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TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

The Lomakin Effect in Annular Gas Seals Under Choked Flow Conditions

[+] Author and Article Information
Mihai Arghir, Cyril Defaye, Jean Frêne

LMS (UMR 6610 CNRS), Université de Poitiers, France

By deriving Eq. 8, one obtains dP¯dx¯=(χMinlet*P¯)[(Minlet*)2P¯2].

J. Eng. Gas Turbines Power 129(4), 1028-1034 (Aug 30, 2006) (7 pages) doi:10.1115/1.2434344 History: Received May 29, 2006; Revised August 30, 2006

The paper deals with the static stability of annular gas seals under choked flow conditions. For a centered straight annular seal, choking can occur only in the exit section because the gas is constantly accelerated by friction forces. From the mathematical standpoint, the flow choking corresponds to a singularity that was never dealt with numerically. The present work introduces an original numerical treatment of this singularity that is validated by comparisons to the analytical solution for planar channel flow. An interesting observation stemming from these results is that the usual hypothesis of considering the flow as being isothermal is not correct anymore for a gas accelerated by a pressure gradient; the characteristics of the flow are the same but the quantitative results are different. The analysis of eccentric annular seals then shows that choked flow conditions produce a change in the static stiffness. For a subsonic exit section, the Lomakin effect is represented by a centering radial force opposed to the rotor displacement. For a choked exit section, the radial force stemming from an eccentricity perturbation has the same direction as the rotor displacement. The annular seal becomes then statically unstable. From the physical standpoint, this behavior is explained by the modification of the Lomakin effect, which changes sign. The pressure and Mach number variations along the seal depict the influence of high compressible flow regimes on the Lomakin effect. This characteristic has never been depicted before.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Mach number in a straight stator-grooved annular seal

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Figure 2

Pressure and Mach number variations in a parallel channel

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Figure 3

Mass flow rate in a parallel channel

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Figure 4

Exit pressure and Mach number in a parallel channel

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Figure 5

Forces in an annular seal

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Figure 6

Centering Lomakin effect for an incompressible flow regime

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Figure 7

Pressure and Mach number variation for a subsonic exit

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Figure 8

Pressure and Mach number variation for a sonic exit

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Figure 9

Mach number variation in the unwrapped annular seal for a choked exit section (blue line: minimum film section; red line: maximum film section)

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Figure 10

Pressure and Mach number variation in the unwrapped annular seal for Pexit=1.25bar and εX=0.6 (blue line: minimum film section; red line: maximum film section)

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