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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
71

Contribution à la description théorique de la dynamique des processus élémentaires hétérogènes : collisions de l'azote moléculaire et de l'hydrogène atomique avec des surfaces de tungstène / Theoretical study of gas-solid elementary processes dynamics : collision of molecular nitrogen and atomic hydrogen with tungsten

Petuya-Poublan, Rémi 17 September 2014 (has links)
Les processus élémentaires hétérogènes à l’interface gaz-solide présentent un intérêt fondamental dans de nombreux domaines tels que la catalyse hétérogène, la chimie atmosphérique et des milieux interstellaires, la rentrée atmosphérique de véhicules spatiaux ou encore la description des interactions plama-paroi. Cette thèse a pour objet l’étude de la dynamique des processus de collision non réactive de l’azote N2 sur une surface de tungstène W(100) et des processus de recombinaison moléculaire de l’hydrogène H2 sur des surfaces de tungstène W(100) et W(110). Leur dynamique quasi classique est simulée au moyen de surfaces d’énergie potentielle préalablement construites à partir de calculs de théorie de la fonctionnelle de la densité. Un potentiel multi-adsorbats est notamment développé pour tenir compte du taux de couverture de surface afin d’étudier la compétition entre la recombinaison directe, de type Eley-Rideal et la recombinaison par « atomes chauds » après diffusion hyperthermique d’un atome sur la surface. / Heterogeneous elementary processes at the gas-solid interface are ofgreat interest in many domains such as heterogeneous catalysis, atmospheric and interstellar media chemistry, spacecraft atmospheric re-entry and plasma-wall interactions description. This thesis focus on the dynamics of nitrogen, N2, non reactive scattering on a tungsten W(100) surface and hydrogen, H2, recombination processes on tungsten surfaces W(100) and W(110). The quasiclassical dynamics of these processes is simulated using potential energy surfaces based on density functional theory calculations. In particular, a multi-adsorbate potential is developed to include surface coverage in the dynamics simulation in order to scrutinize the interplay between both direct abstraction, the so-called Eley-Rideal recombination,and the Hot-Atom recombination process after hyperthermal diffusion on the surface
72

高温・加圧型熱重量分析装置の開発研究

松田, 仁樹, 板谷, 義紀, 渡辺, 藤雄, 武田, 詔平, 前田, 幸雄 03 1900 (has links)
科学研究費補助金 研究種目:基盤研究(A)(1) 課題番号:07555545 研究代表者:松田 仁樹 研究期間:1995-1996年度
73

Simulation of heat conduction and soot combustion in diesel particulate filter

Nakamura, Masamichi, Yamamoto, Kazuhiro January 2012 (has links)
No description available.
74

Modification of Carbonaceous Materials with Sulfur and Its Impact on Mercury Capture and Sorbent Regenertion

Morris, Eric Adde 16 August 2013 (has links)
Physical activation of oil-sands fluid coke, a dense carbonaceous material, using sulfur dioxide (SO2) was investigated as a means of utilizing a plentiful and inexpensive waste for elemental mercury (Hg) removal. A new model was developed to elucidate physical activation of dense carbonaceous materials. Experiments and model simulations revealed that, during activation with SO2, a sulfur-rich porous layer is formed around the periphery of the coke particles; this porous layer reaches a maximum thickness as a result of diffusion limitations; the maximum porous layer thickness is controlled by activation conditions and determines the maximum achievable specific surface area (SSA). Pre-oxidation in air prior to activation, acid washing after activation and smaller coke particle size all result in higher SSA. The highest SSA achieved was 530 m2/g, the highest yet found for oil-sands fluid coke with physical activation. If present, oxygen out-competed SO2 for carbon during activation. SO2 activation and porous layer formation did not occur until oxygen was depleted. Sulfur added to coke through SO2 activation is mainly in reduced forms which are more thermally stable than elemental sulfur in commercial sulfur-impregnated activated carbons (SIACs). TGA and elemental analyses revealed that only 17% of sulfur was removed at 800°C from SO2-activated coke under inert conditions, compared with 100% from a commercial SIAC. The role of sulfuric acid (H2SO4) in vapor Hg capture by activated carbon (AC) was studied due to conflicting findings in the recent literature. In the absence of other oxidizing species, it was found that Hg could be oxidized by oxygen which enhanced vapor Hg adsorption by AC and Hg absorption in H2SO4 solution at room and elevated temperatures. At 200°C, AC treated with 20% H2SO4 reached a Hg loading of more than 500 mg/g, which is among the highest Hg capacities yet reported. When oxygen was not present, S6+ in H2SO4 was found to act as an oxidizer of Hg, thus enabling Hg uptake by H2SO4-treated AC at 200°C. Treating the AC with SO2 at 700°C improved the initial rate of Hg uptake, with and without subsequent H2SO4 treatment.
75

Modification of Carbonaceous Materials with Sulfur and Its Impact on Mercury Capture and Sorbent Regenertion

Morris, Eric Adde 16 August 2013 (has links)
Physical activation of oil-sands fluid coke, a dense carbonaceous material, using sulfur dioxide (SO2) was investigated as a means of utilizing a plentiful and inexpensive waste for elemental mercury (Hg) removal. A new model was developed to elucidate physical activation of dense carbonaceous materials. Experiments and model simulations revealed that, during activation with SO2, a sulfur-rich porous layer is formed around the periphery of the coke particles; this porous layer reaches a maximum thickness as a result of diffusion limitations; the maximum porous layer thickness is controlled by activation conditions and determines the maximum achievable specific surface area (SSA). Pre-oxidation in air prior to activation, acid washing after activation and smaller coke particle size all result in higher SSA. The highest SSA achieved was 530 m2/g, the highest yet found for oil-sands fluid coke with physical activation. If present, oxygen out-competed SO2 for carbon during activation. SO2 activation and porous layer formation did not occur until oxygen was depleted. Sulfur added to coke through SO2 activation is mainly in reduced forms which are more thermally stable than elemental sulfur in commercial sulfur-impregnated activated carbons (SIACs). TGA and elemental analyses revealed that only 17% of sulfur was removed at 800°C from SO2-activated coke under inert conditions, compared with 100% from a commercial SIAC. The role of sulfuric acid (H2SO4) in vapor Hg capture by activated carbon (AC) was studied due to conflicting findings in the recent literature. In the absence of other oxidizing species, it was found that Hg could be oxidized by oxygen which enhanced vapor Hg adsorption by AC and Hg absorption in H2SO4 solution at room and elevated temperatures. At 200°C, AC treated with 20% H2SO4 reached a Hg loading of more than 500 mg/g, which is among the highest Hg capacities yet reported. When oxygen was not present, S6+ in H2SO4 was found to act as an oxidizer of Hg, thus enabling Hg uptake by H2SO4-treated AC at 200°C. Treating the AC with SO2 at 700°C improved the initial rate of Hg uptake, with and without subsequent H2SO4 treatment.
76

S?ntese e caracteriza??o de CuNb2O6 e CuNbC atrav?s de rea??o s?lido- s?lido e g?s- s?lido a baixa temperatura / Synthesis and characterization of CuNb2O6 and CuNbC through reaction solid-solid and gas-solid low temperature

Souto, Maria Veronilda Macedo 31 October 2013 (has links)
Made available in DSpace on 2014-12-17T14:07:15Z (GMT). No. of bitstreams: 1 MariaVMS_Parcial.pdf: 533267 bytes, checksum: dfba6ad9f2b0c2ad0d26dac46721fabf (MD5) Previous issue date: 2013-10-31 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The refractory metal carbides have proven important in the development of engineering materials due to their properties such as high hardness, high melting point, high thermal conductivity and high chemical stability. The niobium carbide presents these characteristics. The compounds of niobium impregnated with copper also have excellent dielectric and magnetic properties, and furthermore, the Cu doping increases the catalytic activity in the oxidation processes of hydrogen. This study aimed to the synthesis of nanostructured materials CuNbC and niobium and copper oxide from precursor tris(oxalate) oxiniobate ammonium hydrate through gas-solid and solid-solid reaction, respectively. Both reactions were carried out at low temperature (1000?C) and short reaction time (2 hours). The niobium carbide was produced with 5 % and 11% of copper, and the niobium oxide with 5% of copper. The materials were characterized by X-Ray Diffraction (XRD), Rietveld refinement, Scanning Electron Microscopy (SEM), X-Ray Fluorescence Spectroscopy (XRF), infrared spectroscopy (IR), thermogravimetric (TG) and differential thermal analysis (DTA , BET and particle size Laser. From the XRD analysis and Rietveld refinement of CuNbC with S = 1.23, we observed the formation of niobium carbide and metallic copper with cubic structure. For the synthesis of mixed oxide made of niobium and copper, the formation of two distinct phases was observed: CuNb2O6 and Nb2O5, although the latter was present in small amounts / Os carbetos de metais refrat?rios t?m se revelado importantes no desenvolvimento de materiais de engenharia devido as suas propriedades, tais como: alta dureza, alto ponto de fus?o, alta condutividade t?rmica e alta estabilidade qu?mica. O carbeto de ni?bio apresenta essas caracter?sticas. Os compostos de ni?bio impregnados com cobre tamb?m possuem excelentes propriedades diel?tricas e magn?ticas e, al?m disso, a dopagem com Cu aumenta a atividade catal?tica em processos de oxida??o de hidrog?nio. Este trabalho teve como objetivo a s?ntese dos materiais CuNbC e ?xido de ni?bio e cobre nanoestruturados a partir do precursor tris(oxalato)oxiniobato de am?nio hidratado, atrav?s de rea??o g?s-s?lido e s?lido-s?lido, respectivamente. Para ambos, as rea??es foram realizadas a baixa temperatura (1000?C) e curto tempo de rea??o (2 horas). O carbeto de ni?bio foi produzido com 5% e 11% de cobre e o ?xido de ni?bio e cobre com 5% de cobre. Os materiais obtidos foram caracterizados atrav?s dos ensaios de Difra??o de Raios X (DRX), Refinamento Rietveld, Microscopia Eletr?nica de Varredura (MEV), Espectroscopia por Fluoresc?ncia de Raios-X (FRX), Espectroscopia de Infravermelho (IV), Termogravim?trica (TG), An?lise Termodiferencial (DTA), BET e granulometria a Laser. A partir das an?lises de DRX e do refinamento Reitiveld para o CuNbC com S= 1,23, observou-se a forma??o do carbeto de ni?bio e cobre puro com estrutura c?bica. Na s?ntese realizada do ?xido misto de ni?bio e cobre correu a forma??o de duas fases distintas: CuNb2O6 e Nb2O5, embora a ?ltima tenha sido formada em pequena quantidade / 2020-01-01
77

Efeitos numéricos na simulação de escoamentos gás-sólido em leito fuidizado borbulhante utilizando a teoria cinética dos escoamentos granulares

Souza, Meire Pereira de [UNESP] 12 January 2009 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:26:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-01-12Bitstream added on 2014-06-13T20:54:32Z : No. of bitstreams: 1 souza_mp_me_bauru.pdf: 1121017 bytes, checksum: 8ed8fe65e5cd46111ec16064bc42b009 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho desenvolve-se um estudo de modelagem matemática e simulação numérica do escoamento bifásico gás-sólido em leito fluidizado borbulhante. Utiliza-se o modelo Euleriano de duas fases separadas formulando o tensor das tensões da fase sólida através da teoria cinética dos escoamentos granulares. As simulações numéricas são realizadas através do código fonte MFIX (Multiphase Flow with Interphase eXchanges) desenvolvido no NETL (National Energy Technology Laboratory). Os resultados de simulação numérica são avaliados por meio da análise da influência dos seguintes parâmetros: malha computacional e esquemas de discretização dos termos convectivos das equações de conservação. Com base nos estudos teóricos e resultados obtidos durante o trabalho conclui-se que esquemas de primeira, tais como FOUP são altamente difusivos, já os resultados obtidos utilizando o esquema de alta ordem, Superbee, produziu resultados de melhor qualidade para as malhas testadas neste trabalho. Além disso, os resultados mostraram-se bastante dependentes do tamanho da malha computacional. / In the present work is described a mathematical model and numerical simulation of gas-solid two-phase flow in a bubbling fluidized bed. It is used the Eulerian gas-solid two-fluid model and the solid phase stress tensor is modeled considering the kinetic theory of granular flows. The numerical simulations were developed using the MFIX (Multiphase Flow with Interphase eXchanges) code developed in NETL (National Energy Technology Laboratory). The numerical diffusion is analyzed considering a single bubbling detachment and its movement process in a two-dimensional bubbling fluidized bed using the bubble shape as a metric for results description. The influence of computacional grid it is also analyzed. It is concluded that SuperBee scheme produces the better results and analysis about estimating uncertainty in grid refinement should be studied.
78

Dinâmica das partículas em leito fluidizado circulante / Particle phase dynamics in a circulating fluidized bed riser

Utzig, Jonathan 19 August 2016 (has links)
CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico / A presente tese e voltada à investigação da dinâmica das partículas em um riser de leito fluidizado circulante (CFB). Os leitos fluidizados sao comumente encontrados em aplicações de diversas areas industriais, como na secagem e revestimento de partículas, na polimerizaçao, na combustao e gaseificacao de carvão ou biomassa, no craqueamento catalítico de gasóleo. Dada a importancia da compreensão fenomenologica dos mecanismos que ocorrem nestes equipamentos, este trabalho utiliza de experimentacães física material e numerica para investigar, descrever e prever o escoamento gas-solido ascendente em escala piloto. Para isso, a Unidade Piloto de Riser e Ciclones foi projetada e construída, bem como seu controle e sistema de medicão optica, a Anemometria por Efeito Doppler (PDA). O escoamento tambem foi avaliado por Fluidodinamica Computacional, como um segundo pilar sobre o qual a presente tese esta suportada, atraves da solucao de um modelo matematico euleriano-lagrangeano transiente de partícula pontual, que considera colisães entre partículas e delas com paredes rugosas do riser, implementado no codigo UNSCYFL3D. Os resultados de ambas simulacoes física material e numerica dos estudos de caso propostos, evidenciaram a formaçcaão de estruturas de macro e mesoescala, derivadas de efeitos geometricos e fluido dinâmicos, respectivamente. Ocorre segregacao do escoamento da fase sólida na base do riser e recirculacao no topo, devido a saída em T. A PDA evidenciou: a formacao da estrutura core-annulus desde a alimentacao das partículas nos maiores carregamentos, a tendâencia de segregaçcãao radial e axial de diametros de partículas e a deposiçao nas regioes próximas à parede, onde as partículas tem maior flutuacao de velocidade. As soluçoes numericas indicaram pouca influencia das forcas de Saffman e Magnus, porem grande influencia da rugosidade da parede e do efeito da turboforese. O modelo matematico foi comparado frente as mediçoes físicas, mostrando bom grau de validacao para concentraçao de partículas no centro do riser e para velocidade axial media das partículas. / This thesis is focused on the particle phase dynamics in a circulating fluidized bed riser (CFB). Fluidized beds are commonly encountered in many industrial applications such as drying and coating of particles, polimerizations, combustion and gasification of coal and biomass, gasoil fluid catalytic cracking. Given the importance of the physical understanding about CFBs, in this work experiments and simulations are carried out to explore, describe and predict the upward gas-solid flow in pilot scale. Therefore, the Pilot Unit of Riser and Cyclones was designed and built, as well as its control and optical measuring systems, the last one by using Phase Doppler Anemometry (PDA). Besides that, the flow was solved by Computational Fluid Dynamics, as the second pillar on which this thesis is based, through the solution of an Eulerian-Lagrangian unsteady point-particle model, with inter-particles collisions and impact on rough walls, implemented on the in-house code UNSCYFL3D. The results from both experiments and simulations have shown the macro- and meso-scale structures formation, caused by geometrical and fluid dynamics effects, respectively. Particle phase flow segregation occurs near the particle inlet and also recirculation at the top of the riser, due to the T shape outlet. The PDA results show the core-annulus structure formation from the bottom of the riser in the higher mass loadings, the tendency of radial and axial segregation of particle diameters and the particle deposition near the riser wall, where the discrete phase has higher velocity fluctuations. On the other hand, the simulation results show little influence of Saffman and Magnus forces over the particles flow, however great impact of the roughness wall model and of the turbophoresis effect. About the model validation, good agreement is found mainly to particle concentration at the riser centre and to the particle phase axial velocity. / Tese (Doutorado)
79

Effects of inter particle friction on the meso-scale hydrodynamics of dense gas-solid fluidized flows / Efeitos da fricção inter-partículas na hidrodinâmica de meso-escala de escoamentos gás-sólido fluidizados densos

Seyed Reza Amini Niaki 21 November 2018 (has links)
Gas-solid fluidized bed reactors are widely applied in chemical and energy industries, and their design and scale-up are virtually empirical, extremely expensive and time consuming. This scenario has motivated the development of alternative theoretical tools, and two-fluid modeling, where gas and particulate are both treated as interpenetrating continuum phases, has appeared as a most promising approach. Owing to the large domains to be resolved in real-scale fluidized bed reactors, only filtered modeling approaches are feasible, and closure models become necessary to recover sub-grid effects that are filtered by the very coarse numerical grids that are imposed owing to computational limitations. Those closure models, which in hydrodynamic formulations account for filtered interphase momentum exchanges and filtered and residual stresses in the phases, can be derived from results of highly resolved simulations (HRS) performed over small size domains under refined numerical grids. One widely practiced approach consists of applying two-fluid modeling under micro-scale defined closures, generally known as microscopic two-fluid modeling. This approach includes microscopic closures for solid phase stresses derived from the kinetic theory of granular flows (KTGF), which accounts for kinetic-collisional effects only, and is adequate to dilute flows. Otherwise, the conventional KTGF does not account for interparticle friction effects, and its application to dense flow conditions is quite questionable. In this work a literature available modified version of KTGF is applied which also accounts for interparticle friction, and highly resolved simulations are performed for dense flow conditions in order to evaluate the effects of friction over relevant filtered parameters (namely effective drag coefficient, filtered and residual stresses). Ranges of domain average solid volume fractions and gas Reynolds numbers are considered (macro-scale conditions) embracing dense gas-solid fluidized flows from suspensions up to pneumatic transport. The MFIX open source code is used in all the simulations, which are performed over 2D periodical domains for a unique monodisperse particulate. The HRS results (i.e. meso-scale flow fields) are filtered over regions compatible with grid sizes in large scale simulations, and the relevant filtered parameters of concern are derived and classified by ranges of other filtered parameters taken as independent variables (filtered solid volume fraction, filtered slip velocity, and filtered kinetic energy of solid velocity fluctuations, which are referred to as markers). Results show that the relevant filtered parameters of concern are well correlated to all of those filtered markers, and also to all of the imposed macro-scale conditions. Otherwise, interparticle friction showed no significant effects over any filtered parameter. It is recognized that this issue clearly requires further investigation notably regarding the suitability of the markers that were assumed for classifying the filtered results. The current work is intended as a contribution for future developments of more accurate closure models for large scale simulations of gas-solid fluidized flows. / Reatores de leito fluidizado de escoamento gás-sólido são largamente utilizados nas indústrias química e de energia, e o seu projeto e escalonamento são virtualmente empíricos, extremamente caros e demorados. Este cenário tem motivado o desenvolvimento de ferramentas teóricas alternativas, e a modelagem de dois fluidos, onde gás e particulado são ambos tratados com fases contínuas interpenetrantes, tem surgido como uma aproximação muito promissora. Devido aos grandes domínios a serem resolvidos em reatores de leito fluidizado de escala real, apenas aproximações de modelagem filtradas são viáveis, e modelos de fechamento tornam-se necessários para recuperar efeitos sub-malha que são filtrados pelas malhas numéricas grosseiras que são impostas devido as limitações computacionais. Estes modelos de fechamento, que em formulações hidrodinâmicas respondem principalmente por trocas de momentum filtradas entre fases e tensões filtradas e residuais nas fases, podem ser obtidos de resultados de simulações altamente resolvidas (SAR) realizadas em domínios de dimensões reduzidas sob malhas numéricas refinadas. Uma aproximação largamente praticada consiste na aplicação de modelagem de dois fluidos sob fechamentos definidos na micro-escala, genericamente conhecida como modelagem microscópica de dois fluidos. Esta aproximação inclui fechamentos microscópicos para tensões da fase sólida obtidos da teoria cinética dos escoamentos granulares (TCEG), que considera apenas efeitos cinéticos-colisionais, e é adequada para escoamentos diluídos. Por outro lado, a TCEG convencional não leva em conta efeitos de fricção interpartículas, e sua aplicação para condições densas de escoamento é bastante questionável. Neste trabalho aplica-se uma versão modificada da TCEG disponível na literatura que também leva em conta fricção interpartículas, e simulações altamente resolvidas são realizadas para condições de escoamentos densos visando avaliar os efeitos da fricção sobre os parâmetros filtrados relevantes (coeficiente de arrasto efetivo, tensões filtradas e residuais). Considera-se faixas de frações volumétricas de sólido e números de Reynolds do gás médios no domínio (condições de macro-escala) abrangendo escoamentos gás-sólido fluidizados densos desde suspensões até transporte pneumático. O código aberto MFIX é utilizado em todas as simulações, que foram executadas sobre domínios periódicos 2D para um único particulado monodisperso. Os resultados das SAR (i.e., campos de escoamento de meso-escala) foram filtrados sobre regiões compatíveis com tamanhos de malha praticados em simulações de grandes escalas, e os parâmetros filtrados relevantes de interesse são calculados e classificados por faixas de outros parâmetros filtrados tomados como variáveis independentes (fração volumétrica de sólido filtrada, velocidade de deslizamento filtrada, e energia cinética das flutuações de velocidade da fase sólida filtrada, que são referidos como marcadores). Os resultados mostram que os parâmetros filtrados relevantes de interesse são bem correlacionados com todos os marcadores, e também com todas as condições de macro-escala impostas. Por outro lado, a fricção interpartículas não mostrou efeitos significativos sobre qualquer parâmetro filtrado. Reconhece-se que este aspecto claramente requer investigações adicionais, notadamente com respeito à adequação dos marcadores que foram considerados para classificação dos resultados filtrados. O trabalho corrente é posto como uma contribuição para o desenvolvimento futuro de modelos de fechamento mais acurados para simulações de grandes escalas de escoamentos gás-sólido fluidizados.
80

Modelagem do particulado em sistemas gás-sólido utilizando o modelo de dois fluidos e o método dos elementos discretos / Study of the dynamic in gas-solid systems using the two-fluid model and the Discrete Element Method

Meire Pereira de Souza Braun 04 July 2013 (has links)
A presente pesquisa tem como objetivo realizar um estudo teórico e desenvolver simulações computacionais envolvendo a dinâmica de sistemas gás-sólido. O foco principal do trabalho é a modelagem do particulado através da análise das forças de contato entre partículas de materiais granulares utilizando modelos contínuos baseados na mecânica dos solos e na teoria cinética dos escoamentos granulares (sistemas grandes com muitas partículas, formulação Euleriana - Volumes Finitos) e modelos discretos baseados nas características físicas dos materiais (sistemas intermediários e número limitado de partículas, formulação Lagrangeana - Método dos Elementos Discretos). Investigam-se os modelos existentes na literatura com intuito de melhorar os modelos contínuos e discretos baseados na interação entre as partículas que caracterizam a dinâmica do particulado em sistemas gás-sólido. Propõe-se uma nova abordagem para a determinação do coeficiente de rigidez da mola baseada em uma equivalência entre os modelos lineares e não-lineares. Utiliza-se o código fonte MFIX para realizar simulações computacionais da dinâmica de sistemas gás-sólido, analisando o processo de fluidização, mistura e segregação de partículas, influência das correlações de arrasto, e análise das forças de contato entre as partículas através do novo método para a determinação do coeficiente de rigidez da mola . Os resultados obtidos são comparados com dados numéricos e experimentais da literatura. / The purpose of the present study is to perform a theoretical study and develop numerical simulations involving dynamic in gas-solid systems. The focus of the work is the modeling of particulate matter using continuous models based on soil mechanics and the kinetic theory of granular flows (large systems with many particles, Eulerian formulation - Finite Volume) and discrete models based on physical characteristics of the particles (intermediate systems and limited number of particles, Lagrangian formulation - Discrete Element Method). It is proposed a new approach to determine the normal spring stiffness coefficient of the linear model through the numerical solution for the overlap between particles in non-linear models. The linear spring stiffness is determined using an equivalence between the linear and the non-linear models. It is used the MFIX computational code to perform numerical simulations of the dynamics of gas-solid systems. It is analyzed the processes of fluidization, mixing and particle segregation and the influence of drag correlations. The proposed approach for normal spring stiffness coefficient is applied in the numerical simulations of two problems: single freely falling particle and bubbling fluidized bed. The results were compared with numerical and experimental data from literature.

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