<p>The broad implementation of three-dimensional full-core modeling, with pin-resolved detail, for computational simulation and analysis of nuclear reactors highlights the importance of accuracy and efficiency in simulation codes for accurate and precise analysis. The primary objective of this dissertation is to develop a high-fidelity code capable of solving time-dependent neutron transport problems with 3D whole-core pin-resolved detail in nuclear reactor cores. Additionally, the dissertation explores the optimization of the code's parallelism to enhance its computational efficiency. To reduce the computational intensity associated with the direct 3D calculation of the neutron transport equation, a high-fidelity neutron transport code called PANDAS-MOC is developed using the 2D/1D approach. The 2D radial solution is obtained using the 2D Method of Characteristics (MOC), the axial 1D solution is determined through the Nodal Expansion Method (NEM), and then two solutions are coupled using transverse leakages to find the 3D solution. The convergence of the iterative scheme is accelerated using the multi-level coarse finite different mesh (ML-CMFD) technique. The code's validation and verification are carried out using the C5G7-TD benchmark exercises.</p> <p><br></p> <p>The significant and innovative aspect of this work involves parallelizing and optimizing the PANDAS-MOC code. Three parallel models are developed and evaluated based on the distributed memory and shared memory architecture: MPI parallel model (PMPI), Segment OpenMP threading hybrid model (SGP), and Whole-code OpenMP threading hybrid model (WCP). When computing the steady state of the C5G7 3D core with the same resources, the obtained speedup relationship between the three models is PMPI \(>\) WCP \(>\) SGP, whereas the WCP model only consumed 60\% of the memory of the PMPI model. Furthermore, the hybrid reduction in the ML-CMFD solver and the parallelism design of the MOC sweep are significant issues that decreased the speedup of WCP. Therefore, this study also addresses further optimizations of these two modules.</p> <p><br></p> <p>Concerning the MOC parallelism, two improvements are discussed: No-atomic schedule and Additional Axial Decomposition (AAD) parallelism. The No-atomic schedule evenly distributed the workload among threads and removes the \textit{omp atomic} clause from the code by predefining the MOC calculation sequence for each launched OpenMP thread while ensuring a thread-safe parallel environment. It can significantly reduce the calculation time and improve parallel efficiency. Furthermore, AAD divides the axial layers and OpenMP threads into multiple groups and restricts each thread to work on the layers designated to the same group. </p> <p>Meanwhile, Flag-Save-Update reduction is designed to increase the computational efficiency of the hybrid MPI/OpenMP reduction operations in the ML-CMFD module. It is accomplished by using the global arrays and status flags and establishing a tree configuration of all threads, and it includes no implicit and explicit barriers. In the case of the C5G7 3D core, the parallel efficiency of the MOC solver is about 0.872 when using 32 threads (=\#MPI \(\times\)\#OpenMP), and the Flag-Save-Update reduction yielded better speedup than the traditional hybrid MPI/OpenMP reduction, and its superiority is more obvious as more OpenMP threads are utilized. As a result, the WCP model outperforms the PMPI model for the overall steady-state calculation.</p> <p><br></p> <p>This research also investigates parallelizable preconditioners to accelerate the convergence of the generalized minimal residual method (GMRES) in the CMFD solver. Preconditioners such as Incomplete LU factorization (ILU), Symmetric Successive Over-relaxation (SOR), and Reduced Symmetric Successive Over-Relaxation (RSOR), are implemented in PANDAS-MOC. Except for RSOR, others are unsuitable for hybrid MPI/OpenMP parallel machines due to their inherent sequential nature and dependency on computation order. Their counterparts using the Red-Black ordering algorithm, namely RB-SOR, RB-RSOR, and RB-ILU, are formatted and examined on benchmark reactors such as TWIGL-2D, C5G7-2D, C5G7-3D, and their corresponding subplane models (TWIGL-2D(5S), C5G7-2D(5S), C5G7-3D(5S)), with relaxed convergence criteria (\(10^{-3}\)). Results show that all preconditioners significantly reduce the required number of iterations to converge the GMRES solutions, and RB-SOR is the best one for most reactors. In the case of C5G7-3D(5S), preconditioners exhibit similar sublinear speedup but demonstrate varying runtimes across all tests for both MG-GMRES and 1G-GMRES. However, the speedup results in 1G-GMRES are more than twice as high as those in MG-GMRES. RB-RSOR has an optimal efficiency of 0.6967 at (4,8), while RB-SOR and RB-ILU have optimal efficiencies of 0.6855 and 0.7275 at (32,1), respectively.</p>

<p dir="ltr">A fast model of a Rotating Detonation Combustor (RDC) is developed based on the Method of Characteristics (MOC). The model provides a CFD-like solution of an unwrapped 2D RDC flow field in under 10 seconds with similar fidelity as 2D Reacting URANS simulations. Parametric studies are conducted using the simplified model, and the trends are analyzed to gain insight into the underlying physics of rotating detonation combustors. A methodology to assess the performance of operation with multiple waves is presented. The main effect of increasing waves is found to be the increase in the exit Mach number of the combustion chamber. The design process of a mixer component is also presented. The mixer lies downstream of a channel-cooled RDC with subsonic exit and upstream of a Rolls-Royce M250 helicopter engine in open-loop configuration. The mixer dilutes the RDC exhaust with approximately 250% air to condition the flow for the M250 turbine at steady state operation, while also acting as an isolator with a choked throat to prevent back propagation of pressure waves. The mixer aerodynamic design was completed using 2D axisymmetric RANS simulations, and the mechanical design was evaluated using Ansys Mechanical FEA and was found to be able to survive the high thermal stresses present both during the transient heating and steady state operating condition.</p>

Ce travail présente une étude théorique et expérimentale portant sur le concept de Moteur Hybride Pneumatique ( MHP). En première approche, un modèle 0D d’un MHP monocylindre, incluant un sous-modèle cinématique original pour l’actuateur entièrement variable muant la soupape de charge, est présenté puis exploité. La modélisation 1D de la dynamique des gaz dans chaque tubulure est traitée, incluant différents modèles de Condition Limite de Soupape (CLS), basées sur la méthode des caractéristiques et issues de la littérature. Il est montré que ces CLS ne sont pas adaptées à la modélisation d’un MHP : existence de chocs numériques, problème de non-convergence et mise en défaut face à des relevés expérimentaux. Un modèle original de CLS, évitant ces problèmes et demeurant basé sur la méthode des caractéristiques, est alors développé puis validé expérimentalement à la foi sur bancs d’essais moteurs et de dynamique des gaz à la soupape. Une étude expérimentale des échanges de chaleur convectifs, en mode pneumatique et sans combustion, est conduite et débouche alors sur une modification nécessaire de la corrélation standard de Woschni, afin de correctement décrire l’extinction du mouvement de tumble en fin de course de compression. Une exploitation de la plate-forme de simulation 1D de MHP monocylindre, incluant l’ensemble des éléments développés, est finalement conduite afin de déterminer les phasages optimums d’ouverture et de fermeture de la soupape de charge, pour différents mode et conditions opératoires. Cette étude, nécessaire à de futures simulations de cycles routier, confirme d’une part, la viabilité du concept et d’autre part, montre l’importance que revêt la prise en compte de la cinématique de l’actuateur soupape et de la dynamique des gaz dans la tubulure de charge. / This work presents an experimental and theoretical study on the concept of Pneumatic Hybrid Engine (PHE). In a first approach, a 0D model of a single cylinder PHE, including an original kinematic sub-model of the fully variable actuator that moves the charging valve, is presented and exploited. Then, the 1D modelling of the gaz dynamics inside each pipes is treated, including several valve boundary conditions (VBC), based on the method of characteristics and issued from literature. It is shown that these VBC are not suitable for a PHE modelling : numerical shocks, non-convergence and contraticted when compared to measurements. An original VBC, avoiding these problems and still based on the method of characteristics, is then developed and experimentally validated on both engine and valve gas dynamics tests benches. An experimental study on the convective heat transfer, in pneumatic mode without combustion, is conducted and leads to a necessary modification of the standard Woschni correlation in order to correctly describe the decay of the tumble motion near the end of the compression stroke. The 1D simulation platform, including all components developed, has finally been conducted in order to determine the optimum timings for the charging valve opening and closing, for different modes and operating conditions. This study, necessary for future driving cycle simulations, first confirms the viability of the PHE concept and second, shows the importance of taking into account the kinematic capability of the charing valve actuator and the gas dynamics inside the charging pipe.

This diploma thesis deals with problem of water hammer in pipes affected by viscoelastic behavior of pipe material. Mathematical model uses pressure dependent speed of sound in water air mixture. For purpose of numerical solution the Method of Characteristics with independent time step is introduced. This method is compared with commonly used methods such as Method of Characteristics (MOC) and Lax Wendroff scheme. Derived model, solved with Method of Characteristics with independent time step, is verified with experimental simulation.

This diploma thesis deals with research and study of soil impedance measurement and soil resistivity. Currently, the issue of measuring and determining soil resistance is ensured through the gradual measurement of certain soil parameters at individual points of the surface (or depth of the ground). This thesis focuses on the idea of measuring soil resistance on a certain area using a network of electrodes through a suitably designed test, measurement and evaluation system. Such an approach may find application in the need to determine soil parameters (such as resistivity) on a specific demarcated area (or depth). The prospect of such an application can be seen in saving time, energy and money needed to measure the soil resistivity of a certain area (as opposed to gradual point measurements). The configuration possibilities of OMICRON CPC 100 measuring instrument were used for the design and implementation of the measuring system for the mentioned purpose. The work is completed by verification of the proposed solution by real measurement with evaluation of the results.

No description available.

Le sujet de ce travail de thèse est l’application de la méthode de caractéristiques longues (MOC) pour résoudre l’équation du transport des neutrons pour des géométries à trois dimensions extrudées. Les avantages du MOC sont sa précision et son adaptabilité, le point faible était la quantité de ressources de calcul requises. Ce problème est même plus important pour des géométries à trois dimensions ou le nombre d’inconnues du problème est de l’ordre de la centaine de millions pour des calculs d’assemblage.La première partie de la recherche a été dédiée au développement des techniques optimisées pour le traçage et la reconstruction à-la-volé des trajectoires. Ces méthodes profitent des régularités des géométries extrudées et ont permis une forte réduction de l’empreinte mémoire et une réduction des temps de calcul. La convergence du schéma itératif a été accélérée par un opérateur de transport dégradé (DPN) qui est utilisé pour initialiser les inconnues de l’algorithme itératif and pour la solution du problème synthétique au cours des itérations MOC. Les algorithmes pour la construction et la solution des opérateurs MOC et DPN ont été accélérés en utilisant des méthodes de parallélisation à mémoire partagée qui sont le plus adaptés pour des machines de bureau et pour des clusters de calcul. Une partie importante de cette recherche a été dédiée à l’implémentation des méthodes d’équilibrage la charge pour améliorer l’efficacité du parallélisme. La convergence des formules de quadrature pour des cas 3D extrudé a aussi été explorée. Certaines formules profitent de couts négligeables du traitement des directions azimutales et de la direction verticale pour accélérer l’algorithme. La validation de l’algorithme du MOC a été faite par des comparaisons avec une solution de référence calculée par un solveur Monte Carlo avec traitement continu de l’énergie. Pour cette comparaison on propose un couplage entre le MOC et la méthode des Sous-Groupes pour prendre en compte les effets des résonances des sections efficaces. Le calcul complet d’un assemblage de réacteur rapide avec interface fertile/fissile nécessite 2 heures d’exécution avec des erreurs de quelque pcm par rapport à la solution de référence.On propose aussi une approximation d’ordre supérieur du MOC basée sur une expansion axiale polynomiale du flux dans chaque maille. Cette méthode permet une réduction du nombre de mailles (et d’inconnues) tout en gardant la même précision.Toutes les méthodes développées dans ce travail de thèse ont été implémentées dans la version APOLLO3 du solveur de transport TDT. / The topic of our research is the application of the Method of Long Characteristics (MOC) to solve the Neutron Transport Equation in three-dimensional axial geometries. The strength of the MOC is in its precision and versatility. As a drawback, it requires a large amount of computational resources. This problem is even more severe in three-dimensional geometries, for which unknowns reach the order of tens of billions for assembly-level calculations.The first part of the research has dealt with the development of optimized tracking and reconstruction techniques which take advantage of the regularities of three-dimensional axial geometries. These methods have allowed a strong reduction of the memory requirements and a reduction of the execution time of the MOC calculation.The convergence of the iterative scheme has been accelerated with a lower-order transport operator (DPN) which is used for the initialization of the solution and for solving the synthetic problem during MOC iterations.The algorithms for the construction and solution of the MOC and DPN operators have been accelerated by using shared-memory parallel paradigms which are more suitable for standard desktop working stations. An important part of this research has been devoted to the implementation of scheduling techniques to improve the parallel efficiency.The convergence of the angular quadrature formula for three-dimensional cases is also studied. Some of these formulas take advantage of the reduced computational costs of the treatment of planar directions and the vertical direction to speed up the algorithm.The verification of the MOC solver has been done by comparing results with continuous-in-energy Monte Carlo calculations. For this purpose a coupling of the 3D MOC solver with the Subgroup method is proposed to take into account the effects of cross sections resonances. The full calculation of a FBR assembly requires about 2 hours of execution time with differences of few PCM with respect to the reference results.We also propose a higher order scheme of the MOC solver based on an axial polynomial expansion of the unknown within each mesh. This method allows the reduction of the meshes (and unknowns) by keeping the same precision.All the methods developed in this thesis have been implemented in the APOLLO3 version of the neutron transport solver TDT.

This thesis aims at automotive starters, their construction, characteristics and problems with starting at low temperatures. There are kinds of starters, function principle, construction, advantages and disadvantages in the first part of thesis. Issues with combustion engine starting and basic technical requirements are also mentioned here; characteristics and importance of starters and combustion engines are also described. Last chapters of this part are dedicated to finite element method and its implication. There are analytical calculations of starter in the second part of thesis. Results are compared with experimental obtained (measured) values and results from RMxprt. Finite element method results are compared, too. Magnetic induction improvement in stator is also suggested.

Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie admissibles selon la force choisie est effectuée. Pour chaque type de force, les champs de vecteurs sont présentés. L’algèbre ayant la dimension la plus élevée possible a été obtenues en considérant les forces monogéniques et elle a été classifiée en classes de conjugaison. La méthode de réduction par symétrie est appliquée pour obtenir des solutions explicites et implicites de plusieurs types parmi lesquelles certaines s’expriment en termes d’une ou deux fonctions arbitraires d’une variable et d’autres en termes de fonctions elliptiques de Jacobi. Plusieurs solutions sont interprétées physiquement pour en déduire la forme de filières d’extrusion réalisables. Dans la seconde partie, on s’intéresse aux solutions s’exprimant en fonction d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre. La méthode des caractéristiques généralisées ainsi qu’une méthode basée sur les symétries conditionnelles pour les invariants de Riemann sont étendues pour être applicables à des systèmes dans leurs régions elliptiques. Leur applicabilité est démontrée par des exemples de la plasticité idéale non-stationnaire pour un flot irrotationnel ainsi que les équations de la mécanique des fluides. Une nouvelle approche basée sur l’introduction de matrices de rotation satisfaisant certaines conditions algébriques est développée. Elle est applicable directement à des systèmes non-homogènes et non-autonomes sans avoir besoin de transformations préalables. Son efficacité est illustrée par des exemples comprenant un système qui régit l’interaction non-linéaire d’ondes et de particules. La solution générale est construite de façon explicite. / The objects under consideration in this thesis are systems of first-order quasilinear equations. In the first part of the thesis, a study is made of an ideal plasticity model from the point of view of the classical Lie point symmetry group. Planar flows are investigated in both the stationary and non-stationary cases. Two new vector fields are obtained. They complete the Lie algebra of the stationary case, and the subalgebras are classified into conjugacy classes under the action of the group. In the non-stationary case, a classification of the Lie algebras admissible under the chosen force is performed. For each type of force, the vector fields are presented. For monogenic forces, the algebra is of the highest possible dimension. Its classification into conjugacy classes is made. The symmetry reduction method is used to obtain explicit and implicit solutions of several types. Some of them can be expressed in terms of one or two arbitrary functions of one variable. Others can be expressed in terms of Jacobi elliptic functions. Many solutions are interpreted physically in order to determine the shape of realistic extrusion dies. In the second part of the thesis, we examine solutions expressed in terms of Riemann invariants for first-order quasilinear systems. The generalized method of characteristics, along with a method based on conditional symmetries for Riemann invariants are extended so as to be applicable to systems in their elliptic regions. The applicability of the methods is illustrated by examples such as non-stationary ideal plasticity for an irrotational flow as well as fluid mechanics equations. A new approach is developed, based on the introduction of rotation matrices which satisfy certain algebraic conditions. It is directly applicable to non-homogeneous and non-autonomous systems. Its efficiency is illustrated by examples which include a system governing the non-linear superposition of waves and particles. The general solution is constructed in explicit form.

Les objets d’étude de cette thèse sont les systèmes d’équations quasilinéaires du premier ordre. Dans une première partie, on fait une analyse du point de vue du groupe de Lie classique des symétries ponctuelles d’un modèle de la plasticité idéale. Les écoulements planaires dans les cas stationnaire et non-stationnaire sont étudiés. Deux nouveaux champs de vecteurs ont été obtenus, complétant ainsi l’algèbre de Lie du cas stationnaire dont les sous-algèbres sont classifiées en classes de conjugaison sous l’action du groupe. Dans le cas non-stationnaire, une classification des algèbres de Lie admissibles selon la force choisie est effectuée. Pour chaque type de force, les champs de vecteurs sont présentés. L’algèbre ayant la dimension la plus élevée possible a été obtenues en considérant les forces monogéniques et elle a été classifiée en classes de conjugaison. La méthode de réduction par symétrie est appliquée pour obtenir des solutions explicites et implicites de plusieurs types parmi lesquelles certaines s’expriment en termes d’une ou deux fonctions arbitraires d’une variable et d’autres en termes de fonctions elliptiques de Jacobi. Plusieurs solutions sont interprétées physiquement pour en déduire la forme de filières d’extrusion réalisables. Dans la seconde partie, on s’intéresse aux solutions s’exprimant en fonction d’invariants de Riemann pour les systèmes quasilinéaires du premier ordre. La méthode des caractéristiques généralisées ainsi qu’une méthode basée sur les symétries conditionnelles pour les invariants de Riemann sont étendues pour être applicables à des systèmes dans leurs régions elliptiques. Leur applicabilité est démontrée par des exemples de la plasticité idéale non-stationnaire pour un flot irrotationnel ainsi que les équations de la mécanique des fluides. Une nouvelle approche basée sur l’introduction de matrices de rotation satisfaisant certaines conditions algébriques est développée. Elle est applicable directement à des systèmes non-homogènes et non-autonomes sans avoir besoin de transformations préalables. Son efficacité est illustrée par des exemples comprenant un système qui régit l’interaction non-linéaire d’ondes et de particules. La solution générale est construite de façon explicite. / The objects under consideration in this thesis are systems of first-order quasilinear equations. In the first part of the thesis, a study is made of an ideal plasticity model from the point of view of the classical Lie point symmetry group. Planar flows are investigated in both the stationary and non-stationary cases. Two new vector fields are obtained. They complete the Lie algebra of the stationary case, and the subalgebras are classified into conjugacy classes under the action of the group. In the non-stationary case, a classification of the Lie algebras admissible under the chosen force is performed. For each type of force, the vector fields are presented. For monogenic forces, the algebra is of the highest possible dimension. Its classification into conjugacy classes is made. The symmetry reduction method is used to obtain explicit and implicit solutions of several types. Some of them can be expressed in terms of one or two arbitrary functions of one variable. Others can be expressed in terms of Jacobi elliptic functions. Many solutions are interpreted physically in order to determine the shape of realistic extrusion dies. In the second part of the thesis, we examine solutions expressed in terms of Riemann invariants for first-order quasilinear systems. The generalized method of characteristics, along with a method based on conditional symmetries for Riemann invariants are extended so as to be applicable to systems in their elliptic regions. The applicability of the methods is illustrated by examples such as non-stationary ideal plasticity for an irrotational flow as well as fluid mechanics equations. A new approach is developed, based on the introduction of rotation matrices which satisfy certain algebraic conditions. It is directly applicable to non-homogeneous and non-autonomous systems. Its efficiency is illustrated by examples which include a system governing the non-linear superposition of waves and particles. The general solution is constructed in explicit form.