It is well known that for a reduced Reynolds number Re*=ρVH/μs˙H/L greater than unity, inertia forces have a dominant effect in the transport equations, thus rendering the classical lubrication equation inapplicable. The so called “bulk flow” system of equations is then the appropriate mathematical model for describing the flow in bearing and seals operating at Re*1. The difficulty in integrating this system of equations is that one has to deal with coupled pressure and velocity fields. Analytic methods have a very narrow application range so a numerical method has been proposed by Launder and Leschziner in 1978. It represents a natural extrapolation of the successful SIMPLE algorithm applied to the bulk flow system of equations. The algorithm used rectangular, staggered control volumes and represented the state of the art at that moment. In the present work we introduced a method using triangular control volumes. The basic advantage of triangles versus rectangles is that non rectangular domains can be dealt without any a priori limitation. The present paper is focused on the description of the discretized equations and of the solution algorithm. Validations for bearings and seals operating in incompressible, laminar and turbulent flow regime are finally proving the accuracy of the method.

1.
Constantinescu, V. N., 1995, Laminar Viscous Flow, Springer-Verlag, New York, NY.
2.
Milne
,
A. A.
,
1959
, “
On the Effect of Lubricant Inertia in the Theory of Hydrodynamic Lubrication
,”
ASME J. Basic Eng.
,
81
, pp.
239
244
.
3.
Kahlert
,
N.
,
1948
, “
Der Einfluss der Tra¨gheitskra¨fte in der hydrodynamischer Schmiermitteltheorie
,”
Ing. Arch.
,
16
, pp.
321
342
.
4.
Slezkin
,
N. A.
, and
Targ
,
S. M.
,
1946
, “
On the Solution of Reynolds Equation
,” (in Russian),
Dokl. Akad. Nauk SSSR
,
54
, pp.
25
208
.
5.
Childs, D. W., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling and Analysis, Wiley Interscience, New York.
6.
Launder
,
B. E.
, and
Leschziner
,
M.
,
1978
, “
Flow in Finite-Width, Thrust Bearings Including Inertial Effects
,”
ASME J. Lubr. Technol.
,
100
, pp.
330
338
.
7.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.
8.
Donea
,
J.
,
1991
, “
Generalized Galerkin Methods for Convection Dominated Transport Phenomena
,”
Appl. Mech. Rev.
44
, pp.
205
214
.
9.
Glowinski
,
R.
, and
Pironneau
,
O.
,
1992
, “
Finite Element Methods for Navier-Stokes Equations
,”
Annu. Rev. Fluid Mech.
,
24
, pp.
167
204
.
10.
Rhie
,
C. M.
, and
Chow
,
W. L.
,
1983
, “
A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation
,”
AIAA J.
,
21
, pp.
1525
1532
.
11.
Peric, M., 1985, “A Finite Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts,” Ph.D. thesis, University of London.
12.
Mathur
,
S. R.
, and
Murthy
,
J. Y.
,
1997
, “
A Pressure-Based Method for Unstructured Meshes
,”
Numer. Heat Transfer, Part B
,
31
, pp.
195
215
.
13.
Lai
,
Y. G.
,
1997
, “
An Unstructured Grid Method for A Pressure-Based Flow and Heat Transfer Solver
,”
Numer. Heat Transfer, Part B
,
32
, pp.
267
281
.
14.
Hirs
,
G.
,
1973
, “
A Bulk Flow Theory for Turbulence in Lubricant Films
,”
ASME J. Lubr. Technol.
,
95
, April, pp.
137
146
.
15.
Ferziger, J. H., and Peric, M., 1996, Computational Methods for Fluid Dynamics, Springer-Verlag.
16.
Venkatakrishnan
,
V.
,
1995
, “
Convergence to Steady State Solutions of the Euler Equations on Unstructured Grids with Limiters
,”
J. Comput. Phys.
118
, pp.
120
130
.
17.
Majumdar
,
S.
,
1988
, “
Role of Underrelaxation on Momentum Interpolation for Calculation of Flow With Nonstaggered Grids
,”
Numer. Heat Transfer
,
13
, pp.
125
132
.
18.
Constantinescu, V. N., et al., 1985, Sliding Bearings, Allerton Press.
19.
George, P. L., 1991, Automatic Mesh Generation. Application to Finite Element Methods, Wiley, New York.
20.
Fre^ne, J., Nicolas, D., Degueurce, B., Berthe, D., and Godet, M., 1990, Lubrification Hydrodynamique. Paliers et bute´es, Editions Eyrolles.
21.
Amoser, M., 1995, “Stro¨mungsfelder und Radialkra¨fte in Labyrinthdichtungen hydraulischer Stro¨mungsmascinen,” Dissertation ETH Zurich Nr. 11150.
22.
Arghir
,
M.
, and
Fre^ne
,
J.
,
1999
, “
A Quasi-Two-Dimensional Method for The Rotordynamic Analysis of Centered Labyrinth Liquid Seals
ASME J. Eng. Gas Turbines Power
,
121
, pp.
144
152
.
23.
Kanki, H., and Kawakami, T., 1984, “Experimental Study on the Dynamic Characteristics of Pump Annular Seals,” Proceedings of the Institution of Mechanical Engineers, Paper C297/84, London, United Kingdom, pp. 159–166.
24.
San Andre`s
,
L. A.
,
1991
, “
Analysis of Variable Fluid Properties, Turbulent Annular Seals
,”
ASME J. Tribol.
,
113
, pp.
694
702
.
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