Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/75798 |
Resumo: | This paper aims to present Galerkin Least-Squares approximations for flows of Bingham plastic fluids. These fluids are modeled using the Generalized Newtonian Liquid (GNL) constitutive equation. Their viscoplastic behavior is predicted by the viscosity function, which employs the Papanastasiou’s regularization in order to predict a highly viscous behavior when the applied stress lies under the material’s yield stress. The mechanical modeling for this type of flow is based on the conservation equations of mass and momentum, coupled to the GNL constitutive equation for the extra-stress tensor. The finite element methodology concerned herein, the well-known Galerkin Least-Squares (GLS) method, overcomes the two greatest Galerkin shortcomings for mixed problems. There is no need to satisfy Babuška-Brezzi condition for velocity and pressure subspaces, and spurious numerical oscillations, due to the asymmetric nature of advective operator, are eliminated. Some numerical simulations are presented: first, the lid-driven cavity flow of shear-thinning and shear-thickening fluids, for the purpose of code validation; second, the flow of shear-thinning fluids with no yield stress limit, and finally, Bingham plastic creeping flows through 2:1 planar and axisymmetric expansions, for Bingham numbers between 0.2 and 133. The numerical results illustrate the arising of two distinct unyielded regions: one near the expansion corner and another along the flow centerline. For those regions, velocity and pressure fields are investigated for the various Bingham numbers tested. |
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Zinani, Flávia Schwarz FranceschiniFrey, Sérgio Luiz2013-07-11T02:22:13Z20071806-3691http://hdl.handle.net/10183/75798000640856This paper aims to present Galerkin Least-Squares approximations for flows of Bingham plastic fluids. These fluids are modeled using the Generalized Newtonian Liquid (GNL) constitutive equation. Their viscoplastic behavior is predicted by the viscosity function, which employs the Papanastasiou’s regularization in order to predict a highly viscous behavior when the applied stress lies under the material’s yield stress. The mechanical modeling for this type of flow is based on the conservation equations of mass and momentum, coupled to the GNL constitutive equation for the extra-stress tensor. The finite element methodology concerned herein, the well-known Galerkin Least-Squares (GLS) method, overcomes the two greatest Galerkin shortcomings for mixed problems. There is no need to satisfy Babuška-Brezzi condition for velocity and pressure subspaces, and spurious numerical oscillations, due to the asymmetric nature of advective operator, are eliminated. Some numerical simulations are presented: first, the lid-driven cavity flow of shear-thinning and shear-thickening fluids, for the purpose of code validation; second, the flow of shear-thinning fluids with no yield stress limit, and finally, Bingham plastic creeping flows through 2:1 planar and axisymmetric expansions, for Bingham numbers between 0.2 and 133. The numerical results illustrate the arising of two distinct unyielded regions: one near the expansion corner and another along the flow centerline. For those regions, velocity and pressure fields are investigated for the various Bingham numbers tested.application/pdfengJournal of the Brazilian Society of Mechanical Sciences and Engineering. Rio de Janeiro, RJ. Vol. 29, no. 4, (Oct./Dec. 2007), 432-443Elementos finitosViscoplasticidadeMecânica dos fluidosBingham plasticCarreau fluidsYield StressPapanastasiou’s approximationGalerkin Least-SquaresGalerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluidsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/otherinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSORIGINAL000640856.pdf000640856.pdfTexto completo (inglês)application/pdf614159http://www.lume.ufrgs.br/bitstream/10183/75798/1/000640856.pdf953839f90d981d328b5b58a8f0469683MD51TEXT000640856.pdf.txt000640856.pdf.txtExtracted Texttext/plain43652http://www.lume.ufrgs.br/bitstream/10183/75798/2/000640856.pdf.txtc4b2ed7c818f385da1551af6dea34cc0MD52THUMBNAIL000640856.pdf.jpg000640856.pdf.jpgGenerated Thumbnailimage/jpeg2129http://www.lume.ufrgs.br/bitstream/10183/75798/3/000640856.pdf.jpgf9001bda6f3bfa85700fe320190d3b0cMD5310183/757982022-04-20 04:54:43.096835oai:www.lume.ufrgs.br:10183/75798Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2022-04-20T07:54:43Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
title |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
spellingShingle |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids Zinani, Flávia Schwarz Franceschini Elementos finitos Viscoplasticidade Mecânica dos fluidos Bingham plastic Carreau fluids Yield Stress Papanastasiou’s approximation Galerkin Least-Squares |
title_short |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
title_full |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
title_fullStr |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
title_full_unstemmed |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
title_sort |
Galerkin least-squares solutions for purely viscous flows of shear-thinning fluids and regularized yield stress fluids |
author |
Zinani, Flávia Schwarz Franceschini |
author_facet |
Zinani, Flávia Schwarz Franceschini Frey, Sérgio Luiz |
author_role |
author |
author2 |
Frey, Sérgio Luiz |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Zinani, Flávia Schwarz Franceschini Frey, Sérgio Luiz |
dc.subject.por.fl_str_mv |
Elementos finitos Viscoplasticidade Mecânica dos fluidos |
topic |
Elementos finitos Viscoplasticidade Mecânica dos fluidos Bingham plastic Carreau fluids Yield Stress Papanastasiou’s approximation Galerkin Least-Squares |
dc.subject.eng.fl_str_mv |
Bingham plastic Carreau fluids Yield Stress Papanastasiou’s approximation Galerkin Least-Squares |
description |
This paper aims to present Galerkin Least-Squares approximations for flows of Bingham plastic fluids. These fluids are modeled using the Generalized Newtonian Liquid (GNL) constitutive equation. Their viscoplastic behavior is predicted by the viscosity function, which employs the Papanastasiou’s regularization in order to predict a highly viscous behavior when the applied stress lies under the material’s yield stress. The mechanical modeling for this type of flow is based on the conservation equations of mass and momentum, coupled to the GNL constitutive equation for the extra-stress tensor. The finite element methodology concerned herein, the well-known Galerkin Least-Squares (GLS) method, overcomes the two greatest Galerkin shortcomings for mixed problems. There is no need to satisfy Babuška-Brezzi condition for velocity and pressure subspaces, and spurious numerical oscillations, due to the asymmetric nature of advective operator, are eliminated. Some numerical simulations are presented: first, the lid-driven cavity flow of shear-thinning and shear-thickening fluids, for the purpose of code validation; second, the flow of shear-thinning fluids with no yield stress limit, and finally, Bingham plastic creeping flows through 2:1 planar and axisymmetric expansions, for Bingham numbers between 0.2 and 133. The numerical results illustrate the arising of two distinct unyielded regions: one near the expansion corner and another along the flow centerline. For those regions, velocity and pressure fields are investigated for the various Bingham numbers tested. |
publishDate |
2007 |
dc.date.issued.fl_str_mv |
2007 |
dc.date.accessioned.fl_str_mv |
2013-07-11T02:22:13Z |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/other |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/75798 |
dc.identifier.issn.pt_BR.fl_str_mv |
1806-3691 |
dc.identifier.nrb.pt_BR.fl_str_mv |
000640856 |
identifier_str_mv |
1806-3691 000640856 |
url |
http://hdl.handle.net/10183/75798 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
Journal of the Brazilian Society of Mechanical Sciences and Engineering. Rio de Janeiro, RJ. Vol. 29, no. 4, (Oct./Dec. 2007), 432-443 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
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