This paper presents an approximate solution of Muijderman's model for compressible spiral grooved gas film. The approximate solution is derived from Muijderman's equations by Adomian decomposition method. The obtained approximate solution expresses the gas film pressure as a function of the gas film radius. The traditional Runge–Kutta method is avoided. The accuracy of the approximate solution is acceptable, and it brings convenience for performance calculation of spiral grooved gas seal. A complete Adomian decomposition procedure of Muijderman's equations is presented. The approximate solution is validated with published results.
Issue Section:
Hydrodynamic Lubrication
References
1.
Tacon
, K.
, Twiss
, C.
, Mammadov
, V.
, and Aslan-Zada
, F.
, 2014
, “Dry Gas Sealing Solutions for High-Pressure Compressor Applications
,” Proc. Inst. Mech. Eng. Part E
, 228
(3
), pp. 238
–252
.2.
Malanoski
, S. B.
, and Pan
, C. H. T.
, 1965
, “The Static and Dynamic Characteristics of the Spiral-Grooved Thrust Bearing
,” ASME J. Basic Eng.
, 87
(3
), pp. 547
–555
.3.
Whipple
, R. T. P.
, 1951
, “Theory of the Spiral Grooved Thrust Bearing With Liquid or Gas Lubricant
,” Great Britain Atomic Energy Research Establishment
, Harwell, UK.4.
Faria
, M. T. C.
, 2001
, “An Efficient Finite Element Procedure for Analysis of High-Speed Spiral Groove Gas Face Seals
,” ASME J. Tribol.
, 123
(1
), pp. 205
–210
.5.
Yue
, Y.
, and Stolarski
, T. A.
, 1997
, “Numerical Prediction of the Performance of Gas-Lubricated Spiral Groove Thrust Bearings
,” Proc. Inst. Mech. Eng. Part J
, 211
(2
), pp. 117
–128
.6.
Vohr
, J. H.
, and Pan
, C. H. T.
, 1964
, “On the Spiral-Grooved, Self-Acting, Gas Bearing
,” MTI Paper No. 63TR52
.7.
Vohr
, J. H.
, and Chow
, C. Y.
, 1965
, “Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings
,” ASME J. Basic Eng.
, 87
(3
), pp. 568
–576
.8.
Muijderman
, E. A.
, 1966
, Spiral Groove Bearings
, Springer-Verlag
, New York
.9.
Constantinescu
, V. N.
, and Castelli
, V.
, 1969
, “On the Local Compressibility Effect in Spiral-Groove Bearings
,” ASME J. Lubr. Technol.
, 91
(1
), pp. 79
–86
.10.
Roberts-Haritonov
, L.
, 2006
, “Design and Performance Analysis of a Novel Face Gas Seal
,” Ph.D. thesis
, Brunel University, Uxbridge, UK.11.
Gabriel
, R. P.
, 1994
, “Fundamentals of Spiral Groove Noncontacting Face Seals
,” Lubr. Eng.
, 50
(3
), pp. 215
–224
.12.
Sedy
, J.
, 1980
, “Improved Performance of Film-Riding Gas Seals Through Enhancement of Hydrodynamic Effects
,” ASLE Trans.
, 23
(1
), pp. 35
–44
.13.
Shapiro
, W.
, Walowit
, J.
, and Jones
, H. F.
, 1984
, “Analysis of Spiral-Groove Face Seals for Liquid Oxygen
,” ASLE Trans.
, 27
(3
), pp. 177
–188
.14.
Wang
, B.
, Zhang
, H.
, and Cao
, H.
, 2013
, “Flow Dynamics of a Spiral-Groove Dry-Gas Seal
,” Chin J. Mech. Eng.
, 26
(1
), pp. 78
–84
.15.
Xu
, J.
, Peng
, X.
, Bai
, S.
, and Meng
, X.
, 2012
, “CFD Simulation of Microscale Flow Field in Spiral Groove Dry Gas Seal
,” 2012 IEEE/ASME
International Conference on Mechatronics and Embedded Systems and Applications (MESA)
, Suzhou, China, July 8–10, IEEE, pp. 211
–217
.16.
Liu
, Z.
, Wang
, M.
, Zhou
, Y.
, and Wu
, N.
, 2014
, “Dynamic Coupling Correlation of Gas Film in Dry Gas Seal With Spiral Groove
,” Chin. J. Mech. Eng.
, 27
(4
), pp. 853
–859
.17.
Song
, P.
, 2009
, “Discussion About the Calculation Methods of the Gas Film Pressure of the Spiral Groove Dry Gas Seals
,” Lubr. Eng.
, 34
(7
), pp. 7
–17
(in Chinese).18.
Polyanin
, A. D.
, and Zaitsev
, V. F.
, 2003
, Handbook of Exact Solutions for Ordinary Differential Equations
, 2nd ed., Chapman & Hall/CRC Press
, Boca Raton, FL
.19.
Adomian
, G.
, 1986
, Nonlinear Stochastic Operator Equations
, Academic Press
, New York
.20.
Adomian
, G.
, 1988
, “A Review of the Decomposition Method in Applied Mathematics
,” J. Math. Anal. Appl.
, 135
(2
), pp. 501
–544
.21.
Adomian
, G.
, and Rach
, R.
, 1992
, “Generalization of Adomian Polynomials to Functions of Several Variables
,” Comput. Math. Appl.
, 24
(5–6
), pp. 11
–24
.22.
Wazwaz
, A. M.
, 2010
, Partial Differential Equations and Solitary Waves Theory
, Higher Education Press
, Beijing, China
.23.
Wazwaz
, A. M.
, 2000
, “A New Algorithm for Calculating Adomian Polynomials for Nonlinear Operators
,” Appl. Math. Comput.
, 111
(1
), pp. 33
–51
.Copyright © 2017 by ASME
You do not currently have access to this content.
