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TECHNICAL PAPERS

Compressible Stokes Flow in Thin Films

[+] Author and Article Information
D. E. A. van Odyck, C. H. Venner

University of Twente, Faculty of Mechanical Engineering, Tribology Group, P.O. Box 217, 7500 AE Enschede, The Netherlands

J. Tribol 125(3), 543-551 (Jun 19, 2003) (9 pages) doi:10.1115/1.1539058 History: Received January 08, 2002; Revised October 22, 2002; Online June 19, 2003
Copyright © 2003 by ASME
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References

Reynolds,  O., 1886, “On the Theory of Lubrication and Its Application to Mr. Beauchamps Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Philos. Trans. R. Soc. London, 177, pp. 157–234.
Sun,  D. C., and Chen,  K. K., 1977, “First Effects of Stokes Roughness on Hydrodynamic Lubrication,” J. Lubr. Technol., 99 pp. 2–9.
Phan-Thien,  N., 1981, “On the Effects of the Reynolds and Stokes Surface Roughnesses in a Two-Dimensional Slider Bearing,” Proc. R. Soc. London, Ser. A, 377, pp. 349–362.
Myllerup, C. M., and Hamrock, B. J., 1992, “Local Effects in Thin Film Lubrication,” Proceedings of the 19th Leeds Lyon conference on tribology.
Myllerup,  C. M., and Hamrock,  B. J., 1994, “Perturbation Approach to Hydrodynamic Lubrication Theory,” ASME J. Tribol., 116, pp. 110–118.
Noordmans, J., 1996, “Solutions of Highly Anisotropic Stokes Equations for Lubrication Problems,” ECCOMAS 96.
Schäfer, C. T., Giese, P., and Woolley, N. H., 1999, “Elastohydrodynamically Lubricated Line Contact Based on the Navier-Stokes Equations,” Proceedings of the 26th Leeds Lyon conference on tribology.
Odyck van, D. E. A., 2001. “Stokes Flow in Thin Films,” Ph.D. thesis, University of Twente, The Netherlands.
Odyck van,  D. E. A., and Venner,  C. H., 2003. “Stokes Flow in Thin Films,” ASME J. Tribol., 125, pp. 1–14.
Bair,  S., Khonsari,  M., and Winer,  W. O., 1998, “High-Pressure Rheology of Lubricants and Limitations of the Reynolds Equation,” Tribol. Int., 31)(10), pp. 573–586.
Batchelor, G. K., 2000, An Introduction to Fluid Dynamics, Cambridge University Press, UK, ISBN 0521663962.
Langlois, W. E., 1964, Slow Viscous Flow, The Macmillan Company, New York.
Constantinescu, V. N., 1969, Gas Lubrication, ASME, New York.
Dowson,  D., and Taylor,  C. M., 1979, “Cavitation in Bearings,” Annu. Rev. Fluid Mech., 11, pp. 35–66.
Elrod,  H. G., 1981, “A Cavitation Algorithm,” ASME J. Lubr. Technol., 103, pp. 350–354.
Delannoy, Y., and Kueny, J. L., 1990, “Two-Phase Flow Approach in Unsteady Cavitation Modeling,” Cavitation and Multiphase Flow, 98 , ASME FED, pp. 153–158.
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Jakobsson, B., and Floberg, L., 1957, “The Finite Journal Bearing, Considering Vaporization,” Trans. Chalmers Univ. Tech., Göteborg, 190.
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Figures

Grahic Jump Location
(a) Pressure profile as function of x and z; and (b) and Streamlines as function of x and z.ε=0.01,βρ=10.0,pv=−3.0.
Grahic Jump Location
(a) The pressure at z=0 as function of x for the Reynolds solution without cavitation (pr (no cav.)), the Reynolds solution with cavitation (pr) and the Stokes solution with cavitation (ps); and (b) enlargement of the pressure and density at z=0 as function of x for the Reynolds and the Stokes solution with cavitation in the cavitation region, ε=0.01,pv=−3.0, and βρ=10.0. The Reynolds and the Stokes solution with cavitation overlap in both figures.
Grahic Jump Location
Contour plot of the density for ε=0.01 and pv=−3.0, (a) βρ=10.0; and (b) βρ=5.0×103
Grahic Jump Location
Contour plot of the density for ε=0.01 and pv=−3.0; (a) βρ=1.0×104; and (b) βρ=4.0×104.
Grahic Jump Location
Density as function of z at x=0.5 for ε=0.01 and pv=−3.0
Grahic Jump Location
(a) Contour plot of the density; and (b) density as function of z at x=0.5. For ε=0.5,pv=−4.0 and βρ=20.0.
Grahic Jump Location
(a) Contour plot of the iso-density contour ρ=0.5 for the Stokes solution on different grids; and (b) Density as function of z at x=0.5 for the Stokes solution on different grids. ε=0.01,pv=−3.0, and βρ=1.0×104.
Grahic Jump Location
Geometry and boundary conditions for gas bearing model problem
Grahic Jump Location
Cavitation bubble in the downstream portion of the contact
Grahic Jump Location
Pressure-density diagram for the liquid/vapor mixture
Grahic Jump Location
Stokes solution: (a) streamlines; and (b) pressure field. Both as function of x and z for ε=0.005,us=10.0 and κs=1343.
Grahic Jump Location
Pressure as function of x for ε=0.005,κs=1343 and different us for the Stokes solution to the gas bearing problem. (a) Pressure at z=0; and (b) pressure at z=h. In (a) the Reynolds solution overlaps the Stokes solution for us=2, 10, 50.
Grahic Jump Location
Pressure as function of x for ε=0.005,us=5.0×103 and different κs for the Stokes (ps) and Reynolds (prey) solutions to the gas bearing problem: (a) pressure at z=0; and (b) pressure at z=h
Grahic Jump Location
(a) Pressure as a function of x at z=0 for the Stokes solution on different grids; and (b) contour plot of the pressure for the Stokes solution on different grids. ε=0.005,us=5.0×103 and κs=1343.

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