Fluid dynamics of the slip boundary condition for isothermal rimming flow with moderate inertial effects

Nicholson, J.M.P.; Power, H.; Tammisola, O.; Hibberd, S.; Kay, E.D.

Abstract

Motivated by evaluating coating oil films within bearing chambers in an aero-engine application, an analysis is presented for the fluid dynamics relevant in their dual capacity as both coolant and lubricant in highly sheared flows that may approach microscale thickness. An extended model is developed for isothermal rimming flow driven by substantial surface shear within a stationary cylinder. In particular, a partial slip condition replaces the no-slip condition at the wall whilst retaining inertial effects relevant to an intrinsic high speed operation. A depth-averaged formulation is presented that includes appropriate inertial effects at leading-order within a thin film approximation that encompass a more general model of assessing the impact of surface slip. Non-dimensional mass and momentum equations are integrated across the film depth yielding a one dimensional problem with the a priori assumption of local velocity profiles. The film flow solutions for rimming flow with wall slip are modelled to a higher order than classical lubrication theory. We investigate the impact of wall slip on the transition from pooling to uniform films. Numerical solutions of film profiles are provided for progressively increased Reynolds number, within a moderate inertia regime, offering evaluation into the effect of film slippage on the dynamics of rimming flow. We find that slip allows non-unique solution regions and existence of multiple possible steady state solutions evaluated in transforming from smooth to pooling film solutions. Additionally, boundary slip is shown to enhance the development of recirculation regions within the film which are detrimental to bearing chamber flows.

Citation

Nicholson, J., Power, H., Tammisola, O., Hibberd, S., & Kay, E. (2019). Fluid dynamics of the slip boundary condition for isothermal rimming flow with moderate inertial effects. Physics of Fluids, 31(3), 1-17. https://doi.org/10.1063/1.5085497

• Journal Article Type: Article
• Acceptance Date: Mar 8, 2019
• Online Publication Date: Mar 29, 2019
• Publication Date: Mar 29, 2019
• Deposit Date: Mar 29, 2019
• Publicly Available Date: Mar 29, 2019
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: AIP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 31
• Issue: 3
• Article Number: 033602
• Pages: 1-17
• DOI: https://doi.org/10.1063/1.5085497
• Keywords: Condensed Matter Physics
• Public URL: https://nottingham-repository.worktribe.com/output/1711369
• Publisher URL: https://aip.scitation.org/doi/full/10.1063/1.5085497
• Additional Information: Received: 2018-12-13; Accepted: 2019-03-08; Published: 2019-03-29