Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear

Kay, E.D. and Hibberd, S. and Power, H. (2013) Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear. Physics of Fluids, 25 (10). 102108-1-102108-24. ISSN 1089-7666

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Abstract

In this paper, we study two-dimensional thin-film flow inside a stationary circular cylinder driven by an imposed surface shear stress. Modelling is motivated by a need to understand the cooling and film dynamics provided by oil films in an aero-engine bearing chamber characterised by conditions of very high surface shear and additional film mass flux from oil droplets entering the film through the surface. In typical high-speed operation, film inertial effects can provide a significant leading-order mechanism neglected in existing lubrication theory models. Inertia at leading-order is included within a depth-averaged formulation where wall friction is evaluated similar to hydraulic models. This allows key nonlinear inertial effects to be included while retaining the ability to analyse the problem in a mathematically tractable formulation and compare with other approaches. In constructing this model, a set of simplified mass and momentum equations are integrated through the depth of the film yielding a spatially one-dimensional depth-averaged formulation of the problem. An a priori assumed form of velocity profile is needed to complete the system. In a local Stokes flow analysis, a quadratic profile is the exact solution for the velocity field though it must be modified when inertial effects become important. Extension of the velocity profile to a cubic profile is selected enabling specification of a wall friction model to include the roughness of the cylinder wall. A modelling advantage of including the inertia term, relevant to the applications considered, is that a smooth progression in solution can be obtained between cases of low Reynolds number corresponding to lubrication theory, and high Reynolds number corresponding to uniform rimming-flow. Importantly, we also investigate the effect of inertia on some typical solutions from other studies and present a greater insight to existing and new film solutions which arise from including inertia effects.

Item Type: Article
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
University of Nottingham, UK > Faculty of Engineering > Department of Mechanical, Materials and Manufacturing Engineering
University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1063/1.4825134
Depositing User: LIN, Zhiren
Date Deposited: 16 Oct 2017 10:38
Last Modified: 17 Oct 2017 20:08
URI: http://eprints.nottingham.ac.uk/id/eprint/47275

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