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.

References

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.1932.0169
3.
Nikolajsen
,
J. L.
,
1999
, “
Viscosity and Density Models for Aerated Oil in Fluid-Film Bearings©
,”
Tribol. Trans.
,
42
(
1
), pp.
186
191
.10.1080/10402009908982207
4.
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-X
5.
Tonder
,
K.
,
1977
, “
Effect of Gas Bubbles on Behavior of Isothermal Michell Bearings
,”
ASME J. Tribol.
,
99
(
3
), pp.
354
358
.10.1115/1.345322
6.
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
.10.1243/13506501JET279
7.
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-X
8.
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)90108-4
9.
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
.10.1080/10402009908982190
10.
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
.10.1115/1.2920999
11.
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.45.802
12.
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
.10.1115/1.1330742
13.
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
.10.1115/1.1510878
14.
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.2011.04.042
15.
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/cherd06243
16.
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.5450800406
17.
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.2003.08.025
18.
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.690250513
19.
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-Y
20.
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.2006.07.003
21.
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.2006.06.020
22.
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.2007.11.002
23.
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/ie049447x
25.
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)90086-8
26.
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.690481103
27.
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)00022-7
28.
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.2010.08.023
29.
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/ie0489002
30.
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.2011.04.001
31.
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.2004.09.070
32.
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.2007.08.081
33.
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.2008.01.013
34.
Pan
,
C. H. T.
,
1965
, “
A Linearized Turbulent Lubrication Theory
,”
ASME J. Fluids Eng.
,
87
(
3
), pp.
675
688
.10.1115/1.3650640
35.
Szeri
,
A. Z.
,
2011
,
Fluid Film Lubrication
,
Cambridge University Press
,
Cambridge/New York
, p.
186
.10.1017/CBO9780511782022
36.
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-x
37.
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
.10.1115/1.3243624
38.
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
.
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