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Research Papers: Hydrodynamic Lubrication

An Approximate Solution of Muijderman's Model for Performance Calculation of Spiral Grooved Gas Seal

[+] Author and Article Information
Wanjun Xu

National Engineering Research Center
of Turbo Generator Vibration,
Southeast University,
Nanjing 210096, China
e-mail: 230149022@seu.edu.cn

Jiangang Yang

National Engineering Research Center
of Turbo Generator Vibration,
Southeast University,
Nanjing 210096, China
e-mail: jgyang@seu.edu.cn

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received June 24, 2016; final manuscript received December 19, 2016; published online May 26, 2017. Assoc. Editor: Min Zou.

J. Tribol 139(5), 051706 (May 26, 2017) (6 pages) Paper No: TRIB-16-1200; doi: 10.1115/1.4035774 History: Received June 24, 2016; Revised December 19, 2016

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.

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Figures

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Fig. 1

Geometry of a spiral grooved gas film

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Fig. 2

Comparison of the solution processes for the two methods: (a) traditional method and (b) present method

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Fig. 3

Variation of gas film pressure with gas film radius: (a) h = 3.05 μm and (b) h = 5.08 μm

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Fig. 4

Variation of gas film force with outer radius pressure

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Fig. 5

Comparison of the approximate solution with the Runge–Kutta method solution for different parameters: (a) rotational speed, (b) outer radius pressure, (c) gas film thickness, (d) spiral angle, and (e) groove depth

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