Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2020.tde-08092020-164651
Document
Author
Full name
Caroline Viezel
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Tomé, Murilo Francisco (President)
Cruz, Daniel Onofre de Almeida
Kurokawa, Fernando Akira
Souza, Leandro Franco de
Title in Portuguese
Solução numérica do modelo Oldroyd-B para valores pequenos da razão de viscosidades: aplicação em escoamentos com superfícies livres
Keywords in Portuguese
Diferenças finitas
Escoamentos viscoelásticos
Oldroyd-B
Superfície livre
UCM
Abstract in Portuguese
Title in English
Numerical solution of the Oldroyd-B model for small values of the viscosity ratio: application to free surface flows
Keywords in English
Finite differences
Free surface
Oldroyd-B
UCM
Viscoelastic flows
Abstract in English
This work deals with the development of a numerical method to simulate axisymmetric free surface flows governed by the constitutive equation Oldroyd-B. A methodology employing the finite difference method to solve the governing equations for axisymmetric free surface flows of Oldroyd-B fluids where the parameter β covers the interval [0; 1] is proposed. Thus, this new methodology allows the numerical solutions of the Oldroyd-B model which involves a solvent viscosity (β > 0) and purely elastic flows described by the Upper Convected-Maxwell (UCM) (β = 0). Moreover, in this approach the extra-stress tensor is combined with the conformation tensor which is approximated implicitly by finite differences which are solved exactly. The momentum equations coupled with the free surface stress conditions are solved using an Elastic Viscous Stress Splitting (EVSS) transformation: this avoid numerical instabilities that can appear when β is small. This new technique is verified by an analytic solution for tube flows and also by comparing results from the literature obtained for the flows impacting drop,dieswell and delayed dieswell using the Oldroyd-B model. New results for bouncing drops, dieswell and delayed dieswell using the UCM model are presented. The existing studies for these flows involve constitutive models that employs solvent viscosities such as Oldroyd-B, Phan-Thien- Tanner (PTT) and Finitely Extensibility Nonlinear Elastic (FENE-P) models.