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Research Papers: Gas Turbines: Structures and Dynamics

# About the Negative Direct Static Stiffness of Highly Eccentric Straight Annular Seals

[+] Author and Article Information
Mihai Arghir

Institut Pprime,
UPR CNRS 3346,
Université de Poitiers,
Poitiers 86962, France
e-mail: mihai.arghir@univ-poitiers.fr

Antoine Mariot

Institut Pprime,
UPR CNRS 3346,
Université de Poitiers,
Poitiers 86962, France
e-mail: antoine.mariot@univ-poitiers.fr

A supersonic exit is a rare case; it could be encountered only when seal is very long and has convergent-divergent axial clearance variation.

Static misalignement and tilt perturbations are discarded in this analysis.

The same kind of results is obtained for a typical water lubricated annular seal operating at high εx and Ω = 0 but are omitted for brevity.

For the RHS of Eq. (15) it was taken into account that $∂P/∂x=0$ along h = hmin.

All calculations were performed with zero prerotation speed.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received November 13, 2014; final manuscript received January 16, 2015; published online February 10, 2015. Editor: David Wisler.

J. Eng. Gas Turbines Power 137(8), 082508 (Aug 01, 2015) (9 pages) Paper No: GTP-14-1619; doi: 10.1115/1.4029624 History: Received November 13, 2014; Revised January 16, 2015; Online February 10, 2015

## Abstract

Experimental results indicating negative direct static stiffness of highly eccentric straight gas annular seals were very recently presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). This instability occurred at zero rotation speed and at high eccentricities. Up to then only gas annular seals with zero rotation speed, operating in centered position and with choked exit section were known as being susceptible of developing negative direct static stiffness. The seals and the working conditions presented by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201) had clearly no choked exit section. The present work advances a theoretical explanation of results reported by Childs and Arthur (2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201). The analysis is based on the numerical solution of the bulk flow equations of the flow in the annular seal. Theoretical results show a negative static stiffness at high eccentricities and zero rotation speeds. Other seal geometries and working conditions were tested and showed that the decrease of the direct static stiffness at high eccentricities and zero rotation speeds is a characteristic of all straight annular seals whether the fluid is compressible or not. Nevertheless with increasing rotation speed, the static stiffness becomes again positive and may increase with increasing eccentricity. The negative static stiffness is then limited to very specific working conditions: high eccentricities and zero rotation speed.

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## References

Childs, D. W., 1993, Turbomachinery Rotordynamics, Wiley, New York.
Childs, D. W., and Arthur, S. P., 2013, “Static Destabilizing Behavior for Gas Annular Seals at High Eccentricity Ratios,” ASME Paper No. GT2013-94201.
Arghir, M., Defaye, C., and Frêne, J., 2007, “The Lomakin Effect in Anular Gas Seals Under Choked Flow Conditions,” ASME J. Eng. Gas Turbines Power, 129(14), pp. 1028–1034.
Hassini, M. A., and Arghir, M., 2013, “Phase Change and Choked Flow Effects on Rotordynamic Coefficients of Cryogenic Annular Seals,” ASME J. Tribol., 135(4), p. 042201.
Massey, I., 1985, “Subsynchronous Vibration Problems in High-Speed Multistage Centrifugal Pumps,” 14th Turbomachinery Symposium, Texas A&M University, Houston, TX, Oct. 22–24, pp. 11–16.
Valantas, R., and Bolleter, U., 1988, “Solutions to Abrasive Wear-Related Rotordynamic Instability Problems in Prudhoe Bay Injection Pumps,” Fifth International Pump Users Symposium, Texas A&M University, Houston, May 10–12, pp. 3–10.
Black, H., and Jenssen, D., 1969, “Dynamic Hybrid Bearing Characteristics of Annular Controlled Leakage Seals,” Proc. Inst. Mech. Eng., Part 3N, 184(14), pp. 92–100.
Marquette, O., Childs, D. W., and San Andrés, L., 1997, “Eccentricity Effects on the Rotordynamic Coefficients of Plain Annular Seals: Theory Versus Experiment,” ASME J. Tribol., 119(3), pp. 443–448.
Constantinescu, V. N., 1995, Laminar Viscous Flow, Springer-Verlag, New York, pp. 403–412.
Launder, B. E., and Leschziner, M., 1978, “Flow in Finite-Width, Journal Bearings Including Inertia Effects,” ASME J. Lubr. Technol., 100(13), pp. 330–338.
San Andrés, L., 1991, “Analysis of Variable Fluid Properties, Turbulent Annular Seals,” ASME J. Tribol., 113(14), pp. 694–702.
Hirs, G., 1973, “A Bulk Flow Theory for Turbulence in Lubricant Films,” ASME J. Lubr. Technol., 95(12), pp. 137–146.
Colebrook, C. F., 1939, “Turbulent Flow in Pipes, With Particular Reference to the Transition Between the Smooth and Rough Pipe Laws,” J. Inst. Civ. Eng., 11(14), pp. 133–156.
Zirkelback, N., and San Andrés, L., 1998, “Bulk-Flow Model for the Transition to Turbulence Regime in Annular Seals,” STLE Tribol. Trans., 39(14), pp. 835–845.
Arghir, M., and Frêne, J., 2001, “A Triangle Based Finite Volume Method for the Integration of Lubrication's Incompressible Bulk Flow Equation,” ASME J. Tribol., 123(11), pp. 118–124.
Arghir, M., and Frêne, J., 2001, “Numerical Solution of Lubrication's Compressible Bulk-Flow Equations: Applications to Annular Seals Analysis,” ASME Paper No. 2001-GT-0117.
Kerr, B. G., 2001, “Experimental and Theoretical Rotordynamic Coefficients and Leakage of Straight Smooth Annular Gas Seals,” Master's thesis, Texas A&M University, College Station, TX.
Alexander, C. R., Childs, D. W., and Yang, Z., 1995, “Theory Versus Experiment for the Rotordynamic Characteristics of a Smooth Annular Gas Seal at Eccentric Positions,” ASME J. Tribol., 117(1), pp. 148–152.

## Figures

Fig. 1

Pressure, Mach number in a choked annular seal

Fig. 2

Typical flow and pressure pattern in a centered annular seal

Fig. 3

Mass flow rate of the seal presented in Ref. [2]

Fig. 4

Restoring radial force for the seal presented in Ref. [2]

Fig. 5

Static direct stiffness of the seal presented in Ref. [2]

Fig. 6

Total Reynolds number in the unwrapped annular seal for εx = 0.95 (PR = 50%)

Fig. 7

Pressure, temperature surface for εx = 0.95 (PR = 50%)

Fig. 8

Mach number isolines for εx = 0.95 (PR = 50%)

Fig. 9

Restoring force and direct static stiffness KXX for incompressible flow regime

Fig. 10

Isolines of pressure finite differences (PR = 50%)

Fig. 11

Isolines of the circumferential bulk velocity U (PR = 50%). The difference between two consecutive isolines is 0.25 m/s.

Fig. 12

Isolines of the axial bulk velocity W, (PR = 50%)

Fig. 13

Isolines of dU/dx, (εx = 0.95 and PR = 50%)

Fig. 14

Generic pressure variation along h = hmin

Fig. 15

Static stiffness KXX for the annular seal described in Ref. [2]

Fig. 20

Isolines of pressure finite differences (PR = 50%, incompressible flow regime)

Fig. 21

Isolines of the circumferential bulk velocity U, (PR = 50%, incompressible flow regime). The differences between two consecutive isolines is 0.25 m/s.

Fig. 22

Isolines of the axial bulk velocity W (PR = 50%, incompressible flow regime)

Fig. 17

Static direct stiffness KXX for the annular seal described in Ref. [17] CR = 0.11 mm and PR = 0.53

Fig. 16

Variation of the Zxx impedance with the excitation speed for the annular seal described in Ref. [2]

Fig. 19

Static direct stiffness KXX for the annular seal described in Ref. [18] CR = 0.41 mm and PR = 0.67

Fig. 18

Static direct stiffness KXX for the annular seal described in Ref. [17] CR = 0.21 mm and PR = 0.65

Fig. 23

Isolines of dU/dx (εx = 0.95, PR = 50%, incompressible flow regime)

## Errata

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