Dang, Thuy Duong;
(2024)
Three-dimensional flow analysis for (a) Hele-Shaw configurations, (b) melting of wall-mounted ice.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
This study initially examines the three-dimensional fluid flow in a channel which is rendered three-dimensional by means of a thin semi-infinite divider spanning from one wall to the other. The effect is thus that of a three-dimensional bifurcation. The relative flow rate as represented by the Reynolds number is assumed to be large. A combination of matched asymptotic expansions and numerical methods is used to interpret the behaviour of the boundary layer(s) near the divider and the channel walls, and the quasi-inviscid flow in the region between them. The model here is simulating laminar flow with the incident oncoming flow being steady plane Poiseuille flow ahead of the junction with the bifurcation. It is also assumed that there is no significant flow in the cross-plane geometry over the streamwise length scales. The solution in the channel cross section immediately after the junction is in fact broken down into four different regions, where the fluid behaviour is determined by interaction with the channel walls, the divider, the corners at which the wall and divider meet and finally, the core flow. The core flow especially is studied using both analytical and numerical techniques with the results showing agreement. In a follow-up study, using many of the above findings, the thin semi-infinite divider plate is replaced by a thin elliptical divider and the effects of flow far downstream from varying the ellipse's thickness are investigated. This aspect has connections with the classical Hele-Shaw configuration but, unlike most studies, the present work focusses on the regime where the inertial influence is a strong one. In the second half of the thesis, melting of ice in uniform shear flow near a fixed wall is studied in both two and three dimensions. The scenario in question involves a body of ice resting on a warm wall, with oncoming fluid of the same temperature as the wall. The unsteady interaction of the flow, heat transfer and phase change are studied analytically and numerically. Evolution of the ice shape subject to initial conditions, heat transfer effects and sub-melting wall temperature are considered. Melting times, vanishing points and the induced pressure gradient caused by the flow are computed for different ice heights. Analyses of varying background heat transfer are presented, addressing cases where this caused accretion of ice. Examination of the effects of static and oscillating sub-melting temperatures underneath the ice are addressed using analytical techniques and numerical results are presented in support of this.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Three-dimensional flow analysis for (a) Hele-Shaw configurations, (b) melting of wall-mounted ice |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2025. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10202735 |
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