Thèse de Doctorat
DOI
https://doi.org/10.11606/T.55.2006.tde-02102006-161603
Document
Auteur
Nom complet
Gilcilene Sanchez de Paulo
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2006
Directeur
Jury
Tomé, Murilo Francisco (Président)
Castelo Filho, Antonio
Devloo, Philippe Remy Bernard
Frey, Sérgio Luiz
Naccache, Mônica Feijó
Titre en portugais
Solução numérica do modelo PTT para escoamentos viscoelásticos com superfícies livres
Resumé en portugais
Titre en anglais
Numerical solution of the PTT model for viscoelastic surface flows
Mots-clés en anglais
Analytic solution
Finite difference technique
Free surface
PTT model
Viscoelastic flows
Resumé en anglais
The aim of this work is to develop a numerical method capable of simulating viscoelastic free surface flows governed by the non-linear constitutive equation PTT (Phan-Thien-Tanner). In this work three numerical methods to simulate vicoelastic Flows of fluids modelled by the PTT equation are presented. Two of these methods were developed to simulate two-dimensional viscoelastic flows while the third method was developed to simulate three-dimensional viscoelastic flows. These numerical methods were incorporated into the codes FreeFlow2D and FreeFlow3D, extending these codes to viscoelastic flows described by the non-linear constitutive equation PTT. Initially, a description of FreeFlow2D and FreeFlow3D is presented. The governing equations for flows described by the PTT model are given in index form and the mathematical formulations for obtaining the numerical methods are presented. The equations describing the numerical methods are solved by the finite difference method on a staggered grid and the fluid is modelled using a Marker-and-Cell type method. The boundary conditions for each type of boundary are described in details and the calculation of the extra-stress tensor on rigid boundaries is performed using the ideas of Tomé et al. [84] for an Oldroyd-B Fluid. Following the methodology presented by Alves et al. [2], the analytic solution of the PTT model for fully developed flows in a two-dimensional channel is presented in details. This analytic solution is then used to validate the numerical method developed in this work. Finally, the numerical methods developed in this work were applied to simulate viscoelastic flows such as a viscoelastic jet flowing onto a rigid plate, the extrudate swell of viscoelastic fluids and the simulation of a viscoelastic drop hitting a rigid plate

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Date de Publication
2006-10-03

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