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Numerical analysis of viscoelastic flows with singularities

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Author(s):
Irineu Lopes Palhares Junior
Total Authors: 1
Document type: Doctoral Thesis
Press: São Carlos.
Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
Defense date:
Examining board members:
José Alberto Cuminato; Gustavo Carlos Buscaglia; Roney Leon Thompson; Frédéric Gérard Christian Valentin
Advisor: José Alberto Cuminato; Cássio Machiaveli Oishi
Abstract

In this work we present an asymptotic and numerical study of viscoelastic flows with stress singularities. These singularities arise as a consequence of an abrupt change in the boundary conditions, as in the case of the stick-slip flow, or due to the presence of corners in the geometry of the problem, as in the contraction flow. For the stick-slip problem, we define the asymptotic behavior of the Oldroyd-B fluid over a Newtonian velocity field. This analysis was done with the method of matched asymptotic expansions, which can be extended to other types of fluids. The asymptotic study of the stick-slip flow for the Oldroyd-B model revealed that the equations of this model are not well defined for this problem, because this fluid extends the singularity throughout the free surface, generating results with no physical meaning. Besides that, the asymptotic results of the stick-slip and 4:1 contraction problems were verified numerically by integrating the constitutive equations along streamlines. It is worth mentioning that we performed asymptotic and numerical studies with the natural stress formulation (NSF) in addition to the Cartesian stress formulation (CSF). The NSF can capture the numerical results in a more accurate manner near singularities. Furthermore, we developed a numerical method to solve the Navier-Stokes equations combined with the constitutive equations of the CSF and NSF formulations for the PTT and Giesekus in the two problems studied. It is worth noting that there is no numerical results, for the transient case, with the NSF formulation for the PTT and Giesekus. Finally, we verified numerically the asymptotic behavior of stresses close to the singularities, as well as the configuration of the boundary layers for the problems mentioned above. (AU)

FAPESP's process: 14/17348-2 - Stability of Numerical methods for Viscoelastic high Weissenberg number flows
Grantee:Irineu Lopes Palhares Junior
Support type: Scholarships in Brazil - Doctorate