Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear
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...
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| Format: | Article |
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American Institute of Physics
2013
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| Online Access: | https://eprints.nottingham.ac.uk/47275/ |
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| author | Kay, E.D. Hibberd, S. Power, H. |
| author_facet | Kay, E.D. Hibberd, S. Power, H. |
| author_sort | Kay, E.D. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:04:57Z |
| format | Article |
| id | nottingham-47275 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:04:57Z |
| publishDate | 2013 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-472752020-05-04T16:39:18Z https://eprints.nottingham.ac.uk/47275/ Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear Kay, E.D. Hibberd, S. Power, H. 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. American Institute of Physics 2013-10-18 Article PeerReviewed Kay, E.D., 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 http://aip.scitation.org/doi/10.1063/1.4825134 doi:10.1063/1.4825134 doi:10.1063/1.4825134 |
| spellingShingle | Kay, E.D. Hibberd, S. Power, H. Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear |
| title | Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear |
| title_full | Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear |
| title_fullStr | Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear |
| title_full_unstemmed | Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear |
| title_short | Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear |
| title_sort | inertial effects at moderate reynolds number in thin-film rimming flows driven by surface shear |
| url | https://eprints.nottingham.ac.uk/47275/ https://eprints.nottingham.ac.uk/47275/ https://eprints.nottingham.ac.uk/47275/ |