A complete formulation of the recently developed. F_N method in kinetic theory is presented and the accuracy of this advanced semi-analytical-numerical technique is demonstrated by testing the method to several classical problems in rarefied gas dynamics. The method is based on the existing analysis for the vector transport equation arising from the decomposition of the linearized BGK equation. Using full-range orthogonality, a system of singular integral equations for the distribution functions at the boundaries is established. The unknown distribution functions are then approximated by a finite expansion in terms of a set of basis functions and the coefficients of the expansion are found by requiring the set of the reduced algebraic equations to be satisfied at certain collocation points. By studying the half-space heat transfer and weak evaporation problems and the problem of heat transfer between two parallel plates it is demonstrated that the F_N method is a viable solution technique yielding results of benchmark accuracy. Two different sets of basis functions are provided for half-space and finite media problems, respectively. In all cases, highly accurate numerical results are computed and compared to existing exact solutions. The obtained numerical results help in judging the accuracy to expect of the method and indicate that the F_N method may be applied with confidence to problems for which, more exact methods of analysis do not appear possible. Then, the cylindrical Poiseuille flow and thermal creep problems, which are not amenable to exact treatment, are solved. The F_N method is formulated and tested successfully for the first time in cylindrical geometry in kinetic theory. The complete solution of the two aforementioned problems is presented with the numerical results quoted as converged being of reference-quality good for benchmark accuracy. / Ph. D. / incomplete_metadata

<p align="justify">Ce travail consiste à étudier des systèmes constitués par un grand nombre de grains, auxquels de l’énergie cinétique est fournie, et à étudier leurs similarités et leurs différences avec des fluides traditionnels. Je me concentre principalement sur la nature de non-équilibre de ces fluides granulaires, en montrant que, même si les méthodes de méchanique statistique y sont applicables, leurs propriétés sont très différentes de celles de systèmes à l’équilibre ou proches de l’équilibre :</p><p><p><ul><li>Les fluides granulaires présentent des phénomènes de transport qui n’ont pas d’équivalent dans des fluides moléculaires, tels qu’un couplage spécifique entre flux de chaleur et gradient de densité.<p><li>Leur distribution de vitesse est en général différente de la distribution de Maxwell-Boltzmann, et présente une surpopulation pour les grandes vitesses. <p><li>Dans le cas de mélanges, différentes espèces de grains sont en général caractérisées par des énergies cinétiques différentes, i.e. ces systèmes sont sujet à une non-equipartition de leur énergie.<p><li>Ces fluides ont tendance à former des inhomogénéités spatiales spontanément. Cette propriété est illustrée en étudiant l’expérience du Demon de Maxwell appliquée aux systèmes granulaires.</ul><p><p align="justify">Chacune de ces particularités est discutée en détail dans des chapitres distincts, où l’on applique différentes méthodes de méchanique statistique (équation de Boltzmann, transition de phase, mean field models…) et où l’on vérifie les prédictions théoriques par simulations numériques (MD, Monte Carlo…).</p> / Doctorat en sciences, Spécialisation physique / info:eu-repo/semantics/nonPublished

Ce travail porte sur la dynamique de la matière granulaire dans l'état fluide, et sa réponse à une excitation localisée dans deux limites : une faible perturbation suite à laquelle le système relaxe rapidement vers un état homogène, ou une agitation intense donnant lieu à une onde de choc telle qu'un souffle d'explosion. Cette réponse est affectée par deux caractéristiques des fluides granulaires : les particules macroscopiques qui les composent sont d'une part inélastiques, de sorte que leur dynamique est dissipative et ne possède pas d'état d'équilibre, et d'autre part polydisperses, c'est-à-dire hétérogènes en taille et en masse. Nous isolons d'abord un effet dynamique de la polydispersité en montrant qu'il existe un mélange optimal qui minimise le temps de relaxation du fluide vers son état asymptotique. Nous nous intéressons ensuite au cas où une seule des espèces est perturbée par l'application d'un champ extérieur, et étudions l'état stationnaire hors d'équilibre ainsi établi, dans la limite du traceur où les autres espèces constituent un bain stationnaire. Enfin, nous modélisons la croissance de formes autosimilaires dans ce bain suite à une intense libération ponctuelle d'énergie, que nous comparons au souffle d'une explosion dans un gaz moléculaire. / This work focuses on the dynamics of the fluid state of granular matter, and its response to a localized perturbation in two limiting cases : relaxation toward a homogeneous state or growth of a blast wave. This response is shaped by two distinctive features of granular media: their macroscopic constituent particles are both inelastic, entailing intrinsically non-equilibrium dynamics, and polydisperse or heterogeneous in their material properties. First, we isolate the effects of polydispersity in the return of a gas to its homogeneous asymptotic state, and evidence the existence of an optimal mixture for which the relaxation time is minimal. We then restrict the perturbation to accelerating a single species with an external field in order to study the induced non-equilibrium stationary state in the tracer limit, where other species are undisturbed by this process. Finally, we model the self-similar shock wave generated in such a dissipative bath by an intense yet localized release of energy, and contrast it with blast waves in molecular gases.

Orientador: Hélio Aparecido Navarro / Banca: Paulo Cesar Razuk / Banca: Luben Cabezas Gomez / Resumo: No presente trabalho desenvolve-se um estudo de modelagem matemática e simulação numérica do escoamento gás-sólido em um leito fuidizado borbulhante. É apresentado o modelo hidrodinâmico, A, para escoamentos bifásicos gás-solido considerando a Teoria Cinética dos Escoamentos Granulares. É usado o modelo Euleriano de duas fases separadas considerando a modelagem do tensor das tensões da fase sólida através do atrito entre as partículas e da teoria cinética dos escoamentos granulares. O código fonte MFIX (Multiphase Flow with Interphase eXchanges) desenvolvido no NETL (National Energy Technology Laboratory) é utilizado para as simulações numéricas. Os resultados de simulação são obtidos resolvendo a temperatura granular algebricamente ou através de uma equação diferencial parcial. Obtêm-se resultados mais realísticos no uso da EDP com condição de contorno de deslizamento parcial na parede. Uma variação no diâmetro das partículas (partículas do grupo B e do grupo A/B) é investigada, concluindo-se que deve ser acrescentado ao código MFIX outros parâmetros físico para simulações com partículas do grupo A/B. / Abstract: In the present work is described a mathematical model and numerical simulation of gas-solid flow in the bubbling fluidized bed. It is presented the hydrodynamic model, A, for gas-solid flow considering the Kinetic Theory of Granular Flows. It is used the two fluids Eulerian model where the solid phase stress tensor is modeled considering the friction between the particles and the kinetic theory of granular flows. The code MFIX (Multiphase Flow with Interphase eXchanges) developed in NETL (National Energy Tecnology Laboratory) is used for numerical simulations. The results are obtained with the compute of the granular temperature using a partial differential equation or an algebraic expression. It was obtained more realistic results when is used a PDE with boundary conditions of the partial slip. A variation in the diameter of the particles (particles in Group B and Group A/B) it is analyzed. It is also concluded that should be added to the code MFIX other physical parameters for simulations with particles of group A/B. / Mestre

Desenvolvemos urna teoria cinética para urna mistura de gases ionizados em presença de campos elétricos e magnéticos. As leis de Ohm, Fourier e Navier-Stokes são obtidas por dois métodos distintos que se baseiam na equação de Boltzmann. Verificamos que o emprego de teoremas de representação torna o método de Chapman-Enskog mais direto. Entretanto o método combinado mostrou-se extremamente simples, onde os coeficientes de transporte são determinados através da inversão de tensores de segunda e quarta ordens. Calculamos também a integral de colisão para as possíveis interações em gases ionizados tais como, entre partículas carregadas, partícula carregada e partícula neutra e entre partículas neutras. Como uma aplicação do método combinado, determinamos os coeficientes de condutividade elétrica, condutividade térmica, coeficiente termo-elétrico e o coeficiente de viscosidade cisalhante para um gás totalmente ionizado. Obtemos seus respectivos gráficos, considerando então um gás ionizado formado a partir do gás de hélio. / We develop a kinetic theory for ionized gases mixtures under the presence of electric and magnetic fields. The laws of Ohm, Fourier and Navier-Stokes are obtained by two different methods based on the Boltzmann equation. We verify that the use of representation theorems makes the Chapman-Enskog method more direct. However the combined method shows up as extremely simple where the transport coefficients are determined through inversion of second-order and fourth order tensors. We calculate also the collision integrals for possible interactions in ionized gases like: between charged particles, between charged particles and neutral particles and between neutral particles. As an application of the combined method, we determine the electrical and thermal conductivity coefficients, thermo-electric and shear viscosity coefficients for a completely ionized gas. We obtain their respective graphics considering an ionized gas of helium.

No description available.

In this dissertation, an experimental and numerical study of dense coarse solids-liquid flows has been performed. The experimental work mainly involved pressure drop measurements in a vertical flow loop. A limited number of measurements of solids velocity profiles were also obtained in the upward flow section of the flow loop. The numerical work involved simulations of coarse particles-in-water flows in vertical and horizontal pipes. The vertical flow simulations were performed using the commercial CFD software, ANSYS CFX-4.4, while ANSYS CFX-10 was used to simulate the flows in the horizontal pipes. The simulations were performed to investigate the applicability of current physically-based models to very dense coarse-particle flows.<p> In the experimental study, measurements of pressure drop and local solids velocity profiles were obtained. The experiments were conducted in a 53 mm diameter vertical flow loop using glass beads of 0.5 mm and 2.0 mm diameter solids for concentration up to 45%. The liquid phase was water. The measured pressure drop exhibited the expected dependence on bulk velocity and solids mean concentration. The wall shear stress was determined by subtracting the gravitational contribution from the measured pressure drop. For flow with the 0.5 mm particles at high bulk velocities, the values of the wall shear stress were essentially similar for each concentration in the upward flow sections but more variation, indicating the effect of concentration, was noted in the downward flow section. At lower bulk velocities, the wall shear stresses with the 0.5 mm glass beads-water flow showed a dependence on concentration in both test sections. This was attributed to an increase in the slip velocity. For the large particle (2.0 mm glass beads), similar observations were made but the effect of concentration was much less in the upward test section. In the downward test section, the wall shear stress for the flow of the 2.0 mm glass beads increased by almost a constant value for the bulk velocities investigated. The solids velocity profiles showed that the solids velocity gradient is large close to the wall. In addition, the solids velocity profiles indicated that the slip velocity increased at lower velocities due to increase in the bulk concentration in the upward flow section.<p> For the vertical flow simulations, different physical models based on the kinetic theory of granular flows were programmed and implemented in ANSYS CFX-4.4. These models, referred to as the kf-ef-ks-es, kf-ef-ks-es-Ts and kf-ef-ks-kfs models, were investigated by focusing on the closure laws for the solids-phase stress. The treatment of the granular temperature Ts depends on whether small- or large-scale fluctuating motion of the particles is considered. The models were implemented via user-Fortran routines. The predicted results were compared with available experimental results. The predicted solids-phase velocity profiles matched the measured data quite well close to the pipe wall but over-predicted it in the core region. The solids concentration, on the other hand, was significantly under-predicted for concentrations higher than 10%. Variations in the predictions of the phasic turbulent kinetic energy and the eddy viscosity were noted; the effect of solids concentration on them was mixed. A general conclusion drawn from the work is that a more accurate model is required for accurate and consistent prediction of coarse particle flows at high concentrations (less than 10%). In a related study, attention was given to wall boundary conditions again focusing on the effect of the solids-phase models at the wall. Comparison between numerical predictions, using some of the existing wall boundary condition models for the solids phase in particulate flows, with experimental results indicated that the physical understanding of the influence of the fluid and solids-phase on each other and their effect on frictional head loss is far from complete. The models investigated failed to reproduce the experimental results. At high solids concentration, it was apparent from the present study that the no-slip and free-slip wall boundary conditions are not appropriate for liquid-solid flows.<p> For the horizontal flow case, three-dimensional simulations were performed with a focus on the velocity and concentration distributions. Medium and coarse sand-in-water flows in three pipe diameters were considered to investigate the default solids stress models in ANSYS CFX-10. Simulations were performed for three cases by considering: 1) no additional solids-phase stress, i.e. no model for Ts; 2) a zero equation, and 3) an algebraic equilibrium model for the granular temperature. The model predictions were compared to experimental results. The effect of particle size, solids-phase concentration, and pipe diameter was explored using the algebraic equilibrium model. All the cases for the models considered exhibited the characteristic features of horizontal coarse particle slurry flows. The zero equation and the algebraic equilibrium model for the granular temperature produced similar results that were not significantly different from the prediction obtained when no solids-phase stress was considered. The comparison with experimental results was mixed. Locally, the measured solids-phase velocity distributions were over-predicted, whereas the solids concentration was reasonably reproduced in the core of all the pipes. The concentration at the bottom and top walls were over-, and under-predicted, respectively. This was attributed to the inappropriate phasic wall boundary condition models available.

In this dissertation, an experimental and numerical study of dense coarse solids-liquid flows has been performed. The experimental work mainly involved pressure drop measurements in a vertical flow loop. A limited number of measurements of solids velocity profiles were also obtained in the upward flow section of the flow loop. The numerical work involved simulations of coarse particles-in-water flows in vertical and horizontal pipes. The vertical flow simulations were performed using the commercial CFD software, ANSYS CFX-4.4, while ANSYS CFX-10 was used to simulate the flows in the horizontal pipes. The simulations were performed to investigate the applicability of current physically-based models to very dense coarse-particle flows.<p> In the experimental study, measurements of pressure drop and local solids velocity profiles were obtained. The experiments were conducted in a 53 mm diameter vertical flow loop using glass beads of 0.5 mm and 2.0 mm diameter solids for concentration up to 45%. The liquid phase was water. The measured pressure drop exhibited the expected dependence on bulk velocity and solids mean concentration. The wall shear stress was determined by subtracting the gravitational contribution from the measured pressure drop. For flow with the 0.5 mm particles at high bulk velocities, the values of the wall shear stress were essentially similar for each concentration in the upward flow sections but more variation, indicating the effect of concentration, was noted in the downward flow section. At lower bulk velocities, the wall shear stresses with the 0.5 mm glass beads-water flow showed a dependence on concentration in both test sections. This was attributed to an increase in the slip velocity. For the large particle (2.0 mm glass beads), similar observations were made but the effect of concentration was much less in the upward test section. In the downward test section, the wall shear stress for the flow of the 2.0 mm glass beads increased by almost a constant value for the bulk velocities investigated. The solids velocity profiles showed that the solids velocity gradient is large close to the wall. In addition, the solids velocity profiles indicated that the slip velocity increased at lower velocities due to increase in the bulk concentration in the upward flow section.<p> For the vertical flow simulations, different physical models based on the kinetic theory of granular flows were programmed and implemented in ANSYS CFX-4.4. These models, referred to as the kf-ef-ks-es, kf-ef-ks-es-Ts and kf-ef-ks-kfs models, were investigated by focusing on the closure laws for the solids-phase stress. The treatment of the granular temperature Ts depends on whether small- or large-scale fluctuating motion of the particles is considered. The models were implemented via user-Fortran routines. The predicted results were compared with available experimental results. The predicted solids-phase velocity profiles matched the measured data quite well close to the pipe wall but over-predicted it in the core region. The solids concentration, on the other hand, was significantly under-predicted for concentrations higher than 10%. Variations in the predictions of the phasic turbulent kinetic energy and the eddy viscosity were noted; the effect of solids concentration on them was mixed. A general conclusion drawn from the work is that a more accurate model is required for accurate and consistent prediction of coarse particle flows at high concentrations (less than 10%). In a related study, attention was given to wall boundary conditions again focusing on the effect of the solids-phase models at the wall. Comparison between numerical predictions, using some of the existing wall boundary condition models for the solids phase in particulate flows, with experimental results indicated that the physical understanding of the influence of the fluid and solids-phase on each other and their effect on frictional head loss is far from complete. The models investigated failed to reproduce the experimental results. At high solids concentration, it was apparent from the present study that the no-slip and free-slip wall boundary conditions are not appropriate for liquid-solid flows.<p> For the horizontal flow case, three-dimensional simulations were performed with a focus on the velocity and concentration distributions. Medium and coarse sand-in-water flows in three pipe diameters were considered to investigate the default solids stress models in ANSYS CFX-10. Simulations were performed for three cases by considering: 1) no additional solids-phase stress, i.e. no model for Ts; 2) a zero equation, and 3) an algebraic equilibrium model for the granular temperature. The model predictions were compared to experimental results. The effect of particle size, solids-phase concentration, and pipe diameter was explored using the algebraic equilibrium model. All the cases for the models considered exhibited the characteristic features of horizontal coarse particle slurry flows. The zero equation and the algebraic equilibrium model for the granular temperature produced similar results that were not significantly different from the prediction obtained when no solids-phase stress was considered. The comparison with experimental results was mixed. Locally, the measured solids-phase velocity distributions were over-predicted, whereas the solids concentration was reasonably reproduced in the core of all the pipes. The concentration at the bottom and top walls were over-, and under-predicted, respectively. This was attributed to the inappropriate phasic wall boundary condition models available.

abstract: Need-based transfers (NBTs) are a form of risk-pooling in which binary welfare exchanges occur to preserve the viable participation of individuals in an economy, e.g. reciprocal gifting of cattle among East African herders or food sharing among vampire bats. With the broad goal of better understanding the mathematics of such binary welfare and risk pooling, agent-based simulations are conducted to explore socially optimal transfer policies and sharing network structures, kinetic exchange models that utilize tools from the kinetic theory of gas dynamics are utilized to characterize the wealth distribution of an NBT economy, and a variant of repeated prisoner’s dilemma is analyzed to determine whether and why individuals would participate in such a system of reciprocal altruism. From agent-based simulation and kinetic exchange models, it is found that regressive NBT wealth redistribution acts as a cutting stock optimization heuristic that most efficiently matches deficits to surpluses to improve short-term survival; however, progressive redistribution leads to a wealth distribution that is more stable in volatile environments and therefore is optimal for long-term survival. Homogeneous sharing networks with low variance in degree are found to be ideal for maintaining community viability as the burden and benefit of NBTs is equally shared. Also, phrasing NBTs as a survivor’s dilemma reveals parameter regions where the repeated game becomes equivalent to a stag hunt or harmony game, and thus where cooperation is evolutionarily stable. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2018

Made available in DSpace on 2014-06-11T19:30:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-03-15Bitstream added on 2014-06-13T21:00:47Z : No. of bitstreams: 1 nova_cv_me_bauru.pdf: 1980542 bytes, checksum: 9aad1da39bf5c30c6e4d38ca0be07fef (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A teoria cinética dos gases tem como primeira aproximação o comportamento observado considerando o gás como tendo um comportamento ideal, isto é, pode ser modelado através da lei do gás ideal. As equações de estado conhecidas, como a equação do gás ideal e de van der Waals descrevem, dentro das aproximações do modelo, situações bastante diversas. Neste trabalho iremos utilizar a lei dos gases ideais, ou mais especificamente a implementação da Equação de van der Waals para o entendimento do fenômeno de colisões que entre átomos e moléculas / The kinetic theory of gases has a a first approximation the observed behavior considering the gas to have an ideal behavior, ie it can be modeled by the ideal bas law. The equations of state known as the ideal gas equation and Van der Waals describe, within the approximations of the model, very different situations. In this paper we use the ideal gas law, or more specifically the implementation of the Vann der Waals equation for understandign the phenomenon of collisions between atoms and molecules