Modeling particle-fluid interaction in a coupled CFD-DEM framework

In this work, we present an alternative methodology to solve the particle-fluid interaction in the resolved CFDEM coupling framework. This numerical approach consists of coupling a Discrete Element Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark, we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study the settling terminal velocity of a sphere under confined conditions

Motion of a sphere in a viscous fluid towards a wall confined versus unconfined conditions

In the present work, we investigate experimentally and numerically the motion of solid macroscopic spheres (Brownian and colloidal effects are negligible) when settling from rest in a quiescent fluid toward a solid wall under confined and unconfined configurations. Particle trajectories for spheres of two types of materials are measured using a high-speed digital camera. For unconfined configurations, our experimental findings are in excellent agreement with well-established analytical frameworks, used to describe the forces acting on the sphere. Besides, the experimental values of the terminal velocity obtained for different confinements are also in very good agreement with previous theoretical formulations. Similar conditions are simulated using a resolved CFD-DEM approach. After adjusting the parameters of the numerical model, we analyze the particle dynamic under several confinement conditions. The simulations results are contrasted with the experimental findings, obtaining a good agreement. We analyze several systems varying the radius of the bead and show the excellent agreement of our results with previous analytical approaches. However, the results indicate that confined particles have a distinct dynamics response when approaching the wall. Consequently, their motion cannot be described by the analytical framework introduced for the infinite system. Indeed, the confinement strongly affects the spatial scale where the particle is affected by the bottom wall and, accordingly, the dimensionless results can not be collapsed in a single master curve, using the particle size as a characteristic length. Alternatively, we rationalize our findings using a kinematic approximation to highlight the relevant scale of the problem. Our outcomes suggest it is possible to determine a new spatial scale to describe the collisional process, depending on the specific confining conditions

Estudo da correlação entre propriedades estatísticas de verbetes

As investigações das línguas naturais através da aplicação de métodos matemáticos e estatísticos que buscam caracterizar propriedades de textos literários têm sido objeto de intensa investigação nas últimas décadas, constituindo uma área denominada de linguística quantitativa. Os primeiros trabalhos nessa área surgiram entre as décadas de 1930 e 1950, com os trabalhos de George Zipf no estudo da distribuição de frequências e Claude Shannon com seu trabalho em previsão de letras e palavras e entropia como medida de redundância em língua inglesa. Nesta dissertação serão investigadas a autocorrelação e correlações cruzadas das séries temporais utilizando técnicas comuns ao estudo de séries temporais não-estacionárias. Discutiremos também quais propriedades emergem dessas correlações e suas implicações no processo de escrita. Ao longo dessa análise, todos os resultados foram obtidos para um conjunto de 250 textos literários escritos em 10 línguas distintas. No momento fi nal desse trabalho, analisaremos as propriedades de textos genéricos obtidos através de dois modelos de distribuições de distância: uma que leva em consideração as distâncias entre os números primos consecutivos e outra que utiliza a distribuição de Weibull. Exploraremos as características que surgem em cada um dos modelos comparando-as com seus equivalentes nos textos em linguagem natural.The application of mathematical and statistical methods to exploit properties in natural languages has a recent and proli c history. These methods and the quantitative tecnhiques adapted and created through the study of languages are part of an area usually called quantitative linguistics. The rst work on such area was performed by George Zipf from 1930 to 1950 in which the distribution of word frequencies were studied. His works were followed by Claude Shannon's analysis on entropy and letters prediction as a measure of redundancy in written english. In this work, we firstly present a study on correlation and cross-correlation through the time series extracted from texts by using common approaches to investigate non-stationary time series. To perform the required analysis we have used a corpora as large as 250 literary texts from 10 diferent languages. The properties emerging from these correlations will also be discussed and properly explained. Secondly, we move to the description of the distance distribution responsible for the long-range structure observed on written language. We devise those distributions by assuming the distance distribution from consecutive prime numbers and distances taken from a Weibull distributed process. The revenues from such models will be put under scrutiny by using the techniques presented during the work and comparing them to properties emerging in natural language.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPE

Modeling particle-fluid interaction in a coupled CFD-DEM framework

In this work, we present an alternative methodology to solve the particle-fluid interaction in the resolved CFDEM ® coupling framework. This numerical approach consists of coupling a Discrete Element Method (DEM) with a Computational Fluid Dynamics (CFD) scheme, solving the motion of immersed particles in a fluid phase. As a novelty, our approach explicitly accounts for the body force acting on the fluid phase when computing the local momentum balance equations. Accordingly, we implement a fluid-particle interaction computing the buoyant and drag forces as a function of local shear strain and pressure gradient. As a benchmark, we study the Stokesian limit of a single particle. The validation is performed comparing our outcomes with the ones provided by a previous resolved methodology and the analytical prediction. In general, we find that the new implementation reproduces with very good accuracy the Stokesian dynamics. Complementarily, we study the settling terminal velocity of a sphere under confined conditions

Motion of a sphere in a viscous fluid towards a wall confined versus unconfined conditions

In the present work, we investigate experimentally and numerically the motion of solid macroscopic spheres (Brownian and colloidal effects are negligible) when settling from rest in a quiescent fluid toward a solid wall under confined and unconfined configurations. Particle trajectories for spheres of two types of materials are measured using a high-speed digital camera. For unconfined configurations, our experimental findings are in excellent agreement with well-established analytical frameworks, used to describe the forces acting on the sphere. Besides, the experimental values of the terminal velocity obtained for different confinements are also in very good agreement with previous theoretical formulations. Similar conditions are simulated using a resolved CFD-DEM approach. After adjusting the parameters of the numerical model, we analyze the particle dynamic under several confinement conditions. The simulations results are contrasted with the experimental findings, obtaining a good agreement. We analyze several systems varying the radius of the bead and show the excellent agreement of our results with previous analytical approaches. However, the results indicate that confined particles have a distinct dynamics response when approaching the wall. Consequently, their motion cannot be described by the analytical framework introduced for the infinite system. Indeed, the confinement strongly affects the spatial scale where the particle is affected by the bottom wall and, accordingly, the dimensionless results can not be collapsed in a single master curve, using the particle size as a characteristic length. Alternatively, we rationalize our findings using a kinematic approximation to highlight the relevant scale of the problem. Our outcomes suggest it is possible to determine a new spatial scale to describe the collisional process, depending on the specific confining conditions