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Research Papers

Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime With a Swirl Brake for Three Clearances

[+] Author and Article Information
Ovais Ahmed Bin Najeeb

Turbomachinery Laboratory,
Texas A&M University,
College Station, TX 77843

Dara W. Childs

Emeritus Professor of Mechanical Engineering,
Texas A&M University,
College Station 77843, TX
e-mail: dchilds@tamu.edu

Manuscript received August 9, 2018; final manuscript received January 19, 2019; published online February 11, 2019. Assoc. Editor: Tae Ho Kim.

J. Eng. Gas Turbines Power 141(8), 081002 (Feb 11, 2019) (11 pages) Paper No: GTP-18-1557; doi: 10.1115/1.4042650 History: Received August 09, 2018; Revised January 19, 2019

Tests are reported for a smooth seal with radial clearances 127 μm, 254 μm, 381 μm (1×, 2×, and 3×); length 45.72 mm, diameter 101.6 mm. An insert induced upstream preswirl. Swirl brakes (SBs), comprising 36 square cuts with axial depth 5.08 mm, radial height 6.35 mm, and circumferential width 6.35 mm each. Static and rotordynamic data were produced at ω = 2, 4, 6, 8 krpm, ΔP = 2.07, 4.14, 6.21, 8.27 bar, and eccentricity ratios ε0 = e0/Cr = 0.00, 0.27, 0.53, and 0.80. ISO VG 46 oil at a range of 46–49 °C was used, netting laminar flow (total Re ≤ 650). Dynamic measurements included components of the following vectors: (a) stator–rotor relative displacements, (b) acceleration, and (c) applied dynamic force in a stationary coordinate system. SBs were effective at the 3× clearance only. With the 3× seal, the cross-coupled stiffness coefficients have the same sign (not destabilizing). However, the seal has a negative direct stiffness K that could potentially “suck” the rotor into contact with the stator wall, along with dropping the pump rotor's natural frequency, further reducing its dynamic stability. Measurements were compared to predictions from a code by Zirkelback and San Andrés. Most predictions agree well with test data. Notable exceptions are the direct and cross-coupled stiffness coefficients for the 3× clearance. Predictions showed positive direct stiffness and opposite signs for the cross-coupled stiffness coefficients.

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References

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Lomakin, A. , 1958, “ Calculation of Critical Number of Revolutions and the Conditions Necessary for Dynamic Stability of Rotors in High-Pressure Hydraulic Machines When Taking Into Account Forces Originating in Sealings,” J. Power Mech. Eng., 14 (in Russian).
Pinkus, O. , and Sternlicht, B. , 1961, Theory of Hydrodynamic Lubrication, McGraw-Hill, New York.
Childs, D. , Norrbin, C. , and Phillips, S. , 2014, “ A Lateral Rotordynamics Primer on Electrical Submersible Pumps (ESP's) for Deep Subsea Applications,” 30th Pump Users Symposia, Houston, TX, Sept. 23–25, pp. 13–16. https://pdfs.semanticscholar.org/1a84/018a79cf26f9743f7165e8ae59cafa045feb.pdf
Childs, D. W. , 2013, Turbomachinery Rotordynamics With Case Studies, Minter Spring Publishing, Wellborn, TX.
Black, H. F. , Allaire, P. , and Barret, L. , 1981, “ Inlet Flow Swirl in Short Turbulent Annular Seal Dynamics,” Ninth International Conference on Fluid Sealing, Noordwijkerhout, The Netherlands, Apr. 1–3, pp. 141–152.
Benckert, H. , and Wachter, J. , 1980, “ Flow Induced Spring Constants of Labyrinth Seals for Applications in Rotor Dynamics,” First Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery, College Station, TX, May 12–14, pp. 189–212.
Massey, I. , 1985, “ Subsynchronous Vibration Problems in High-Speed Multistage Centrifugal Pumps,” 14th Turbomachinery Symposium, College Station, TX, pp. 11–16. https://oaktrust.library.tamu.edu/handle/1969.1/163638
Najeeb, O. A. , 2017, Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime With a Swirl Brake for Three Clearances, Texas A&M University, College Station, TX.
Kaul, A. , 1999, Design and Development of a Test Setup for the Experimental Determination of the Rotordynamic and Leakage Characteristics of Annular Bushing Oil Seals, Texas A&M University, College Station, TX.
Moreland, A. J. , 2016, “ Moreland-Effect of Eccentricity and Pre-Swirl on Smooth Stator Grooved Rotor Liquid Annular Seals, Measured Static and Dynamic Results,” M.S. thesis, Texas A&M University, College Station, TX.
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Figures

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Fig. 2

Effect of changing inlet swirl on WFR for a smooth seal[5]

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Fig. 3

Balance-piston seal SB [5]

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Fig. 4

Detailed drawing of new clearance seal with SBs. All dimensions are in mm.

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Fig. 5

Cross-sectional view of the main test section

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Fig. 6

Drive side view of the shaker assembly. Adapted from Ref. [10]

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Fig. 7

1× clearance seal with SBs

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Fig. 8

Cross-sectional view of high preswirl insert

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Fig. 9

Stator assembly schematic

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Fig. 10

Stator and lubricant flow path

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Fig. 11

Assembled stator and instrumentation

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Fig. 12

Measured and predicted Q˙ versus ε0 for ω = 6 krpm at: (a) ΔP = 2.07 bar and (b) ΔP = 8.27 bar

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Fig. 13

(a) Axial positions of the pitot tubes. (b) Radial view of the inlet pitot tube location. All dimensions in mm. Adapted from Ref. [11]

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Fig. 14

Radial position of the inlet preswirl pitot tube. Note that the figure is not drawn to scale

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Fig. 15

vi  versus ω at ε0 = 0.00: (a) ΔP = 2.07 bar and (b) ΔP = 8.27 bar

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Fig. 16

Preswirl ratio versus ω at ΔP = 8.27 bar

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Fig. 17

(a) Ideal load control and (b) ideal position control

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Fig. 18

Coordinate transformation from Cartesian coordinate system to r and t coordinate system

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Fig. 19

ω = 8 krpm and ΔP = 2.07 bar: (a) measured ϕ versus ε0 and (b) measured Fs versus ε0

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Fig. 20

ΔP = 2.07 bar and ω = 4 krpm: (a) measured and predicted Krr versus ε0 and (b) Measured and predicted Ktt versus ε0

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Fig. 21

ΔP = 2.07 bar and ω = 4 krpm: (a) measured Ktr and Krt versus ε0 and (b) predicted Ktr and Krt versus ε0

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Fig. 22

ΔP = 2.07 bar and ω = 2 krpm: (a) measured and predicted Crr versus ε0 and (b) measured and predicted Ctt versus ε0

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Fig. 23

ΔP = 6.21 bar and ω = 4 krpm: (a) measured and predicted Ctr versus ε0 and (b) measured and predicted Crt versus ε0

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Fig. 24

ΔP = 2.07 bar and ω = 4 krpm: (a) measured and predicted Mrr versus ε0 and (b) measured and predicted Mtt versus ε0

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Fig. 25

Measured Mtr and Mrt versus ε0 at ΔP = 6.21 bar and ω = 6 krpm

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Fig. 26

Measured and predicted WFR versus ε0 at ΔP = 4.14 bar and ω = 6 krpm

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