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Load and loss for high-speed lubrication flows of pressurized gases between non-concentric cylinders

Published online by Cambridge University Press:  20 March 2019

S. Y. Chien Open the ORCID record for S. Y. Chien [Opens in a new window]  and
M. S. Cramer
S. Y. Chien*
Affiliation:
Engineering Mechanics Program, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
M. S. Cramer
Affiliation:
Engineering Mechanics Program, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
*
†Email address for correspondence: [email protected]
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Abstract

We examine the high-speed flow of pressurized gases between non-concentric cylinders where the inner cylinder rotates at constant speed while the outer cylinder is stationary. The flow is taken to be steady, two-dimensional, compressible, laminar, single phase and governed by a Reynolds lubrication equation. Approximations for the lubricating force and friction loss are derived using a perturbation expansion for large speed numbers. The present theory is valid for general Navier–Stokes fluids at nearly all states corresponding to ideal, dense and supercritical gases. Results of interest include the observation that pressurization gives rise to large increases in the lubricating force and decreases in the fluid friction. The lubrication force is found to scale with the bulk modulus. Within the context of the Reynolds equation an exact relation between total heat transfer and power loss is developed.

JFM classification

Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 1 - 25
Copyright
© 2019 Cambridge University Press 

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