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A comparison study between navier-stokes equation and reynolds equation in lubricating flow regime

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Abstract

For practical calculations, the Reynolds equation is frequently used to analyze the lubricating flow. The full Navier-Stokes Equations are used to find validity limits of Reynolds equation in a lubricating flow regime by result comparison. As the amplitude of wavy upper wall increased at a given average channel height, the difference between Navier-Stokes and lubrication theory decreased slightly ; however, as the minimum distance in channel throat increased, the differences in the maximum pressure between Navier-Stokes and lubrication theory became large.

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Abbreviations

h:

Height of channel

h0, h1 :

Average channel distance, amplitude of the cosine wavy wall, repectively

p:

Pressure

P0, p2 :

Perturbation pressure of order 0, 2

Re:

Reynolds number ρvlref/β

Q:

Volume flow rate

u, v, w:

Velocity component

x, y, z:

Rectangular Cartesian coordinates

ε:

Perturbation parameter, h/L

Ψ:

Stream function

Ψ0, Ψ2, Ψ4 :

perturbation stream function of order 0, 2, 4

μ:

Viscosity

ν:

Kinematic viscosity

() ’:

Derivative

min:

minimum

max:

maximum

L:

Lower surface

U:

Upper surface

( )x :

Derivative with respect to x

References

  • Carvalho, M. S. and Scriven, L. E., 1997. “Flows in Forward Deformable Roll Coating Gaps: Comparison between Spring and Plain-Strain Models of Roll Cover,”Journal of Computational Physics, Vol. 138, No. 2, pp. 449–479.

    Article  Google Scholar 

  • Choi. B. L., Lee, A. S., and Choi, D. H., 2001, “A Lubrication Performance Analysis of Mechanical Face Seals Using Galerkin Finite Element Method,”KSME J. part A, vol. 25, pp. 916–922.

    Google Scholar 

  • Dowson, D. and Wang, D., 1994, “Analysis of the Normal Bouncing of a Solid Elastic Ball on an Oily Plate,”Wear, Vol. 179, pp. 29–37.

    Article  Google Scholar 

  • Dusey, M., 1993,Numerical Analysis of Lubrication Theory and Peristaltic Transport in The Esophagus, Ph. D. Thesis, Pennsylvania State University, University park, PA.

    Google Scholar 

  • Fluid Dynamics Analysis Package Ver. 7.0, 1993, Fluid Dynamics International, Inc.,

  • Hsu, C. H. and Lee, R., 1994, “Advanced Multilevel Solution of Elastohydrodynamic Lubrication Circular Contact Problem,”Wear, Vol. 177, pp. 117–127.

    Article  Google Scholar 

  • Hua, D. Y. and Kohnsari, M. M., 1995, “Application of Transient Elastohydrodynamic Lubrication Analysis for Gear Transmissions,”Tribology Trans. Vol. 38, pp. 905–913.

    Article  Google Scholar 

  • Schmuck, M. R., Chung, J. B., Schultz, W. W. and KannateyAsibu, E. Jr., 1991, “Analysis of Fluid Flow Under a Grinding Wheel. ”Trans. ASME, Vol. 113, pp. 190–197.

    Google Scholar 

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Authors and Affiliations

  1. Yeungnam University, 214-1, Daedong, 712-749, Gyongsan, Korea

    Dong Joo Song & Duck Kyo Seo

  2. University of Michigan, 48109, Ann Arbor, Ml, USA

    William W. Schultz

Authors
  1. Dong Joo Song
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  2. Duck Kyo Seo
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  3. William W. Schultz
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Correspondence to Dong Joo Song.

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Song, D.J., Seo, D.K. & Schultz, W.W. A comparison study between navier-stokes equation and reynolds equation in lubricating flow regime. KSME International Journal 17, 599–605 (2003). https://doi.org/10.1007/BF02984461

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  • DOI: https://doi.org/10.1007/BF02984461

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