition (i.e. magnesium content) of the samples were varied. For particle sizes in the range from 0.85 to 3.35 mm, experimental data show that the cake strength increased linearly with initial moisture content for each drying method and particle size, and decreased with increasing particle size for each initial moisture content and drying method. As well, it was also found that cake strength will increase essentially linearly with magnesium content from 0.02% to 0.1% for samples with the same initial moisture content, particle size and drying method. All data show that potash samples tend to form a stronger cake with a slower drying process. <p>A theoretical/numerical model is presented in this thesis to simulate ion diffusion and crystallization near one contact point between two potash (KCl) particles during a typical drying process. The effects of three independent factors are investigated: initial moisture content; evaporation rate; and degree of supersaturation on the surface surrounding the contact point. The numerical results show that the mass of crystal deposition near the contact point will increase with increased initial moisture content and decreased evaporation rate. These numerical predictions for recrystallization near the contact point are consistent with the experimental data for the cake strength of test samples of particle beds. With variations in the solid crystal surface degree of supersaturation near the contact point, simulations showed up to 5 times the increase in the crystal mass deposition near the contact point. This prediction of increased roughness is consistent with another experimental investigation which showed that the surface roughness of NaCl and KCl surfaces increased by a factor of five after one wetting and drying process.