Elastoviscoplastic Fluid Flow in Non-Circular Tubes: Transversal Field and Interplay of Elasticity and Plasticity

Mario F. Letelier, Cristian Barrera, A. Gonzalez, Siginer Dennis

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

An analytical study of elastoviscoplastic fluid flow in tubes of non-circular cross section is presented. The constitutive structure of the fluid is described by a linear frame invariant combination of the Phan-Thien−Tanner model of viscoelastic fluids and the Bingham model of plastic fluids. Non-circular tube cross sections are modeled by the shape factor method a one-to-one mapping of the circular base contour into a wide spectrum family of arbitrary tube contours. Field variables are expanded into asymptotic series in terms of the elasticity measure, the Weissenberg number We, coupled with an asymptotic expansion in terms of the geometrical mapping parameter ε leading to a set of hierarchical momentum balance equations which are solved successively up to and including the third order in We when the secondary field appears for the first time. The computational algorithm developed is applied to the study of the non-rectilinear flow in tubes with triangular and square cross sections. We find that the presence of the yield stress dampens the intensity of the purely viscoelastic vortices, the higher the yield stress the lower the intensity of the vortices in the cross-section, and the further away the vortices are from the center of the cross section as compared to the purely viscoelastic vortices. The results also evidence that viscoelasticity increases the axial flow for given viscoplastic conditions and pressure drop, and consequently increases the rate of flow, a phenomenon that may find applications in optimizing material transportation.
Original languageEnglish
JournalApplied Mathematical Modelling
DOIs
Publication statusPublished - 2016

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Plasticity
Fluid Flow
Elasticity
Flow of fluids
Tube
Vortex flow
Cross section
Vortex
Yield Stress
Fluids
Yield stress
Axial flow
Viscoelasticity
Fluid
Asymptotic series
Viscoelastic Fluid
Pressure drop
Pressure Drop
Balance Equations
Computational Algorithm

Cite this

@article{f517aee7adbe40acb08fb6e5955b2cb9,
title = "Elastoviscoplastic Fluid Flow in Non-Circular Tubes: Transversal Field and Interplay of Elasticity and Plasticity",
abstract = "An analytical study of elastoviscoplastic fluid flow in tubes of non-circular cross section is presented. The constitutive structure of the fluid is described by a linear frame invariant combination of the Phan-Thien−Tanner model of viscoelastic fluids and the Bingham model of plastic fluids. Non-circular tube cross sections are modeled by the shape factor method a one-to-one mapping of the circular base contour into a wide spectrum family of arbitrary tube contours. Field variables are expanded into asymptotic series in terms of the elasticity measure, the Weissenberg number We, coupled with an asymptotic expansion in terms of the geometrical mapping parameter ε leading to a set of hierarchical momentum balance equations which are solved successively up to and including the third order in We when the secondary field appears for the first time. The computational algorithm developed is applied to the study of the non-rectilinear flow in tubes with triangular and square cross sections. We find that the presence of the yield stress dampens the intensity of the purely viscoelastic vortices, the higher the yield stress the lower the intensity of the vortices in the cross-section, and the further away the vortices are from the center of the cross section as compared to the purely viscoelastic vortices. The results also evidence that viscoelasticity increases the axial flow for given viscoplastic conditions and pressure drop, and consequently increases the rate of flow, a phenomenon that may find applications in optimizing material transportation.",
author = "Letelier, {Mario F.} and Cristian Barrera and A. Gonzalez and Siginer Dennis",
year = "2016",
doi = "10.1016/j.apm.2017.10.008",
language = "English",
journal = "Applied Mathematical Modelling",
issn = "0307-904X",
publisher = "Elsevier Inc.",

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Elastoviscoplastic Fluid Flow in Non-Circular Tubes: Transversal Field and Interplay of Elasticity and Plasticity. / Letelier, Mario F.; Barrera, Cristian; Gonzalez, A.; Dennis, Siginer.

In: Applied Mathematical Modelling, 2016.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Elastoviscoplastic Fluid Flow in Non-Circular Tubes: Transversal Field and Interplay of Elasticity and Plasticity

AU - Letelier, Mario F.

AU - Barrera, Cristian

AU - Gonzalez, A.

AU - Dennis, Siginer

PY - 2016

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N2 - An analytical study of elastoviscoplastic fluid flow in tubes of non-circular cross section is presented. The constitutive structure of the fluid is described by a linear frame invariant combination of the Phan-Thien−Tanner model of viscoelastic fluids and the Bingham model of plastic fluids. Non-circular tube cross sections are modeled by the shape factor method a one-to-one mapping of the circular base contour into a wide spectrum family of arbitrary tube contours. Field variables are expanded into asymptotic series in terms of the elasticity measure, the Weissenberg number We, coupled with an asymptotic expansion in terms of the geometrical mapping parameter ε leading to a set of hierarchical momentum balance equations which are solved successively up to and including the third order in We when the secondary field appears for the first time. The computational algorithm developed is applied to the study of the non-rectilinear flow in tubes with triangular and square cross sections. We find that the presence of the yield stress dampens the intensity of the purely viscoelastic vortices, the higher the yield stress the lower the intensity of the vortices in the cross-section, and the further away the vortices are from the center of the cross section as compared to the purely viscoelastic vortices. The results also evidence that viscoelasticity increases the axial flow for given viscoplastic conditions and pressure drop, and consequently increases the rate of flow, a phenomenon that may find applications in optimizing material transportation.

AB - An analytical study of elastoviscoplastic fluid flow in tubes of non-circular cross section is presented. The constitutive structure of the fluid is described by a linear frame invariant combination of the Phan-Thien−Tanner model of viscoelastic fluids and the Bingham model of plastic fluids. Non-circular tube cross sections are modeled by the shape factor method a one-to-one mapping of the circular base contour into a wide spectrum family of arbitrary tube contours. Field variables are expanded into asymptotic series in terms of the elasticity measure, the Weissenberg number We, coupled with an asymptotic expansion in terms of the geometrical mapping parameter ε leading to a set of hierarchical momentum balance equations which are solved successively up to and including the third order in We when the secondary field appears for the first time. The computational algorithm developed is applied to the study of the non-rectilinear flow in tubes with triangular and square cross sections. We find that the presence of the yield stress dampens the intensity of the purely viscoelastic vortices, the higher the yield stress the lower the intensity of the vortices in the cross-section, and the further away the vortices are from the center of the cross section as compared to the purely viscoelastic vortices. The results also evidence that viscoelasticity increases the axial flow for given viscoplastic conditions and pressure drop, and consequently increases the rate of flow, a phenomenon that may find applications in optimizing material transportation.

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JO - Applied Mathematical Modelling

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