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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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References

Bell, I. H., Wronski, J., Quoilin, S. & Lemort, V. 2014 Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library CoolProp. Ind. Engng Chem. Res. 53 (6), 2498–2508.Google Scholar
Briggs, M. H., Prahl, J. M., Bruckner, R. & Dykas, B. 2008 High pressure performance of foil journal bearings in various gases. In STLE/ASME 2008 International Joint Tribology Conference, pp. 403–405. American Society of Mechanical Engineers.Google Scholar
Chien, S. Y. & Cramer, M. S. 2019 Pressure, temperature, and heat flux in high speed lubrication flows of pressurized gases. Tribol. Intl 129, 468–475.Google Scholar
Chien, S. Y., Cramer, M. S. & Untaroiu, A. 2017a Compressible Reynolds equation for high-pressure gases. Phys. Fluids 29 (11), 116101.Google Scholar
Chien, S. Y., Cramer, M. S. & Untaroiu, A. 2017b A compressible thermohydrodynamic analysis of journal bearings lubricated with supercritical CO2 . In ASME Conference Paper FEDSM2017-69310.Google Scholar
Chung, T. H., Ajlan, M., Lee, L. L. & Starling, K. E. 1988 Generalized multiparameter correlation for nonpolar and polar fluid transport properties. Ind. Engng Chem. Res. 27 (4), 671–679.Google Scholar
Chung, T. H., Lee, L. L. & Starling, K. E. 1984 Applications of kinetic gas theories and multiparameter correlation for prediction of dilute gas viscosity and thermal conductivity. Ind. Engng Chem. Fundam. 23 (1), 8–13.Google Scholar
Conboy, T. M. 2013 Real-gas effects in foil thrust bearings operating in the turbulent regime. J. Tribol. 135 (3), 031703.Google Scholar
Conboy, T. M., Wright, S. A., Pasch, J., Fleming, D., Rochau, G. & Fuller, R. 2012 Performance characteristics of an operating supercritical CO2 Brayton cycle. Trans. ASME J. Engng Gas Turbines Power 134 (11), 111703.Google Scholar
Crespi, F., Gavagnin, G., Sánchez, D. & Martínez, G. S. 2017 Supercritical carbon dioxide cycles for power generation: a review. Appl. Energy 195, 152–183.Google Scholar
DellaCorte, C., Radil, K. C., Bruckner, R. J. & Howard, S. A. 2008 Design, fabrication, and performance of open source generation I and II compliant hydrodynamic gas foil bearings. Tribol. Trans. 51 (3), 254–264.Google Scholar
Dostal, V., Driscoll, M. J. & Hejzlar, P.2004 A supercritical carbon dioxide cycle for next generation nuclear reactors. Tech. Rep. MIT-ANP-TR-100.Google Scholar
Dousti, S. & Allaire, P. 2016 A compressible hydrodynamic analysis of journal bearings lubricated with supercritical carbon dioxide. In Proceeding of Supercritical CO2 Power Cycle Symposium. San Antonio, TX.Google Scholar
Gross, W. A., Matsch, L. A., Castelli, V., Eshel, A., Vohr, J. H. & Wildmann, M. 1980 Fluid Film Lubrication. Wiley.Google Scholar
Guenat, E. & Schiffmann, J. 2018 Real-gas effects on aerodynamic bearings. Tribol. Intl 120, 358–368.Google Scholar
Hamrock, B. J., Schmidt, S. R. & Jacobson, B. O. 2004 Fundamentals of Fluid Film Lubrication. CRC Press.Google Scholar
Heshmat, H., Walton, J. F. & Cordova, J. L. 2018 Technology readiness of 5th and 6th generation compliant foil bearing for 10 MWE s-CO2 turbomachinery systems. In Proceeding of the 6th International Supercritical CO2 Power Cycles Symposium. Pittsburg, PA.Google Scholar
Howard, S. A., Bruckner, R. J., DellaCorte, C. & Radil, K. C. 2007 Gas foil bearing technology advancements for closed Brayton cycle turbines. In AIP Conference Proceedings, vol. 880, pp. 668–680. AIP.Google Scholar
Kim, D. 2016 Design space of foil bearings for closed-loop supercritical CO2 power cycles based on three-dimensional thermohydrodynamic analyses. J. Engng Gas Turbines Power 138 (3), 032504.Google Scholar
Lemmon, E. W., Huber, M. L. & McLinden, M. O. 2002 NIST Reference fluid thermodynamic and transport properties – REFPROP. NIST Standard Reference Database 23, v7.Google Scholar
Peng, Z. C. & Khonsari, M. M. 2004 On the limiting load-carrying capacity of foil bearings. J. Tribol. 126 (4), 817–818.Google Scholar
Pinkus, O. & Sternlicht, B. 1961 Theory of Hydrodynamic Lubrication. McGraw-Hill.Google Scholar
Qin, K.2017, Development and application of multiphysics simulation tools for foil thrust bearings operating with carbon dioxide. PhD thesis, University of Queensland.Google Scholar
Reid, R. C., Prausnitz, J. M. & Poling, B. E. 1987 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
Reynolds, O. 1886 On the theory of lubrication and its application to Mr. Beauchamp Tower’s experiments, including an experimental determination of the viscosity of olive oil. Proc. R. Soc. Lond. 40 (242–245), 191–203.Google Scholar
Szeri, A. Z. 2010 Fluid Film Lubrication. Cambridge University Press.Google Scholar
Wright, S. A., Radel, R. F., Vernon, M. E., Robert, G. E. & Pickard, P. S.2010 Operation and analysis of a supercritical $\text{CO}_{2}$ Brayton cycle. Sandia Report, No. SAND2010-0171.Google Scholar