Thesis

Reduced-order modelling of fluid flows using analytical and numerical methods

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Awarding institution
  • University of Strathclyde
Date of award
  • 2024
Thesis identifier
  • T16870
Person Identifier (Local)
  • 201882192
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • Coating the exterior of a cylinder with a layer of fluid is a fundamental problem in fluid mechanics and occurs in numerous natural processes and industrial applications, such as heat and mass transfer and the production of orthopaedic implants. This thesis formulates and analyses novel models for two different coating flow problems which are not restricted by the common assumptions that the cylinder has circular cross-section and/or that the film is thin. The first problem involves the unsteady, two-dimensional flow on the exterior of a uniformly rotating horizontal cylinder with elliptical cross-section. By using a long-wave approximation we derive a thick-film model, and by using a thin-film approximation we derive a thin-film model. Both models incorporate the effects of cylinder eccentricity, rotation, gravity, centrifugation, viscosity, and surface tension. By studying the thin-film model, we demonstrate both analytically and numerically that the behaviour of the film coating the elliptical cylinder significantly differs from that in the circular case. In particular, it is shown that even a relatively mild departure from circularity produces significant qualitative and quantitative differences from the behaviour in the circular case. The second problem involves the unsteady, three-dimensional flow of a thick film on the exterior of a vertical fibre with circular cross-section. By using a longwave approximation and the method of weighted residuals, we derive a thick-film weighted-residual model, which incorporates the effects of gravity, viscosity, surface tension, and inertia. We study the thick-film weighted-residual model in the linear regime in order to elucidate the mechanics that determine both the stability and the axisymmetry of the flow. We demonstrate that these results in the linear regime, in general, correctly predict the results of the linear calculations of the Navier–Stokes equations and the results of numerical simulations of the thick-film weighted-residual model in the nonlinear regime.
Advisor / supervisor
  • Wilson, Stephen K.
  • Wray, Alexander
Resource Type
DOI
Date Created
  • 2023

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