1

ON THE LEAKAGE AND ROTORDYNAMIC

FORCE COEFFICIENTS OF PUMP

ANNULAR SEALS OPERATING WITH

AIR/OIL MIXTURES:

MEASUREMENTS AND PREDICTIONS

Funded by Turbomachinery Research Consortium

Luis San AndrésPerforms research in lubrication and rotordynamics. Luis is a Fellow of

ASME and STLE, and a member of the Industrial Advisory Committees for

the Texas A&M Turbomachinery Symposia. Luis has published over 260

peer reviewed papers in various journals and conferences; several papers

recognized as best by the professional societies.

Xueliang Lu Ph.D. student working for Dr. San Andrés at Texas A&M University. So

far, Xueliang has published 7 papers during his Ph.D. studies,

onerecognized as a best paper at the ASME Turbo Expo Conference

(2017). Xueliang’s research focuses on the experimental identification

and prediction of force coefficients for two phase flow annular seals and

fluid film bearings.

Authors

2

3

Abstract

In the subsea oil and gas industry, multiphase pumps and wet

gas compressors enable long distance tie back systems and

eliminate oil and gas separation stations.

In these systems, seals must operate without affecting the

system efficiency and dynamic stability for a distinct services

changing through the life of the pump/compressor.

The lecture presents measurements of leakage and force

coefficients for six annular seals operating with an air in oil

mixture ranging from pure liquid to most air. The test results

show the effect of gas content on the performance of these

seals and make patent unusual behavior.

Outline

1. Justification

2. About wet (bubbly) annular seals.

3. Test rig at TAMU

4. Seals’ leakage and shear drag vs gas

content.

5. Seals’ dynamic force coefficients

6. Gas injection to increase seal direct stiffness

in pumps/turbines

7. Conclusion

4

Introduction to wet

(bubbly) annular seals

5

6

Annular Pressure Seals

Seals in a Multistage Centrifugal Pump or Compressor

Seals (annular, labyrinth or textured) separate regions of high pressure

and low pressure and their main function is to minimize leakage(secondary flow); thus improving the overall efficiency of a machine

extracting or delivering power to a fluid.

Impeller eye or

neck ring sealBalance piston seal

Inter-stage

seal

Compressor stage (LVF: 0 to 5%)Electrical submersible pump

stage (GVF: 0 to 100%) Hydraulic pump/turbine

impeller section

Seals in pumps, compressors & turbines

Bubbly/Wet seals affect pump/compressor

performance (leakage and torque) and are prone

to reduce system stability.

A change in mixture gas volume fraction (GVF) affects physical

properties: density and viscosity. 7

GVF: Gas volume fraction (pump) LVF: Liquid volume fraction (compressor)

8

Pros and cons of two-phase flow operation

Multiphase

pumping

Wet gas

compression

Hydraulic

turbine/pumps

Applications Onshore, offshore,

subsea and

downhole

GVF 0 -100% [1]

Subsea and

downhole

LVF 0 – 5% [2]

Power generation

Benefits Add pressure to process fluids,

enabling long distance tie back

system to reduce Oil/Gas separation

station, dropping cost by 30%

Clean energy

Challenges Rotor sub-synchronous vibrations Sometimes suffer from

non-synchronous

vibration even at null

speed [3]

[1] Gong, H., et al., 2012, “Comparison of Multiphase Pumping Technologies for Subsea and Downhole Applications.” Oil and Gas

Facilities, 1(01), pp. 36-46.

[2] Vannini, G., et al., 2014, “Centrifugal Compressor Rotordynamics in Wet Gas Conditions.” Proc. of the 43th Turbomachinery & 30th

Pump Users Symposia, Houston, TX, September 23-25.

[3] Smith, et al., 1996, “Centrifugal Pump Vibration Caused by Supersynchronous Shaft Instability Use of Pumpout Vanes to Increase

Pump Shaft Stability.” Proc. 13th International Pump Users Symposium, Houston, TX, Mar. 5-7.

Ransom et al., 2011, “Mechanical Performance of a Two Stage Centrifugal Compressor under Wet

Gas Conditions,” 40th Turbomachinery Symposium, Houston.

Shaft speed:

8 krpm (133 Hz)Fluids:

Air and water

Issues related to wet gas compression

Rotor axial vibration

• Axial vibration (0.5 Hz) appears

with low LVF.

• No SSV with dry gas (LVF=0)

• Increasing LVF: vibration

amplitude increases with

frequency (10 – 15 Hz)

• Axial vibration stops when liquid

injection is turned off.

Variation of LVF produces a

change in balance piston sealthrust load, thus axial vibration.

9

Vannini et al., 2016, “Experimental Results and CFD Simulations of Labyrinth and Pocket Damper

Seals for Wet Gas Compression,” ASME J. Eng. Gas Turb. Power, 138, p. 052501.

0.45 X SSV increases in

magnitude with LVF

13.5 krpm, 10 bar

Balance piston:

Labyrinth seal

Fluids:

Air and water

Rotor lateral vibration

LVF: 0~3%

Trapped liquid in seal

rotates with great

momentum and causes

0.45X SSV

1 X

0.45 X

Two-phase flow in a wet gas compressor

10

Vannini et al., 2016, “Experimental Results and CFD Simulations of Labyrinth and Pocket Damper

Seals for Wet Gas Compression,” ASME J. Eng. Gas Turb. Power, 138, p. 052501.

13.5 krpm, 10 bar

Balance piston:

Pocket damper

seal

Rotor lateral vibration

0.45 X SSV reduces from 20 μm

to a few microns.

Liquid does not accumulate

in PDS, thus mitigating SSV.

1 X

0.45 X

Two-phase flow in a wet gas compressor

11

Helico-axial pump (1.5 to 4.6 krpm)

Rotor SSV appears under some

two-phase flow conditions : low

differential pressure with a

high-viscosity mixture.

Bibet, P. J., et al., 2013, "Design and Verification Testing of a New Balance Piston for High Boost

Multiphase Pumps," Proc. 29th International Pump User Symposium, Houston, TX.

Bibet et al. (2013)

Two-phase flow in a Multiple Phase pump

Pump operates stable with liquid.

(600 cPoise)

When SSV occurs, rotor whirl

frequency ratio > 1.0.

high amplitude

SSVs

12

• Wet gas compression and multiphase oil boosting save

up to 30% of capital investment compared with a L/G

separation station.

• Subsea facilities must handle gas in liquid mixtures with

a varying gas content:

Wet gas compressor: LVF < 5%

Multiphase pump: 0< GVF< 100%

Justification subsea facilities

13

Need of concerted effort to quantify

effect of two phase flow in sealing

components

Towards improving reliability and

reducing operating cost.

Test Rig at TAMU- TL

14

Air InletOil Inlet

(ISO VG 10)

Test seal

section

Valve

Valve

Sparger

(mixing)

element

Oil

Air

Ps/Pa=2.5, inlet GVF=

50%, stationary shaft

Wet seal test rig

journal speed: 3.5 krpm (23.3 m/s)15

D = 26 mm

L=

46 m

m

Seal

Diameter (D ) 127 mm (5 in)

Length (L) 46 mm (1.8 in)

Clearance (c) 0.203 mm (8 mil) at

34 ºC

Supply pressure (Ps) 1.0~3.5 bar (abs)

Oil ISO VG 10

density(ρl) 830 kg/m3

viscosity (μl) 10.6 cP at 34 ºC

Air density (ρga) 1.2 kg/m3 at 1bar

viscosity(μga) 0.02 cP at 20 ºC, 1

bar (abs)

Shaft speed (Ωmax) 3.5 krpm

Rotor surface

speed ½ DΩmax

23 m/s

Flow

Seal

Rotor and seal

L/D=0.36

X

ZY

Seal geometry and fluids

16

Air and oil circulation systems

Oil

Air

GVF at inlet:

/

/in

g a s

l g a s

Q P P

Q +Q P P

17

α : Gas volume fraction

Ps: pressure at seal inlet plane

Pa: ambient pressure= 1 bar(a)

Qg: gas flow rate at Ps

Ql: liquid flow rate

Six test seals

Four types :

Smooth surface

plain sealNominal c and worn (>c)

Three-wave seal:Large dynamic stiffness

Groove seal: Applied with large pressure

drops (turbulent flow)

Step clearance

seals: Often used in water

turbines/pumps.

18

Clearance (c) ~ 0.2 mm

Plain seals #1 & 2:(c1= 0.203 mm, c2 = 0.274 mm)

#3

Three-wave seal(cm=0.191 mm)

#4

Grooved seal (cr=0.211 mm, dg=0.543 mm,

lg=1.5 mm, ll=0.904 mm,

Ng=14)

#5

Upstream step clearance (cT=0.164mm, cB=0.274 mm,

LT=0.11L).

#6

Downstream step

clearance (cT=0.274 mm, cB=0.164 mm,

LT=0.82L).

Flow visualization inlet GVF = 0-0.9. Ps/Pa=2.5. Speed 0 rpm

19

• Leakage increases

with inlet LVF.

• Reynolds # drops

from >1000 (air) to a

very low magnitude

with (air in oil).

Ps/Pa=1.5, inlet LVF= 2%

1

10

100

1000

10000

0.0 0.2 0.4 0.6 0.8 1.0

Ax

ial

flo

w R

eyn

old

s n

um

be

r

Liquid volume fraction at seal inlet

Reynolds #

8

10

12

14

16

18

20

22

24

0.0 0.2 0.4 0.6 0.8 1.0

Ma

ss

flo

w r

ate

of

mix

ture

[g

/s]

Liquid volume fraction at Seal Inlet

Measurement,

Ps/Pa= 3.0

Prediction

Prediction,

Ps/Pa = 3.5

Measurement

Leakage

20

Plain seal : flow rate vs LVF (0 rpm)

Clearance ~ 0.2 mm

Flow with shaft spinning Ps/Pa = 2, speed 1.8 krpm

21

Inlet

outlet Direction of rotation

Stroboscope light

with frequency 30

Hz freezes shaft

motion

Air bubbles coalesce

and merges to make

streamlets

Laminar flow with Reynolds #: Rec = 153, Rez = 245 at exit plane

(12 m/s)

Seals’ leakage and

drag torque

22

0.0

0.5

1.0

1.5

2.0

1 3 4 5 6

Dim

en

sio

nle

ss m

ass

flo

w r

ate

Seal type

Uniform

clearance

Three-

wave

Grooved

seal

Upstream

step sealDownstream

step seal

31

12

l

pl

l

Pm Dc

L

Normalized toPlain seals #1 & 2:

(c1= 0.203 mm, c2 = 0.274 mm)

#3

Three-wave seal(cm=0.191 mm)

#4

Grooved seal (cr=0.211 mm, dg=0.543 mm, lg=1.5

mm, ll=0.904 mm, Ng=14)

#5

Upstream step clearance (cT=0.164mm, cB=0.274 mm,

LT=0.11L).

#6

Downstream step clearance (cT=0.274 mm, cB=0.164 mm,

LT=0.82L).

Leakage (oil only) LVF=1

Grooved seal not as effective as plain seal

since flow is laminar.23

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.00 0.20 0.40 0.60 0.80 1.00

Grooved seal-4

(3.5 krpm)

Three-wave seal

(4 krpm)

Three wave seal

(0 rpm)

Plain seal-1, (0 rpm)

Cseal#1 = 0.203 mm; Cseal#2 = 0.274 mm

Cseal#3 = 0.191 mm; Cseal#4 = 0.211 mm

Mass f

low

/ l

iqu

id m

ass f

low

Plain seal-2

(0 rpm)

Gas volume fraction at seal inlet

Leakage for all seals shows

same trend as GVF

increases it drops!Three-wave seal leaks a little

more.

Grooved seal shows fastest

reduction.

Predictions agree with test

data.

Leakage (Mixture) gas volume fraction increases

mixture

liquid

mm

m

24

Normalized with respect to liquid

(GFV=0)

normalized to liquid condition

3

0

2 L

seal m

RT dz

c

Drag torque (mixture)

Torque linearly

decreases with GVF.

GVF = 0 0.9

85% reduction in

torque

Grave implication for

pump and motor

reliable performance.

Tseal

Shaft speed:1.5, 2.5 3.5 krpm

25

prediction

Air in ISO VG 10 oil

Seals’ Dynamic

Force Coefficients

26

27

Seal reaction force is a function of the

fluid properties, flow regime, operating

conditions and geometry.

For small amplitudes of rotor

motion, the force is represented

with stiffness, damping and inertia

force coefficients:

X

Y

F K k x C c x M 0 x

F k K y c C y 0 M y

Dynamic force coefficients

X

Y

K k C cF x x

F k K y c C y

For two-

phase

flow

or a gas

frequency dependent

Dynamic load tests

Excite test system

with periodic loads

and measure test

system forced

response and

perform parameter

identification.

room temperature 20oC.

journal speed: 3.5 krpm(RΩ: 23 m/s)

Inlet GVF: 0 to 0.9

28

29

Structure (pipe) stiffness,

Ks = 690 kN/m

Structure damping,

Cs= 0.2 kN.s/m

Housing mass & seal

MBC = 7 kg

Test rig structure parameters

Dry system

natural frequency,

fn= 50 Hz

& damping ratio, ξ = 4.5 %

EOM: Time Domain

' ')SEAL SEAL SEAL S S SK z+C z+M z = F-M a-(K z C z

Relative displacement Absolute acceleration Absolute displacement

30

Model system (2-DOF): structure + seal

Measure:

Load F=Fo sin(t)

Displacement z,

acceleration a

( ) ( )

( ) ( )

Re

Im

H K

H C

31

Estimated components of complex dynamic stiffness

Parallel to displacement

(or –acceleration)

Parallel to velocity

'iω iω

SEAL S S SK+ C z = F-M A- K + C z H z

EOM: Frequency Domain

Force coefficients identification

Test results for plain cylindrical

seals and three-wave seals

32

#1 & # 2

Plain sealsc1=0.203 mm, c2=0.274 mm (worn)

#3

Three-wave seal cm=0.191 mm

Direct dynamic stiffness K (MN/m)

33

Symbols: test results Lines: predictionsGVF = 0.0

GVF = 0.2

GVF = 0.9

Direct dynamic stiffness K (MN/m)

34

Symbols: test results Lines: predictionsGVF = 0.0

GVF = 0.9Worn seal (#2) shows lowest K.

Three wave seal (#3) shows

largest K (promotes static

stability).

K : soft to hard as GVF increases.

Lesser added mass!

35

Symbols: test results Lines: predictionsGVF = 0.0

GVF = 0.2

GVF = 0.9

Cross coupled dynamic stiffness k (MN/m)

36

Symbols: test results Lines: predictionsGVF = 0.0

GVF = 0.9 Worn seal (#2) shows

smallest k.

Three wave seal (#3) shows

largest k.

No cross coupled mass m.

k reduces with GVF

Cross coupled dynamic stiffness k (MN/m)

37

Direct damping coefficient C (kN.s/m)

Worn seal (#2) shows

smallest C.

Three wave seal (#3)

shows largest C.

C drops with GVF

C ~ Cpl (1-GVF)

C is frequency

independent

Symbols: test results

38

Effective damping (kN.s/m) Ceff =C –k /ω

Symbols: test results Lines: predictions

GVF = 0.0

GVF = 0.2

GVF = 0.9

39

Effective damping (kN.s/m) Ceff =C –k /ω

For stability, Ceff >0 is a

must.

Cross frequency drops

from ~ ½ X

to a lower magnitude.

Increase in GVF Ceff

drops.

GVF = 0.0

GVF = 0.9

Symbols: test results Lines: predictions

Test results for a

grooved seal (#4)

Seal #4Clearance: c=0.211 mm

Groove depth: dg= 0.543 mm

length: lg=1.5 mm

Land length: ll=0.904 mm

Number of grooves: Ng= 14

40

Direction of

flow

dg/c=2.6 shallow depth groove

GVF > 0.2:

Seal does not show

any dynamic

stiffness

GVF = 0 (liquid):

K decreases with

frequency large

added mass.

Direct dynamic stiffness

3,500 rpm. GVF: 0 to 0.7

K (MN/m)

41

Cross coupled stiffness

42

3,500 rpm. GVF: 0 to 0.7

k (MN/m)

GVF = 0 (liquid):k ~ constant - small

cross coupled mass.

k reduces for

large GVF > 0.2

43

Direct damping

C is same for

GVF=0.1 and 0.2and

decreases

quickly as GVF=

0.30.7.

3,500 rpm. GVF: 0 to 0.7

C (kNs/m)

Effective damping

44

Ceff =C –k /ω (kN.s/m)

3,500 rpm. GVF: 0 to 0.7

Ceff same for

GVF = 0.1 & 0.2

(>1X).

Little effective

damping for

GVF=0.7.

Whirl frequency ratio

= 1/3 (liquid)

Test results for stepped seals (#5, #6)

45

Direction of flow

#5

Upstream step

clearance cT=0.164 mm, cB=0.274

mm, LT=0.11L

#6

Downstream step

clearance cT=0.274 mm, cB=0.164

mm, LT=0.82L.

Step clearance seals in hydraulic turbines

• Hydraulic pump/turbines

installed with a band

upstream step clearance

seal vibrate at their natural

frequency (below than

structural), even w/o shaft

rotation.

• But these units do not

vibrate when installed with

a downstream step

clearance seal.

Nishimura, H., et al., 2016, “Sub- and Super-Synchronous Self-Excited Vibrations of a Columnar Rotor

Due to Axial Clearance Flow,” 28th IAHR Symposium on Hydraulic Machinery and Systems, Grenoble,

France, July 4-8. 46

Dynamic stiffness for stepped clearance seals

47

Re(H)=K-ω2M (MN/m)

Flow rate

increases

K< 0, C >0

0 rpm, Liquid only

Flow rate

increases

|K| grows with flow rate (supply pressure)

K > 0, C >0

|K| grows with flow rate (supply pressure)

48

Direct stiffness for stepped clearance seals K(MN/m)

|K| ~ supply pressure

(flow)

K not a function of

shaft speed

Model predicts

observed behavior.

negative stiffness

for narrow clearance

step seal

0 -3.5 krpm, Liquid only

49

Cross stiffness for upstream step seal k (MN/m)

k ~ shaft speed, not a

function of supply

pressure.

0 -3.5 krpm, Liquid only

50

Direct damping for stepped clearance seals C(kN.s/m)

C > 0, not a function of

shaft speed, and

not a function of

supply pressure

0 -3.5 krpm, Liquid only

51

Direct mass for stepped clearance seals M (kg)

M > 0, not a function of

shaft speed, and

not a function of

supply pressure

0 -3.5 krpm, Liquid only

Air injection to increase

seal direct stiffness K

52

53

Ql = 11.4 L/min,

Ps=2.9 bara

Re(H)=K-ω2M (MN/m)Ima(H)=ωC (MN/m)

Air injection to increase K (upstream step seal)

• All liquid seal, K <0 and drops

quickly with frequency.

• Air injection reduces damping but

increases dynamic stiffness

K >0 (stiffness hardening)

Symbols: test results

0 rpm

1

2 2

G G 

VF 1 VF

g g l i

aa a

Sound speed in a

mixture [1]

[1] Andrews, M. J., and O’Rourke, P. J., 1996, “The Multiphase Particle-in-Cell (MP-PIC) Method for

Dense Particulate Flows,” Int. J. Multiphase Flow, 22(2), pp. 379–402.

Normalized sound speed

a/al

al = 1,470 m/s in mineral oil

Sound speed in a

mixture drops from

seal inlet to outlet

because GVF

increases

Fluid compressibility hardening of K

54

+ Reduced sound

speed makes

mixture highly

compressible

causing increase in

direct stiffness K

(useful in statically

unstable vertical

pumps)

Seal #1, prediction from a BFM (bulk flow model)

Air Injection to Increase K

55

ConclusionON THE LEAKAGE AND ROTORDYNAMIC

FORCE COEFFICIENTS OF PUMP

ANNULAR SEALS OPERATING WITH

AIR/OIL MIXTURES: MEASUREMENTS AND

PREDICTIONS

56

(a) Three wave seal leaks more than plain seal. The

downstream step clearance seal leaks the least.

(b) Mass flow rate and drag torque drop continuously with an

increase in gas volume fraction (GVF).

(c) Force coefficients are frequency dependent for operation

with gas/oil mixture.

(d) Three wave seal shows largest direct stiffness K.

(e) Cross–coupled k decreases with both frequency and GVF.

(f) Direct damping C decreases with GVF C~Cl (1-GVF)

(g) Ceff = (C-k/) drops with GVF. Cross over frequency at ~ ½ X.

(h) Air injection produces stiffness hardening albeit drops

damping.

Conclusion

57

Acknowledgments

Thanks to Turbomachinery Research Consortium

Questions (?)

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

58

59

Luis San AndrésPerforms research in lubrication and rotordynamics. Luis is a Fellow of ASME and

STLE, and a member of the Industrial Advisory Committees for the Texas A&M

Turbomachinery Symposia. Luis has published over 160 peer reviewed papers in

various journals and with several papers recognized as best in various

conferences.

Xueliang Lu Ph.D. student working for Dr. San Andrés at Texas A&M University. So far,

Xueliang has published 7 papers during his Ph.D. studies, onerecognized as a

best paper at the ASME Turbo Expo Conference (2017). Xueliang’s research

focuses on the experimental identification and prediction of force coefficients for

two phase flow annular seals and fluid film bearings.

Zhu JieChief engineer at Hunan Sund Industrial and Technology Company (PR China).

Zhu has +10 years’ experience in hydrodynamic bearings and seals, published

more than 10 papers and holds 50 patents. Zhu Jie is a member of the Asia

Turbomachinery Symposium Advisory Committee since 2014.

Authors

60