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Doctoral Thesis
DOI
Document
Author
Full name
Irineu Lopes Palhares Junior
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2019
Supervisor
Committee
Cuminato, José Alberto (President)
Buscaglia, Gustavo Carlos
Thompson, Roney Leon
Valentin, Frédéric Gérard Christian
Title in Portuguese
Análise numérica de escoamentos viscoelásticos com singularidades
Keywords in Portuguese
Escoamento viscoleástico
Estudo assintótico
Estudo numérico
Formulação natural do tensor
Problema stick-slip
Abstract in Portuguese
Neste trabalho apresentamos um estudo assintótico e numérico de escoamentos viscoelásticos com singularidades de tensão. Estas singularidades surgem como consequência de uma mudança abrupta nas condições de contorno, como no caso do stick-slip, ou devido a presença de quinas na geometria do problema, como no escoamento da contração. Para o problema stick-slip definimos o comportamento assintótico do fluido Oldroyd-B sobre um campo de velocidade Newtoniano. Esta análise foi feita com o método assintótico das expansões, que pode ser estendida para outros tipos de fluidos. O estudo assintótico do stick-slip com o modelo Oldroyd-B revelou que as equações deste modelo não estão bem definidas para este problema, pois este fluido estende o valor singular ao longo de toda a superfície livre, gerando resultados sem sentido físico. Além disso, os resultados assintóticos dos problemas stick-slip e da contração 4:1 foram verificados numericamente através da integração das equações constitutivas ao longo de linhas de corrente. Vale destacar que, além da tradicional formulação Cartesiana do tensor (CSF), também utilizamos a formulação natural do tensor (NSF), que tem a vantagem de capturar de modo mais acurado os resultados próximos às singularidades. Além do mais, desenvolvemos um método numérico para resolver as equações de Navier-Stokes combinadas com as equações constitutivas das formulações CSF e NSF para os modelos PTT e Giesekus nos dois problemas estudados. Vale ressaltar que, não há na literatura resultados numéricos, para o caso transiente, com a formulação NSF para os modelos PTT e Giesekus. Por fim, verificamos numericamente o comportamento assintótico das tensões próximo as singularidades, bem como a configuração das camadas limites para os problemas mencionados.
Title in English
Numerical analysis of viscoelastic flows with singularities
Keywords in English
Asymptotic study
Natural stress formulation
Numerical study
Stick-slip problem
Viscoelastic flow
Abstract in English
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.
 
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Publishing Date
2019-04-29
 
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