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Master's Dissertation
DOI
10.11606/D.55.2017.tde-18122017-142923
Document
Author
Full name
Marcela Alexandra da Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2005
Supervisor
Committee
Tomé, Murilo Francisco (President)
Carvalho, Márcio da Silveira
Ferreira, Valdemir Garcia
Title in Portuguese
Desenvolvimento de um método numérico para simular escoamentos viscoelásticos axissimétricos com superfícies livres
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Neste trabalho são apresentadas as equações governantes para um fluido Oldroyd-B juntamente com as condições de contorno para escoamentos viscoelásticos axissimétricos com superfícies livres. Um método numérico para simular escoamentos com superfícies livres é apresentado e as equações resultantes são resolvidas utilizando o método de diferenças finitas numa malha deslocada. São desenvolvidas formulações para o cálculo do tensor extra-tensão em contornos rígidos e no eixo de simetria. As condições de contorno na superfície livre são discutidas em detalhes. Os termos convectivos são aproximados pelo método 'upwind' de alta ordem CUBISTA ('A convergent and universally bounded interpolation scheme for the treatment of advection'). O fluido é modelado utilizando a técnica 'Marker-and-Cell' o que permite visualizar e localizar a superfície livre do fluido. Para evitar ondulações, a superfície livre é suavizada pela técnica TSUR ('Trapezoidal Surface Removal'). O método numérico descrito neste trabalho foi implementado no sistema de simulação Freeflow-AXI e validado comparando os resultados numéricos do escoamento em um tubo com a respectiva solução analítica. Resultados numéricos incluem: simulação do inchamento do extrudado, gota incidindo contra uma superfície rígida e a simulação do 'splashing drop' para vários números de Reynolds e de Weissenberg.
Title in English
Not available
Keywords in English
Not available
Abstract in English
This work presents the governing equations together with the corresponding boundary conditions for the flow of an Oldroyd-B fluid with free surfaces in axisymmetric geometries. A numerical method for simulating free surface flows is presented and the resulting equations are solved by the finite difference method on a staggered grid. A formulation for the computation of the extra-stress tensor on rigid boundaries and on the symmetry axis is developed. The boundary conditions of the free surface are discussed in details. One feature of the numerical technique presented in this work is the approximation of the convective terms appearing in the equations of motion and in the constitutive equation by the high order CUBISTA scheme (A convergent and universally bounded interpolation scheme for the treatment of advection). The fluid is modeled by the Marker-and-Cell method which permits the visualization and the location of the free surface. In order to avoid ondulations the free surface is smoothed by the TSUR (Trapezoidal Surface Removal) method which is a mass conserving procedure. The resulting difference equations are then implemented into the Freeflow-AXI simulation system. The code implementation is validated by simulating the flow of an Oldroyd-B fluid in a pipe. Numerical results include the simulation of the transient extrudate swell, impacting drop and the splashing drop of an Oldroyd-B fluid at high Reynolds numbers and various Weissenberg numbers.
 
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Publishing Date
2017-12-18
 
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