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Research Papers: Gas Turbines: Structures and Dynamics

Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals

[+] Author and Article Information
Luis San Andrés

Mast-Childs Tribology Professor Fellow ASME, Mechanical Engineering Department,  Texas A&M University, College Station, TX 77843-3123 e-mail: Lsanandres@tamu.edu

J. Eng. Gas Turbines Power 134(2), 022503 (Dec 14, 2011) (8 pages) doi:10.1115/1.4004130 History: Received April 11, 2011; Revised April 13, 2011; Published December 14, 2011; Online December 14, 2011

Abstract

As oil fields deplete, in particular in deep sea reservoirs, pump and compression systems work under more strenuous conditions with gas in liquid and liquid in gas mixtures, mostly inhomogeneous. Off-design operation affects system overall efficiency and reliability, including penalties in leakage and rotordynamic performance of secondary flow components, namely seals. The paper details a bulk-flow model for annular damper seals operating with gas in liquid mixtures. The analysis encompasses all-liquid and all-gas seals, as well as seals lubricated with homogenous (bubbly) mixtures, and predicts the static and dynamic force response of mixture lubricated seals; namely: leakage, power loss, reaction forces, and rotordynamic force coefficients, etc., as a function of the mixture volume fraction (βS ), supply and discharge pressures, rotor speed, whirl frequency, etc. A seal example with a nitrogen gas mixed with light oil is analyzed. The large pressure drop (70 bar) causes a large expansion of the gas within the seal even for (very) small gas volume fractions (βS ). Predictions show leakage and power loss decrease as $β→1$; albeit at low βS (< 0.3) (re)laminarization of the flow and an apparent increase in mixture viscosity, produce a hump in power loss. Cross-coupled stiffnesses and direct damping coefficients decrease steadily with increases in the gas volume fraction; however, some anomalies are apparent when the flow turns laminar. Mixture lubricated seals show frequency-dependent force coefficients. The equivalent damping decreases above and below βS  ∼ 0.10. The direct stiffness coefficients show atypical behavior: a low βS  = 0.1 produces stiffness hardening as the excitation frequency increases. Recall that an all liquid seal has a dynamic stiffness softening as frequency increases due to the apparent fluid mass. The predictions call for an experimental program to quantify the static and dynamic forced performance of annular seals operating with (bubbly) mixtures and to validate the current predictive model results.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Figure 1

Geometry of an annular pressure seal and coordinate system

Figure 2

Seal leakage (mass flow rate) versus inlet gas volume fraction (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 3

Mixture exit volume fraction (βa ) and mixture mass fraction (λ) versus inlet gas volume fraction (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 4

Axial pressure profile in seal for increasing inlet gas volume fractions (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 5

Drag power loss versus inlet gas volume fraction (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 6

Reynolds numbers: maximum and at exit plane versus inlet gas volume fraction (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 7

Seal (synchronous) stiffness and damping coefficients versus inlet gas volume fraction (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 8

Seal stiffness coefficients versus whirl frequency ratio (ω/Ω) for increasing inlet gas volume fractions (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 9

Seal damping coefficients versus whirl frequency ratio (ω/Ω) for increasing inlet gas volume fractions (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

Figure 10

Seal equivalent stiffness (Ke ) and damping (Ce ) coefficients versus whirl frequency ratio (ω/Ω) for increasing inlet gas volume fractions (βS ). Mixture N2 in ISO VG 2 oil (ΔP = 71 bar, 10 krpm).

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