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

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

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), https://doi.org/10.1063/1.4825134

• Journal Article Type: Article
• Acceptance Date: Sep 25, 2013
• Online Publication Date: Oct 18, 2013
• Deposit Date: Oct 16, 2017
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 25
• Issue: 10
• DOI: https://doi.org/10.1063/1.4825134
• Public URL: https://nottingham-repository.worktribe.com/output/718648
• Publisher URL: http://aip.scitation.org/doi/10.1063/1.4825134
• Contract Date: Oct 15, 2017