Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations

ABSTRACT Non-Newtonian rheology effects, such as pseudoplasticity and viscoplasticity, are understood as shear stresses, incorporated to the energy slope term in the Shallow-Water Equations (SWE). However, non-Newtonian shear stresses are dependent of the shear rate, whose formulation is a function...

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Main Authors: Yuri Taglieri Sáo, João Batista Pereira, Geraldo de Freitas Maciel
Format: Article
Language:English
Published: Associação Brasileira de Recursos Hídricos 2023-08-01
Series:Revista Brasileira de Recursos Hídricos
Subjects:
Online Access:http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312023000100501&tlng=en
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author Yuri Taglieri Sáo
João Batista Pereira
Geraldo de Freitas Maciel
author_facet Yuri Taglieri Sáo
João Batista Pereira
Geraldo de Freitas Maciel
author_sort Yuri Taglieri Sáo
collection DOAJ
description ABSTRACT Non-Newtonian rheology effects, such as pseudoplasticity and viscoplasticity, are understood as shear stresses, incorporated to the energy slope term in the Shallow-Water Equations (SWE). However, non-Newtonian shear stresses are dependent of the shear rate, whose formulation is a function of the gradient of the velocity profile in the bottom. This study investigated two shear rate formulations that are commonly applied in the SWE literature: 1) a non-parameterized function; and 2) a function based on the Herschel-Bulkley rheological model. Their influence in steady uniform flows of non-Newtonian fluids was evaluated through numerical-theoretical comparisons. A Lax-Friedrichs scheme was implemented to solve the SWE system and allowed employing the shear rate formulations. Experimental tests were carried out and numerical simulations of hypothetical scenarios were performed. It was found that the non-parameterized formulation presented deviation in normal depth up to 14% in comparison with theoretical solution, while the formulation based on the Herschel-Bulkley model provided a good agreement, corroborated by punctual Computational Fluid Dynamics simulations (deviation less than 2%) and experimental data. The ratio of both shear rate formulations is strongly correlated to the deviation of normal depth, indicating that the non-parameterized shear rate function does not provide an acceptable result in the steady uniform flow.
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spelling doaj.art-9dff229f865d4149b143e114f140ac7b2023-08-15T07:45:14ZengAssociação Brasileira de Recursos HídricosRevista Brasileira de Recursos Hídricos2318-03312023-08-012810.1590/2318-0331.282320230005Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equationsYuri Taglieri Sáohttps://orcid.org/0000-0003-2037-5451João Batista Pereirahttps://orcid.org/0000-0001-7136-917XGeraldo de Freitas Macielhttps://orcid.org/0000-0003-1272-9045ABSTRACT Non-Newtonian rheology effects, such as pseudoplasticity and viscoplasticity, are understood as shear stresses, incorporated to the energy slope term in the Shallow-Water Equations (SWE). However, non-Newtonian shear stresses are dependent of the shear rate, whose formulation is a function of the gradient of the velocity profile in the bottom. This study investigated two shear rate formulations that are commonly applied in the SWE literature: 1) a non-parameterized function; and 2) a function based on the Herschel-Bulkley rheological model. Their influence in steady uniform flows of non-Newtonian fluids was evaluated through numerical-theoretical comparisons. A Lax-Friedrichs scheme was implemented to solve the SWE system and allowed employing the shear rate formulations. Experimental tests were carried out and numerical simulations of hypothetical scenarios were performed. It was found that the non-parameterized formulation presented deviation in normal depth up to 14% in comparison with theoretical solution, while the formulation based on the Herschel-Bulkley model provided a good agreement, corroborated by punctual Computational Fluid Dynamics simulations (deviation less than 2%) and experimental data. The ratio of both shear rate formulations is strongly correlated to the deviation of normal depth, indicating that the non-parameterized shear rate function does not provide an acceptable result in the steady uniform flow.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312023000100501&tlng=enShallow-water equationsHEC-RASNon-Newtonian fluid
spellingShingle Yuri Taglieri Sáo
João Batista Pereira
Geraldo de Freitas Maciel
Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations
Revista Brasileira de Recursos Hídricos
Shallow-water equations
HEC-RAS
Non-Newtonian fluid
title Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations
title_full Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations
title_fullStr Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations
title_full_unstemmed Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations
title_short Evaluation of shear rate formulations through steady uniform non-Newtonian fluid flows in the context of shallow-water equations
title_sort evaluation of shear rate formulations through steady uniform non newtonian fluid flows in the context of shallow water equations
topic Shallow-water equations
HEC-RAS
Non-Newtonian fluid
url http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2318-03312023000100501&tlng=en
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AT geraldodefreitasmaciel evaluationofshearrateformulationsthroughsteadyuniformnonnewtonianfluidflowsinthecontextofshallowwaterequations