Transcript Document

ASME Turbo Expo 2011: Power for Land, Sea and Air June 6-10, 2011, Vancouver, BC
Rotordynamic Force
Coefficients of Bubbly Mixture
Annular Pressure Seals
Luis San Andres
Mast-Childs Tribology Professor
Turbomachinery Laboratory
Texas A&M University
ASME GT2011-45264
Accepted for publication J Eng. Gas Turb. Power
Presentation available at http://rotorlab.tamu.edu
1
Supported by TAMU Turbomachinery Laboratory (Prof. D. Childs)
Annular Pressure Seals
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.
Inter-stage seal
Impeller eye or
neck ring seal
Balance piston seal
Seals in a Multistage Centrifugal Pump or Compressor
2
Annular Pressure Seals
The dynamic force response of pressure seals has a
primary influence on the stability response of highperformance 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.
3
Seals and rotordynamics
Due to their relative
position within a rotorbearing system, seals
modify the system
dynamic behavior.
Seals typically "see"
large amplitude rotor
motions. This is
particularly important in
back-to-back
compressors and longflexible multiple stage
pumps
Straight-Through and Back-to-back Compressors
and 1st Mode Shapes
Childs, D., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis,
John Wiley & Sons, Inc., New York, New Yor, Chap. 4.
4
Force Coefficients in Annular Seals
L
Y
c
stator
rotorrotor

X
D

Pa
W
Axial
velocity

Film thickness
H=c+eX coseY sin
Pe
Axial pressure
field (liquid)
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
PS
 FX 
 K XX
   
 FY 
 KYX
K XY   x  CXX CXY   x   M XX
 
 


KYY   y   CYX CYY   y   M YX
coefficients:
M XY   x 
 

M YY   y 
5
Annular Pressure Seals
Intentionally roughened stator
surfaces (macro texturing) reduce
the impact of undesirable crosscoupled 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
6
Bubbly Mixture Annular Pressure Seals
Justification
Seals operate with either liquids or gases, but not both……
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.
7
Background literature
Annular Seals
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.
Hendricks, R.C., 1987, "Straight Cylindrical Seals for High Performance Turbomachinery," NASA
TP-1850
Computational – Seals (two phase)
Beatty, P.A., and Hughes, W.F., 1987, "Turbulent Two-Phase Flow in Annular Seals," ASLE Trans.,
30, pp. 11-18.
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, 228233
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,
8
Background literature
Mxx
Annular Seals
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.
Cxx
NO description of water lubricated seal (L, D,
c) or gas type…..
Tests conducted at various speeds (1,5003,500 rpm) and supply pressures=1.2 - 4.7 bar.
Air/liquid volume fraction b=0, 0.25, 0.45, 0.70
Kxx
b, gas volume
fraction
increases
9
Background literature
Squeeze film dampers
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
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
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., 2002, “Pressure
Measurements and Flow Visualization in a Squeeze Film
Damper Operating with a Bubbly Mixture,” ASME J. Tribol.,
124, pp. 346-350.
Sponsored by National Science Foundation and TAMU Turbomachinery Research
Consortium, June 1998- May 2002
10
Background literature
Squeeze film dampers
Effect of bubbly mixtures and air ingestion on SFD forced performance
CCO
L=31.1 mm
D=129 mm
c=0.254 mm
Sponsored by National Science Foundation and TAMU Turbomachinery Research
Consortium, June 1998- May 2002
11
Background literature
Bubbly SFD
0.6
Diaz, S., Beets, T., and San Andrés, L., 2000, “Pressure
Measurements and Flow Visualization in a Squeeze Film
Damper Operating With a Bubbly Mixture”
hmin
hmax
+ squeeze - squeeze
0
0
b=0.540
0.4
time [sec]
6
5
open end
30o
sealed end
open end
sealed end
4
open end
0.3
sealed end
h[mm]
0
31.1 mm
Uniform Pressure Zone:
Maximum Pressure Zone:
Minimum Pressure Zone:
Maximum Film Thickness
Film Thickness Decreasing
Film Thickness Increasing
Onset of Positive Squeeze
Minimum Gas Volume Fraction
Onset of Air Ingestion
Maximum Gas Volume Fraction
Uniform Mixture
Incoming gas from Discharge
Non-Uniform Streaks (fingering)
See digital videos at http://rotorlab.tamu.edu
12
SFD (CCO): c=0.254 mm, e=0.180 mm, 500 rpm, ISO VG 68
A simple model for bubbly mixtures
- Homogenous mixture of 2-components; isothermal & static equilibrium
- Both components move with same speed & occupy same volume
Ps
z
Mixture density
  b G  1 b  L
W

Pa
Ideal gas
P
G 
Z G TS
Quasi-static model –
ignores bubble dynamics
Gas volume fraction (known at inlet)
b
1

P  PV  2c S  1
1
 1

PGS
b
 S

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
13
U
A simple model for bubbly mixtures
All liquid
McAdams model
Mixture
viscosity
All gas
1.4
1.3
1.2
1.1
i
for b  0.3 
   0.4 

1  2.5 
b ;
L


1



 G
L
1  
1   1
1  
1
for b  0.3 
 



 
 
  G     G      1
 
0.3

0.3  0.7 L
G
;
1
0.9
mi
0.8
 Cicc hitti 0.7
i
 Isbin
i
1.3 L2  1.75 L G
 
 L  G
Realistic model, not depending on mass fraction
0.6
0.5
0.4
0.3
0.2
*
0.1
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
b_i
Dukkler
McAdams
Cicchitti
Isbin
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
b
14
1
Bulk-flow Analysis of Annular Seals
Ps
z
W
Flow
Continuity



 H  H d  
 UH    WH   0

t
x
z
U
Pa

Circumferential
Momentum
transport
Axial momentum
transport
H
H


P




H
  x 0   UH   U   H d  
U 2 H   UWH 
x
t
t
x
z

P




H
  z 0 
W 2 H
 WH   W   H d    UWH  
z
t
t
x
z
- 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)
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
15

Wall shear stress differences
Shear stresses

H
z 0


H
 k zW  ;
H
 x 0

RΩ 
   k x U  kr
H
2 
  r
 
1

g
k  f Re; f  am 1  cm
 bm
 
  H
Rer , s  


am=0.001375; bm=5 x 105; cm=104
z
1/3
Friction factors
Other
Ps
W
U
Pa

- Moody’s friction factor
- Not affected by flow condition (single or two component)
- Actual to be determined
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
16
Bulk-flow Analysis of Annular Seals
-Inlet pressure loss due to fluid inertia (Lomakin effect)
- Inlet swirl determined by upstream condition (swirl-brake)
-Exit pressure without recovery loss, typically.
Boundary
Conditions
Pe  Ps -
1
 (1+  ) W 2, U    R
2
Numerical solution for
Numerical
Solution
realistic geometries use
CFD technique (staggered
grids, upwinding, etc) and
predict (4) K,C,M force
coefficients.
Radial baffles
retarding fluid swirl
Ps
Fluid path
Seal
Rotor speed
z
Vz

rotor
Vx
Anti swirl brake at inlet or
pressure seal
17
Model validation
Air in Oil Mixture SFD
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.
Tangential force
t
Circular
Centered
orbit
r
b, mixture volume fraction
Lines:
predictions,
Radial force
Symbols:
experiments
Quasi-static bubbly
flow model adequate
for whole range of
gas volume fractions
(b=0.0-1.0)
18
SFD (CCO): c=0.254 mm, e=0.120 mm, 1000 rpm, ISO VG 68
Example of analysis
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
mixture
at PS, TS

Physical
properties
ISO VG 2
Based on a proposed test rig
0.50
Nitrogen (N2)
Viscosity, 
2.14 c-Poise
Viscosity, 
0.0182 c-Poise
Density, 
784 kg/m3
Density, 
80.2 kg/m3
Bulk-modulus, k
20,682 bar
Molecular weight
28
Surface tension, S
0.035 N/m
Compressibility, Z
1.001
Vapor pressure
0.010 bar
g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
Centered seal (e=0):
No static load
~ smooth surfaces;
L/D=0.75, c/R=0.002
MIX OIL with N2
Mixture
volume
fraction b
varies
(0.0-1.0)
Based on available test rig
Predict seal
Table 1
Geometry and operating conditions of seal with mixture
performance
19
Seal Flow rate vs. inlet gas volume fraction
Figure 2 Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
kg/s
1.4
Flow rate
1.2
ALL liquid (24.2 GPM)
inlet and exit
1.0
ALL gas:
0.8
66 GPM at seal inlet
4,694 GPM at seal exit
0.6
Leakage
decreases
continuou
sly as gas
content
increases
0.4
0.2
0.0
0.0
All liquid
0.2
0.4
0.6
0.8
1.0
bS : G/L volume fraction at inlet
All gas
20
Gas Mass fraction vs. inlet gas volume fraction
Gas/liquid mass fraction
Figure 3b Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Gas/liquid
mass
content
increases
exponenti
ally with
gas
volume
content
0.0
All liquid
0.2
0.4
0.6
0.8
1.0
bS : G/L volume fraction at inlet
All gas
21
Exit gas volume fraction vs. inlet volume fraction
Gas/liquid volume fraction
Figure 3b Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Ps
z
W
U

Pa
0.0
All liquid
0.2
0.4
0.6
0.8
bS : G/L volume fraction at inlet
1.0
Gas
volume
fraction at
exit plane
increases
quickly
because
of large
pressure
drop
All gas
22
Axial pressure drop as gas fraction increases
Figure 4
Land pressure
bar
Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
80
inlet pressure loss
70
Gas bs=1.0
60
50
bs0.75
40
bs0.5
Liquid
bs0.0
30
20
bs0.25
10
exit pressure = 1 bar
0
0.000
All liquid:
linear
pressure
drop.
All gas:
nonlinear
with rapid
changes
near exit
plane
Ps
0.020
0.040
0.060
0.080
0.100
z
W
axial coordinate
m
Exit
inlet

Pa
23
U
Drag power loss vs. inlet volume fraction
Figure 5
Power loss
kW
Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
8.0
Steady
decrease
in power;
but in
region of
flow
transition
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0.0
All liquid
0.2
bS
0.4
0.6
0.8
1.0
: G/L volume fraction at inlet
All gas
24
Max. Reynolds # vs. inlet volume fraction
Reynolds number (max)
Figure 6 Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
100000
axial flow
10000
Reynolds # (max)
Re-circ (exit)
Re-axial (exit)
laminar flow region
1000
circumferential flow
100
0.0
All liquid
0.2
0.4
0.6
0.8
1.0
bS : G/L volume fraction at inlet
All gas
Axial flow
dominates
at high
volume
fractions.
Circumf.
flow Re#
decreases.

Re ~ V c

25
Rotordynamic coefficients – lateral motions
Seal reaction forces:
 FX 
 K XX
-
  
 FY 
 KYX
K XY   x  CXX CXY   x   M XX
 
 


KYY   y   CYX CYY   y   M YX
M XY   x 
 

M YY   y 
Model for centered operation
KXX = KYY, KXY = -KYX
CXX = CYY, CXY = -CYX
MXX = MYY, MXY = -MYX
Whirl frequency ratio WFR ~
KXY
Assumes:
No static load
: measure of rotordynamic stability
CXX 
Y
X
Force coefficients are functions of frequency w for
gases, and also for a two-component (gas/liquid)
mixture.
26
Seal stiffnesses vs. inlet volume fraction
Figure 7a Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm) SYNCHRONOUS SPEED
2.0E+08
N/m
Mixture viscosity decreases
Stiffnesses
1.5E+08
KXY=-KYX
KXY
XY=-K
=-KYX
YX
K
1.0E+08
5.0E+07
K
KXX
XX=K
=KYY
YY
0.0E+00
0.0
0.2
0.4
0.6
0.8
1.0
-5.0E+07
-1.0E+08
bS : G/L volume fraction at inlet
All liquid
Liquid
seal (oil)
has large
crosscoupled
stiffness.
Gas seal
shows
strong
direct
stiffness
All gas
27
Synchronous speed force coefficient w
Seal damping vs. inlet volume fraction
Figure 7b Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm) SYNC SPEED
4.0E+05
Mixture viscosity decreases
N-s/m
-s/m
Damping
3.0E+05
CCYY
=C
XX
=CYYYY
2.0E+05
1.0E+05
CCXY
=-C
XY
=-CYXYX
0.0E+00
0.0
-1.0E+05
All liquid
0.2
0.4
0.6
0.8
1.0
bS : G/L volume fraction at inlet
All gas
Direct
damping
decrease
s as gas
content
increases,
but in
flow
transition
zone
Crossdamping
small.
28
Whirl frequency ratio
Whirl frequency ratio – Stability indicator
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
WFR
- WFR always
0.50 for inlet
swirl = 0.50 –
Stable
operation up
to 2 x critical
speed
0.0
0.2
0.4
0.6
0.8
1.0
: G/L volume fraction at inlet
Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm) SYNC SPEED
29
force coefficients – frequency dependency
Seal reaction forces (centered seal):
 FX   K XXw 
  
 FY   K XYw 
K XYw    x   CXXw  CXYw    x 
  
 
K XXw    y   CXYw  CXXw    y 



Force coefficients are functions of frequency w for
gases, and also for a two-component (gas/liquid)
mixture.
Y
X
30
Seal direct stiffnesses vs. whirl frequency
Figure 8a Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
KXX
XX=K
=KYY
YY
K
3.0E+08
N/m
2.0E+08
B=0.0 (all liquid)
B=0.05
K
bs0.10
bs0.75 bs1.0 Gas
1.0E+08
bs0.05
bs0.50
0.0E+00
bs0.25
B=0.10
B=0.25
-1.0E+08
Liquid
B=0.5
All liquid
shows
added mass
effect
(K-w2M).
All gas
(b=1) has
large KXX.
Note
increase (*)
in KXX for
small b=0.1
-2.0E+08
bs0.0
B=0.75
B=1.00 (all gas)
-3.0E+08
0.0
0.5
1.0
1.5
2.0
whirl
frequency/rotational
speed
Frequency
(Hz)
w/
(*) b=0.1: Stiffness hardening is typical in textured gas
damper seals (= negative added mass)
31
Seal cross-stiffnesses vs. whirl frequency
Figure 8b Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
KK
XY
=-K
YXYX
XY
=-K
3.0E+08
N/m
2.5E+08
B=0.0 (all liquid)
B=0.0125
k
2.0E+08
1.5E+08
B=0.025
B=0.05
B=0.10
B=0.25
B=0.5
1.0E+08
5.0E+07
0.0E+00
0.0
All liquid
shows
largest
bs0.10
k.
Liquidbs=0
bs0.025
Crossstiffness
bs0.05
decreases
bs
bs0.25
bs0.50
with gas
bs0.75
content.
bs1.0 Gas
Small effect
of
0.5
1.0
1.5
2.0 frequency
B=0.75
B=1.00 (all gas)
whirl
frequency/rotational
speed
Frequency
(Hz)
w/
32
Seal direct damping vs. whirl frequency
Figure 9a Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
CXX
CXX
=C=C
YYYY
N.s/m
B=0.0 (all liquid)
4.0E+05
C
bs0.025
3.5E+05
bs0.05
2.5E+05
B=0.025
2.0E+05
B=0.05
1.5E+05
B=0.25
B=0.5
B=0.75
B=1.00 (all gas)
Liquidbs=0
3.0E+05
bs
bs0.25
B=0.0125
B=0.10
All liquid
shows
largest
C.
Same as
cross-K.
Small effect
of
frequency
bs0.50
bs0.75
1.0E+05
5.0E+04
Gas,
bs=1.0
0.0E+00
0.0
0.5
1.0
1.5
2.0
whirl
frequency/rotational
speed
Frequency
(Hz)
w/
Cross damping coefficients are one order of magnitude lower
33
Equivalent force coefficients (Ke,Ce)
Seal reaction forces (circular orbits):
Ft
 x  cos( wt ) 
x
 sin( wt ) 

e



e
w
  

 


y
sin(
w
t
)
y

cos(
w
t
)
  

 


Y
Radial and tangential components of force
 Fr   K e 
     e
 Ft  Cew 
e
X
Ke  K XX( w )  w CXY ( w )
Ce  C XX w 
 
1
wt
Fr
w K XY w
 
34
Seal equivalent stiffness vs. whirl frequency
N/m
2.0E+08
Keq
Figure 10a Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
1.5E+08
1.0E+08
B=0.0 (all
liquid)
B=0.0125
5.0E+07
B=0.025
0.0E+00
B=0.05
B=0.10
-5.0E+07
B=0.25
B=0.5
B=0.75
-1.0E+08
0.0
B=1.00 (all gas)
Ke  K XX  w CXY
Cross
damping
bs0.10
small.
Gas, bs=1.0
All liquid
bs0.05
bs0.75
shows
added mass
bs0.5
effect .
bs0.025
All gas
bs0.25
bs0.0125
(b=1) has
large Ke.
Liquid,bs=0
Note
0.5
1.0
1.5
2.0 increase (*)
in Ke for
whirl frequency/rotational speed
small b=0.1
w/
35
Seal equivalent damping vs. whirl frequency
Figure 10a Mixture N2 in ISO VG 2 oil (DP=71 bar, 10 krpm)
Ceq
Ns/m
3.E+05
Liquidbs=0
bs0.10
2.E+05
1.E+05
B=0.0 (all
liquid)
B=0.0125
0.E+00
B=0.025
-1.E+05
bs0.25
bs0.025
B=0.05
B=0.10
B=0.25
B=0.5
bs
-2.E+05
bs0.05
bs0.5
bs0.75
Gas
bs1.0
Note Ce=0
at w/=0.5
-3.E+05
0.0
B=0.75
B=1.00 (all gas)
Ce  CXX 
All liquid
shows
largest
C e.
Steady
decrease of
Ce with gas
content.
1
0.5
1.0
1.5
2.0
whirl frequency/rotational speed
w K XY
w/
36
Conclusions
GT2011-45264
Rotordynamic force coefficients of bubbly mixture annular pressure seals
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 (DP=71 bar, 10 krpm)
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 bS=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
37
GT2011-45264
Rotordynamic force coefficients of bubbly mixture annular pressure
seals
Questions (?)
Learn more at http://rotorlab.tamu.edu
© 2011 Luis San Andres
38