Abstract

Though simple and fast, bulk-flow models (BFMs) for gas labyrinth seals (LSs) often predict the mass flow inaccurately. The BFM models rely on classical Neumann's equation model to characterize the flow through a labyrinth tooth. Presently, a computational fluid dynamics (CFD) analysis quantifies the effects of tip clearance (Cr) and operating conditions on the prediction of LS mass flow, and then derives an updated kinetic energy carry-over coefficient (μ1i) to improve the accuracy of Neumann's leakage equation. μ1i is a function of the seal tip clearance (Cr), the tooth pitch, and the total teeth number; but it does not depend on the seal supply or discharge pressures. The analysis selects a 14-teeth on stator LS (length/diameter = L/D = 0.29) with clearance Cr = (1/733)D and operating at nominal supply (Pin) and discharge (Pout) pressures equal to 73 bar and 51 bar, respectively, and at a rotor speed of 12 krpm (surface speed = 138 m/s). The CFD produces flow fields for LSs with a clearance varying from 80% to 200% of the nominal Cr, a gas supply pressure from 60 bar to 100 bar, and with various discharge pressures giving a pressure ratio (PR = Pout/Pin) ranging from 0.40 to 0.85. The numerous predictions deliver the mass flow as well as the bulk-flow velocities and cavity pressures within the seals. The kinetic energy carry-over coefficient (μ1i) increases with respect to the seal radial clearance (Cr). μ1i shows a parabolic correlation with PR; at first, μ1i increases with a rise in PR from a low value; and then, a further increase in PR leads to a decrease in μ1i. The coefficient μ1i is only sensitive to the PR and not to the magnitude of either the supply or discharge pressures. Lastly, for use with Neumann's leakage model, the CFD predictions produce an updated μ1i, a function of the seal geometry and the PR condition. Integration of the new μ1i correlation into a BFM code improves its accuracy to predict LS mass flow rate, a 19% difference against test data reduces to within 6%. A TOS LS tested by Ertas et al. (2012, Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbine Power, 134(4), p. 4250301) serves to further validate the accuracy of the modified leakage model.

References

1.
Childs
,
D. W.
,
1993
, “
Rotordynamic Models for Annular Gas Seals
,”
Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis
,
Wiley
,
New York
, pp.
209
306
.
2.
Martin
,
H.
,
1908
, “
Labyrinth Packings
,”
Engineering
,
85
(
10
), pp.
35
38
.
3.
Egli
,
A.
,
1935
, “
The Leakage of Steam Through Labyrinth Seals
,”
Trans. ASME
,
57
(
3
), pp.
115
122
.
4.
Hodkinson
,
B.
,
1939
, “
Estimation of the Leakage Through a Labyrinth Gland
,”
Proc. Inst. Mech. Eng.
,
141
(
1
), pp.
283
288
.10.1243/PIME_PROC_1939_141_037_02
5.
Neumann
,
K.
,
1964
, “
Zur Frage Der Verwendung Von Durchblickdichtungen im Dampfturbinenbau
,”
Maschinenbautechnik
,
13
(
4
), pp.
188
195
.
6.
Dai
,
Y.
,
Tyacke
,
J.
, and
Tucker
,
P.
,
2016
, “
Effect of Labyrinth Seal Configurations on Leakage Performance Using LES
,”
AIAA
Paper No. 2016-2127.10.25146/6.2016-2127
7.
Migliorini
,
P. J.
,
Untaroiu
,
A.
,
Wood
,
H. G.
, and
Allaire
,
P. E.
,
2012
, “
A Computational Fluid Dynamics/Bulk-Flow Hybrid Method for Determining Rotordynamic Coefficients of Annular Gas Seals
,”
ASME J. Tribol.
,
134
(
2
), p.
022202
.10.1115/1.4006407
8.
Migliorini
,
P. J.
,
Untaroiu
,
A.
,
Witt
,
W. C.
,
Morgan
,
N. R.
, and
Wood
,
H. G.
,
2014
, “
Hybrid Analysis of Gas Annular Seals With Energy Equation
,”
ASME J. Tribol.
,
136
(
3
), p.
031704
.10.1115/1.4026590
9.
Childs
,
D. W.
, and
Wade
,
J.
,
2004
, “
Rotordynamic Coefficient and Leakage Characteristics for Hole-Pattern-Stator Annular Gas Seals-Measurements Versus Predictions
,”
ASME J. Tribol.
,
126
(
2
), pp.
326
333
.10.1115/1.1611502
10.
San Andrés
,
L.
,
Wu
,
T.
,
Maeda
,
H.
, and
Ono
,
T.
,
2018
, “
A Computational Fluid Dynamics Modified Bulk-Flow Analysis for Circumferentially Shallow Grooved Liquid Seals
,”
ASME J. Eng. Gas Turbine Power
,
140
(
1
), p.
012504
.10.1115/1.4037614
11.
Nordmann
,
R.
,
Dietzen
,
F. J.
,
Janson
,
W.
,
Frei
,
A.
, and
Florjancic
,
S.
,
1986
, “
Rotordynamic Coefficients and Leakage Flow of Parallel Grooved Seals and Smooth Seals
,”
Texas A&M University
,
College Station, TX
, accessed Sept. 5, 2013, https://ntrs.nasa.gov/search.jsp?R=19870012773
12.
Cangioli
,
F.
,
Vannini
,
G.
,
Pennacchi
,
P.
,
Ciuchicchi
,
L.
,
Nettis
,
L.
, and
Chatterton
,
S.
,
2018
, “
Rotordynamic Characterization of a Staggered Labyrinth Seal: Experimental Test Data and Comparison With Predictions
,”
ASME J. Eng. Gas Turbine Power
,
141
(
1
), p.
011009
.10.1115/1.4040688
13.
Wu
,
T.
, and
San Andrés
,
L.
,
2019
, “
Gas Labyrinth Seals: On the Effect of Clearance and Operating Conditions on Wall Friction Factors—A CFD Investigation
,”
Tribol. Int.
,
131
, pp.
363
376
.10.1016/j.triboint.2018.10.046
14.
San Andrés
,
L.
,
Wu
,
T.
,
Barajas-Rivera
,
J.
,
Zhang
,
J.
, and
Kawashita
,
R.
,
2019
, “
Leakage and Cavity Pressures in an Interlocking Labyrinth Gas Seal: Measurements vs. Predictions
,”
ASME J. Eng. Gas Turbine Power
,
141
(
10
), p.
101007
.10.1115/1.4044284
15.
Wu
,
T.
, and
San Andrés
,
L.
,
2018
, “
Leakage and Dynamic Force Coefficients for Two Labyrinth Gas Seals: Teeth-on-Stator and Interlocking Teeth Configurations. A CFD Approach to Their Performance
,”
ASME J. Eng. Gas Turbine Power
,
141
(
4
), p.
042501
.10.1115/1.4041123
16.
Wu
,
T.
, and
San Andrés
,
L.
,
2019
, “
Pump Grooved Seals: A Computational Fluid Dynamics Approach to Improve Bulk-Flow Model Predictions
,”
ASME J. Eng. Gas Turbine Power
,
141
(
10
), p.
101005
.10.1115/1.4044283
17.
Vannini
,
G.
,
Cioncolini
,
S.
,
Del Vescovo
,
G.
, and
Rovini
,
M.
,
2014
, “
Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data
,”
ASME J. Eng. Gas Turbine Power
,
136
(
2
), p.
022501
.10.1115/1.4025360
18.
Cangioli
,
F.
,
Pennacchi
,
P.
,
Riboni
,
G.
,
Vannini
,
G.
,
Ciuchicchi
,
L.
,
Vania
,
A.
, and
Chatterton
,
S.
,
2017
, “
Sensitivity Analysis of the One-Control Volume Bulk-Flow Model for a 14 Teeth-on-Stator Straight-Through Labyrinth Seal
,”
ASME
Paper No. GT2017-63014.10.1115/GT2017-63014
19.
Iwatsubo
,
T.
,
1980
, “
Evaluation of Instability Forces of Labyrinth Seals in Turbines or Compressors
,”
Texas A&M University
,
College Station, TX
, accessed Sept. 4, 2013, https://ntrs.nasa.gov/search.jsp?R=19800021205
20.
Iwatsubo
,
T.
,
Motooka
,
N.
, and
Kawai
,
R.
,
1982
, “
Flow Induced Force of Labyrinth Seal
,”
Texas A&M University
,
College Station, TX
, Aug. 11, 2013, https://ntrs.nasa.gov/search.jsp?R=19830007372
21.
Childs
,
D. W.
, and
Scharrer
,
J. K.
,
1986
, “
Experimental Rotordynamic Coefficient Results for Teeth-on-Rotor and Teeth-on-Stator Labyrinth Gas Seals
,”
ASME J. Eng. Gas Turbine Power
,
108
(
4
), pp.
599
604
.10.1115/1.3239953
22.
Gurevich
,
M. I.
,
1966
,
The Theory of Jets in an Ideal Fluid
,
Pergamon Press
,
Oxford
, pp.
235
256
.
23.
Yèucel
,
U.
,
1996
, “
Leakage and Swirl Velocities in Labyrinth Seals
,”
M.S. thesis
, Department of Applied Mathematics,
Lehigh University
,
Bethlehem, PA
.https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.835.5880&rep=rep1&type=pdf
24.
San Andrés
,
L.
, and
Wu
,
T.
,
2017
, “
An Improved Bulk-Flow Analysis for Interlocking Labyrinth Gas Seals: Leakage and Force Coefficients
,” Turbomachinery Research Consortium (TRC),
Texas A&M University
,
College Station, TX
, Report No.
TRC-Seal-02-17
.https://rotorlab.tamu.edu/TRIBGROUP/2017%20San%20Andres%20TRC/7%20Software%20Needs%20CFD/TRC-Seal-02-17%20Software%20Needs%20Seals%20PRESENTATION.pdf
25.
Wu
,
T.
,
2019
, “
A Computational Fluid Dynamics Modified Friction Factor and Leakage Model for an Improved Bulk-Flow Analysis of Labyrinth Gas Seals
,”
Ph.D. dissertation
,
Mechanical Engineering Department, Texas A&M University
,
College Station, TX
.https://oaktrust.library.tamu.edu/handle/1969.1/189225
26.
Marquette
,
O.
,
Childs
,
D.
, and
San Andres
,
L.
,
1997
, “
Eccentricity Effects on the Rotordynamic Coefficients of Plain Annular Seals: Theory Versus Experiment
,”
ASME J. Tribol.
,
119
(
3
), pp.
443
447
.10.1115/1.2833515
27.
Delgado
,
I.
, and
Proctor
,
M.
,
2006
, “
Continued Investigation of Leakage and Power Loss Test Results for Competing Turbine Engine Seals
,”
AIAA
Paper No. 2006-4754.10.25146/6.2006-4754
28.
Ertas
,
B. H.
,
Delgado
,
A.
, and
Vannini
,
G.
,
2012
, “
Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio
,”
ASME J. Eng. Gas Turbine Power
,
134
(
4
), p.
042503
.10.1115/1.4004537
29.
Li
,
Z.
,
Li
,
J.
, and
Feng
,
Z.
,
2016
, “
Labyrinth Seal Rotordynamic Characteristics Part II: Geometrical Parameter Effects
,”
J. Propul. Power
,
32
(
5
), pp.
1281
1291
.10.2514/1.B35817
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