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Computational modelling of non-Newtonian fluids based on the stabilised finite element method. / Sava Slijepcevic

Swansea University Author: Sava Slijepcevic

Abstract

This work considers numerical modelling of non-Newtonian fluid flow. The motivation for this is the need for simulating industrial processes that involve non- Newtonian fluids. The non-Newtonian fluids that are included belong to the group of generalised Newtonian fluids. Generalised Newtonian fluid...

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Published: 2002
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42378
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spelling 2018-08-02T16:24:29.0257825 v2 42378 2018-08-02 Computational modelling of non-Newtonian fluids based on the stabilised finite element method. f2d4562ee3108662ac5232fdca07f840 NULL Sava Slijepcevic Sava Slijepcevic true true 2018-08-02 This work considers numerical modelling of non-Newtonian fluid flow. The motivation for this is the need for simulating industrial processes that involve non- Newtonian fluids. The non-Newtonian fluids that are included belong to the group of generalised Newtonian fluids. Generalised Newtonian fluids have a non-linear dependence between the shear stain rate and the shear stress, implying a non constant viscosity. Depending on the type of non-linearity generalised Newtonian fluids can be divided into three groups; shear-thinning, shear-thickening and visco-plastic fluids In this work all three groups are considered. The numerical modelling is performed by using a semi-discrete finite element method. The spatial domain is discretized with finite elements while the time domain is discretized with a discrete time stepping scheme. The finite element method that is used belongs to the group of stabilised finite element methods. Two types of stabilisation are employed. The first is the streamline upwind Petrov-Galerkin method (SUPG) stabilisation that is used to prevent the occurrence of spurious node- to-node oscillations that appear in the presence of dominant advective terms. The second type of stabilisation is pressure stabilisation This stabilisation is necessary to remove pressure oscillations and allow for greater flexibility when choosing interpolation functions. Thus the main unknown variables, velocity and pressure are discretized by linear equal order interpolation functions which offers substantial implementation advantages. The time stepping scheme is a single step method with a generalised midpoint rule. The scheme includes a parameter that can be used to obtain a variety of time stepping schemes from backward Euler to trapezoidal rule. The highly non linear system of equations obtained after discretization is solved via the Newton-Raphson solution procedure. After the finite element formulation was discretized, consistently linearised and implemented into a finite element program, several tests were performed to verify the implementation, to determine the accuracy and to prove suitability of this type numerical modelling for industrial applications. Several large scale problems from industrial practice have finally been solved to illustrate capabilities of the methodology. E-Thesis Computational physics.;Fluid mechanics. 31 12 2002 2002-12-31 COLLEGE NANME Engineering COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:29.0257825 2018-08-02T16:24:29.0257825 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sava Slijepcevic NULL 1 0042378-02082018162449.pdf 10798086.pdf 2018-08-02T16:24:49.7130000 Output 5495402 application/pdf E-Thesis true 2018-08-02T16:24:49.7130000 false
title Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
spellingShingle Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
Sava Slijepcevic
title_short Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
title_full Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
title_fullStr Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
title_full_unstemmed Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
title_sort Computational modelling of non-Newtonian fluids based on the stabilised finite element method.
author_id_str_mv f2d4562ee3108662ac5232fdca07f840
author_id_fullname_str_mv f2d4562ee3108662ac5232fdca07f840_***_Sava Slijepcevic
author Sava Slijepcevic
author2 Sava Slijepcevic
format E-Thesis
publishDate 2002
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description This work considers numerical modelling of non-Newtonian fluid flow. The motivation for this is the need for simulating industrial processes that involve non- Newtonian fluids. The non-Newtonian fluids that are included belong to the group of generalised Newtonian fluids. Generalised Newtonian fluids have a non-linear dependence between the shear stain rate and the shear stress, implying a non constant viscosity. Depending on the type of non-linearity generalised Newtonian fluids can be divided into three groups; shear-thinning, shear-thickening and visco-plastic fluids In this work all three groups are considered. The numerical modelling is performed by using a semi-discrete finite element method. The spatial domain is discretized with finite elements while the time domain is discretized with a discrete time stepping scheme. The finite element method that is used belongs to the group of stabilised finite element methods. Two types of stabilisation are employed. The first is the streamline upwind Petrov-Galerkin method (SUPG) stabilisation that is used to prevent the occurrence of spurious node- to-node oscillations that appear in the presence of dominant advective terms. The second type of stabilisation is pressure stabilisation This stabilisation is necessary to remove pressure oscillations and allow for greater flexibility when choosing interpolation functions. Thus the main unknown variables, velocity and pressure are discretized by linear equal order interpolation functions which offers substantial implementation advantages. The time stepping scheme is a single step method with a generalised midpoint rule. The scheme includes a parameter that can be used to obtain a variety of time stepping schemes from backward Euler to trapezoidal rule. The highly non linear system of equations obtained after discretization is solved via the Newton-Raphson solution procedure. After the finite element formulation was discretized, consistently linearised and implemented into a finite element program, several tests were performed to verify the implementation, to determine the accuracy and to prove suitability of this type numerical modelling for industrial applications. Several large scale problems from industrial practice have finally been solved to illustrate capabilities of the methodology.
published_date 2002-12-31T03:52:51Z
_version_ 1763752616876048384
score 11.014358

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