In the classical Reynolds equation-based modeling of lubrication, the exit area is only considered through a pressure boundary condition which fails to predict the remaining amount of lubricant on each moving surface after the film rupture. A two-phase flow model using the Navier-Stokes equations and a diffuse interface approach is developed to analyze the lubricant behavior at the exit of rolling and sliding lubricated line contacts. After physical and numerical descriptions of the two-phase flow model, results are compared with experimental data from the literature. Good agreements are found concerning pressure profiles and meniscus exit abscissas. The model is then used to study in detail the flow behavior at the exit for different surface tensions. It is shown that when surface tension effects are important, recirculation areas occur downstream the air/oil meniscus. Sliding effects on fluid distribution are then investigated. Finally, an analytical approach is proposed, as a synthesis of the numerical results.
Issue Section:
Elastohydrodynamic Lubrication
References
1.
Dowson
, D.
, and Taylor
, C. M.
, 1975, “Fundamental Aspects of Cavitation on Bearings
,” Leeds-Lyon Symposium on Tribology: Cavitation and Related Phenomena in Lubrication 1st: Proceedings
, D.
Dowson
, M.
Godet
, and C. M.
Taylor
, eds., Institution of Mechanical Engineers
, London
, pp. 15
–28
.2.
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
,” Philos. Trans. R. Soc. A
, 177
, pp. 157
–234
.3.
Braun
, M. J.
, and Hannon
, W. M.
, 2010, “Cavitation Formation and Modelling for Fluid Film Bearings: A Review
,” Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
, 224
, pp. 839
–863
.4.
Elrod
, H. G.
, 1981, “A Cavitation Algorithm
,” J. Lubr. Technol.
, 103
(3
), pp. 350
–354
.5.
Coyne
, J. C.
, and Elrod
, H. G.
, 1971, “Conditions for the Rupture of a Lubricating Film - Part II: New Boundary Conditions for Reynolds’ Equation
,” Trans. ASME, J. Lubric. Technol.
, 93
, pp. 156
–166
.6.
Coyne
, J. C.
, and Elrod
, H. G.
, 1970, “Conditions for the Rupture of a Lubricating Film. Part I: Theoretical Model
,” Trans. ASME, J. Lubric. Technol.
, 92
, pp. 451
–456
.7.
Jacqmin
, D.
, 1999, “Calculation of Two-Phase Navier-Stokes Flows using Phase-Field Modeling
,” J. Comput. Phys.
, 155
, pp. 96
–127
.8.
Anderson
, D. M.
, McFadden
, G. B.
, and Wheeler
, A. A.
, 1998, “Diffuse Interface Methods in Fluid Dynamics
,” Ann. Rev. Fluid Mech.
, 30
, pp. 139
–165
.9.
Donald Brooke Jenkins
, H.
, 2007, Chemical Thermodynamics at a Glance
, Wiley
, New York
.10.
Cahn
, J.
, and Hilliard
, J.
, 1957, “Free Energy of a Nonuniform System. I. Interfacial Free Energy
,” J. Chem. Phys.
, 28
, pp. 258
–267
.11.
Cahn
, J.
, and Hilliard
, J.
, 1959, “Free Energy of a Nonuniform System. III. Nucleation in a Two-Component Incompressible Fluid
,” J. Chem. Phys.
, 31
, pp. 688
–699
.12.
Yue
, P.
, Zhou
, C.
, and Feng
, J. J.
, 2007, “Short Note: Spontaneous Shrinkage of Drops and Mass Conservation in Phase-Field Simulations
,” J. Comput. Phys.
, 223
, pp. 1
–9
.13.
Yue
, P.
, Feng
, J.
, Liu
, C.
, and Shen
, J.
, 2004, “A Diffuse Interface Method for Simulating Two-Phase Flows of Complex Fluids
,” J. Fluid Mech.
, 515
, pp. 293
–317
.14.
Feng
, J. J.
, Liu
, C.
, Shen
, J.
, and Yue
, P.
, 2005, “An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges
,” Modeling of Soft Matter (The IMA Volumes in Mathematics and its Applications)
, M. -C. T. T.
Calderer
and E. M.
Terentjev
, eds., Springer
, New York
, pp. 1
–26
.15.
Ding
, H.
, and Spelt
, P. D. M.
, 2007, “Wetting Condition in Diffuse Interface Simulations of Contact Line Motion
,”Phys. Rev. E
, 75
, p. 046708
.16.
Brown
, P. N.
, Hindmarsh
, A. C.
, and Petzold
, L. R.
, 1994, “Using Krylov Methods in the Solution of Large-Scale Differential-Algebraic Systems
,” SIAM J. Sci. Comput.
, 15
, pp. 1467
–1488
.17.
Gresho
, P. M.
, and Sani
, R. L.
, 1998, Incompressible Flow and the Finite Element Method
, Wiley
, New York
.18.
Yue
, P.
, Zhou
, J.
, and Feng
, J.
, 2010, “Sharp-Interface Limit of the Cahn–Hilliard Model for Moving Contact Lines
,” J. Fluid Mech.
, 645
, pp. 279
–294
.19.
Dalmaz
, G.
, 1980, “Formation and Separation of Thin Viscous Film in Hertzian Line Contacts
,” Trans. ASME J. Lubr. Technol.
, 102
, pp. 466
–477
.20.
Dalmaz
, G.
, 1979, “Le Film Mince Visqueux dans les Contacts Hertziens en Régimes Hydrodynamique et Elastohydrodynamique
,” Ph.D. thesis, INSA de Lyon, Lyon, France.21.
Floberg
, L.
, 1965, “On Hydrodynamic Lubrication with Special Reference to Sub-cavity Pressures and Number of Streamers in Cavitation Regions
,” ed. Royal Swedish Acad. of Engineering Sciences Acta Poly. Scan Mech. Eng.
, 19
, pp. 3
–35
.22.
Cameron
, A.
, 1966, The Principles of Lubrication
, Wiley
, New York
.23.
Hopkins
, M. R.
, 1957, “Viscous Flow Between Rotating Cylinders and a Sheet Moving Between Them
,” Br. J. Appl. Phys.
, 8
, pp. 442
–444
.24.
Ceniceros
, H. D.
, Nós
, R. L.
, and Roma
, A. M.
, 2010, “Three-Dimensional, Fully Adaptive Simulations of Phase-Field Fluid Models
,” J. Comput. Phys.
, 229
(17
), pp. 6135
–6155
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.
