Thin film rimming flow subject to droplet impact at the surface

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Williams, Joanne, 1978- (2009) Thin film rimming flow subject to droplet impact at the surface. PhD thesis, University of Nottingham.

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Abstract

A bearing chamber may be modelled as a horizontal cylinder, stationary or rotating about its axis, with a film of fluid coating the inside of the cylinder wall. The impact of droplets from a two-phase flow in the core of the chamber drives the motion of the oil film. In this thesis we develop a model for the film based on conservation of mass and momentum across the interface between the film and the core, droplet-laden flow.

We derive a fourth-order partial differential equation for the film thickness which can be applied to a range of droplet parameters. Solution of this equation is primarily numerical, but approximating it by a cubic also provides useful analytical results.

The equation for film thickness contains terms omitted by previous models of the bearing chamber. In particular, we show that terms due to the azimuthal component of droplet motion have a significant effect on film profiles, as they tend to destabilise shock solutions. A dominance of surface tension over the azimuthal droplet momentum is critical for stable steady shock solutions to exist.

We consider the effect of the droplet impact being non-uniform about the cylinder, and the positioning of a sink to remove the mass added to the film by the droplets. We will also examine the underlying flow in the film, with particular note of recirculation regions and the residence time of the fluid in the chamber. These factors may be key to the effectiveness of the fluid as a coolant. We also show that Marangoni stresses on the film surface, one of the effects of heating the cylinder, can be modelled using the same film equation and also has a destabilizing effect.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Hibberd, S.
Power, H.
Riley, D.S.
Subjects: Q Science > QA Mathematics > QA299 Analysis
Q Science > QC Physics > QC170 Atomic physics. Constitution and properties of matter
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 10670
Depositing User: EP, Services
Date Deposited: 09 Feb 2009 11:32
Last Modified: 16 Oct 2017 12:56
URI: https://eprints.nottingham.ac.uk/id/eprint/10670

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