Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639057
Title: Computational modelling of non-Newtonian fluids based on the stabilised finite element method
Author: Slijepcevic, S.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2000
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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 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 was discretized with finite elements and time was discretized with a discrete time stepping scheme. The finite element method that is used belongs to the group of stabilised finite element method. The main unknown variables, velocity and pressure are discretized by equal order interpolation functions. 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 that is pressure stabilisation that is necessary to remove pressure oscillations. The stabilisation allows use of equal order interpolation for pressure and velocity fields. Equal order interpolation function had been chosen because of the implementation advantage. The time stepping scheme that is used 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. The highly non linear system of equations that is 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 run 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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.639057  DOI: Not available
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