Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99</m...

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Autores principales:	Juliana Bertoco, Rosalía T. Leiva, Luís L. Ferrás, Alexandre M. Afonso, Antonio Castelo
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	viscoelastic fluids generalised PTT model finite-differences development length Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/c5b10d0a48c34e5a9acccc1cc53686fa
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spelling	oai:doaj.org-article:c5b10d0a48c34e5a9acccc1cc53686fa2021-11-11T15:23:42ZDevelopment Length of Fluids Modelled by the gPTT Constitutive Differential Equation10.3390/app1121103522076-3417https://doaj.org/article/c5b10d0a48c34e5a9acccc1cc53686fa2021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10352https://doaj.org/toc/2076-3417In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99</mn><mo>%</mo></mrow></semantics></math></inline-formula> of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is presented. The numerical results showed that in the creeping flow limit (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>. For low values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, the highest value of the development length is obtained for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>β</mi><mo>=</mo><mn>0.5</mn></mrow></semantics></math></inline-formula>; for high values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, the highest value of the development length is obtained for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>β</mi><mo>=</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>. This work also considers the influence of the elasticity number.Juliana BertocoRosalía T. LeivaLuís L. FerrásAlexandre M. AfonsoAntonio CasteloMDPI AGarticleviscoelastic fluidsgeneralised PTT modelfinite-differencesdevelopment lengthTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10352, p 10352 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	viscoelastic fluids generalised PTT model finite-differences development length Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	viscoelastic fluids generalised PTT model finite-differences development length Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Juliana Bertoco Rosalía T. Leiva Luís L. Ferrás Alexandre M. Afonso Antonio Castelo Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
description	In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>99</mn><mo>%</mo></mrow></semantics></math></inline-formula> of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> is presented. The numerical results showed that in the creeping flow limit (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>e</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>. For low values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, the highest value of the development length is obtained for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>β</mi><mo>=</mo><mn>0.5</mn></mrow></semantics></math></inline-formula>; for high values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>W</mi><mi>i</mi></mrow></semantics></math></inline-formula>, the highest value of the development length is obtained for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mi>β</mi><mo>=</mo><mn>1.5</mn></mrow></semantics></math></inline-formula>. This work also considers the influence of the elasticity number.
format	article
author	Juliana Bertoco Rosalía T. Leiva Luís L. Ferrás Alexandre M. Afonso Antonio Castelo
author_facet	Juliana Bertoco Rosalía T. Leiva Luís L. Ferrás Alexandre M. Afonso Antonio Castelo
author_sort	Juliana Bertoco
title	Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
title_short	Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
title_full	Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
title_fullStr	Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
title_full_unstemmed	Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation
title_sort	development length of fluids modelled by the gptt constitutive differential equation
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/c5b10d0a48c34e5a9acccc1cc53686fa
work_keys_str_mv	AT julianabertoco developmentlengthoffluidsmodelledbythegpttconstitutivedifferentialequation AT rosaliatleiva developmentlengthoffluidsmodelledbythegpttconstitutivedifferentialequation AT luislferras developmentlengthoffluidsmodelledbythegpttconstitutivedifferentialequation AT alexandremafonso developmentlengthoffluidsmodelledbythegpttconstitutivedifferentialequation AT antoniocastelo developmentlengthoffluidsmodelledbythegpttconstitutivedifferentialequation
_version_	1718435391929843712

Development Length of Fluids Modelled by the gPTT Constitutive Differential Equation

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