This thesis presents models and simulations of dielectrophoretic separation of micro and nano particles. The fluid dynamics involved and the dielectric properties of water inside single-walled carbon nanotube are studied as well. Based on the effective dipole moment method, the particle dynamic model focuses on the translational motions of micro particles. The hydrodynamic force between the particles and the particle-particle electrostatic interactions are considered as well. By comparing the dimensionless parameters, the dominating force can be determined. Based on a simplified version of the particle dynamic model, two numerical simulations are carried out to predict the efficiency of dielectrophoretic separation of micro size particles. The first calculation suggests a strategy to improve the trapping efficiency of E.coli bacteria by applying superimposed AC electric fields. The second calculation discusses the concept of mobility and improves the separation rate of particles by a multi-step trapping-releasing dielectrophoresis strategy. The model is extended down scale to calculate the separation of metallic and semiconducting single-walled carbon nanotubes by the modified effective dipole moment method for prolate ellipsoids. The steeply changed gradient of electric field results in the local joule heating therefore creates gradient of dielectric properties in the solution. As a result, certain pattern of fluid flow with a considerable strength is created and affects the motion of carbon nanotubes especially close to the electrode gap, which indicates that the so-called electrothermal flow should be considered in designing the experiment to separate single-walled carbon canotubes. When the length scale of particles is comparable to that of the electrodes, the calculation of dielectrophoretic force by the effective dipole moment is considered not to be accurate since only the electric field in the center point is taken into account. Hence in the thesis a new method based on distributed induced charge is suggested. By approximating a straight slender body as a prolate ellipsoid, the electric field of multiple points along the centerline are all considered in the calculation and the interaction between particles could be concurrently taken care. This method is expected to be an improved method to calculate the dielectrophoretic force of rod-like virus, DNA, nanowires and carbon nanotubes. The dielectric property of water confined in carbon nanotubes is expected to be dramatically different from that of bulk water. The thesis also contains a molecular dynamics study to reveal the difference also a dependence on the diameter of carbon nanotubes. The results show that along the axial direction, both the static permittivity and the relaxation time are larger than the isotropic bulk water, and in the cross-section plane it is opposite. When the radius of the carbon nanotubes increases, the properties of water inside become closer to the bulk water. / QC 20100820

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.

<p>We investigate the dielectrophoretic separation of microparticles. Two different models are formulated in two characteristic time scales. The first model mainly accounts for the orientation behavior and rotational motion of non-spheric microparticles. The concept of effective charge is suggested to calculate the finite size non-spheric particles. It is combined with the fluid particle dynamics method to calculate hydrodynamic as well as dielectrophoretic forces and torques. The translational motion and the particle-particle interaction are calculated also, but they take much longer time to be observed due to the different time scales of the rotational and translational motions By viewing the particle as spheres, the second model focus on the translational motion of spheres. The hydrodynamic force between particles and particle-particle electrostatic interactions are also taken into account. We check the relative magnitude ratio between these forces in order to determine the importance of these forces. To predict and guide the design of experimental dielectrophoretic separation, two numerical applications are carried out. The first calculation suggests optimum patterns to improve the trapping efficiency of<em> E.coli.</em> cells by applying superimposed AC electric fields. The second calculation finds out the mobility and separation rate of particles which differs in size and electric properties by a multi-step trapping-releasing strategy.</p>

Recent experiments revealed micrometer (µm)-sized Selenium (Se)-doped Germanium (Ge) particles forming a network of inactive phase (Li-Ge-Se) bring superior performance in cycling stability and capacity over un-doped Ge particles. Therefore, based on two states of Li (one for diffusion and another for alloyed reaction), a phaseield model (PFM) is developed incorporating both chemical reaction and Li diffusion to investigate remaining elusive underpinning mechanism. The reaction-diffusion PFM enables us to directly determine the conditions under which the lithiation process is diffusion- and/or reaction-controlled. Moreover, coupling the elasto-plastic deformation, the model allows us to investigate the role of the inactive phase in morphology and stress variation of Se-doped Ge electrode upon lithiation. The numerical results reveal that the tensile hoop stress at the surface of the particles is significantly suppressed due to softness of the inactive Li-Ge-Se phase, in line with the experimental observation of surface fractureree behavior. Further, we find that the soft Li-Ge-Se phase reduces a compressive mean stress at the reaction front, thus alleviating the stress retardation effect on the lithiation kinetics. And, the high Li diffusivity of the amorphous Li-Ge-Se network provides an effective Li diffusion path for inter-particle diffusion, reducing stress difference between the surfaces of neighboring particles. Besides, the constraint between the adjacent particles induces a higher compressive stress at the reaction front impeding the mobile Li insertion during lithiation. Though small c-Ge nano-particle in the Ge0.9Se0.1 microparticle is lithiated faster than large one, the compressive stress is generated at the center of small one for stress equilibrium which causes more retardation effect. Meanwhile, the size difference between adjacent particles increases the principle and shear stresses in the inactive Li-Ge-Se network near adjacent surfaces, which could potentially lead to mechanical failure and debonding of the amorphous network. We believe that the results of this investigation can shed some light on the optimization design of electrodes.

We investigate the dielectrophoretic separation of microparticles. Two different models are formulated in two characteristic time scales. The first model mainly accounts for the orientation behavior and rotational motion of non-spheric microparticles. The concept of effective charge is suggested to calculate the finite size non-spheric particles. It is combined with the fluid particle dynamics method to calculate hydrodynamic as well as dielectrophoretic forces and torques. The translational motion and the particle-particle interaction are calculated also, but they take much longer time to be observed due to the different time scales of the rotational and translational motions By viewing the particle as spheres, the second model focus on the translational motion of spheres. The hydrodynamic force between particles and particle-particle electrostatic interactions are also taken into account. We check the relative magnitude ratio between these forces in order to determine the importance of these forces. To predict and guide the design of experimental dielectrophoretic separation, two numerical applications are carried out. The first calculation suggests optimum patterns to improve the trapping efficiency of E.coli. cells by applying superimposed AC electric fields. The second calculation finds out the mobility and separation rate of particles which differs in size and electric properties by a multi-step trapping-releasing strategy. / QC 20101118

Orientador: Milton Mori / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica / Made available in DSpace on 2018-08-14T18:54:23Z (GMT). No. of bitstreams: 1 Bastos_JaciCarloSchrammCamara_D.pdf: 4353350 bytes, checksum: 0de3633c8edcc4ae2ec7fc57a3b590d0 (MD5) Previous issue date: 2009 / Resumo: Apresenta-se nesta pesquisa uma análise experimental e numérica do comportamento da fase dispersa em um jato circular bifásico confinado e uma comparação com jato circular bifásico livre. Nas análises experimentais, uma câmara pentagonal em acrílico foi utilizada como sistema de confinamento para a obtenção de perfis axiais e radiais de velocidade média, flutuação de velocidade (RMS) e intensidade de turbulência. Estes dados foram analisados a fim de desenvolver uma análise completa da região desenvolvida do jato. Três diferentes jatos foram utilizados para a alimentação da fase gás no topo da câmara, mas apenas o jato central foi carregado com partículas entre 60 e 90µm de diâmetro. Os outros dois foram utilizados para proporcionar uma maior interação entre as fases no interior da câmara. A técnica óptica Phase Doppler Anemometry (PDA), foi empregada na medição da velocidade instantânea da fase sólida e do diâmetro das partículas nas diferentes posições axiais a partir do bico do jato. Nove casos de estudo distintos são investigados individualmente e, em seguida, comparados entre si. Estes casos fornecem informações importantes sobre o comportamento e o efeito do confinamento dos jatos sobre o transporte macrocóspico e turbulento das partículas entre o centro e as regiões de contorno do jato. As análises numéricas tratam da modelagem matemática tridimensional, turbulenta e transiente do escoamento no jato bifásico confinado. O modelo trata as fases gás e sólida a partir de uma abordagem Euleriana. O fechamento das equações de transporte foi realizado utilizando o modelo de turbulência de duas equações k-e para a fase gás e modelos de turbulência de zero-equação para a fase sólida, e ainda em alguns casos esta última apenas sofreu efeitos turbulentos advindos da fase contínua. A acurácia das previsões do modelo em um jato de partículas confinadas com as características médias no tempo, assim como os coeficientes da correlação de turbulência foram avaliados. Perfis radiais de velocidade média e fração volumétrica das partículas foram capturados em quarenta e dois níveis, subdivididos em nove casos e comparados aos dados experimentais adquiridos. O diâmetro médio das partículas utilizado nas simulações foi de 75µm e as velocidades iniciais utilizadas variam entre 3 e 11m/s no jato central. O modelo matemático previu um escoamento desenvolvido semelhante ao que foi encontrado experimentalmente. / Abstract: It is presented in this research an experimental and numerical analisys of the dispersed phase behavior in a circular confined two-phase jet and a comparison with circular free two-phase jet. In the experimental analysis, a pentagonal plexiglass chamber was used as confined system for the axial and radial profiles investigation of mean velocity, fluctuation velocity known as RMS velocity and turbulence intensity. These data were analyzed in order to develop a complete analysis in the developed region of the jet. Three different nozzles were used to feed the gas phase at the top of the chamber, but just the central nozzle was loaded with particles between 60 and 90µm of diameter. The other two were used to increase the interaction between the phases in the chamber. An optical technique known as Phase Doppler Anemometry was used to measure the instantaneous velocity of the solid phase and particle diameter in different axial positions of the jet nozzle. Nine different cases of study are investigated individually and then compared among each other. These cases provide important information about the jets behavior and the confinement effect on the macrocospic and turbulent transport of particles between the jet center and the jet contour regions. The numerical analysis deals with three-dimensional, turbulent and transient mathematical modeling of a confined two-phase jet flow. The model treats the gas and the solid phases from an Eulerian approach. The closure of the transport equations have been accomplished by using the k-e turbulence model for the gas phase and the zero-equation turbulence model for the solid phase, and in some cases the latter suffered turbulent effects occuring only from the continuos phase. The accuracy of the model predictions in a particle-laden confined jet with the characteristics as well as turbulence correlation coefficients have been evaluated. Radial mean velocity profiles for the solid phase were computed on forty two axial levels, subdivided in nine cases and compared to the obtained experimental data. The mean particle diameter used in the simulations was 75µm and the initial velocities used vary between 3 and 11m/s. The mathematical model predicted a flow development similar to that found experimentally. / Doutorado / Desenvolvimento de Processos Químicos / Mestre em Engenharia Química

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.

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.

The transport or the separation of solid particles or droplets suspended in a fluid flow is a common task in mechanical and process engineering. To improve machinery and physical processes (e.g. for coal combustion, reduction of NO_x and soot) an optimization of complex phenomena by simulation applying the fundamental conservation equations is required. Fluid-particle flows are characterized by the ratio of density of the two phases gamma=rho_P/rho_F, by the Stokes number St=tau_P/tau_F and by the loading in terms of void and mass fraction. Those numbers (Stokes number, gamma) define the flow regime and which relevant forces are acting on the particle. Dependent on the geometrical configuration the particle-wall interaction might have a heavy impact on the mean flow structure. The occurrence of particle-particle collisions becomes also more and more important with the increase of the local void fraction of the particulate phase. With increase of the particle loading the interaction with the fluid phase can not been neglected and 2-way or even 4-way coupling between the continous and disperse phases has to be taken into account. For dilute to moderate dense particle flows the Euler-Lagrange method is capable to resolve the main flow mechanism. An accurate computation needs unfortunately a high number of numerical particles (1,...,10^7) to get the reliable statistics for the underlying modelling correlations. Due to the fact that a Lagrangian algorithm cannot be vectorized for complex meshes the only way to finish those simulations in a reasonable time is the parallization applying the message passing paradigma. Frank et al. describes the basic ideas for a parallel Eulererian-Lagrangian solver, which uses multigrid for acceleration of the flow equations. The performance figures are quite good, though only steady problems are tackled. The presented paper is aimed to the numerical prediction of time-dependend fluid-particle flows using the simultanous particle tracking approach based on the Eulerian-Lagrangian and the particle-source-in-cell (PSI-Cell) approach. It is shown in the paper that for the unsteady flow prediction efficiency and load balancing of the parallel numerical simulation is an even more pronounced problem in comparison with the steady flow calculations, because the time steps for the time integration along one particle trajectory are very small per one time step of fluid flow integration and so the floating point workload on a single processor node is usualy rather low. Much time is spent for communication and waiting time of the processors, because for cold flow particle convection not very extensive calculations are necessary. One remedy might be a highspeed switch like Myrinet or Dolphin PCI/SCI (500 MByte/s), which could balance the relative high floating point performance of INTEL PIII processors and the weak capacity of the Fast-Ethernet communication network (100 Mbit/s) of the Chemnitz Linux Cluster (CLIC) used for the presented calculations. Corresponding to the discussed examples calculation times and parallel performance will be presented. Another point is the communication of many small packages, which should be summed up to bigger messages, because each message requires a startup time independently of its size. Summarising the potential of such a parallel algorithm, it will be shown that a Beowulf-type cluster computer is a highly competitve alternative to the classical main frame computer for the investigated Eulerian-Lagrangian simultanous particle tracking approach.