Perturbation Solutions for Annular Flow of Small Gap

DOI: 10.4236/jamp.2015.37092   PDF   HTML   XML   2,215 Downloads   2,551 Views  


The perturbation method is used to solve the control equations of a three-dimensional annular flow inside a small gap. The nonlinear equations are separated into zeroth-order and first-order perturbation equations. The velocity and pressure distributions are solved successively by different numerical methods with the zeroth-order and first-order equation. Agreement in results is found with the present method and software ANSYS-CFX, which illustrates the applicability of perturbation method in solving complicated flow field inside small gaps.

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Cao, X. and Wang, Y. (2015) Perturbation Solutions for Annular Flow of Small Gap. Journal of Applied Mathematics and Physics, 3, 761-765. doi: 10.4236/jamp.2015.37092.

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The authors declare no conflicts of interest.


[1] Fritz, R.J. (1970) The Effects of an Annular Fluid on the Vibrations of a Long Rotor, Part 1-Theory. Journal of Basic Enginneering, 1970, 923-929.
[2] Hirs, G.G. (1973) A Bulk-Flow Theory for Turbulence in Lubrication Film. ASME Journal of Lubrication Technology, 95, 137-146.
[3] Childs, D.W. (1983) Dynamic Analysis of Turbulent Annular Seals Base on Hirs’ Lubrication Equation. ASME Journal of Lubrication Technology, 105, 429-436.
[4] Nelson, C.C. (1987) Comparison of Hirs’ Equation with Moody’s Equation for Determining Rotor Dynamic Coefficients of Annular Pressure Seals. ASME Journal of Trilogy, 109, 144-148.
[5] Massey, B.S. and Smith, J.W. (1979) Mechanics of Fluids. 4th Edition, Van Nostrand Reinhold Company, New York.
[6] Antunes, J. (1996) Dynamics of Rotors Immersed in Eccentric Annular Flow. Part 1: Theory. Journal of Fluids and Structures, 10, 893-918.
[7] Sun, Q.G. and Yu, L. (2000) Effect of Stator and Rotor Wall Roughness on Dynamic Coefficients of Eccentric Rotor in Large Gap Annular Flow. Tribology, 20, 365-369.
[8] Chen, J.Y. (1995) An Improved Perturbation Method for Free Vibration Analysis. Journal of Sound and Vibration, 180, 519-523.
[9] Stepanova, L.V. and Igonin, S.A. (2014) Perturbation Method for Solving the Nonlinear Eigenvalue Problem Arising from Fatigue Crack Growth Problem in a Damaged Medium. Applied Mathematical Modeling, 38, 3436-3455.
[10] Wang, Z.X. and Qiao, P. (2015) Vibration Analysis of Laminated Composite Plates with Damage Using the Perturbation Method. Composites: Part B, 72, 160-174.
[11] Pu, G.Y. (2011) ANSYS Workbench 12 Basic Tutorial and Example Explanation, China Waterpower Press, Beijing. (In Chinese)

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