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Previous issue date: 2015-03-25 / Neste trabalho investigamos alguns aspectos do fluxo bidimensional de um fluido viscoso Newtoniano
atrav?s de um meio poroso desordenado, modelado por um sistema fractal aleat?rio,
semelhante ao tapete de Sierpinski. Este fractal ? formado por obst?culos de diversos tamanhos,
cuja fun??o de distribui??o segue uma lei de pot?ncia. Al?m do mais, est?o aleatoriamente
dispostos em um canal retangular. O campo de velocidades e outros detalhes da din?mica
dos fluidos s?o obtidos resolvendo-se, numericamente, as equa??es de Navier-Stokes e as da
continuidade no n?vel de poros, onde ocorre realmente o fluxo de fluidos em meios porosos.
Os resultados das simula??es num?ricas permitiram-nos fazer uma an?lise da distribui??o das
tens?es de cisalhamento desenvolvidas nas interfaces s?lido-fluido, e encontrar rela??es alg?bricas
entre as for?as viscosas ou de atrito e par?metros geom?tricos do modelo, inclusive a sua
dimens?o fractal. Com base nos resultados num?ricos propusemos rela??es de escala que envolve
os par?metros relevantes do fen?meno, quantificando as fra??es dessas for?as com rela??o ?s
classes de tamanhos dos obst?culos. Finalmente, foi poss?vel, tamb?m, fazer infer?ncias sobre
as flutua??es na forma da distribui??o das tens?es viscosas desenvolvidas na superf?cie dos
obst?culos. / In this work we have investigated some aspects of the two-dimensional flow of a viscous Newtonian
fluid through a disordered porous medium modeled by a random fractal system similar
to the Sierpinski carpet. This fractal is formed by obstacles of various sizes, whose distribution
function follows a power law. They are randomly disposed in a rectangular channel. The velocity
field and other details of fluid dynamics are obtained by solving numerically of the Navier-Stokes
and continuity equations at the pore level, where occurs actually the flow of fluids in porous
media. The results of numerical simulations allowed us to analyze the distribution of shear
stresses developed in the solid-fluid interfaces, and find algebraic relations between the viscous
forces or of friction with the geometric parameters of the model, including its fractal dimension.
Based on the numerical results, we proposed scaling relations involving the relevant parameters
of the phenomenon, allowing quantifying the fractions of these forces with respect to size classes
of obstacles. Finally, it was also possible to make inferences about the fluctuations in the form of
the distribution of viscous stresses developed on the surface of obstacles.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/20107 |
| Date | 25 March 2015 |
| Creators | Barbosa, Iderval Alves |
| Contributors | 00405663404, http://lattes.cnpq.br/7151949476055522, Barroca Neto, ?lvaro, 20053380444, http://lattes.cnpq.br/2194067631173871, Leite, Francisco Edcarlos Alves, 02529744416, http://lattes.cnpq.br/3650123589671260, Silva, Luciano Rodrigues da, 07416407400, http://lattes.cnpq.br/5182830756789229, Henriques, Marcos Vinicius C?ndido, 00978165403, Lucena, Liacir dos Santos |
| Publisher | Universidade Federal do Rio Grande do Norte, PROGRAMA DE P?S-GRADUA??O EM CI?NCIA E ENGENHARIA DE PETR?LEO, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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