Spectral element methods for predicting the die-swell of Newtonian and viscoelastic fluids

Russo, Giancarlo 2009. Spectral element methods for predicting the die-swell of Newtonian and viscoelastic fluids. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

This thesis is concerned with the development of numerical methods for free surface problems. In particular, the die-swell problem is analyzed for Newtonian and viscoelastic fluids. For several materials comparisons with experiments are presented. The viscoelastic models explored are the Upper Convective Maxwell model, single and multi-mode Oldroyd B and the single and multi-mode eXtended Pom-Pom models. The numerical method employed is based on a spectral element method. The time marching scheme follows a pseudo-transient approach. Discretization in time is performed by means of the Operator-Integration FActor Splitting method of first and second order. The free surface evolves according to an Adams-Bashforth scheme of order three. Comparison with first and second order schemes are also presented for the Newtonian case. The viscoelastic scheme is uncoupled. The fully discretized constitutive equation is solved using a Bi-Conjugate Gradient Stabilized method, while the mass and momentum equations are solved simultaneously by means of the Conjugate Gradient method. Preconditioners are used to accelerate the inversion process. The die-swell of a Newtonian fluid is investigated. The physical interpretation of the phenomenon for Newtonian fluids is also revisited, with the goal of reanalyzing findings from the literature and enrich them by means of specifically addressed numerical simulations. The effect of inertia and surface tension are considered. Analysis of convergence is performed and comparison with available results are presented. Numerical simulations of viscoelastic die-swell are performed for the UCM, Oldroyd-B and XPP models. The effect of elasticity is analyzed through the stress fields, normal stress difference, pressure drops and swelling ratios. For the Oldroyd-B and XPP models, several materials are fully characterized for quantitative comparisons. For the XPP model, the effect of orientation and polydispersity on extrusion is discussed.

Item Type:	Thesis (PhD)
Status:	Unpublished
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Date of First Compliant Deposit:	30 March 2016
Last Modified:	19 Mar 2016 23:19
URI:	https://orca.cardiff.ac.uk/id/eprint/47063

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