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TECHNICAL PAPERS

Finite Element Solution of Inertia Influenced Flow in Thin Fluid Films

[+] Author and Article Information
Noël Brunetière

Laboratoire de Mécanique des Solides, UMR CNRS 6610, Université de Poitiers, SP2MI, BP 30179, 86962 Futuroscope Chasseneuil Cedex, Francenoel.brunetiere@lms.univ-poitiers.fr

Bernard Tournerie

Laboratoire de Mécanique des Solides, UMR CNRS 6610, Université de Poitiers, SP2MI, BP 30179, 86962 Futuroscope Chasseneuil Cedex, France

J. Tribol 129(4), 876-886 (May 30, 2007) (11 pages) doi:10.1115/1.2768089 History: Received September 18, 2006; Revised May 30, 2007

The aim of this paper is to present a numerical model to compute laminar, turbulent, and transitional incompressible fluid flows in thin lubricant films where inertia effects cannot be neglected. For this purpose, an averaged inertia method is used. A numerical scheme based on the finite element method is presented to solve simultaneously the momentum and continuity equations. The numerical model is then validated by confronting it with previously published analytical, experimental, and numerical results. Particular attention is devoted to analyzing the numerical conservation of mass and momentum. The influence of mesh size on numerical precision is also analyzed. Finally, the model is applied to a misaligned hydrostatic seal. These seals operate with a substantial leakage flow, where nonlaminar phenomena occur. The influence of inertia and misalignment of the faces on the seal behavior is analyzed through a comparison with an inertialess solution. Significant differences are observed for high values of the tilt angle when the flow is nonlaminar. Inertia effects increase when the flow is laminar.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Geometric configuration

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Figure 2

Radial pressure distributions in laminar flow between stationary disks: (a) coarse regular mesh leading to oscillations and (b) coarse mesh becoming finer near the inner radius, leading to a smooth solution

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Figure 3

Comparison of analytical and numerical radial pressure distributions in laminar flows between stationary and rotating flat disks

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Figure 4

Comparison of experimental and numerical pressure distributions in the laminar flow between two stationary misaligned flat disks (ε=0.44)

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Figure 5

Influence of the mesh size on the numerical precision

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Figure 6

Influence of the mesh size on the mass and momentum conservation

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Figure 7

Misaligned hydrostatic seal

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Figure 8

Fluid flow regime in aligned and misaligned configurations for an angular velocity of 1500rpm

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Figure 9

Centerline clearance versus the misalignment angle

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Figure 10

Minimum film thickness versus the misalignment angle

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Figure 11

Leakage rate versus the misalignment angle

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Figure 12

Restoring moment versus the misalignment angle

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Figure 13

Transverse moment versus the misalignment angle

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