## The fluid and thermal dynamics of rimming flows with boundary slip

Nicholson, Jonathon M. P. (2020) The fluid and thermal dynamics of rimming flows with boundary slip. PhD thesis, University of Nottingham.

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## Abstract

This thesis intends to provide the reader with a detailed understanding of the current research into aero-engine bearing chambers, providing a description of their function and importance to the aerospace industry. The bearing chambers are a complex component where there is a chaotic mix of oil droplets, splashing, heating and geometric complexities which makes conventional analysis techniques costly to implement. The aim of this research is to describe the important physical effects pertinent to the rotational flow found in bearing chambers within a mathematical modelling strategy.

In developing a mathematical model of the flow inside a bearing chamber, it is useful to simplify the geometry. This geometry is a stationary horizontal cylinder. The model includes effects that are specifically important to the bearing chamber. These effects can relate to the film’s inertia or internal pressure which are normally ignored due to the scale of problem under investigation. The proposed model utilises an averaging method of the governing equations, known as depth-averaging, which provides a reasonable estimation of the temporally averaged flow with significant reductions in both time and costs associated with simulations. This method contains the key mechanisms of the film, as well as introducing a new effect that has not been previously considered. This is an effect known as fluid slip, which is typically associated to either; small scale flows, of which the bearing chamber flows can be, or certain texturing methods which can also induce this flow behaviour. This phenomenon is investigated under a variety of flow configurations using the microscopic effects to generate macro scale changes. The thorough exploration of these changes is the main aim of this thesis.

The model is shown to be a well posed extension to classical lubrication theory, which includes both wall slip and inertia. The inertial effects lead to a series of transitional profiles between a stagnating pool and the uniformly distributed film. The film behaviour with fluid slip was shown to create flow recirculation and to have multiple steady profiles in a non-unique solution region. The impact of slip during high levels of inertia is minimal, but in moderate to low levels the imposed surface slip is significant as a flow control technique.

The effect of fluid slip on the film temperatures is relatively small in comparison to thermal convection, which has a direct effect on temperature. When thermal convection is of equal or greater strength relative to conduction, there is a significant increase in the amount of heat contained within the fluid. The main effect of slip is to accelerate the film, which in turn amplifies the rate of convection.

The physical characteristics have been thoroughly detailed, with an emphasis on which values are most important in determining the film profile. Minor variations in these values can lead to drastic deviation from the expected behaviour and necessitates a mindfulness of the temporal problem at large.

Importantly, the quantification of the slip condition is discussed in depth. This includes the range of slip scales that are expected with examples of the structures thought to produce sustainable slip. The most important findings of this thesis are contained in the analysis of the different scales of slip on flows which are characteristic of the bearing chamber.

Item Type: Thesis (University of Nottingham only) (PhD) La Rocca, AntoninoGiddings, DonaldTammisola, OutiPower, HenryHibberd, Stephen Rotational motion; Bearings (Machinery); Fluid-structure interaction; Thin films; T Technology > TA Engineering (General). Civil engineering (General) > TA 357 Fluid mechanics UK Campuses > Faculty of Engineering 60635 Nicholson, Jonathon 31 Jan 2023 08:24 31 Jan 2023 08:28 https://eprints.nottingham.ac.uk/id/eprint/60635

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