Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2010 / Made available in DSpace on 2012-10-24T22:38:24Z (GMT). No. of bitstreams: 1 282117.pdf: 4037789 bytes, checksum: 27a0af29d5c4ffcce813cbe3959ff1ec (MD5) / Shan e colaboradores (SHAN, X.; YUAN, X.-F.; CHEN, H. "Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation". Journal of Fluid Mechanics, v. 550, p.413-441) e Philippi e colaboradores (PHILIPPI, P. C. et al. "From the continuous to the lattice Boltzmann equation: The discretization problem and thermal models". Physical Review E, v. 73, n. 5, p. 056702), em 2006, reabriram a perspectiva de uso do lattice Boltzmann para a simulação de escoamentos não isotérmicos e/ou a alto número de Knudsen através da resolução direta da equação de Boltzmann ao estabelecerem uma ligação sistemática e consistente entre a Teoria Cinética dos Gases e os métodos de lattice Boltzmann (LBM), determinando condições necessárias para a discretização do espaço de velocidades em diferentes ordens do número de Knudsen. As redes obtidas através do método proposto por eles, de abscissas prescritas, provaram ser estáveis em escoamentos em uma ampla faixa de parâmetros. Levando em consideração que as redes obtidas através deste método aumentaram significativamente o número de velocidades moleculares necessárias para a discretização do espaço de velocidades e os fenômenos físicos descritos por esta formulação possuem grande complexidade, exigindo uma maior quantidade de parâmetros para que os coeficientes de transporte do fluido simulado em várias escalas de Knudsen possam ser corretamente ajustados, diversas adaptações aos LBMs convencionais precisaram ser realizadas. Modelos de colisão a múltiplos tempos de relaxação, adequados ao ajuste dos coeficientes de transporte do fluido simulado, foram propostos. Um modelo de colisão a dois tempos de relaxação será discutido e analisado nesta tese. Do ponto de vista numérico, métodos mais acurados em relação a sua discretização espacial e temporal foram testados com o objetivo de melhorar a representação numérica dos efeitos físicos relacionados a números de Knudsen finitos, de forma que o comportamento do modelo de colisão utilizado fosse representado com mais acurácia, evitando que ele se confundisse com erros numéricos do método de solução. Condições de contorno adequadas à simulação destes escoamentos também tiveram que ser propostas. Seu uso em simulações utilizando diferentes métodos numéricos revela a dificuldade em ajustá-las quando fenômenos em uma escala inferior a da fluidodinâmica são considerados. Todos os métodos propostos foram analisados através da expansão de Chapman-Enskog. O objetivo destas análises foi comparar os métodos numéricos e os modelos de colisão no contínuo teoricamente, prevendo as equações macroscópicas que eles deveriam obedecer em diversas ordens do número de Knudsen. Depois de uma extensa discussão teórica sobre o método de lattice Boltzmann, diversas simulações foram realizadas com o objetivo de testar: i) o efeito que a correta representação de ordens crescentes dos momentos da distribuição de equilíbrio do contínuo no espaço discreto de velocidades possui, ii) a acurácia dos diferentes métodos de diferenças finitas empregados em diversas ordens de Knudsen, iii) a acurácia das análises de Chapman-Enskog realizadas e por fim, iv) a influência das condições iniciais e de contorno na evolução de escoamentos simulados a diversas ordens do número de Knudsen.

This work is focused on the development of a hybrid DSMC/CFD solver to examine hypersonic boundary layer flow over discrete surface roughness. The purpose of these investigations is to identify and quantify the non-equilibrium effects that influence the roughness-induced disturbance field and surface quantities of interest for engineering applications. To this end, a new hybrid framework is developed for high-fidelity hybrid solutions involving five-species air hypersonic boundary layer flow applications. A novel approach is developed for DSMC particle generation at a hybrid interface for gas mixtures with internal degrees of freedom. The appropriate velocity distribution function is formulated in the framework of Generalized Chapman-Enskog Theory, and includes contributions from species mass diffusion, shear stress and heat fluxes (both translational and internal) on the perturbation of the equilibrium distribution function. This formulation introduces new breakdown parameters for use in hybrid DSMC/CFD applications, and the new sampling algorithm allows for the generation of DSMC internal energies from the appropriate non-equilibrium distribution for the first time in the literature. The contribution of the internal heat fluxes to the overall perturbation is found to be of the same order as the stress tensor components, underscoring the importance of DSMC particle generation from the Generalized Chapman-Enskog distribution. A detailed comparison of the transport coefficients is made between the DSMC and CFD solvers, and a general best-fit approach is developed for the consistent treatment of diffusion, viscosity and thermal conductivity for a five-species air gas mixture. The DSMC VHS/VSS model parameters are calibrated through an iterative fitting approach using the Nelder-Mead Simplex Algorithm. The VSS model is found to provide the best fit (within 5% over the temperature range) to the transport models used in the CFD solver. The best-fit five-species air parameters are provided for general use by the DSMC community, either for hybrid applications or to provide improved consistency in general DSMC/CFD applications. This hybrid approach has been applied to examine hypersonic boundary layer flow over discrete surface roughness for a variety of roughness geometries and flow conditions. An (asymmetric) elongated hump geometry and (symmetric) diamond shaped roughness geometry are examined at high and low altitude conditions. Detailed comparisons among the hybrid solution and the CFD no-slip and slip wall solutions were made to examine the differences in surface heating, translational/vibrational non-equilibrium in the flow near the roughness, and the vortex structures in the wake through the Q-criterion. In all cases examined, the hybrid solution predicts a lower peak surface heating to the roughness compared to either CFD solution, and a higher peak surface heating in the wake due to vortex heating. The observed differences in vortex heating are a result of the predicted vortex structures which are highlighted using the Q-criterion. The disturbance field modeled by the hybrid solution organizes into a system of streamwise-oriented vortices which are slightly stronger and have a greater spanwise extent compared to the CFD solutions. As a general trend, it was observed that these differences in the predicted heating by the hybrid and CFD solutions increase with increasing Knudsen number. This trend is found for both peak heating values on the roughness and in the wake. / text

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Mecânica. / Made available in DSpace on 2012-10-20T00:39:29Z (GMT). No. of bitstreams: 1 241551.pdf: 755978 bytes, checksum: 7a86bbf486f9fdec5cc61339710e48c6 (MD5) / O método de Boltzmann para redes tem obtido grande êxito na simulação de problemas hidrodinâmicos à temperatura constante. Entretanto, apesar dos diversos modelos propostos na literatura, este método foi incapaz de descrever escoamentos não isotérmicos de forma satisfatória, devido, principalmente, à presença de instabilidade numérica e de discrepâncias nas equações macroscópicas que descrevem a dinâmica do fluido. Neste contexto, o presente trabalho estuda uma série de modelos derivados como formas discretas da equação de Boltzmann. O estudo compreende uma análise multiescala, de modo a averiguar a concordância entre o comportamento macroscópico dos modelos e as equações de Navier-Stokes, e uma análise da estabilidade linear, com o objetivo de obter os limites de aplicabilidade dos modelos. Por fim, são apresentadas medições numéricas dos coeficientes de transporte, com a finalidade de corroborar os resultados da análise multiescala.

Cette thèse porte sur le développement de modèles multi-échelles et de méthodes de calcul pour les applications aérothermodynamiques. Le travail de recherche sur les modèles multi-échelles met l’accent sur l’excitation énergétique et la dissociation. L’objectif était double : mieux comprendre la dynamique des processus d'excitation énergétique et dissociation et développer des modèles réduits en diminuant la résolution d’un modèle détaillé de collisions rovibrationnelles. Les résultats obtenus ont montré que les modèles réduits permettent de reproduire avec précision la dynamique d’écoulement prédites par le modèle détaillé de collisions rovibrationnelles. Le travail de recherche sur les méthodes de calcul a porté sur les écoulements raréfiés. L’objectif était de formuler une méthode numérique de type déterministe pour résoudre l’équation de Boltzmann dans le cas de gaz à plusieurs composants y compris l’énergie interne. La méthode numérique est basée sur la structure de convolution pondérée de la transformée de Fourier de l’équation de Boltzmann. La précision de la méthode numérique proposée a été évaluée en comparant les moments extraits de la fonction de distribution de vitesse avec les prédictions de la méthode de simulation directe Monte Carlo (DSMC). Dans toutes les applications étudiées, un excellent accord a été trouvé. / This thesis aimed at developing multi-scale models and computational methods for aerother-modynamics applications. The research on multi-scale models has focused on internal energy excitation and dissociation of molecular gases in atmospheric entry flows. The scope was two-fold: to gain insight into the dynamics of internal energy excitation and dissociation in the hydrodynamic regime and to develop reduced models for Computational Fluid Dynamics applications. The reduced models have been constructed by coarsening the resolution of a detailed rovibrational collisional model developed based on ab-initio data for the N2 (1Σ+g)-N (4Su) system provided by the Computational Quantum Chemistry Group at NASA Ames Research Center. Different mechanism reduction techniques have been proposed. Their appli-cation led to the formulation of conventional macroscopic multi-temperature models and vi-brational collisional models, and innovative energy bin models. The accuracy of the reduced models has been assessed by means of a systematic comparison with the predictions of the detailed rovibrational collisional model. Applications considered are inviscid flows behind normal shock waves, within converging-diverging nozzles and around axisymmetric bodies, and viscous flows along the stagnation-line of blunt bodies. The detailed rovibrational colli-sional model and the reduced models have been coupled to two flow solvers developed from scratch in FORTRAN 90 programming language (SHOCKING_F90 and SOLV-ER_FVMCC_F90). The results obtained have shown that the innovative energy bin models are able to reproduce the flow dynamics predicted by the detailed rovibrational collisional model with a noticeable benefit in terms of computing time. The energy bin models are also more accurate than the conventional multi-temperature and vibrational collisional models. The research on computational methods has focused on rarefied flows. The scope was to formu-late a deterministic numerical method for solving the Boltzmann equation in the case of multi-component gases with internal energy by accounting for both elastic and inelastic collisions. The numerical method, based on the weighted convolution structure of the Fourier trans-formed Boltzmann equation, is an extension of an existing spectral-Lagrangian method, valid for a mono-component gas without internal energy. During the development of the method, particular attention has been devoted to ensure the conservation of mass, momentum and en-ergy while evaluating the collision operators. Conservation is enforced through the solution of constrained optimization problems, formulated in a consistent manner with the collisional in-variants. The extended spectral-Lagrangian method has been implemented in a parallel com-putational tool (best; Boltzmann Equation Spectral Solver) written in C programming lan-guage. Applications considered are the time-evolution of an isochoric gaseous system initially set in a non-equilibrium state and the steady flow across a normal shock wave. The accuracy of the proposed numerical method has been assessed by comparing the moments extracted from the velocity distribution function with Direct Simulation Monte Carlo (DSMC) method predictions. In all the cases, an excellent agreement has been found. The computational results obtained for both space homogeneous and space inhomogeneous problems have also shown that the enforcement of conservation is mandatory for obtaining accurate numerical solutions.

Granular materials exist in many forms in nature ranging from space debris to sand dunes and from breakfast cereals to pharmaceutical tablets. They can behave like a solid or a viscous fluid or a gas. The gas-like nature of granular materials in rapid flows allows the use of models based on kinetic theory thus revealing in depth complex physics and phenomena. However unlike conventional fluids here the energy balance requires additional dissipation terms as a consequence of inelasticity. The complexity of their interaction and diversity in application has led to numerous studies using experimental methods and numerical simulations in order to determine the most appropriate constitutive relationships for granular gases. With large dissipation the form of the constitutive relationship becomes particularly important, especially in the presence of non-equipartition and anisotropy. This thesis is focused on constitutive models of simple granular flows. A vibrated bed is often used as an idealisation of granular flows, providing a convenient approximation to the simplest type of flow: binary and instantaneous collisions with no rotations. Using finite element method (FE) based COMSOL modules we solve conservation of mass, momentum and energy resulting from granular kinetic theory in axi-symmetric form to generate time and spatial resolved solutions of packing fraction, velocity and granular temperature and compare the predictions to numerical simulation and experiment. At first we show the comparison for two closure sets, one based on a simple near elastic approach while the second based on revised Enskog theory for dense inelastic flows. The results for the second approach show good agreement with the results of previously validated near elastic models and experimental results. The observed differences between the two closure sets are small except for the observation of temperature upturn in a dilute region of the cell away from base. One cause of this is the presence of additional constitutive terms in the balance equations and are a consequence of inelasticity. The models also consider time varying effects at low frequency of excitation. These solutions show existence of wave-like effects in the cell with associated temperature upturn within the hydrodynamic applicability region. Presence of instantaneous cyclic rolling is also seen in both approaches. Evidence from MD simulations and experiments qualitatively support the findings of hydrodynamic models in phase resolved as well as time average behaviour. Subsequently, the frequency of vibration was varied to unlink the wave motion from the bulk temperature. Lack of agreement between experiment and the model predictions are shown to be due to lack of separation of time scale between the grain-base interaction and the base frequency. A sharp decrease of heat flux is measured showing that the energy input is frequency dependent. Analysis of the bulk behaviour shows that at high frequency, hard sphere based models are able to capture the steady state behaviour reasonably well. Further investigations that modulate the driving with a low frequency amplitude change revealed the dynamic nature of flow with the low frequency component. No significant influence of high frequency signal is noted except the reduction of base heat flux. Independent analysis of bulk behaviour for modulated wave excitation using MD simulations and hydrodynamic models showed wave motion in a pattern similar to non-modulated low frequency vibration. A one-dimensional inviscid model was used to determine the underlying scaling relationships for near elastic granular flows. A form of non-dimensionalisation predicts scaling behaviour for the granular flow. The predictions show good results for the dilute flows using hard sphere MD simulations. Results from MD simulations confirm dilute limit scaling of base temperature, packing fractions and heat flux coefficients. At higher inelasticity and loading condition the model fails to capture the real physics suggesting the need for a more accurate model. This simplified model does, however, set the basis for describing the main scalings for vibrofluidized granular beds, and in the future we anticipate that effects of further inelasticity and enhanced density could be incorporated.

This thesis aimed at developing multi-scale models and computational methods for aerother-modynamics applications. The research on multi-scale models has focused on internal energy excitation and dissociation of molecular gases in atmospheric entry flows. The scope was two-fold: to gain insight into the dynamics of internal energy excitation and dissociation in the hydrodynamic regime and to develop reduced models for Computational Fluid Dynamics applications. The reduced models have been constructed by coarsening the resolution of a detailed rovibrational collisional model developed based on ab-initio data for the N2 (1Σ+g)-N (4Su) system provided by the Computational Quantum Chemistry Group at NASA Ames Research Center. Different mechanism reduction techniques have been proposed. Their appli-cation led to the formulation of conventional macroscopic multi-temperature models and vi-brational collisional models, and innovative energy bin models. The accuracy of the reduced models has been assessed by means of a systematic comparison with the predictions of the detailed rovibrational collisional model. Applications considered are inviscid flows behind normal shock waves, within converging-diverging nozzles and around axisymmetric bodies, and viscous flows along the stagnation-line of blunt bodies. The detailed rovibrational colli-sional model and the reduced models have been coupled to two flow solvers developed from scratch in FORTRAN 90 programming language (SHOCKING_F90 and SOLV-ER_FVMCC_F90). The results obtained have shown that the innovative energy bin models are able to reproduce the flow dynamics predicted by the detailed rovibrational collisional model with a noticeable benefit in terms of computing time. The energy bin models are also more accurate than the conventional multi-temperature and vibrational collisional models. The research on computational methods has focused on rarefied flows. The scope was to formu-late a deterministic numerical method for solving the Boltzmann equation in the case of multi-component gases with internal energy by accounting for both elastic and inelastic collisions. The numerical method, based on the weighted convolution structure of the Fourier trans-formed Boltzmann equation, is an extension of an existing spectral-Lagrangian method, valid for a mono-component gas without internal energy. During the development of the method, particular attention has been devoted to ensure the conservation of mass, momentum and en-ergy while evaluating the collision operators. Conservation is enforced through the solution of constrained optimization problems, formulated in a consistent manner with the collisional in-variants. The extended spectral-Lagrangian method has been implemented in a parallel com-putational tool (best; Boltzmann Equation Spectral Solver) written in C programming lan-guage. Applications considered are the time-evolution of an isochoric gaseous system initially set in a non-equilibrium state and the steady flow across a normal shock wave. The accuracy of the proposed numerical method has been assessed by comparing the moments extracted from the velocity distribution function with Direct Simulation Monte Carlo (DSMC) method predictions. In all the cases, an excellent agreement has been found. The computational results obtained for both space homogeneous and space inhomogeneous problems have also shown that the enforcement of conservation is mandatory for obtaining accurate numerical solutions.

This thesis is concerned with the new formulation of a finite-volume lattice Boltzmann equation method and its implementation on unstructured meshes. The finite-volume discretization with a cell-centered tessellation is employed. The new formulation effectively adopts a total variation diminishing concept. The formulation is analyzed for the modified partial differential equation and the apparent viscosity of the model. Further, the high-order extension of the present formulation is laid out. Parallel simulations of a variety of two-dimensional benchmark flows are carried out to validate the formulation. In Chapter 1, the important notions of the kinetic theory and the most celebrated equation in the kinetic theory, ‘the Boltzmann equation’ are given. The historical developments and the theory of a discrete form of Boltzmann equation are briefly discussed. Various off-lattice schemes are introduced. Various methodologies adopted in the past for the solution of the lattice Boltzmann equation on finite-volume discretization are reviewed. The basic objectives of this thesis are stated. In Chapter2,the basic formulations of lattice Boltzmann equation method with a rational behind different boundary condition implementations are discussed. The benchmark flows are studied for various flow phenomenon with the parallel code developed in-house. In particular, the new benchmark solution is given for the flow induced inside a rectangular, deep cavity. In Chapter 3, the need for off-lattice schemes and a general introduction to the finite-volume approach and unstructured mesh technology are given. A new mathematical formulation of the off-lattice finite-volume lattice Boltzmann equation procedure on a cell-centered, arbitrary triangular tessellation is laid out. This formulation employs the total variation diminishing procedure to treat the advection terms. The implementation of the boundary condition is given with an outline of the numerical implementation. The Chapman-Enskog (CE) expansion is performed to derive the conservation equations and an expression for the apparent viscosity from the finite-volume lattice Boltzmann equation formulation in Chapter 4. Further, the numerical investigations are performed to analyze the apparent viscosity variation with respect to the grid resolution. In Chapter 5, an extensive validation of the newly formulated finite-volume scheme is presented. The benchmark flows considered are of increasing complexity and are namely (1) Posieuille flow, (2) unsteady Couette flow, (3) lid-driven cavity flow, (4) flow past a backward step and (5) steady flow past a circular cylinder. Further, a sensitivity study to the various limiter functions has also been carried out. The main objective of Chapter6is to enhance the order of accuracy of spatio-temporal calculations in the newly presented finite-volume lattice Boltzmann equation formulation. Further, efficient implementation of the formulation for parallel processing is carried out. An appropriate decomposition of the computational domain is performed using a graph partitioning tool. The order-of-accuracy has been verified by simulating a flow past a curved surface. The extended formulation is employed to study more complex unsteady flows past circular cylinders. In Chapter 7, the main conclusions of this thesis are summarized. Possible issues to be examined for further improvements in the formulation are identified. Further, the potential applications of the present formulation are discussed.

No description available.

La thèse porte sur les propriétés thermodynamiques, de transport, de diffusion de rayonnement, et diélectriques des mélanges CO2-N2 contaminés par du cuivre, pour des températures de 300 - 30,000 K et des pressions 0.1 - 16 bar. Les motivations de ce travail ainsi qu'un état de l'art sur le remplacement du SF6 et l'influence des vapeurs métalliques dans de tels dispositifs sont présentés dans le chapitre 1. Le chapitre 2 étudie les compositions à l'équilibre calculées à partir de la méthode de minimisation de l'énergie libre de Gibbs, en considérant la présence de phases condensées dans le plasma. A partir de ces compositions, nous présentons les propriétés thermodynamiques comme la densité de masse, l'enthalpie et la chaleur spécifiques à pressions constante. Les corrections de Virial et Debye-Hückel sont prises en compte pour tenir compte de l'effet des ions et des hautes pressions. Dans le chapitre 3, les coefficients de transport (conductivité électrique, viscosité, et conductivité thermique) et les coefficients de diffusion combinés (coefficients de diffusion ordinaires combinés, ceux liés au champ électrique, aux gradients de pression et de température) sont calculés selon la théorie de Chapman-Enskog. Les intégrales de collision nécessaires au calcul de ces coefficients sont obtenues pour les interactions neutre-neutre et neutre-ion à partir d'un potentiel de Lennard-Jones modifié. Dans le chapitre 4, les coefficients d'émission nette (CEN) sont calculés en considérant le rayonnement des raies atomiques, du continuum atomique, des raies moléculaires et du continuum moléculaire. Les élargissements en pression des raies (élargissements de Van der Waals et de résonance), les élargissements Stark, et l'élargissement sont pris en compte dans la détermination d'un facteur de fuite qui permet de simplifier le calcul du coefficient d'émission des raies. Le rayonnement du continuum atomique tient compte de l'attachement radiatif, de la recombinaison radiative et du Bremsstrahlung. Dans le chapitre 5, les propriétés diélectriques de claquage (incluant la fonction de distribution d'énergie des EEDF), le coefficient réduit d'ionisation réduit, le coefficient réduit d'attachement électronique, le coefficient effectif réduit d'ionisation, et le champ critique réduit) du gaz chaud ont été calculés sur la base de l'approximation à deux termes de l'équation de Boltzmann. Les interactions, incluant les collisions élastiques, excitation, ionisation et attachement entre électrons et espèces neutres sont pris en compte dans la résolution de l'équation de Boltzmann. Les sections efficaces d'ionisation de Cu2 et CuO non disponibles dans la littérature ont été calcules selon la méthode DM. La conclusion des travaux et leurs perspectives sont présentés dans le chapitre. / Sulfur hexafluoride (SF6) is a greenhouse gas designated by the Kyoto Protocol because of its extremely high global warming potential (GWP). CO2, N2, and their mixtures have the potential to replace SF6 in certain applications, such as circuit breakers. In these electric apparatus, copper vapour resulting from the heating of electrodes can modify the characteristics of arc plasmas, which must be taken into account when setting up physical models. This dissertation, therefore, investigates the thermodynamic, transport, diffusion, radiation, and dielectric breakdown properties of CO2-N2 mixtures contaminated by copper at temperatures of 300 - 30,000 K and pressures of 0.1 - 16 bar. The equilibrium compositions are calculated using the minimization of Gibbs free energy with consideration of condensed species. Copper vapour is found to condense at temperatures below 3000 K. Based on the compositions, the thermodynamic properties, including mass density, specific enthalpy, and specific heat at constant enthalpy, are determined according to their definitions. The Debye-Hückel corrections are also considered in the calculation of compositions and thermodynamic properties. The transport coefficients (including electrical conductivity, viscosity, thermal conductivity) and combined diffusion coefficients (including the combined ordinary diffusion coefficient, combined electric field diffusion coefficient, combined temperature diffusion coefficient and combined pressure diffusion coefficient) are calculated based on the Chapman-Enskog theory. The newly developed Lennard-Jones like phenomenological model potential is adopted to describe the neutral-neutral and neutral-ion interactions in determining collision integrals. The net emission coefficients (NEC) of gas mixtures are calculated with considering atomic lines and continuum and molecular bands and continuum. The pressure broadening (Van der Waals broadening and the resonance broadening), Stark broadening, and Doppler broadening are taken into account in the determination of escape factors. The continuum radiation of atoms is described by radiative attachment, radiative recombination, and Bremsstrahlung. The dielectric breakdown properties (including EEDF, reduced ionization coefficient, reduced electron attachment coefficient, reduced effective ionization coefficient, and reduced critical electric field strength) of hot gas mixtures are calculated based on the two-term approximation of the Boltzmann equation. The interactions, including elastic, excitation, ionization and attachment collisions, between electrons and neutral species are taken into account in solving the Boltzmann equation. The ionization cross sections of Cu2 and CuO which are unavailable in literatures are calculated using the DM method. Compared with SF6-Cu mixtures, CO2-N2-Cu mixtures present much different thermophysical, radiation, and dielectric breakdown properties. As an arc quenching gas, CO2-N2-Cu mixtures have lower ??Cp and thermal conductivity at low temperatures but present higher ??Cp, thermal conductivity, and NEC in the medium temperature range. As an insulating medium, the hot CO2-N2-Cu mixtures have much poorer dielectric strength below 2000 K, whereas above 2000 K, they present better dielectric breakdown performance than SF6-Cu mixtures.

The main objective of this thesis is to study the fundamental behaviour of multi-component gas mixture flows in micro/nano-channels undergoing catalytic chemical reactions on the walls. This work is primarily focused on nano-scale reacting flows seen in related applications; especially, miniaturized energy sources such as micro-fuel cells and batteries. At these geometries, the order of the characteristic length is close to the mean free path of the flowing gas, making the flow highly rarefied. As a result, non-equilibrium conditions prevail even the bulk flow and therefore, continuum assumptions are not held anymore. Hence, discrete methods should be adopted to simulate molecular movements and interactions described by the Boltzmann equation. The Direct Simulation Monte Carlo (DSMC) method was employed for the present research due to its natural ability for simulating a broad range of rarefied gas flows, and its flexibility to incorporate surface chemical reactions. In the first step, fluid dynamics and the heat transfer of H₂/N₂ and H₂/N₂/CO₂ gas mixture slip flows in a plain micro-channel are simulated. The obtained results are compared to the corresponding data achieved from Navier-Stokes equations with slip/jump boundary conditions. Generally, very good agreements are observed between the two methods. It proves the ability of DSMC in replicating the fluid properties of multi-component gas mixtures even when high mass discrepancies exist among the species. Based on this comparison, the proper parameters are set for the prepared DSMC code, and the appropriate intermolecular collision model is identified. It is also found that stream variables should be calculated more accurately at flow boundaries in order to simulate the intense upstream diffusion emerging at low velocity flows frequently seen in micro/nano-applications. Therefore, in the second step, a novel pressure boundary condition is introduced for gas mixture flows by substituting the commonly used Maxwell velocity distribution with the Chapman-Enskog distribution function. It is shown that this new method yields better results for lower velocity and higher rarefaction level cases. In the last step, a new method is proposed for coupling the flow field simulated by DSMC and surface reactions modelled by the species conservation ODE system derived from the reaction mechanism. First, a lean H₂/air slip flow subjected to oxidation on platinum coated walls in a flat micro-channel 4μm in height is simulated as a verification test case. The results obtained are validated against the solutions of the Navier-Stokes equations with slip/jump boundary conditions and very good conformity is achieved. Next, several cases undergoing the same reaction with Reynolds numbers ranging from 0.2 to 3.6 and Knudsen numbers ranging from 0.025 to 0.375, are simulated using the verified code to investigate the effects of the channel height ranging from 0.5μm to 2μm , the inlet mass flow rate ranging from 5 kg/m².s to 25 kg/m².s, the inlet temperature ranging from 300K to 700K, the wall temperature ranging from 300K to 1000K, and the fuel/air equivalence ratio ranging from 0.28 to 1.5. Some of the findings are as follows: (1) increasing the surface temperature from 600K to 1000K and/or the inlet temperature from 300K to 700K results in negligible enhancement of the conversion rate, (2) the optimum value of the equivalence ratio is on the fuel lean side (around 0.5), (3) the efficiency of the reactor is higher for smaller channel heights, and (4) increasing the inlet mass flux elevates the reaction rate especially for the smaller channels; this effect is not linear and is more magnified for lower mass fluxes.