The bulk-flow equations used for inertia dominated thin-film flows is an attractive model for the analysis of circumferentially grooved annular seals because the solutions based on the numerical integration of the complete Navier-Stokes equations can be very time-consuming. By using three types of control volumes and some user-tuned constants, the bulk-flow model can be used for calculating the static and the dynamic characteristics. Until now, this has been carried out for centered seals where the flow is governed by ordinary differential equations but no solutions have yet been given for eccentric working conditions. In this latter case, the model is governed by partial differential equations of an elliptic type. The main problem is that for describing the groove effects, the pressure field must incorporate the concentrated drop or recovery effects that occur at the interface between the groove and the land zone. This means that the numerical procedure used for solving the elliptic equations should be able to handle a pressure field having discontinuous values and discontinuous first order derivatives. In the present work, the method used for integrating the system of bulk-flow equations is the SIMPLE algorithm. The algorithm is extended for handling pressure jumps by adding two pressure values on each side of the discontinuity. These values are then expressed in terms of cell centered pressures by imposing the mass conservation and the generalized Bernoulli equation at the discontinuity. This numerical solution is original and has never previously been presented in the finite volume related literature. Comparisons between the numerical predictions (leakage flow rate and rotordynamic coefficients) and experimental data taken from the literature Marquette and Childs (1997) are subsequently presented for an eccentric ten-groove annular seal.

Issue Section:
Technical Papers
Keywords:
Navier-Stokes equations, damping, lubrication, rotation, friction
Topics:
Flow (Dynamics), Pressure, Algorithms, Navier-Stokes equations
1.
Childs, D. W., 1984, “Finite-Length Solutions for Rotordynamic Coefficients of Constant-Clearance and Convergent-Tapered Annular Seals,” in Vibrations in Rotating Machinery, Proceedings, ImechE, Third International Conference on Vibrations in Rotating Machinery, York, England, pp. 223–231.
2.
Nordmann, R., Dietzen, F. J., Janson, W., Frei, A., and Florjancic, S., 1986, “Rotordynamic Coefficients and Leakage Flow of Parallel Grooved Seals and Smooth Seals,” Rotordynamic Instability Problems in High-Performance Turbomachinery, Proceedings of a Workshop, NASA CP No. 2338, pp. 129–153.
3.
Kim
,
C.-H.
, and
Childs
,
D. W.
,
1987
, “
Analysis for Rotordynamic Coefficients of Helically-Grooved Turbulent Annular Seals
,”
ASME J. Tribol.
,
109
(
1
), pp.
136
–
143
.
4.
Iwatsubo, T., and Sheng, B., 1990, “Evaluation of Dynamic Characteristics of Parallel Grooved Seals by Theory and Experiment,” Proceedings of the Third IFToMM International Conference on Rotordynamics, Lyon, France, pp. 313–318.
5.
Florjancic, S., 1990, “Annular Seals of High Energy Centrifugal Pumps: A New Theory and Full Scale Measurement of Rotordynamic Coefficients and Hydraulic Friction Factors,” Dissertation, ETH Zu¨rich Nr. 9087.
6.
Marquette
,
O. R.
, and
Childs
,
D. W.
,
1996
, “
An Extended Three-Control-Volume Theory for Circumferentially-Grooved Liquid Seals
,”
ASME J. Tribol.
,
118
(
1
), pp.
276
–
285
.
7.
Dietzen, F. J., 1988, “Bestimmung der Dynamischen Koeffizienten von Dichtspalten mit Finite-Differenz-Verfahren,” VDI Fortschrift-Berichte, Reihe 11, Nr. 103, Du¨sseldorf.
8.
Rhode
,
D. L.
,
Hensel
,
S. J.
, and
Guidry
,
M. J.
,
1992
, “
Three-Dimensional Computations of Rotordynamic Force Distribution in a Labyrinth Seal
,”
STLE Tribol. Trans.
,
36
(
3
), pp.
461
–
469
.
9.
Athavale, M. M., Przekwas, A. J., Hendricks, R. C., and Liang, A., 1994, “SCISEAL: A 3D CFD Code for Accurate Analysis of Fluid Flow and Forces in Seals,” Advanced ETO Propulsion Conference, May.
10.
Arghir, M., 1996, “Mode´lisation du Comportement Dynamique des Joints Annulaires a` Fluide Incompressible,” The`se de Docteur de l’Universite´ de Poitiers.
11.
Marquette, O. R., and Childs, D. W., 1997, “Theory Versus Experiment for Leakage and Rotordynamic Coefficients of Circumferentially-Grooved Liquid Annular Seals With L/D of 0.45,” FEDSM97-3333.
12.
Childs, D. W., 1993, Turbomachinery Rotordynamics. Phenomena, Modeling and Analysis, Wiley Interscience, New York.
13.
Hirs
,
G. G.
,
1973
, “
A Bulk-Flow Theory for Turbulence in Lubricant Films
,” J. Lubr. Technol., April, pp. 137–146.
14.
Abramovich, G. N., 1963, The Theory of Turbulent Jets, MIT Press, Cambridge, Mass.
15.
Weiser, H.-P., 1989, “Ein Beitrag zur Berechnung der Dynamischen Koeffizienten von Labyrinthdichtungsystemen bei Turbulenter Durchstro¨mung mit Kompressiblen Medien,” Dissertation der Universita¨t Kaiserslautern, D 386.
16.
Launder
,
B. E.
, and
Leschziner
,
M.
,
1978
, “
Flow in Finite-Width, Thrust Bearings Including Inertial Effects
,”
ASME J. Lubr. Technol.
,
100
, pp.
330
–
338
.
17.
San Andre´s
,
L.
,
1991
, “
Analysis of Variable Fluid Properties, Turbulent Annular Seals
,”
ASME J. Tribol.
,
113
(
4
), pp.
694
–
702
.
18.
Arghir
,
M.
, and
Fre^ne
,
J.
,
2001
, “
A Triangle Based Finite Volume Method for the Integration of Lubrication’s Incompressible Bulk Flow Equations
,”
ASME J. Tribol.
,
123
(
1
), pp.
118
–
124
.
19.
Patankar, S. V., 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation & McGraw Hill B. C..
20.
Arghir
,
M.
,
Alsayed
,
A.
, and
Nicolas
,
D.
,
2002
, “
The Finite Volume Solution of the Reynolds Equation of Lubrication With Film Discontinuities
,”
Int. J. Mech. Sci.
,
44
(
10
), pp.
2119
–
2132
.
21.
Scharrer, J. K., 1987, “A Comparison of Experimental and Theoretical Results for Labyrinth Gas Seals,” TRC-SEAL-3-87, Texas A&M University, College Station, TX.
Copyright © 2004
 by ASME
You do not currently have access to this content.