Aplicação da transformada integral generalizada no escoamento potencial em contrações
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Data
2009-07-30
Autores
Souza, Luís Henrique Gazeta de [UNESP]
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Universidade Estadual Paulista (Unesp)
Resumo
Realiza-se a formulação matemática do escoamento potencial no interior de contrações bidimensionais usando sistemas de coordenadas cartesianas e cilíndricas. Para tal considera-se que as geometrias das contrações sejam bidimensionais no sistema de coordenadas cartesianas e bidimensionais com simetria axial no sistema de coordenadas cilíndricas. A formulação é adaptada a partir das equações tridimensionais de Euler em coordenadas cartesianas e cilíndricas, fazendo-se as hipóteses de bidimensionalidade, regime permanente, fluido invíscido e escoamento irrotacional. O formalismo diferencial do escoamento potencial no interior de contrações bidimensionais é formalmente resolvido utilizando-se a Técnica da Transformada Integral Generalizada – TTIG – cuja fundamentação está na expansão de funções-quadrado-integráveis em séries de funções ortogonais. Desenvolveu-se algoritmos computacionais, em linguagem computacional Fortran 95, para simular as soluções formais obtidas e produzir resultados numéricos que possibilitassem a análise do escoamento potencial nas referidas contrações. Realizou-se extensivos testes numéricos para quatro famílias de geometrias das contrações, sendo que cada família ainda possuía diferentes funções modeladoras do formato de suas paredes, bem como os parâmetros razão e esbeltez e razão de contração. Analisou-se os resultados visando sintetizar aspectos e características de como as contrações operam e que formatos são mais adequados ou não
It was done the mathematical formulation for potential flow inside two-dimensional contractions using both Cartesian and cylindrical coordinate systems. To achieve such aim it was considered that contraction geometries are two-dimensional in the Cartesian coordinate system and two-dimensional with axial symmetry in cylindrical system. Formulation is adapted from tri-dimensional Euler equations in Cartesian and cylindrical coordinate systems, doing hypothesis such as: two-dimensionality, steady flow regime, inviscid fluid and irrotational flow. Differential formulae that models potential flow inside two-dimensional contraction is formally solved using Generalized Integral Transform Technique – GITT – which is based upon orthogonal series expansion of square-integrable functions. It was developed some computational algorithms, using Fortran 95 computational language, to simulate the obtained formal solutions and to produce numerical results that allows potential flow analysis for referred contractions. It was done comprehensive numerical tests for four families of contraction geometries, being that each family yet has different contraction wall modeling functions, as well length and contraction ratios. Results were analyzed aiming to synthesize aspects and characteristics of how contractions operate and which forms are more adequate or not
It was done the mathematical formulation for potential flow inside two-dimensional contractions using both Cartesian and cylindrical coordinate systems. To achieve such aim it was considered that contraction geometries are two-dimensional in the Cartesian coordinate system and two-dimensional with axial symmetry in cylindrical system. Formulation is adapted from tri-dimensional Euler equations in Cartesian and cylindrical coordinate systems, doing hypothesis such as: two-dimensionality, steady flow regime, inviscid fluid and irrotational flow. Differential formulae that models potential flow inside two-dimensional contraction is formally solved using Generalized Integral Transform Technique – GITT – which is based upon orthogonal series expansion of square-integrable functions. It was developed some computational algorithms, using Fortran 95 computational language, to simulate the obtained formal solutions and to produce numerical results that allows potential flow analysis for referred contractions. It was done comprehensive numerical tests for four families of contraction geometries, being that each family yet has different contraction wall modeling functions, as well length and contraction ratios. Results were analyzed aiming to synthesize aspects and characteristics of how contractions operate and which forms are more adequate or not
Descrição
Palavras-chave
Contrações, Transformadas integrais, Potencial de escoamento, Contractions, Integral transform, Potential flow
Como citar
SOUZA, Luís Henrique Gazeta de. Aplicação da transformada integral generalizada no escoamento potencial em contrações. 2009. 123 f. Dissertação (mestrado) – Universidade Estadual Paulista, Faculdade de Engenharia de Ilha Solteira, 2009.