Oil aeration lubricant in high-speed journal bearing is composed of mixture of continuous phase liquid and discrete phase bubbles. This work establishes a thermohydrodynamic (THD) coupling model for this lubrication condition. The generalized Reynolds equation is derived by the continuity equation, Navier–Stokes equation, law of wall turbulence model, and bubble volume distribution function, and then a THD oil aeration turbulent lubrication model is established by coupling the generalized Reynolds equation, energy equation, force equilibrium equation of bubble, and population balance equations (PBEs). The coupled-equations are solved numerically to obtain the pressure distribution under oil aeration lubrication state, the equilibrium distribution of bubble volume, the turbulent velocity distribution, the bubble velocity distribution, and the temperature rise. The results show that the load capacity of a bearing with oil aeration lubrication model is higher than that of the same bearing with a pure oil lubrication model, and heat dissipation performance of the bearing under the oil aeration lubrication state is superior.
Issue Section:
Hydrodynamic Lubrication
References
1.
Hayward
, A. T. J.
, 1962
, “The Viscosity of Bubbly Oil
,” J. Inst. Pet.
, 48
, pp. 156
–164
.2.
Taylor
, G. I.
, 1932
, “The Viscosity of a Fluid Containing Small Drops of Another Fluid
,” Proc. R. Soc. London Ser. A
, 138
(834
), pp. 41
–48
.10.1098/rspa.1932.01693.
Nikolajsen
, J. L.
, 1999
, “Viscosity and Density Models for Aerated Oil in Fluid-Film Bearings©
,” Tribol. Trans.
, 42
(1
), pp. 186
–191
.10.1080/104020099089822074.
Chun
, S. M.
, 2002
, “A Parametric Study on Bubbly Lubrication of High-Speed Journal Bearings
,” Tribol. Int.
, 35
(1
), pp. 1
–13
.10.1016/S0301-679X(01)00072-X5.
Tonder
, K.
, 1977
, “Effect of Gas Bubbles on Behavior of Isothermal Michell Bearings
,” ASME J. Tribol.
, 99
(3
), pp. 354
–358
.10.1115/1.3453226.
Goodwin
, M. J.
, Dong
, D.
, Yu
, H.
, and Nikolajsen
, J. L.
, 2007
, “Theoretical and Experimental Investigation of the Effect of Oil Aeration on the Load-Carrying Capacity of a Hydrodynamic Journal Bearing
,” Proc. Inst. Mech. Eng., Part J
, 221
(7
), pp. 779
–786
.10.1243/13506501JET2797.
Qi
, A.
, Yinsheng
, Z.
, and Yongxin
, Q.
, 1997
, “Study on the Viscosity Properties of Bubbly Oil and the Static Characteristics of Journal Bearing Lubricated With Bubbly Oil
,” Wear
, 213
(1
), pp. 159
–164
.10.1016/S0043-1648(97)00183-X8.
Kiciński
, J.
, 1983
, “Effect of the Aeration of a Lubricating Oil Film and Its Space-and Time-Related Compression on the Static and Dynamic Characteristics of Journal Bearings
,” Wear
, 91
(1
), pp. 65
–87
.10.1016/0043-1648(83)90108-49.
Nikolajsen
, J. L.
, 1999
, “The Effect of Aerated Oil on the Load Capacity of a Plain Journal Bearing©
,” Tribol. Trans.
, 42
(1
), pp. 58
–62
.10.1080/1040200990898219010.
Chamniprasart
, K.
, Al-Sharif
, A.
, Rajagopal
, K. R.
, and Szeri
, A. Z.
, 1993
, “Lubrication With Binary Mixtures: Bubbly Oil
,” ASME J. Tribol.
, 115
(2
), pp. 253
–260
.10.1115/1.292099911.
Choi
, S.
, and Kim
, K. W.
, 2002
, “Analysis of Bubbly Lubrication in Journal Bearings
,” JSME Int. J. Ser. C
, 45
(3
), pp. 802
–808
.10.1299/jsmec.45.80212.
Diaz
, S.
, and San Andrés
, L.
, 2001
, “A Model for Squeeze Film Dampers Operating With Air Entrainment and Validation With Experiments
,” ASME J. Tribol.
, 123
(1
), pp. 125
–133
.10.1115/1.133074213.
San Andrés
, L.
, and Diaz
, S. E.
, 2003
, “Flow Visualization and Forces From a Squeeze Film Damper Operating With Natural Air Entrainment
,” ASME J. Tribol.
, 125
(2
), pp. 325
–333
.10.1115/1.151087814.
Buffo
, A.
, Vanni
, M.
, and Marchisio
, D. L.
, 2012
, “Multidimensional Population Balance Model for the Simulation of Turbulent Gas–Liquid Systems in Stirred Tank Reactors
,” Chem. Eng. Sci.
, 70
, pp. 31
–44
.10.1016/j.ces.2011.04.04215.
Scargiali
, F.
, D'Orazio
, A.
, Grisafi
, F.
, and Brucato
, A.
, 2007
, “Modelling and Simulation of Gas–Liquid Hydrodynamics in Mechanically Stirred Tanks
,” Chem. Eng. Res. Des.
, 85
(5
), pp. 637
–646
.10.1205/cherd0624316.
Deen
, N. G.
, Solberg
, T.
, and Hjertager
, B. H.
, 2002
, “Flow Generated by an Aerated Rushton Impeller: Two-Phase PIV Experiments and Numerical Simulations
,” Can. J. Chem. Eng.
, 80
(4
), pp. 1
–15
.10.1002/cjce.545080040617.
Van Wachem
, B. G. M.
, and Almstedt
, A. E.
, 2003
, “Methods for Multiphase Computational Fluid Dynamics
,” Chem. Eng. J.
, 96
(1
), pp. 81
–98
.10.1016/j.cej.2003.08.02518.
Ishii
, M.
, and Zuber
, N.
, 1979
, “Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows
,” Am. Inst. Chem. Eng. J.
, 25
(5
), pp. 843
–855
.10.1002/aic.69025051319.
Brackbill
, J. U.
, Kothe
, D. B.
, and Zemach
, C.
, 1992
, “A Continuum Method for Modeling Surface Tension
,” J. Comput. Phys.
, 100
(2
), pp. 335
–354
.10.1016/0021-9991(92)90240-Y20.
Bonometti
, T.
, and Magnaudet
, J.
, 2007
, “An Interface-Capturing Method for Incompressible Two-Phase Flows. Validation and Application to Bubble Dynamics
,” Int. J. Multiphase Flow
, 33
(2
), pp. 109
–133
.10.1016/j.ijmultiphaseflow.2006.07.00321.
Sussman
, M.
, Smith
, K. M.
, Hussaini
, M. Y.
, Ohta
, M.
, and Zhi-Wei
, R.
, 2007
, “A Sharp Interface Method for Incompressible Two-Phase Flows
,” J. Comput. Phys.
, 221
(2
), pp. 469
–505
.10.1016/j.jcp.2006.06.02022.
Herrmann
, M.
, 2008
, “A Balanced Force Refined Level Set Grid Method for Two-Phase Flows on Unstructured Flow Solver Grids
,” J. Comput. Phys.
, 227
(4
), pp. 2674
–2706
.10.1016/j.jcp.2007.11.00223.
Pinkus
, O.
, and Sternlicht
, B.
, 1961
, Theory of Hydrodynamic Lubrication
, McGraw-Hill
, New York
, pp. 381
–388
.24.
Jakobsen
, H. A.
, Lindborg
, H.
, and Dorao
, C. A.
, 2005
, “Modeling of Bubble Column Reactors: Progress and Limitations
,” Ind. Eng. Chem. Res.
, 44
(14
), pp. 5107
–5151
.10.1021/ie049447x25.
Guido-Lavalle
, G.
, Carrica
, P.
, Clausse
, A.
, and Qazi
, M. K.
, 1994
, “A Bubble Number Density Constitutive Equation
,” Nucl. Eng. Des.
, 152
(1
), pp. 213
–224
.10.1016/0029-5493(94)90086-826.
Lehr
, F.
, Millies
, M.
, and Mewes
, D.
, 2002
, “Bubble-Size Distributions and Flow Fields in Bubble Columns
,” Am. Inst. Chem. Eng. J.
, 48
(11
), pp. 2426
–2443
.10.1002/aic.69048110327.
Millies
, M.
, and Mewes
, D.
, 1999
, “Interfacial Area Density in Bubbly Flow
,” Chem. Eng. Process.: Process Intensif.
, 38
(4
), pp. 307
–319
.10.1016/S0255-2701(99)00022-728.
Mitre
, J. F.
, Takahashi
, R. S. M.
, Ribeiro
, C. P.
, and Lage
, P. L. C.
, 2010
, “Analysis of Breakage and Coalescence Models for Bubble Columns
,” Chem. Eng. Sci.
, 65
(23
), pp. 6089
–6100
.10.1016/j.ces.2010.08.02329.
Wang
, T.
, Wang
, J.
, and Jin
, Y.
, 2005
, “Population Balance Model For Gas–Liquid Flows: Influence of Bubble Coalescence and Breakup Models
,” Ind. Eng. Chem. Res.
, 44
(19
), pp. 7540
–7549
.10.1021/ie048900230.
Bayraktar
, E.
, Mierka
, O.
, Platte
, F.
, Kuzmin
, D.
, and Turek
, S.
, 2011
, “Numerical Aspects and Implementation of Population Balance Equations Coupled With Turbulent Fluid Dynamics
,” Comput. Chem. Eng.
, 35
(11
), pp. 2204
–2217
.10.1016/j.compchemeng.2011.04.00131.
Chen
, P.
, Sanyal
, J.
, and Duduković
, M. P.
, 2005
, “Numerical Simulation of Bubble Columns Flows: Effect of Different Breakup and Coalescence Closures
,” Chem. Eng. Sci.
, 60
(4
), pp. 1085
–1101
.10.1016/j.ces.2004.09.07032.
Podila
, K.
, Al Taweel
, A. M.
, Koksal
, M.
, Troshko
, A.
, and Gupta
, Y. P.
, 2007
, “CFD Simulation of Gas–Liquid Contacting in Tubular Reactors
,” Chem. Eng. Sci.
, 62
(24
), pp. 7151
–7162
.10.1016/j.ces.2007.08.08133.
Bhole
, M. R.
, Joshi
, J. B.
, and Ramkrishna
, D.
, 2008
, “CFD Simulation of Bubble Columns Incorporating Population Balance Modeling
,” Chem. Eng. Sci.
, 63
(8
), pp. 2267
–2282
.10.1016/j.ces.2008.01.01334.
Pan
, C. H. T.
, 1965
, “A Linearized Turbulent Lubrication Theory
,” ASME J. Fluids Eng.
, 87
(3
), pp. 675
–688
.10.1115/1.365064035.
Szeri
, A. Z.
, 2011
, Fluid Film Lubrication
, Cambridge University Press
, Cambridge/New York
, p. 186
.10.1017/CBO978051178202236.
Huang
, B.
, and Wang
, G. Y.
, 2011
, “A Modified Density Based Cavitation Model for Time Dependent Turbulent Cavitating Flow Computations
,” Chin. Sci. Bull.
, 56
(19
), pp. 1985
–1992
.10.1007/s11434-011-4540-x37.
Kubota
, A.
, Kato
, H.
, Yamaguchi
, H.
, and Maeda
, M.
, 1989
, “Unsteady Structure Measurement of Cloud Cavitation on a Foil Section Using Conditional Sampling Technique
,” ASME J. Fluids Eng.
, 111
(2
), pp. 204
–210
.10.1115/1.324362438.
Sahu
, M.
, Giri
, A. K.
, and Das
, A.
, 2012
, “Thermohydrodynamic Analysis of a Journal Bearing Using CFD as a Tool
,” Int. J. Sci. Res. Publ.
, 2
(9
), pp. 1
–7
.39.
Zhang
, Z.
, Zhang
, Y.
, Xie
, Y.
, Chen
, Z.
, Qiu
, D.
, and Zhun
, J.
, 1986
, Hydrodynamics Lubrication Theory of the Journal Bearing
, Higher Education Press
, Beijing
, pp. 108
–118
.40.
Ni
, J.
, Wang
, G.
, and Zhang
, H.
, 1991
, The Basic Theory of Solid Liquid Two-Phase Flow and Its Latest Applications
, Science Press
, Beijing
, pp. 35
–52
.41.
Guo
, L.
, 2002
, Two-Phase and Multiphase Flow Dynamics
, Xi'an Jiaotong University Press
, Xi'an
, China
, p. 430
.42.
Amer
, W. F.
, 1977
, Numerical Methods for Partial Differential Equations
, Academic Press
, CA
, pp. 133
–231
.43.
Xianfu
, W.
, 2009
, Cavitating and Supercavitating Flows Theory and Applications
, National Defense Industry Press
, Beijing
, pp. 1
–6
.Copyright © 2015 by ASME
You do not currently have access to this content.
