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Title: Spectral element methods for predicting the die-swell of Newtonian and viscoelastic fluids
Author: Russo, Giancarlo
ISNI:       0000 0004 2733 3155
Awarding Body: Cardiff University
Current Institution: Cardiff University
Date of Award: 2009
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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 Split ting 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 vis coelastic 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. Preconditioned 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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics