GT2011-45624 Bubbly_flow Seal

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ASME Turbo Expo 2011: Power for Land, Sea and Air June 6-10, 2011, Vancouver, BC

Luis San AndresMast-Childs Tribology Professor

Turbomachinery LaboratoryTexas A&M University

ASME GT2011-45264

Rotordynamic Force Coefficients of Bubbly Mixture

Annular Pressure Seals

Accepted for publication J Eng. Gas Turb. Power

Presentation available at http://rotorlab.tamu.edu

Supported by TAMU Turbomachinery Laboratory (Prof. D. Childs)

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Seals in a Multistage Centrifugal Pump or Compressor

Radial seals (annular, labyrinth or honeycomb) separate regions of high pressure and low pressure and their principal function is to minimize the leakage (secondary flow); thus improving the overall efficiency of a rotating machine extracting or delivering power to a fluid.

Impeller eye or neck ring seal

Balance piston sealInter-stage seal

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The dynamic force response of pressure seals has a primary influence on the stability response of high-performance turbomachinery.

Annular seals, although geometrically similar to plain journal bearings, show a flow structure dominated by turbulence and fluid inertia effects.

Operating characteristics unique to seals are the * large axial pressure gradients,* large clearance to radius ratio (R/c) < 500, while * the axial development of the circumferential velocity determines the magnitude of cross-coupled (hydrodynamic) forces.

Childs, D., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley & Sons, Inc., New York, New Yor, Chap. 4.

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Seals and rotordynamics

Straight-Through and Back-to-back Compressors and 1st Mode Shapes

Due to their relative position within a rotor-bearing system, seals

modify the system dynamic behavior.

Seals typically "see" large amplitude rotor

motions. This is particularly important in

back-to-back compressors and long-

flexible multiple stage pumps

Childs, D., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley & Sons, Inc., New York, New Yor, Chap. 4.

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Force Coefficients in Annular Seals

Seal reaction forces are functions of the fluid

properties, flow regime, operating conditions

and geometry.

For small amplitudes of rotor lateral motion: forces are linearized

with stiffness, damping and inertia force

coefficients:

c

rotor

L

D

Axial pressure field (liquid)

stator

Pa

PS

Pe

W Axial velocity

X

Y

Film thickness H=c+eX coseY sin

rotor

X XX XY XX XY XX XY

Y YX YY YX YY YX YY

F K K C C M Mx x x

F K K C C M My y y

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Intentionally roughened stator surfaces (macro texturing) reduce

the impact of undesirable cross-coupled dynamic forces and

improve seal stability.

Annular seals acting as Lomakin bearings have potential as support

elements (damping bearings) in high speed compressors and

pumps.

Childs, D., and Vance, J., 1997, “Annular Gas Seals and Rotordynamics of Compressors and Turbines”, Proc. of the 26th Turbomachinery Symposium, Texas A&M University, Houston, TX, September, pp. 201-220

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Bubbly Mixture Annular Pressure Seals

As oil fields deplete compressors work off-design with liquid in gas mixtures, mostly inhomogeneous.

Similarly, oil compression station pumps operate with gas in liquid mixtures

The flow condition affects compressor or pump overall efficiency and reliability.

Little is known about seals operating under 2-phase conditions, except that the mixture affects seal leakage, power loss and rotordynamic force coefficients; perhaps even inducing random vibrations that are transmitted to the whole rotor-bearing system.

Justification

Seals operate with either liquids or gases, but not both……

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Background literature

Experimental – Seals (two phase)Iwatsubo, T., and Nishino, T., 1993, “An Experimental Study on the Static and Dynamic Characteristics of Pump Annular Seals,“ 7th Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery.

Computational – Seals (two phase)

Annular Seals

Hendricks, R.C., 1987, "Straight Cylindrical Seals for High Performance Turbomachinery," NASA TP-1850

Arauz, G., and San Andrés, L., 1998, “Analysis of Two Phase Flow in Cryogenic Damper Seals, I: Theoretical Model, II: Model Validation and Predictions,” ASME J. Tribol., 120, pp. 221-227, 228-233

Beatty, P.A., and Hughes, W.F., 1987, "Turbulent Two-Phase Flow in Annular Seals," ASLE Trans., 30, pp. 11-18.

Arghir, M., Zerarka, M., Pineau, G., 2009 "Rotordynamic analysis of textured annular seals with mutiphase (bubbly) flow, “Workshop : “Dynamic Sealing Under Severe Working Conditions” EDF – LMS Futuroscope, October 5,

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Experimental – Seals (two phase)Iwatsubo, T., and Nishino, T., 1993, “An Experimental Study on

the Static and Dynamic Characteristics of Pump Annular Seals,“ 7th Workshop on Rotordynamic Instability Problems in High

Performance Turbomachinery.

Annular Seals

NO description of water lubricated seal (L, D, c) or gas type…..

Tests conducted at various speeds (1,500-3,500 rpm) and supply pressures=1.2 - 4.7 bar. Air/liquid volume fraction =0, 0.25, 0.45, 0.70

Mxx

Cxx

Kxx

, gas volume fractionincreases

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Experimental & Physical Modeling

Tao, L., Diaz, S., San Andrés, L., and Rajagopal, K.R., 2000, "Analysis of Squeeze Film Dampers Operating with Bubbly Lubricants" ASME J. Tribol., 122, pp. 205-210

Squeeze film dampers

Diaz, S., and San Andrés, L., 2002, “Pressure Measurements and Flow Visualization in a Squeeze Film Damper Operating with a Bubbly Mixture,” ASME J. Tribol., 124, pp. 346-350.

Diaz, S., and San Andrés, L., 2001, “A Model for Squeeze Film Dampers Operating with Air Entrainment and Validation with Experiments,” ASME J. Tribol., 123, pp. 125-133.

Diaz, S., and San Andrés, L., 2001, "Air Entrainment versus Lubricant Vaporization in Squeeze Film Dampers: An Experimental Assessment of their Fundamental Differences,” ASME J. Eng. Gas Turbines Power, 123, pp. 871-877

Sponsored by National Science Foundation and TAMU Turbomachinery Research Consortium, June 1998- May 2002

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Background literature Squeeze film dampers

Sponsored by National Science Foundation and TAMU Turbomachinery Research Consortium, June 1998- May 2002

Effect of bubbly mixtures and air ingestion on SFD forced performance

CCO L=31.1 mmD=129 mmc=0.254 mm

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Background literature Bubbly SFD

Diaz, S., Beets, T., and San Andrés, L., 2000, “Pressure Measurements and Flow Visualization in a Squeeze Film

Damper Operating With a Bubbly Mixture”

0 0.4time [sec]

0

0.3

0.6hmin

- squeeze

hmax

+ squeeze

0

h[m

m]

0 0.40 0.4time [sec]

0

0.3

0.6hmin

- squeeze

hmax

+ squeeze

0

h[m

m]

time [sec]

0

0.3

0.6hmin

- squeeze

hmaxhmax

+ squeeze

0

h[m

m]

seal

ed e

nd

op

en e

nd

44

seal

ed e

nd

op

en e

nd

55

31.1 mm

seal

ed e

nd

op

en e

nd

66

30o

Uniform Pressure Zone:

Maximum Film Thickness

Onset of Positive Squeeze

Maximum Gas Volume Fraction

Non-Uniform Streaks (fingering)

Minimum Pressure Zone:

Film Thickness Increasing

Onset of Air Ingestion

Incoming gas from Discharge

Maximum Pressure Zone:

Film Thickness Decreasing

Minimum Gas Volume Fraction

Uniform Mixture

=0.540

SFD (CCO): c=0.254 mm, e=0.180 mm, 500 rpm, ISO VG 68

See digital videos at http://rotorlab.tamu.edu

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A simple model for bubbly mixtures

Mixture density

Quasi-static model – ignores bubble dynamics

- Homogenous mixture of 2-components; isothermal & static equilibrium- Both components move with same speed & occupy same volume

1G L

GG S

P

Z T

Ideal gas

2

1

11 1

S

V c

G S

P P S

P

Gas volume fraction (known at inlet)

Pa

zW

Ps

U

Pa

zW

Ps

U

zW

Ps

U

For oil, PV~0.010 bar and S=0.035 N/m, and with c=0.152 mm, PV+2S/c=0.0146 bar

Diaz, S., and San Andrés, L., 2001, “A Model for Squeeze Film Dampers Operating with Air Entrainment and Validation with Experiments,” ASME J. Tribol., 123, pp. 125-133

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A simple model for bubbly mixtures

Mixture viscosity

McAdams model

0.4for 0.3 1 2.5 ;

1G

L L

1 1 1 1 1

for 0.31G G

21.3 1.750.3;

0.3 0.7

L L G

L L G

G

McAdams, W.H., Woods, W.K., and Heroman, L.C., Jr., 1942, “Vaporization inside Horizontal Tubes- II -Benzene-Oil Mixtures,” ASME Trans., 64, p.193

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

DukklerMcAdamsCicchittiIsbin

i

mi

Cicchittii

Isbini

_i

*

Realistic model, not depending on mass fraction

All liquid All gas

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Bulk-flow Analysis of Annular Seals

FlowContinuity

Circumferential Momentum transport

Axial momentum transport

- Turbulent flow with fluid inertia effects- Mean flow velocities – average across film (h)- No accounting for strong recirculation zones- Includes round-hole and honeycomb pattern (textured surface seal)

zW

Ps

U

0dH H UH WHt x z

Hx d

PH UH U H U H UWH

x t t x z

2

0

0H

z dP

H WH W H UWH W Hz t t x z

2

San Andrés, L., and Soulas, T., 2007, “A Bulk Flow Model for Off-Centered Honeycomb Gas Seals,” ASME J. Eng. Gas Turbines Power, 129, pp. 185-194

Pa

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Wall shear stress differences

Shear stresses

Friction factors

Other

Pa

- Moody’s friction factor- Not affected by flow condition (single or two component)- Actual to be determined

zW

Ps

U

0 0

Ω

2HH

z z x x rR

k W ; k U kH H

1/3

,

1Re; 1

Reg

m m mr s

rk f f a c b

H

am=0.001375; bm=5 x 105; cm=104

Salhi, A., Rey, C., and Rosant, J.M., 1992, “Pressure Drop in Single-Phase and Two-Phase Couette-Poiseuille Flow,” ASME J. Fluids Eng., 114, pp.80-84

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Bulk-flow Analysis of Annular Seals

Boundary Conditions

Numerical Solution

Numerical solution for realistic geometries use CFD technique (staggered grids, upwinding, etc) and predict

(4) K,C,M force coefficients.

-Inlet pressure loss due to fluid inertia (Lomakin effect)- Inlet swirl determined by upstream condition (swirl-brake) -Exit pressure without recovery loss, typically.

) ,2e s

1P P - (1+ U RW

2

zVz

Ps

Vx

rotor

Radial bafflesretarding fluid swirl Fluid path

Rotor speed

Seal

Anti swirl brake at inlet or pressure seal

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Model validation Air in Oil Mixture SFD

SFD (CCO): c=0.254 mm, e=0.120 mm, 1000 rpm, ISO VG 68

Lines:predictions,

Symbols:experiments

, mixture volume fraction

Tangential force

Radial force

Circular Centered

orbit

Diaz, S., and San Andrés, L., 2001, “A Model for Squeeze Film Dampers Operating with Air Entrainment and Validation with

Experiments,” ASME J. Tribol., 123, pp. 125-133.

r

t

r

t

Quasi-static bubbly flow model adequate

for whole range of gas volume fractions

(=0.0-1.0)

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Example of analysis

Geometry and operating conditions of seal with mixture

Predict seal performance

Mixture volume fraction varies (0.0-1.0)

Based on available test rig

MIX OIL with N2

Table 1

Centered seal (e=0): No static load~ smooth surfaces;L/D=0.75, c/R=0.002

Rotor speed, 1,047 rad/s (10 krpm)

Diameter, D 116.8 mm Supply Temperature, TS 298.3 K (25 C)

Length, L 87.6 mm Supply pressure, PS 71 bar

Clearance, c 126.7 mm Exit pressure, Pa 1 bar

Smooth seal rr=0.0005 rs=0.001

Entrance pressure loss,

0.25 Inlet pre-swirl ratio, a 0.50

Physical properties

mixture at PS, TS

ISO VG 2 Nitrogen (N2)

Viscosity, 2.14 c-Poise Viscosity, 0.0182 c-Poise

Density, 784 kg/m3 Density, 80.2 kg/m3

Bulk-modulus, 20,682 bar Molecular weight 28

Surface tension, S 0.035 N/m Compressibility, Z 1.001

Vapor pressure 0.010 bar CP/CV 1.48

Sound speed, vs 1,624 m/s Sound speed, vs 361 m/s

Density at Pa, a 1.1 kg/m3

Based on a proposed test rig

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0

Flo

w r

ate

kg/s

: G/L volume fraction at inlet

ALL liquid (24.2 GPM) inlet and exit

ALL gas:66 GPM at seal inlet

4,694 GPM at seal exit

S

Seal Flow rate vs. inlet gas volume fraction

Figure 2 Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm)

All liquid All gas

Leakage decreases continuously as gas

content increases

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0.00.10.20.30.40.50.60.70.80.91.0

0.0 0.2 0.4 0.6 0.8 1.0

Ga

s/l

iqu

id m

as

s f

rac

tio

n

: G/L volume fraction at inletS

Gas Mass fraction vs. inlet gas volume fraction

Figure 3b Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm)

All liquid All gas

Gas/liquid mass

content increases exponenti

ally with gas

volume content

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0.00.10.20.30.40.50.60.70.80.91.0

0.0 0.2 0.4 0.6 0.8 1.0

Ga

s/l

iqu

id v

olu

me

fra

cti

on

G/L volume fraction at inlet

S :

Exit gas volume fraction vs. inlet volume fraction


All liquid All gas

Gas volume

fraction at exit plane increases

quickly because of large

pressure drop

Pa

zW

Ps

U

Pa

zW

Ps

U

zW

Ps

U

23

0

10

20

30

40

50

60

70

80

0.000 0.020 0.040 0.060 0.080 0.100

Lan

d p

ress

ure

bar

axial coordinate m

Liquid

Gas s=1.0

s0.25

s0.75

inlet pressure loss

s0.5

s0.0

exit pressure = 1 bar

Axial pressure drop as gas fraction increases


inlet

Exit

All liquid: linear

pressure drop.

All gas: nonlinear with rapid

changes near exit

plane

Pa

zW

Ps

U

Pa

zW

Ps

U

zW

Ps

U

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0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0.0 0.2 0.4 0.6 0.8 1.0

Po

wer

loss

kW


S

Drag power loss vs. inlet volume fraction


All liquidAll gas

Steady decrease

in power; but in

region of flow

transition

25

100

1000

10000

100000

0.0 0.2 0.4 0.6 0.8 1.0Rey

no

lds

nu

mb

er (

max

)

Reynolds # (max)Re-circ (exit)Re-axial (exit)


laminar flow region

S

circumferential flow

axial flow

Max. Reynolds # vs. inlet volume fraction


All liquid All gas

Axial flow dominates

at high volume

fractions.Circumf. flow Re#

decreases.

Re ~ V c

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Rotordynamic coefficients – lateral motions

Seal reaction forces:

-

Model for centered operationKXX = KYY, KXY = -KYX

CXX = CYY, CXY = -CYX

MXX = MYY, MXY = -MYX

Whirl frequency ratio WFR ~ KXY

CXX : measure of rotordynamic stability

Assumes:No static load

X

Y

X XX XY XX XY XX XY

Y YX YY YX YY YX YY

F K K C C M Mx x x

F K K C C M My y y

Force coefficients are functions of frequency for gases, and also for a two-component (gas/liquid) mixture.

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-1.0E+08

-5.0E+07

0.0E+00

5.0E+07

1.0E+08

1.5E+08

2.0E+08

0.0 0.2 0.4 0.6 0.8 1.0

Sti

ffn

esse

s

N/m


KXY=-KYX

KXX=KYY

S

Seal stiffnesses vs. inlet volume fraction

Figure 7a Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm) SYNCHRONOUS SPEED

All liquid All gas

Liquid seal (oil)

has large cross-

coupled stiffness.Gas seal

shows strong direct

stiffness

KXY=-KYX

KXX=KYY

KXY=-KYX

Synchronous speed force coefficient

Mixture viscosity decreases

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-1.0E+05

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

0.0 0.2 0.4 0.6 0.8 1.0

Dam

pin

g

N-s/m


CXY=-CYX

CYY=CYY

S

Seal damping vs. inlet volume fraction

Figure 7b Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm) SYNC SPEED

All liquid All gas

Direct damping

decreases as gas

content increases,

but in flow

transition zone

Cross-damping

small.

CXX=CYY

CXY=-CYX

N-s/mMixture viscosity decreases

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Whirl frequency ratio – Stability indicator

- WFR always 0.50 for inlet

swirl = 0.50 – Stable

operation up to 2 x critical

speed

0.000.100.200.300.400.50

0.600.700.800.901.00

0.0 0.2 0.4 0.6 0.8 1.0

Wh

irl f

req

uen

cy r

atio WFR


Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm) SYNC SPEED

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force coefficients – frequency dependency

Seal reaction forces (centered seal):

X

Y

XX XY XX XYX

Y XY XX XY XX

K K C CF x x

F K K y C C y

Force coefficients are functions of frequency for gases, and also for a two-component (gas/liquid) mixture.

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-3.0E+08

-2.0E+08

-1.0E+08

0.0E+00

1.0E+08

2.0E+08

3.0E+08

0.0 0.5 1.0 1.5 2.0

KXX=KYY

B=0.0 (all liquid)

B=0.05

B=0.10

B=0.25

B=0.5

B=0.75

B=1.00 (all gas)

Frequency (Hz) whirl frequency/rotational speed

N/m

Liquid

Gas

s0.10

s0.05

s0.25

s0.0

s1.0

s0.50

s0.75

Seal direct stiffnesses vs. whirl frequency

Figure 8a Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm) All liquid shows

added mass effect

(K-2M). All gas

(=1) has large KXX.

Note increase (*)

in KXX for small =0.1

KXX=KYY

K

(*) =0.1: Stiffness hardening is typical in textured gas damper seals (= negative added mass)

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0.0E+00

5.0E+07

1.0E+08

1.5E+08

2.0E+08

2.5E+08

3.0E+08

0.0 0.5 1.0 1.5 2.0

KXY=-KYX

B=0.0 (all liquid)

B=0.0125

B=0.025

B=0.05

B=0.10

B=0.25

B=0.5

B=0.75

B=1.00 (all gas) Frequency (Hz) whirl frequency/rotational speed

s

N/mLiquids=0

Gas

s0.10

s0.75

s0.05

s0.25

s0.025

s0.50

s1.0

Seal cross-stiffnesses vs. whirl frequency


KXY=-KYX

All liquid shows

largest k.

Cross-stiffness

decreases with gas content.

Small effect of

frequency

k

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0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

4.0E+05

0.0 0.5 1.0 1.5 2.0

CXX=CYY

B=0.0 (all liquid)

B=0.0125

B=0.025

B=0.05

B=0.10

B=0.25

B=0.5

B=0.75

B=1.00 (all gas)

Frequency (Hz) whirl frequency/rotational speed

N.s/m

Gas, s=1.0

s0.75

s0.05s0.25

s0.025

s0.50

s

Liquids=0

Seal direct damping vs. whirl frequency

Figure 9a Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm)

CXX=CYY

Cross damping coefficients are one order of magnitude lower

C All liquid shows

largest C.

Same as cross-K.

Small effect of

frequency

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Equivalent force coefficients (Ke,Ce)

Seal reaction forces (circular orbits):

X

Y

r e

t e

F Ke

F C

x t x te e

y t y t

cos( ) sin( )

sin( ) cos( )

Radial and tangential components of force

e

t

Fr

Ft

( ) ( )e XX XYK K C

1

e XX XYC C K

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-1.0E+08

-5.0E+07

0.0E+00

5.0E+07

1.0E+08

1.5E+08

2.0E+08

0.0 0.5 1.0 1.5 2.0

Keq

B=0.0 (allliquid)B=0.0125

B=0.025

B=0.05

B=0.10

B=0.25

B=0.5

B=0.75

B=1.00 (all gas) whirl frequency/rotational speed

N/m

Liquid,s=0

s0.10

s0.75s0.05

s0.25

s0.5

Gas, s=1.0

s0.025

s0.0125

Seal equivalent stiffness vs. whirl frequency


e XX XYK K C

Cross damping

small. All liquid

shows added mass

effect . All gas

(=1) has large Ke.

Note increase (*)

in Ke for small =0.1

36

-3.E+05

-2.E+05

-1.E+05

0.E+00

1.E+05

2.E+05

3.E+05

0.0 0.5 1.0 1.5 2.0

Ce

q

B=0.0 (allliquid)B=0.0125

B=0.025

B=0.05

B=0.10

B=0.25

B=0.5

B=0.75

B=1.00 (all gas) whirl frequency/rotational speed

Ns/m

s

Liquids=0

Gas

s0.10

s0.75

s0.05s0.25

s0.025s0.5 s1.0

Seal equivalent damping vs. whirl frequency


1e XX XYC C K

All liquid shows

largest Ce.

Steady decrease of Ce with gas

content.

Note Ce=0 at =0.5

37

Conclusions

Rotordynamic force coefficients of bubbly mixture annular pressure seals

1. Leakage and power loss decrease with the gas in liquid volume content – except in transition region from laminar to turbulent flow

2. Seal force coefficients show strong dependency on whirl frequency. Cross-coupled stiffnesses and direct damping coefficients decrease steadily as gas volume fraction raises.

3. Direct stiffness coefficients show atypical behavior, in particular a mixture of gas volume fraction S=0.1 produces stiffness hardening as the excitation frequency increases.

4. Predictions justify an experimental program to quantify the static and dynamic forced performance of annular seals operating with (bubbly) mixtures

GT2011-45264

Advanced (simple) computational physics bulk-flow model for prediction of seal performance static and dynamic. Assumed homogenous mixture of two components (liquid and gas).

Mixture N2 in ISO VG 2 oil (P=71 bar, 10 krpm)

38

Rotordynamic force coefficients of bubbly mixture annular pressure seals

GT2011-45264

Questions (?)

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

© 2011 Luis San Andres

GT2011-45624 Bubbly_flow Seal

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