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Research Papers

Stratified Two-Phase Flow in Annular Seals

[+] Author and Article Information
Gioacchino Grimaldi

Fellow ASME
Department of Mechanics,
Mathematics and Management,
Polytechnic University of Bari,
V.le Japigia, 182,
Bari 70126, Italy
e-mail: gioacchino.grimaldi@poliba.it

Giuseppe Pascazio

Professor
Department of Mechanics,
Mathematics and Management,
Polytechnic University of Bari,
via Re David, 200,
Bari 70125, Italy
e-mail: giuseppe.pascazio@poliba.it

Giuseppe Vannini

Baker Hughes a GE Company,
Via Felice Matteucci 2,
Firenze 50127, Italy
e-mail: giuseppe.vannini@bhge.com

Luciano Afferrante

Associate Professor,
Department of Mechanics,
Mathematics and Management,
Polytechnic University of Bari,
V.le Japigia, 182,
Bari 70126, Italy
e-mail: luciano.afferrante@poliba.it

1Corresponding author.

Manuscript received October 5, 2018; final manuscript received December 22, 2018; published online January 16, 2019. Assoc. Editor: Tim Allison.

J. Eng. Gas Turbines Power 141(7), 071006 (Jan 16, 2019) (9 pages) Paper No: GTP-18-1642; doi: 10.1115/1.4042396 History: Received October 05, 2018; Revised December 22, 2018

The present study concerns the leakage predictions in pressure annular centered seals operating in a two-phase (gas–liquid) smooth stratified flow pattern. In such systems, the liquid experiences centrifugal forces typically 3–4 orders of magnitude larger than the standard earth gravity. Consequently, it is reasonable to assume the liquid is centrifuged toward the stator, leaving the rotor in contact only with the gas. This specific flow configuration is difficult to investigate experimentally, being the rotor–stator clearance of the order of 100 μm. For this reason, a new bulk model based on a two-phase smooth-stratified flow is proposed for leakage predictions. The (external) liquid flow and the (internal) gas one are assumed in laminar and turbulent regime, respectively. The results show that for convenient values of the inlet and outlet pressure loss coefficients, the stratified model predicts mass flow rates in better agreement with experimental data than a standard homogeneous multiphase bulk model.

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References

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Figures

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Fig. 1

Geometrical parameters of the developed stratified model

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Fig. 2

Variation of Ma−2 and Malim−2 in the axial direction forthree different pressure ratio PR=P0,exit/P0 (L/D=0.75,GVFinlet=0.885, P0=62.1 bar, Ω=1.5×104RPM)

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Fig. 3

Variation of the liquid axial VlH/ν and circumferential Ul,endH/ν Reynolds number with the inlet GVF: (a) axial liquid Reynolds number Rel,m=Ql/μl for L/D = 0.75 and (b) circumferential liquid Reynolds number Rel,c=ρlUl,exitHl,exit/μl for L/D = 0.75

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Fig. 4

Variation of the bulk axial velocities in the axial direction for the long seal case (D =90 mm, L/D =0.75, P0 = 62.1 bar, P0,out = 31 bar, Ω = 15,000 RPM, GVFinlet = 98.2%)

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Fig. 5

Variation of the bulk circumferential velocities in the axial direction for the long seal case (D =90 mm, L/D =0.75, P0 = 62.1 bar, P0,out = 31 bar, Ω = 15,000 RPM, GVFinlet = 98.2%). Prediction of the homogeneous model is also shown for comparison.

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Fig. 6

Comparison between stratified bulk model predictions and measured oil leakage. Results are obtained for D =90 mm, H =0.18 mm, T0 = 295 K, P0 = 62.1 bar, ρl = 900 kg/m3, μl = 3.64 × 10−3 Pl, μg = 1.82 × 10−5 Pl, ζi = 0.2, ζo = 0.5, Ω = 15,000 RPM: (a) oil leakage comparison for L/D = 0.75 and (b) oil leakage comparison for L/D = 0.29.

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Fig. 7

Comparison between stratified and homogeneous bulk model predictions in the case of long seal (D =90 mm, L/D =0.75) and different values of the pressure ratio PR = P0,exit/P0. Results are obtained for H =0.18 mm, T0 = 295 K, P0 = 62.1 bar, ρl = 900 kg/m3, μl = 3.64 × 10−3 Pl, μg = 1.82 × 10−5 Pl, ζi = 0.2, ζo = 0.5, Ω = 15,000 RPM: (a) leakage comparison, P0,exit = 0.6P0, (b) leakage comparison, P0,exit = 0.5P0, and (c) leakage comparison, P0,exit = 0.4P0.

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Fig. 8

Comparison between stratified and homogeneous bulkmodel predictions in the case of long seal (D =90 mm, L/D =0.29) and different values of the pressure ratio PR = P0,exit/P0. Results are obtained for H =0.18 mm, T0 = 295 K, P0 = 62.1 bar, ρl = 900 kg/m3, μl = 3.64 × 10−3 Pl, μg = 1.82 × 10−5 Pl, ζi = 1, ζo = 1, Ω = 15,000 RPM: (a) leakage comparison, P0,exit = 0.7P0, (b) leakage comparison, P0,exit = 0.6P0, and (c) leakage comparison, P0,exit = 0.5P0.

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Fig. 9

Comparison between the shear drag torque predicted by the proposed stratified model and the homogeneous ones (lines with diamonds) in the case of short seal (L/D =0.29)

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Fig. 10

Comparison between the shear drag torque predicted by the proposed stratified model and the homogeneous one (lines with diamonds) in the case of long seal (L/D =0.75)

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Fig. 11

Comparisons between CFD results and Eq. (A9)

Tables

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