Stokes roughness effects on hydrodynamic lubrication are studied in the slip flow regime. Slip flow boundary conditions for Navier-Stokes equations are derived, assuming that the fluid on a surface slips due to the molecular mean free path along the surface, even if the surface is rough. The perturbation method for Navier-Stokes equations, which was derived in Part I of this report, is then applied. Slip flow effects on load carrying capacity and frictional force are numerically clarified for both Stokes and Reynolds roughnesses. In the slip flow regime, second-order quantities induced by Stokes effects, such as flow rate, load carrying capacity, and frictional force are in proportion to the wavenumber squared. This phenomenon relative to the quantities being proportional is also the same as that in the continuum flow regime. As a result of velocity slippage, the load carrying capacity in Stokes roughness is found to decrease more than in Reynolds roughness for incompressible films, while the relationship is reversed for compressible films having a high compressibility number. The simulation of random roughness, which is generated by numerical means, clarifies one important result: the average slip flow effects associated with random Stokes roughness become similar to the slip flow effects in deterministic sinusoidal Stokes roughness, whose wavelength and height are statistically equivalent to those of random roughness. Although attention should be given to the fact that Stokes effects on random roughness demonstrate considerable scattering with the continuum flow, such scattering diminishes with the slip flow.
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April 1986
Research Papers
Stokes Roughness Effects on Hydrodynamic Lubrication. Part II—Effects Under Slip Flow Boundary Conditions
Y. Mitsuya
Y. Mitsuya
Magnetic Storage Section, NTT Electrical Communication Laboratories, Nippon Telegraph and Telephone Corp., Musashino-shi, Tokyo, 180 Japan
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Y. Mitsuya
Magnetic Storage Section, NTT Electrical Communication Laboratories, Nippon Telegraph and Telephone Corp., Musashino-shi, Tokyo, 180 Japan
J. Tribol. Apr 1986, 108(2): 159-166 (8 pages)
Published Online: April 1, 1986
Article history
Received:
July 1, 1983
Online:
October 29, 2009
Connected Content
This is a companion to:
Stokes Roughness Effects on Hydrodynamic Lubrication. Part I—Comparison Between Incompressible and Compressible Lubricating Films
This is a companion to:
Structural Analysis of an LMFBR Shield Assembly Duct Under Thermo-Mechanical and Seismic Loads
Citation
Mitsuya, Y. (April 1, 1986). "Stokes Roughness Effects on Hydrodynamic Lubrication. Part II—Effects Under Slip Flow Boundary Conditions." ASME. J. Tribol. April 1986; 108(2): 159–166. https://doi.org/10.1115/1.3261154
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