A multigrid numerical solution algorithm has been developed for the laminar (Stokes) flow of a compressible medium in a thin film. The solver has been applied to two model problems each representative of lubrication problems in a specific way. For both problems the solutions of the Stokes equations are compared with the solutions of the Reynolds equation. The configurations of both model problems were chosen such that based on the ratio film thickness to contact length (H/L) the difference between the Reynolds and the Stokes solutions will be very small, so the geometry of the gap itself does not lead to a significant cross film dependence of the pressure. It is shown that in this situation the compressibility can still lead to a cross-film pressure dependence which is predicted by the Stokes solution and not by the Reynolds solution. The results demonstrate that limitations exist to the validity of the Reynolds equation related to the compressibility of the medium.
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July 2003
Technical Papers
Compressible Stokes Flow in Thin Films
D. E. A. van Odyck,
D. E. A. van Odyck
University of Twente, Faculty of Mechanical Engineering, Tribology Group, P.O. Box 217, 7500 AE Enschede, The Netherlands
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C. H. Venner
C. H. Venner
University of Twente, Faculty of Mechanical Engineering, Tribology Group, P.O. Box 217, 7500 AE Enschede, The Netherlands
Search for other works by this author on:
D. E. A. van Odyck
University of Twente, Faculty of Mechanical Engineering, Tribology Group, P.O. Box 217, 7500 AE Enschede, The Netherlands
C. H. Venner
University of Twente, Faculty of Mechanical Engineering, Tribology Group, P.O. Box 217, 7500 AE Enschede, The Netherlands
Contributed by the Tribology Division for publication in the ASME JOURNAL OF TRIBOLOGY. Manuscript received by the Tribology Division January 8, 2002; revised manuscript received October 22, 2002. Associate Editor: L. San Andre´s.
J. Tribol. Jul 2003, 125(3): 543-551 (9 pages)
Published Online: June 19, 2003
Article history
Received:
January 8, 2002
Revised:
October 22, 2002
Online:
June 19, 2003
Citation
van Odyck , D. E. A., and Venner, C. H. (June 19, 2003). "Compressible Stokes Flow in Thin Films ." ASME. J. Tribol. July 2003; 125(3): 543–551. https://doi.org/10.1115/1.1539058
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