Leakage and Cavity Pressures in an

Interlocking Labyrinth Gas Seal: Measurements and Predictions

Tingcheng Wu & Jose BarajasGraduate Research Assistants

Luis San AndrésMast-Childs Chair Professor

ASME Fellow

Rimpei KawashitaResearch Engineer

Mitsubishi Heave Industries

Accepted for journal

publication

Jiaxin ZhangREUP Undergraduate Student

Proceedings of ASME Turbo Expo 2019: Turbomachinery Technical

Conference and Exposition, June 17-21, 2019, Phoenix, AZGT2019- 781507

2

Annular Clearance Tip Seals

Seals reduce leakage or

secondary flow in

turbomachinery.

Machine efficiency & cost of

operation rely on the accurate

quantification of seals’ leakage

over the operating speed &

pressure range, and

life including wear of parts.

Childs, D. W., 1993, Turbomachinery Rotordynamics, Chap.5.

3

About Labyrinth Seals1

Types of seals

(1) TOS: all teeth on stator

(2) TOR: all teeth on rotor

(3) ILS : teeth on both rotor and stator

TOS TOR ILS

LSs also affect rotor-bearing system stability.

[1] San Andres & Wu, 2018, ASME GT2018-75205

4

How do LSs restrict leakage?

Increased flow resistance:through vertical flow cells

TOR

TOS

ILS

Current knowledge:• Interlocking Laby Seal (ILS)

offers 30% lesser leakage than

TOR LS or TOS LS.

• Field data for ILS rotor-dynamic

characteristics still vague and

scarce.

5

Prior Art

Childs. 1993 (textbook) – states leakage of LSs (TOR or TOS) is well known though leakage traits for

ILSs are not well publicized.

Childs at al., 1988 – compare leakage for ILS & TOS seals ILS leaks less (30%) than TOS LS.

Wu and San Andrés, 2018 - use CFD to compare the leakage of a TOS LS against that of an ILS and

report the ILS reduces leakage by up to 30%.

Paolillo et al., 2017 – report on the effect of rotor speed on LS leakage and find important the ratio of rotor

surface speed (Urotor= ½ DΩ) to axial flow velocity (W).

Gary and Childs, 2018 - report measured leakage and radial and tangential forces for a test ILS. The test

rig and seals did not produce consistent results.

Benkert and Wachter, 1980 - measure leakage and force coefficients for various types of LS. The test

results show inlet pre-swirl velocity, rather than rotor speed, affects the seal tang. (damping) force.

Cangioli et al., 2017- assess the effect of both negative and positive inlet pre-swirl velocities on the

force coefficients of labyrinth seals.

6

This paper

Quantifies the effect of operating

conditions on the leakage (mass

flow) in an ILS,

1. Measurement: mass flow rate & cavity pressures as a

function of operating conditions.

as a function of

pressure difference DP=(Pin - Pout),

pressure ratio (PR=Pout/Pin),

and rotor surface speed.

2. Compare test data to bulk-flow model (BFM) and a

computational fluid dynamics (CFD) predictions.

GT2019- 781507

7

Photograph of Test Rig

Seal clearance = 0.2 mm

1 m0 m

8

Housing and Seals Test Section

Zoom of seal test section

Two test seals on side

of central inlet plenum.

Flow enters central

plenum through

angled orifices, passes

swirl brakes and flows

through left and right

ILSs, and

discharges into

large plenum.

9

Test Seal Geometry

Rotor diameter, D 150 mm

Overall length, L 45 mm

Radial clearance, Cr 0.200 mm

Teeth Number, NT 5

Tooth Pitch, Li 8.3 mm

Height, B 5.8 mm

Width at tip, Bt 0.25 mm

Three teeth of stator and two teeth

on rotor.

Left ILSRight

(Test)

ILSCentral

plenum

Inlet air

Housing

flowflow

Left ILS Right ILSCentral

plenum

10

Inlet with angled injection holes (swirl vane)

Pressurized air enters the chamber through two rows of 14 parallel holes,

1.5 mm in diameter, equally spaced around the ring circumference, and

angled 75o with respect to a radial line.

Sensors and location

11

Exit LS

Exit LSPitot

tube

Exit

plenum

Inlet

plenum

Exit

plenum

Static

pressure

Shaft – Eddy

current sensors

Differential cavity

pressure sensors

thermocouple

flowflow

Flow diagram

Pressure Sensors and their Location

12

Differential pressure sensors did not deliver reliable dynamic pressure data.

Useless to extract force coefficients!

Connection of ends of differential pressure

transducers into a muffler plenum.

flow

flow

13

Predictive

Models

Bulk-Flow Model (BFM) for Labyrinth Seal

m i = m i+1

Neumann’s Leakage Model

+ circumferential momentum in cavities

 2  21

1 2  

i ii i r

g

P Pm DC

R T

Thorat & Childs, 2010 XLLABY® used for predictions.

14

Flow through clearance under a tooth

San Andrés & Wu, 2017, TRC-Seal-02-17

CFD Model, Mesh and Boundary Conditions

15

45,501 nodes for

leakage calculation

flow

flow

16

Test

Results

Test Conditions

17

Air Properties

Density @ 25 ͦ C 1.2 kg/m3

Temperature, T 298 K

Sound speed, Vs 352 m/s

Kinematic viscosity, n 1.86×10-5 m2/s

Operating

Conditions

Line pressure, Pline 0.96 ~2.16 MPa

ILS Inlet Pressure, Pin 0.29 ~ 1.1 MPa

Pressure ratio,

PR = Pout/Pin0.3, 0.5, 0.8

Rotor speed, Ω 0, 3, 5, 7.5, 10 krpm

Surface Speed, RΩ 0 ~ 78.5 m/s

flow

Note: Estimated centrifugal grow of rotor at 10 krpm = 3.6 m (~

max 2% clearance)

Mass Flow Rate vs. Pressure vs. Rotor Speed

• Flow rate is proportional to DP and increases with PR.

• Shaft speed has an insignificant effect on seal leakage.

• CFD and BFM predictions agree with test data. 18

ILS Clearance=0.2 mmUncertainty : 5% max

Cavity Pressures

• Cavity pressures linearly drop from seal inlet towards exit plane

at pressure Pout.

• Rotor speed or DP do not affect cavity pressures.19

ILS Clearance=0.2 mm

Inlet Pressure 300-600 kPa

choke

Uncertainty : 1% max

20

Cavity Pressures: Models vs Test Data

BFM & CFD predictions agree +well with the measured leakage.

ILS Clearance=0.2 mm

ILS : Pin = 292 ~ 1,150 kPa, PR = 0.3 ~0.8, rotor speed Ω = 0 ~ 10 krpm (RΩ = 0 ~ 79 m/s).

Flow Regime in Test ILS – Pressure ratio increases

Reynolds number

ranges from 4,302

to 10,847

turbulent flow.

For PR=0.3, flow

chokes across

last tooth (at seal

exit plane: cavity

#4)

21

22

Other Findings

• Inlet swirl has a minute effect on

the test seal leakage and cavity

pressures.

• Uswirl is as high as 172 m/s for the

highest Pin and lowest PR.

• No major change (1 or 2 K) in gas

exit temperature.

• Estimated centrifugal grow of

rotor at 10 krpm = 3.6 m (~ max 2

% clearance)

23

Analysis of

ILS Leakage

24

Flow Factor fQuantifies leakage of gas seals to demonstrate

independence of seal size (diameter D) and inlet flow

conditions in pressure (Pin) and temperature (T).

kg KMPa m s

( )inm T P Df

Delgado, I., and Proctor, M., 2006, AIAA–2006–4754.

…. but still a dimensional(ly odd) parameter

25

Flow Factor for test ILS ILS Clearance=0.2 mm( )inm T P Df

kg KMPa m s

f increases as pressure ratio

(PR) drops but is nearly

constant with DP.

Find a better way to

represent flow.

26

An Effective Clearance for test ILS

Use Neumann’s

leakage

equation to

define a

modified flow

factor and to

represent test

ILS as an

equivalent

(single tooth)

seal.

Ceff is an effective

clearance.

 2  2

1 11 21 

 2  2

1

12 12 22 

 2  2

2

2

1  

r

g

r

in

g

N N N rN u

g

o t

P Pm DC

R T

P Pm DC

R T

P Pm DC

R T

 2  2

in out

eff

g

P Pm DC

R T

27

Modified Flow Factor

2 2

1~

1 1eff

gin

m TC

RPR D P PR

f

Ceff = effective clearance = cd Cr

2 2

2

~ 1 out

in

in out Pin

eff eff P

g g

P P Pm DC DC

R T R T

( )inm T P Df

cd loss coefficient.

28

Modified Flow Factor for test ILS

kg KMPa m s

Clearance=0.2 mm

Data collapses to give:

12.75

0.45 (3.2%)

0.25 (2.0%)

kg KMPa m s

kg KMPa m s

kg KMPa m s

Standard deviation

test

prediction

not a function of pressures Pin, Pout, or rotor speed!

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Loss coefficient for test ILS Clearance=0.2 mm

12.75 kg KMPa m s

cd (a fraction of seal clearance) is not a function of

pressures Pin, Pout, or rotor speed!

21

g

eff d r

in

m R TC c C

D P PR

test

prediction

0.36 0.01

0.35 0.01

d

d

c

c

30

Conclusion

Conclusion

31

• ILS mass flow increases linearly with pressure difference (Pin-Pout) and

for all (exit/inlet) pressure ratios (PR).

• Rotor speed has a minute effect on test seal leakage.

• Seal cavity static pressures drop linearly for all Pin and pressure ratios

PR=0.8 and 0.5. For PR=0.3, ILS chokes.

• Both CFD and BFM predictions (leakage and pressure) agree with test

data.

• Flow factor f does not vary with Pin but decreases as PR increases.

• A modified from factor produces a single constant, neither a function of

inlet pressure nor pressure ratio.

• The finding allows to estimate a unique effective clearance Ceff /Cr = cd =

0.36 for all test conditions.

GT2019- 781507

32

Acknowledgements

Questions (?)

Thanks for support to Mitsubishi

Heavy Industries and NSF Research

Experience for Undergraduate

Program

Learn more at http://rotorlab.tamu.edu

Inlet Hole Speed vs. Pressure Difference

33

• Inlet flow velocity

through orifice

increases with pressure

difference and

decreases with both

shaft speed and

pressure ratio

• Velocity tangent to rotor

surface (Pitot tube) is a

fraction of inlet speed

through holes but

higher than rotor

surface speed (same

direction)

0

50

100

150

200

250

300

350

0 100 200 300 400

inle

t ve

locity (

m/s

)

Pressure Difference (kPa)

test data : w rotor spinning. Seal clearance = 0.2 mm

PR=0.3

PR=0.5

PR=0.8

PR=0.3 Pitot

PR=0.5 Pitot

PR=0.8 Pitot

PR=0.3

PR=0.5

Pivot tube

feed holes

speed = 7.5 kRPM (58 m/s)

speed =10 kRPM (79 m/s)

PR=0.8

Sound speed = 352 m/s

34

Pressurized

air in

Pressurized air in

Air out Air out

rotor