This thesis is concerned with the numerical simulation of Newtonian and viscoelastic free-surface flows. This work is novel in advance of hybrid finite volume and free-surface techniques, and in the study of particular industrial flows. The presence of free-surfaces in a number of complex industrial flows, gives rise to instabilities during processing. Consequently, these instabilities impose certain limitations on processing windows and final product quantity. Accordingly, an important aspect of the current work is to investigate these instabilities, with a view to suggesting possible remedies for suppression. A transient semi-implicit Taylor-Galerkin/pressure-correction time-stepping framework is employed, accommodating both finite element (FE) and finite volume (FV) schemes. FE discretisation is used for the momentum-continuity equations, whilst the constitutive equations are resolved through finite volume cell-vertex approximation. To quantify the accuracy, stability and consistency of the proposed FV method, we have chosen a model sink-flow problem, that has an analytical solution. Our interest is to explore the consequences of utilising conventional cell-vertex methodology for an Oldroyd-B model and to demonstrate deficiencies in the presence of complex source terms. In this manner, a consistent approach is derived. The first complex problem addressed is that of industrial reverse-roller coating for Newtonian viscous flows. The evolving position of the free-surface, whose position is unknown a <I>priori, </I>is computed using kinematic boundary adjustment with mesh-stretching algorithms. The problem is analysed first to steady-state, prior to transient considerations. We have found pressure maxima to arise in the nip region, that subsequently produce elevated levels of lift on the foil. In addition, we have investigated the influence of these elevated forces (lift) on the foil, by adjusting nip-width in time. Variation in nip-gap width introduces temporal foil-vibration. This is found to have a significant impact upon pressure and lift on the foil. Such temporal changes in nip-width, also generated free-surface instabilities that act upon the coating layer (film-thickness). A second problem studied is that associated with filament-stretching flows. The long-time, large extensional deformations and break-up of Newtonian fluids is analysed, based on an axisymmetric, time-dependent half-length model. The simulation is performed between two plates, which depart at an exponentially increasing rate. Due to the presence of rigid-end-plates and imposed pinning boundary conditions, the radius of the filament varies along its length. Ultimately, this leads to filament break-up. Various remeshing schemes have been introduced. A cost-effective approach is proposed, that suppresses premature filament breakup and maintains accuracy and stability within the computer predictions up to large Hencky-strain levels. Finally, attention is turned to filament-stretching for viscoelastic fluids. Here, we have recourse to the hybrid FE/FV approach and a coupled/decoupled algorithm is outlined. Various aspects of the problem are addressed and results are compared against those for Newtonian fluids, considering a full-length model. With regard to upwinding discretisation, we have contrasted performance of both LDB and LAX-Wendroff schemes. An optimum choice has emerged that captures stress field accurately in the vicinity of the free-surface.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:636224 |
| Date | January 2000 |
| Creators | Chandio, M. S. |
| Publisher | Swansea University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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