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TECHNICAL PAPERS

Permeability and Inertial Coefficients of Porous Media for Air Bearing Feeding Systems

[+] Author and Article Information
G. Belforte, T. Raparelli, V. Viktorov

Department of Mechanics,  Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129 Italy

A. Trivella

Department of Mechanics,  Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, 10129 Italyandrea.trivella@polito.it

J. Tribol 129(4), 705-711 (Apr 18, 2007) (7 pages) doi:10.1115/1.2768068 History: Received November 29, 2006; Revised April 18, 2007

In porous resistances, Darcy’s law provides a good approximation of mass flow rate when the differences between upstream and downstream pressures are sufficiently small. In this range, the mass flow rates are proportional to the porous resistance’s permeability. For gas bearings, the pressure difference is normally higher, and it is known experimentally that the mass flow rates are lower than would result from Darcy’s law. Forchheimer’s law adds an inertial term to Darcy’s law and, when an appropriate coefficient is selected for this term, provides a good approximation of flow rates for the same applications even with the highest pressure differences. This paper presents an experimental and theoretical investigation of porous resistances used in gas bearing and thrust pad supply systems. The porous resistances considered in the investigation were made by sintering bronze powders with different grain sizes to produce cylindrical inserts that can be installed in bearing supply devices. The paper describes the test setup and experimental results obtained for: (i) mass flow rate through single porous resistances at different upstream and downstream pressures and (ii) mass flow rate and pressure distribution on a pneumatic pad featuring the same porous resistances. The theoretical permeability of the chosen porous resistances was calculated, and the results from setup (i) were then used to obtain experimental permeability and to determine the inertial coefficients. The results, which are expressed as a function of the Reynolds number, confirmed the validity of using Forchheimer’s law. The mass flow rates from setup (ii) were compared to those from setup (i) at the same pressure differentials across the resistance.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Powder with particle size Dp=66μm

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Figure 2

Cylindrical porous resistances

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Figure 3

Magnified view of resistance produced from powder with particle size Dp=66μm

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Figure 4

Single porous resistance test setup

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Figure 5

Flow rates of resistance 1

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Figure 6

Flow rates of resistance 2

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Figure 7

Flow rates of resistance 3

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Figure 10

Center area of pad and stationary bearing member

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Figure 11

Radial absolute pressure distribution across pad with resistance 1

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Figure 12

Radial absolute pressure distribution across pad with resistance 2

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Figure 13

Radial absolute pressure distribution across pad with resistance 3

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Figure 15

Friction factor fK versus Reynolds number ReK, P1=0.6MPa

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Figure 16

Comparison of theoretical (unmarked curves) and experimental (black points) mass flow rate G for the three resistances tested with P1=0.6MPa, using Kth from Table 4 and cth from Table 5 (cth selected for P2∕P1=0.17)

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Figure 17

Comparison of theoretical (unmarked curves) and experimental (black points) mass flow rate G for the three resistances tested with P1=0.6MPa, using Kexp from Table 4 and cexp from Table 5 (cexp selected for P2∕P1=0.17)

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Figure 18

Comparison of theoretical (unmarked curves) and experimental (black points) mass flow rate G for the three resistances tested with P1=0.6MPa, using Kexp from Table 4 and cexp from Table 6 (cexp selected for P2∕P1=0.5)

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Figure 19

Comparison of mass flow rate G for the resistance 3: experimental (white points), theoretical (continuous curve), theoretical without second-order term in G (outlined curve) with P1=0.6MPa, using Kexp from Table 4 and cexp from Table 6

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Figure 21

Comparison of experimental mass flow rate for the three resistances: single (white points) and mounted in the pad (black points), P1=0.6MPa

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Figure 14

Experimental (marked lines) and theoretical (unmarked lines) values of permeability versus v, P1=0.6MPa

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