Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.

Um estudo sobre a aprendizagem de alguns conceitos algébricos e geométricos

The objective of the present work was develop a study about the writing and the algebraic manipulation of symbolical expressions for perimeter and area of some convex polygons, approaching the properties of the operations and equality, extending to the obtaining of the formulas of length and area of the circle, this one starting on the formula of the perimeter and area of the regular hexagon. To do so, a module with teaching activities was elaborated based on constructive teaching. The study consisted of a methodological intervention, done by the researcher, and had as subjects students of the 8th grade of the State School Desembargador Floriano Cavalcanti, located on the city of Natal, Rio Grande do Norte. The methodological intervention was done in three stages: applying of a initial diagnostic evaluation, developing of the teaching module, and applying of the final evaluation based on the Mathematics teaching using Constructivist references. The data collected in the evaluations was presented as descriptive statistics. The results of the final diagnostic evaluation were analyzed in the qualitative point of view, using the criteria established by Richard Skemp s second theory about the comprehension of mathematical concepts. The general results about the data from the evaluations and the applying of the teaching module showed a qualitative difference in the learning of the students who participated of the intervention

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Método híbrido para projeto de superfícies seletivas em frequência

This thesis presents a hybrid technique of frequency selective surfaces project (FSS) on a isotropic dielectric layer, considering various geometries for the elements of the unit cell. Specifically, the hybrid technique uses the equivalent circuit method in conjunction with genetic algorithm, aiming at the synthesis of structures with response single-band and dual-band. The equivalent circuit method allows you to model the structure by using an equivalent circuit and also obtaining circuits for different geometries. From the obtaining of the parameters of these circuits, you can get the transmission and reflection characteristics of patterned structures. For the optimization of patterned structures, according to the desired frequency response, Matlab™ optimization tool named optimtool proved to be easy to use, allowing you to explore important results on the optimization analysis. In this thesis, numeric and experimental results are presented for the different characteristics of the analyzed geometries. For this, it was determined a technique to obtain the parameter N, which is based on genetic algorithms and differential geometry, to obtain the algebraic rational models that determine values of N more accurate, facilitating new projects of FSS with these geometries. The optimal results of N are grouped according to the occupancy factor of the cell and the thickness of the dielectric, for modeling of the structures by means of rational algebraic equations. Furthermore, for the proposed hybrid model was developed a fitness function for the purpose of calculating the error occurred in the definitions of FSS bandwidths with transmission features single band and dual band. This thesis deals with the construction of prototypes of FSS with frequency settings and band widths obtained with the use of this function. The FSS were initially reviewed through simulations performed with the commercial software Ansoft Designer ™, followed by simulation with the equivalent circuit method for obtaining a value of N in order to converge the resonance frequency and the bandwidth of the FSS analyzed, then the results obtained were compared. The methodology applied is validated with the construction and measurement of prototypes with different geometries of the cells of the arrays of FSS.

Simulação de fluxo de fluidos em meios porosos desordenados uma análise de efeito de escala na estimativa da permeabilidade e do coeficiente de arrasto

The present study provides a methodology that gives a predictive character the computer simulations based on detailed models of the geometry of a porous medium. We using the software FLUENT to investigate the flow of a viscous Newtonian fluid through a random fractal medium which simplifies a two-dimensional disordered porous medium representing a petroleum reservoir. This fractal model is formed by obstacles of various sizes, whose size distribution function follows a power law where exponent is defined as the fractal dimension of fractionation Dff of the model characterizing the process of fragmentation these obstacles. They are randomly disposed in a rectangular channel. The modeling process incorporates modern concepts, scaling laws, to analyze the influence of heterogeneity found in the fields of the porosity and of the permeability in such a way as to characterize the medium in terms of their fractal properties. This procedure allows numerically analyze the measurements of permeability k and the drag coefficient Cd proposed relationships, like power law, for these properties on various modeling schemes. The purpose of this research is to study the variability provided by these heterogeneities where the velocity field and other details of viscous fluid dynamics are obtained by solving numerically the continuity and Navier-Stokes equations at pore level and observe how the fractal dimension of fractionation of the model can affect their hydrodynamic properties. This study were considered two classes of models, models with constant porosity, MPC, and models with varying porosity, MPV. The results have allowed us to find numerical relationship between the permeability, drag coefficient and the fractal dimension of fractionation of the medium. Based on these numerical results we have proposed scaling relations and algebraic expressions involving the relevant parameters of the phenomenon. In this study analytical equations were determined for Dff depending on the geometrical parameters of the models. We also found a relation between the permeability and the drag coefficient which is inversely proportional to one another. As for the difference in behavior it is most striking in the classes of models MPV. That is, the fact that the porosity vary in these models is an additional factor that plays a significant role in flow analysis. Finally, the results proved satisfactory and consistent, which demonstrates the effectiveness of the referred methodology for all applications analyzed in this study.