Transcript Parameter Identification of an End Sealed SFD Part II

TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
A novel FE Bulk-Flow Model for Improved
Predictions of Force Coefficients in OffCentered Grooved Oil Seals
Luis San Andrés
Adolfo Delgado
Mast-Childs Professor
Research Assistant
TRC-SEAL-1-08
28th TRC Annual Meeting 2008
TRC Project: 32513/1519 T7
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Oil Seals

Oil seals are commonly used
to prevent leakage of
process fluid in centrifugal
compressors.
- Locked oil seal rings can induce
instability in compressors.
- Seals are grooved to reduce
cross-coupled stiffness and lower
lock-up forces
Oil seal in a compressors[1]
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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Damping, Cross-coupled Stiffness & Inertia
2L
CXX  8
  D L3
4 c3
; K XY
1
  D L3
  CXX ; M XX  8
2
20 c
; K XY
1
  D L3
  CXX ; M XX 
2
20 c
c
Journal
Constant pressure
CXX 
  D L3
4c
3
2-land seal: (deep groove divides lands)
L
30c
5c
Coeffs are ¼ of original seal
c
CXX  2
Short length seal
  D L3
4c
3
; K XY
1
  D L3
  CXX ; M XX  2
2
20 c
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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Mxx
10000 rpm - 24 bars
Mxx
10000 rpm - 45 bars
Mxx
10000 rpm - 70 bars
Test Grooved Oil Seals
70
Added Mass [kg]
50
Childs
et al., (2006)
70
70
50
50
Single
30groove and multiple groove
30 oil seal (single
clearance)
10
10
-10
-10
Childs et al., (2007)
10
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
One groove
with groove
depths
(5c,10c,15c)
-30
Eccentricity
-30
30
0.6
Eccentricity
Results
0.8
-10 0.0
0.2
-30
0.4
0.6
0.8
Eccentricity
Added mass versus eccentricity ratios
[Childs et. al]
Force coefficients are underpredicted (grooved seal)
Groove does not effectively separate seal lands
Large added mass coefficients (~30 kg)
Experimental Results
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Grooved Oil Seal:
Predictions
Groove should reduce crossedcoupled stiffness and damping
coefficients by a factor of four
Kxy (1 land)= 4 Kxy(2 lands)
Cxx (1 land)= 4 Cxx(2 lands)
Null (neglected) added mass
coefficients
c
≠
Experiments
Groove does not effectively
separate seal lands
≠
At most
Kxy (1 land) ~2 Kxy(2 lands)
Cxx (1 land) ~2 Cxx(2 lands)
≠
Large added mass
coefficients , increasing
with increasing groove
depth
Need for better predictive models
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Improved predictive model TRC-SFD-2-07
•Bulk flow, centered operation, incompressible fluid
• Qualitative observations of laminar flow field
• Boundary Conditions
• Characteristic groove depth
oil supply, Ps
feed plenum groove
mid-land groove
Ps- Pd >0
Pd :discharge pressure
Pd
z
y
Streamlines in axially symmetric grooved annular cavity.
Pd
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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Bulk flow model
Centered operation
No fluid advection
Separate flow regions
Oil supply
1
zI
I
2
zII
II
  I , II ,...N
3
III
zIII
4
IV
zIV
n
N
n+1
zN
Reynolds eqn with temporal fluid inertia
  3  P
 h
x
x
   3  P
 h

 z
  z 
2




2

12

h

6

R

h


h
h








2  
t
x
t



TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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Finite Element Solution
Off-centered operation
x= qR
Film thickness
h = h0 + eiwt  eX cos ( q ) + eY sin ( q )
Reynolds eqn. with temporal fluid inertia
h
R
w
e
e
X

   3  P
 h

 z
  z 


12   h   6 R 
 h  
t
x
  3  P
 h
x
x
Y



 h 

2
2
 h 
 t2
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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n pe
P0e    i P0ei
i 1
Flow
domain
n pe
k
j 1
 h 
k   

e  12  

3
e
ij
Nodal pressures
z
e

e
ij
P0ej   q ie  f i e
 j , x   i , z  j , z  dx dz
e
i,x
R
e
fi 
h

i . x dx dz

2 e
e
e
q Flow rate
x=R
Finite element model for pressure field
in fluid film bearing
FEM for solution of Pressure field
Assemble system of
equations, impose
boundary conditions and
solve
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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Excel® GUI: XFEGLOSeal
Lin
c
Lm
Lg
Lout
cg
User inputs:
-Fluid properties: Density and
viscosity
-Operating conditions: Inlet and
outlet pressures, static journal
eccentricity.
(XFiniteElementGroovedLaminarOilSEAL)
-Geometry: Rotor diameter,
clearance, groove depth, number of
grooves, inlet and outlet land
length, inter-groove length, groove
length.
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Outlet plane
Test Grooved Oil Seal & FE mesh
h0
4
1
Inlet
e
3
2
e
Grooves
z
q
2
0
Inlet plane
z
x=R
q
x=R
q
Oil supply
17 mm
25 mm
2 mm
Clearance= 86 m
Seal length
Discharge plenum
136c
76c
Journal diameter: 117 mm
Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007,
“The Influence of Groove Size on the Static and
Rotordynamic Characteristics of Short, Laminar-Flow
Annular Seals,” ASME J. Tribol, 129(2), 398-406.
Journal
c
(0-15) c
Parallel oil seals Configuration [Childs et al]
Buffer seal
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
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Effective groove depth
Ps
CFD simulations show: streamline
separating flow regions IS a physical
boundary delimiting the domain for
squeeze film flow due to journal radial
motions.
Pa
Test seal
Laminar flow
10c
15c
Ps= supply pressure
Pa= ambient pressure
Inner groove close up (CFD -Pressure driven flow)
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Shaft speed: 10,000 rpm
1.0
Test data
smooth seal
Smooth
smooth seal
seal
smooth seal
Grooved seal
0.8
Static eccentricity ratio: 0, 0.3, 0.5, 0.7
Grooved seal
Load
Grooved seal
Grooved seal
0.5
Supply pressure: 70 bar
e y
ey
ey
0.3
-1.0
0.0
-0.8
-0.5
-0.3
0.0
0.3
-0.3
-0.5
-0.8
-1.0
ex
eex
x
0.5
0.8
1.0
Journal center locus
indicates seal
operates with oil
cavitation at the
largest test
eccentricities
Journal locus
x
Seal operating conditions
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
10,000 rpm, 70 bar
0.45
Smooth Seal
0.40
Grooved Seal
0.30
Predicted leakage
correlates well with
experiments for both
smooth land and
grooved seal
0.25
0.20
0.15
0.10
0.05
0.00
0
4000
0.1
0.2
0.3
0.4
0.5
3500
Static journal eccentricity ratio (e/c)
3000
2500
2000
1500
Force [N]
Leakage [kg/s]
0.35
Leakage
0.6
Smooth seal- Predictions
Smooth seal- Experiments
Grooved seal- Predictions
Grooved seal- Experiments
(c = 7c)
(cg= 15c)
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Damping [kN.s/m]
300
10,000 rpm, 70 bar
Cx
200
Smooth Seal
x
100
Grooved Seal
0
0
0.2
0.4
0.6
Static journal eccentricity ratio (e/c)
200
Smooth seal- Predictions
Smooth seal- Experiments
Force [N]
Damping [kN.s/m]
300
4000
3500
Cy
3000
y
2500
2000
1500
1000
0.2
0.4
Static journal eccentricity ratio (e/c )
500
100
0
0
Model predicts
accurately reduction
in direct damping due
to inner land groove.
Smooth Seal
Grooved Seal
Grooved seal- Predictions
(c = 7c)
Grooved seal- Experiments
0.6
Direct Damping
(cg= 15c)
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
60
60
Stiffness
Stiffness[MN/m]
[MN/m]
Stiffness
[MN/m]
70 bar
Eccentricity ratio=0
50
50
Smooth Seal
40
40
30
30
Grooved Seal
20
20
Kxy
10
10
Model effectively
predicts reduction in
cross-coupled stiffness
due to mid-land groove.
00
00
2000
2000
4000
4000
6000
6000
8000
8000
10000
10000
12000
12000
Rotor
(RPM)
Rotor speed
speed (RPM)
60
60
Eccentricity ratio=0.3
50
50
40
40
Force [N]
[MN/m]
Stiffness
Stiffness[MN/m]
Stiffness
[MN/m]
e = 0, 0.3
30
30
20
20
Kxy
10
10
00
00
2000
2000
4000
4000
6000
6000
8000
8000
Rotor
(RPM)
Rotor speed
speed (RPM)
4000
3500
3000
2500
2000
1500
100012000
10000
10000
12000
500
Smooth Seal
Smooth seal- Predictions
Smooth seal- Experiments
Grooved Seal
Grooved seal- Predictions
(c = 7c)
Grooved seal- Experiments (cg= 15c)
Cross-coupled Stiffness
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
10,000 rpm, 70 bar
Experimental data shows
relatively large added mass
coefficients. Predictions
correlate well with
experimental results.
40
Mxx
Added Mass [kg]
35
Grooved Seal
30
Added mass coefficients
are larger for grooved seal
25
Smooth Seal
20
15
10
Classical theory [1]
predicts ~ 1/10 of test
value
5
0
0
0.1
0.2
0.4
4000 0.5
0.3
[1] Reinhardt, F., and Lund, J. W., 1975, “The Influence of Fluid Inertia on
the Dynamic Properties of Journal Bearings,” ASME J. Lubr. Technol., 97(1),
pp. 154-167.
Force [N]
Static journal eccentricity ratio
3500(e/c)
3000
2500
2000
1500
0.6
Smooth seal- Predictions
Smooth seal- Experiments
Grooved seal- Predictions (c = 7c)
Grooved seal- Experiments (cg= 15c)
Added Mass
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Conclusions:
• Predictions accurately capture the reduction of
force coefficients on oil seals due to the
addition of circumferential grooves.
• Predicted force coefficients (K,C,M) correlate
well with experimental data.
• Boundary conditions reproduce well physical
system.
• A groove does not fully uncouple adjacent film
lands!!
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Boundary Conditions
Flow continuity is
automatically satisfied at
boundaries
Outlet plane
Constant static pressure at exit plane
P=Pexit
Null dynamic pressure at exit plane
Zeroth Order Pressure Field
Groove
Laminar flow
First Order Pressure Field
Groove
Constant static pressure at inlet plane z
P=Psupply
Null axial flow rate (geometrical symmetry)
x
Inlet plane
P(q,z)=P(q+2,z)
For both the zeroth and first
order fields the pressure field be
periodic in the circumferential
direction
In the occurrence of
oil cavitation
(Pcav=0), the first
order dynamic
pressure field
vanishes
TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals
TL
Grooved Oil Seals
Semanate and San Andrés, (1993)
Predictive
Models
- Bulk flow equation model
- Grooves should reduce force coefficients
by a factor of four, i.e.
Kxy (1 land)= 4 Kxy(2 lands)
Cxx (1 land)= 4 Cxx(2 lands)
-Fluid inertia effects not predicted (considered negligible)
Baheti and Kirk, (1995)
- Reynolds and energy equation (Finite element solution)
- Grooves should effectively isolate seal lands
- Cross-coupled stiffness and damping coefficients are
reduced by ~60 % for grooved configurations