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

Kay, E.D.; Hibberd, S.; Power, H.

Authors

E.D. Kay

S. Hibberd

H. Power



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.

Citation

Kay, E., Hibberd, S., & Power, H. (in press). Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear. Physics of Fluids, 25(10), doi:10.1063/1.4825134

Journal Article Type Article
Acceptance Date Sep 25, 2013
Online Publication Date Oct 18, 2013
Deposit Date Oct 16, 2017
Publicly Available Date
Journal Physics of Fluids
Print ISSN 1070-6631
Electronic ISSN 1089-7666
Publisher AIP Publishing
Peer Reviewed Peer Reviewed
Volume 25
Issue 10
DOI https://doi.org/10.1063/1.4825134
Public URL http://eprints.nottingham.ac.uk/id/eprint/47275
Publisher URL http://aip.scitation.org/doi/10.1063/1.4825134
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf