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Research Papers: Gas Turbines: Structures and Dynamics

Simulation of Static Performance of Air Foil Bearings Using Coupled Finite Element and Computational Fluid Dynamics Techniques

[+] Author and Article Information
Leonidas I. Paouris

e-mail: leonidas.paouris@gmail.com

Dimitrios A. Bompos

e-mail: dbobos@mech.upatras.gr

Pantelis G. Nikolakopoulos

e-mail: pnikolak@mech.upatras.gr
Machine Design Laboratory,
Department of Mechanical
Engineering and Aeronautics,
University of Patras,
Patras 26504, Greece

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received August 3, 2013; final manuscript received September 22, 2013; published online November 1, 2013. Editor: David Wisler.

J. Eng. Gas Turbines Power 136(2), 022503 (Nov 01, 2013) (11 pages) Paper No: GTP-13-1292; doi: 10.1115/1.4025537 History: Received August 03, 2013; Revised September 22, 2013

The main objective of the current work is to determine a relationship between the top and bump foil's geometry and load-carrying capacity in a journal compliant generation I air foil bearing, as well as determining the effect of the thermohydrodynamic phenomena in the performance of the air foil bearing (AFB). Static and steady-state operation is assumed throughout the analysis. A finite element model is adopted in order to investigate the operational characteristics of the specific bearing. Bump foil's elastic behavior is modeled using two node linear link spring elements. During the hydrodynamic analysis, incompressible viscous steady state Navier–Stokes equations are numerically solved, due to the low bearing compressibility number. During the thermohydrodynamic analysis, compressible, viscous, steady-state Navier–Stokes equations were solved, coupled with the energy equation. The material used during the structural analysis is Inconel X750, and it is assumed that it has linear and elastic behavior. Constant ambient pressure is applied at the free faces of the fluid as well as no slip condition at the surface of the fluid that faces the top foil. Computational fluid dynamics (CFD) and structural models are solved separately. At the beginning of the analysis, the CFD problem is solved with the assumption that the top foil has not yet been deformed. After the solution of the CFD problem, the pressure distribution at the surface of the fluid that faces the top foil is applied at the top foil and then the structural problem is solved. Consequently, the deflections of the top foil are applied on the corresponding surface of the CFD model and the algorithm continues until convergence is obtained. As soon as the converged solution for the pressure distribution is obtained, numerical integration is performed along the surface of the bearing in order to calculate its load-carrying capacity. Static bearing performance characteristics, such as pressure distribution, bump foil deflection, and load capacity are calculated and presented. Furthermore, fluid film thickness, top foil deflection, and fluid pressure are investigated as functions of the bearing angle as well as load-carrying capacity as a function of the bump and top foil stiffness. The same procedure is repeated for the thermohydrodynamic analysis. Moreover, in order to estimate the heat flux from the top foil to the bump foil channel as a function of the top foil temperature, a simple finite element model of the bump foil–cooling channel is constructed.

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References

Carpino, M., Medvetz, L. A., and Peng, J.-P., 1994, “Effects of Membrane Stresses in the Prediction of Foil Bearing Performance,” STLE Tribol. Trans., 37(1), pp. 43–50. [CrossRef]
Carpino, M., Peng, J.-P., and Medvetz, L. A., 1994, “Misalignment in a Complete Shell Gas Foil Journal Bearing,” STLE Tribol. Trans., 37(4), pp. 829–835. [CrossRef]
Kim, T. H., and San Andrés, L., 2006, “Limits for High Speed Operation of Gas Foil Bearings,” ASME J. Tribol., 128(3), pp. 670–673. [CrossRef]
San Andrés, L., and Kim, T. H., 2007, “Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models,” ASME Paper No. GT2007-27249. [CrossRef]
Bensouilah, H., Lahmar, M., and Bou-Said, B., 2012, “Elasto-Aerodynamic Lubrication Analysis of a Self-Acting Air Foil Journal Bearing,” Lubr. Sci., 24, pp. 95–128. [CrossRef]
Dellacorte, C., and Valco, M. J., 2000, “Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications,” Tribol. Trans., 43(4), pp. 795–801. [CrossRef]
San Andrés, L., and Kim, T. H., 2009, “Analysis of Gas Foil Bearings Integrating FE Top Foil Models,” Tribol. Int., 42, pp. 111–120. [CrossRef]
DellaCorte, C., Radil, C. K., Bruckner, J. R., and Howard, A. S., 2006, “A Preliminary Foil Gas Bearing Performance Map,” Annual Meeting and Exhibition sponsored by the Society of Tribologists and Lubrication Engineers, Calgary, AB, Canada, May 7–11, Paper No. ARL-TR-3902.
Carpino, M., and Talmage, G., 2003, “A Fully Coupled Finite Element Formulation for Elastically Supported Foil Journal Bearings,” Tribol. Trans., 46(4), pp. 560–565. [CrossRef]
Feng, K., and Kaneko, S., 2010, “Analytical Model of Bump-Type Foil Bearings Using a Link-Spring Structure and a Finite Element Shell Model,” ASME J. Tribol., 132(2), p. 021706. [CrossRef]
Walowit, J. A., and Anno, J. N., 1975, Modern Developments in Lubrication Mechanics, Applied Science, New York.
Niimi, T., 2012, “High Knudsen Number Flows COE for Education and Research of Nano-Micro Mechatronics, Nagoya University, http://groe.mech.naroyau.ac.jp/basic/pdf/basic-11.pdf
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Figures

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Fig. 1

An air foil bearing

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Fig. 2

Geometry of bump foil

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Fig. 3

Cooling channel geometry

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Fig. 4

Overall model of AFB

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Fig. 5

Validation diagram with Ref. [5]

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Fig. 6

Contour line plot of the top foil deflection for eccentricity ratio 0.6 versus bearing length and angle

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Fig. 7

Fluid film thickness versus angle for various eccentricity ratios

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Fig. 8

Load capacity versus eccentricity ratio

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Fig. 9

Pressure distribution for eccentricity ratio 0.6

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Fig. 10

Von Misses stresses for eccentricity ratio 0.6

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Fig. 11

Top foil deflection versus angle for eccentricity ratios

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Fig. 12

Top foil deflection versus angle for various normalized top foil thicknesses (tfn), ε0 = 0.4 and ftot = 24 N

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Fig. 13

Attitude angle versus normalized top foil thickness

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Fig. 14

Heat flux through top foil versus temperature for two different air speeds

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Fig. 15

Temperature field in the middle of the cooling channel

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Fig. 16

Temperature field in the radial clearance for ε0 = 0.6

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Fig. 17

Pressure versus bearing angle for ε0 = 0.6

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Fig. 18

p.d.c versus bearing angle

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Fig. 19

Bearing compressibility number versus bearing angle

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Fig. 20

Load-carrying capacity for non-THD and TDH versus eccentricity ratio

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Fig. 21

Air velocity flow lines at the inflow region of the bearing

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