Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Williams, Joanne, 1978- (2009)
Languages: English
Types: Unknown

Classified by OpenAIRE into

arxiv: Physics::Fluid Dynamics
A bearing chamber may be modelled as a horizontal cylinder, stationary or rotating about its axis, with a film of fluid coating the inside of the cylinder wall. The impact of droplets from a two-phase flow in the core of the chamber drives the motion of the oil film. In this thesis we develop a model for the film based on conservation of mass and momentum across the interface between the film and the core, droplet-laden flow. We derive a fourth-order partial differential equation for the film thickness which can be applied to a range of droplet parameters. Solution of this equation is primarily numerical, but approximating it by a cubic also provides useful analytical results. The equation for film thickness contains terms omitted by previous models of the bearing chamber. In particular, we show that terms due to the azimuthal component of droplet motion have a significant effect on film profiles, as they tend to destabilise shock solutions. A dominance of surface tension over the azimuthal droplet momentum is critical for stable steady shock solutions to exist. We consider the effect of the droplet impact being non-uniform about the cylinder, and the positioning of a sink to remove the mass added to the film by the droplets. We will also examine the underlying flow in the film, with particular note of recirculation regions and the residence time of the fluid in the chamber. These factors may be key to the effectiveness of the fluid as a coolant. We also show that Marangoni stresses on the film surface, one of the effects of heating the cylinder, can be modelled using the same film equation and also has a destabilizing effect.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [11] A. L. Bertozzi, A. MuÄnch, and M. Shearer. Undercompressive shocks in thin ¯lm °ows. Physica D, 134(4):431{464, 1999.
    • [12] B. R. Du®y and S. K. Wilson. Thin-¯lm and curtain °ows on the outside of a rotating horizontal cylinder. Journal of Fluid Mechanics, 394:29{49, 1999.
    • [23] D.-Y. Hsieh and H. S.P. Wave and Stability in Fluids. World Scienti¯c, 1994.
    • [24] T. P. Hynes. Stability of thin ¯lms. PhD thesis, Cambridge, 1978.
    • [25] R. E. Johnson. Steady-state coating °ows inside a rotating horizontal cylinder. Journal of Fluids Mechanics, 190:321{342, 1988.
    • [26] R. E. Johnson. Coating °ow stability in rotational molding. In G. Yates, editor, Engineering Science, Fluid Dynamics: A symposium to honor T. Y. Wu, pages 435{449. World Scienti¯c, Singapore, 1990.
    • [27] S. Kalliadasis, E. A. Demekhin, C. Ruyer-Quil, and M. G. Velarde. Thermocapillary instability and wave formation on a ¯lm falling down a uniformly heated plane. Journal of Fluid Mechanics, 492:303{338, 2003.
    • [28] S. Kalliadasis, A. Kiyashko, and E. A. Demekhin. Marangoni instability of a thin liquid ¯lm heated from below by a local heat source. Journal of Fluid Mechanics, 475:377{408, 2003.
    • [37] S. B. G. O'Brien. Linear stability of rimming °ow. Quarterly of Applied Mathematics, 60(2):201{211, 2002.
    • [50] P. M. J. Trevelyan and S. Kalliadasis. Wave dynamics on a thin-liquid ¯lm falling down a heated wall. Journal of Engineering Mathematics, 50(2-3):177{208, 2004.
    • [52] M. Villegas-D¶³az, H. Power, and D. S. Riley. On the stability of rimming °ows to two-dimensional disturbances. Fluid Dynamics Research, 33(1-2):141{172, 2003.
    • [53] M. Villegas-D¶³az, H. Power, and D. S. Riley. Analytical and numerical studies of the stability of thin-¯lm rimming °ow subject to surface shear. Journal of Fluid Mechanics, 541:317{344, 2005.
    • [54] Y. Wang, K. Simmons, and S. Hibberd. Numerical study of the e®ect of injected oil droplets on the core air °ow with a HP-IP bearing chamber model. Report to Rolls Royce, (UTC/TF/2000/17/YW), 2000.
    • [55] Y. Wang, K. Simmons, and S. Hibberd. Numerical investigation of the turbulent °ow ¯eld and oil droplet motion in an annulus with co-/contra- rotating shafts. Report to Rolls Royce, (UTC/TF/2001/29/YW), 2001.
    • [56] Y. Wang, K. Simmons, S. Hibberd, and C. Eastwick. CFD study of the single-phase air °ow ¯eld and oil droplet motion in the Rolls-Royce HP-IP bearing chamber. Report to Rolls Royce, (UTC/TF/1999/13/YW), 1999.
  • No related research data.
  • No similar publications.

Share - Bookmark

Cite this article