Thesis
Reduced-order modelling of electrohydrodynamic flows on a circular cylinder
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2024
- Thesis identifier
- T16892
- Person Identifier (Local)
- 201966245
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- This thesis concerns the theoretical modelling and analysis of a two-dimensional film of a perfectly conducting Newtonian liquid coating a uniformly rotating horizontal cylindrical electrode. The system is enclosed by a concentric outer electrode, with the electric potential difference between the inner and outer electrodes inducing electrostatic forces at the liquid-gas interface. The system is investigated for both thin and thick films. A thin-film model, derived using a classical lubrication approximation, incorporates the effects of rotation, gravity, viscosity, capillarity, and electric stress, whilst a thick-film model, derived using long-wave scalings and the method of weighted residuals, also includes the additional effects of viscous dissipation and inertia. First, as an essential precursor to the electrostatic case, the thin-film model is studied in the absence of an electric field in the case in which the inner electrode is stationary. A complete description of the late-time asymptotic behaviour of the film is derived that reveals three distinct regions of behavior, with the interplay between gravity and capillarity resulting in a capillary-ripple structure. Next, the full thin-film model is studied. For a stationary inner electrode, under conditions of weak electrostatic effects, the qualitative behavior is unchanged from the situation in which the electric field is absent. For a rotating inner electrode, a numerical parametric study reveals four distinct behaviors: steady, periodic, transient, and outer contact (in which the film touches the outer electrode in a finite time). Linear stability and multiple-timescale analyses are performed and reveal that electrostatic effects induce instability, leading to outer contact. Finally, the full thick-film model is investigated, revealing qualitatively similar behaviour to that in the thin-film case. The spatiotemporal distribution of the electric potential at the outer electrode is used to control the flow and, in particular, the interface is successfully controlled towards complex target shapes using optimal control.
- Advisor / supervisor
- Wilson, Stephen
- Wray, Alexander
- Resource Type
- DOI
- Funder
Relações
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PDF of thesis T16892 | 2024-04-23 | Público | Baixar |