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ASME Turbo Expo 2011 Power for Land, Sea and Air June 6-10, 2011, Vancouver, BC. A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically. Adolfo Delgado Mechanical Engineer GE Global Research Center. Luis San Andrés

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slide1

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

A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically

Adolfo Delgado

Mechanical Engineer

GE Global Research Center

Luis San Andrés

Mast-Childs Professor

Texas A&M University

ASME GT2011-45274

accepted for journal publication

Presentation available at

http://rotorlab.tamu.edu

Supported by TAMU Turbomachinery Research Consortium

oil seal in a compressor 1

Oil Seals

Oil seal in a compressor [1]

commonly used to prevent leakage of process fluid in centrifugal compressors.

- Locked oil seal rings can induce instability in compressors.

- A common remedy: seals are grooved to reduce cross-coupled stiffness and lower lock-up forces

Kirk, R., 1986, “Oil Seal Dynamic Considerations for Analysis of Centrifugal Compressors,” Proc. 15thTurbomachinery Symposium, Houston, TX, pp. 25-34.

slide3

Baheti and Kirk, (1995)

  • - Reynolds and energy equation (FEM)
  • Grooves should effectively isolate seal lands
  • Cross-coupled stiffness and damping coefficients are reduced by ~60 % for grooved configurations

Predictive Models

Semanate and San Andrés, (1993)

- Bulk flow equation model

  • KXY (1 land)= 4 KXY(2 lands)
  • CXX (1 land)= 4 CXX(2 lands)

- Grooves should reduce force coefficients by a factor of four, i.e.

-Fluid inertia effects not predicted (assumed negligible)

slide4

30c

L

5c

Coeffs are ¼ of original seal

c

Damping, Cross-coupled Stiffness & Inertia

2L

c

Journal

Constant pressure

2-land seal: (deep groove divides lands)

Short length seal

slide5

Smooth& grooved oil seals: test results

17 mm

25 mm

Oil supply

Seal length

136c

76c

c

Journal

Parallel oil seal configuration [1]

Childs et al., (2006, 2007)

Parallel seal configuration (balance thrust force due to pressure drop across the seals)

Includes ‘deep’ inlet (central) groove to feed seals

Parameter identification:FSEAL= 1/2 FTest conf.

Predictions do not consider groove or fluid inertia effects (Zirkelback and San Andrés1996)

Results

Force coefficients are well predicted (C,K) except added mass coefficients

Large added mass coefficients (~15 kg)

Added mass predictions using Classical model (Reinhardt & Lund – 1975) (single land- i.e. not including inlet groove) (2.84 kg)

[1] Graviss, M., 2005, “The Influence of a Central Groove on Static and Dynamic Characteristics of an Annular Liquid Seal with Laminar Flow,” M.S. Thesis, Texas A&M Univ., College Station, TX.

slide6

Old Predictions

Experiments

Inlet (central) groove not considered (null dynamic pressure). Ignores fluid inertia

Large added mass coefficients

Inner land groove should reduce crossed-coupled stiffness and direct damping coefficients by a factor of four

Groove does not effectively separate seal lands

  • At most:

KXY (1 land)= 2 KXY(2 lands)

CXX (1 land)= 2 CXX(2 lands)

Kxy (1 land)= 4 Kxy(2 lands)

Cxx (1 land)= 4 Cxx(2 lands)

Large added mass coefficients, increasing with increasing groove depth

Null (neglected) added mass coefficients

Need for better predictive models

slide7

Fluid flow predictive model

  • Bulk flow for incompressible liquid
  • Qualitative observations of laminar flow field
    • Boundary Conditions
    • Characteristic groove depth

oil supply, Ps

Streamlines in axially symmetric grooved annular cavity.

feed plenum groove

mid-land groove

Ps- Pd >0

Pd :discharge pressure

Pd

Pd

z

y

Delgado, A., and San Andrés, L., 2010, “A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Oil Seal Rings,” ASME J. Tribol., 132

slide8

Linear fluid inertia model

No fluid inertia advection

Oil supply

4

3

n

1

2

N

n+1

IV

III

II

I

zN

zIV

zII

zIII

zI

In each flow region:

Reynolds equation

with temporal fluid inertia

slide9

Finite Element Solution

Off-centered operation

x= qR

h

W

w

e

R

Y

De

Film thickness

X

slide10

Boundary conditions

Oil supply

4

3

n

1

2

N

n+1

IV

III

II

I

zN

zIV

zII

zIII

zI

Laminar flow

Ps= supply pressure

Pa= ambient pressure

Ps

Pa

Pa

First-order pressures and axial flow rates must be equal

Null axial flow rate

(axial symmetry)

No generation of dynamic pressure

slide11

Finite Element for solution of Reynolds Eqn.

Assemble system of equations, impose boundary conditions and solve

slide12

Perturbation analysis of flow equations

Consider small amplitude journal (rotor) motions about a static equilibrium position (SEP)

An applied external static load (Wo) determines the rotor equilibrium position (eX, eY)owith steady pressure fieldPoand film thicknessho

Let the journal whirl with frequencyand small amplitude motions(eX, eY)about the equilibrium position. Hence

Small amplitude journal motions about an equilibrium position

slide13

Seal dynamic reaction forces

  • Lateral displacements (X,Y)

Y

X

Z

Stiffness coefficients

Damping coefficients

Inertia coefficients

Force coefficients are independent of excitation frequency for incompressible fluid. Force coefficients depend on rotor speed & static load

Measure of stability: Whirl frequency ratio

WFR = Kxy/(CxxW)

slide14

Test Grooved Oil Seal & FE mesh

Outlet plane

Grooves

z

q

2p

0

Inlet plane

17 mm

25 mm

Oil supply

Seal length

Discharge plenum

2 mm

136c

76c

c

Buffer seal

Journal

(0-15) c

Parallel oil seals Configuration [Childs et al]

Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static & Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2), 398-406.

x=Rq

Clearance = 86 mm

Journal diameter: 117 mm

slide15

Boundary conditions

Outlet plane

Groove

Groove

z

P=Psupply

Inlet plane

x

P(q,z)=P(q+2p,z)

Laminar flow

Constantstatic pressure at exit plane

P=Pexit

Flow continuity is automatically satisfied at boundaries

Null dynamic pressure at exit plane

If oil cavitation (Pcav=0), the first order dynamic pressure field vanishes

  • Zeroth Order Pressure Field
  • First Order Pressure Field

Constant static pressure at inlet plane

Null axial flow rate (axial symmetry)

Zeroth and first order pressure and flow fields are periodic in circumferential direction

slide16

Groove effective depth

CFD simulations show streamline separating flow regions IS aphysical boundarydelimiting the domain for squeeze film flow due to journal radial motions.

Ps= supply pressure

Pa= ambient pressure

Ps

Pa

Test seal

10c

Laminar flow

15c

Inner land groove close up (CFD -Pressure driven flow)

slide17

Test Grooved Oil Seal

Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static & Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2), 398-406.

x=Rq

Effective depths in model

Central groove = 9c

Inner land groove = 6c

slide18

Test oil seal operating conditions

Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static & Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2), 398-406.

Shaft speed:10,000 rpm

Test data

Static eccentricity ratio:0, 0.3, 0.5, 0.7

Load

Supply pressure:70 bar

Journal center locus shows oil seal operates with oil cavitation at the largest test eccentricities (large static load)

Journal locus

slide19

Oil Seal Leakage

10,000 rpm, 70 bar

Predicted leakage correlates very well with tests for both smooth land and grooved seal

Smooth Seal

Grooved Seal

(ch = 7c)

(cg= 15c)

Figure 14

slide20

Oil Seal Forces

10,000 rpm, 70 bar

Smooth Seal

KXX

Grooved Seal

(ch = 7c)

(cg= 15c)

At high eccentricity, test data shows larger seal reaction force for smooth & grooved seals

Figure 7

slide21

Oil Seal Direct Stiffness

10,000 rpm, 70 bar

Model predicts well direct stiffness for smooth & grooved seals

Smooth Seal

KXX

Grooved Seal

(ch = 7c)

(cg= 15c)

Smooth Seal

KYY

Grooved Seal

Figure 8

slide22

Oil Seal Cross Stiffness

10,000 rpm, 70 bar

KXY

Model predicts well decrease in cross-stiffness when adding inner groove

Smooth Seal

Grooved Seal

KYX

(ch = 7c)

Grooved Seal

(cg= 15c)

Smooth Seal

Figure 9

slide23

Oil Seal Cross-Stiffnesses

70 bar

e = 0.0, 0.3

Eccentricity=0

rotor speed increases

Smooth Seal

Grooved Seal

Model effectively predicts reduction in cross-coupled stiffness due to mid-land groove.

KXY

Eccentricity=0.3

Smooth Seal

Grooved Seal

(ch = 7c)

(cg= 15c)

KXY

Figure 10

slide24

Oil Seal Direct Damping

10,000 rpm, 70 bar

Model predicts accurately reduction in direct damping due to inner land groove.

CXX

Smooth Seal

Grooved Seal

(ch = 7c)

CYY

(cg= 15c)

Smooth Seal

Grooved Seal

Figure 11

slide25

Oil Seal Cross Damping

10,000 rpm, 70 bar

Small cross-damping, test data shows larger magnitude than predictions

Smooth Seal

CXY

Grooved Seal

Smooth Seal

(ch = 7c)

CYX

Grooved Seal

(cg= 15c)

Figure 12

slide26

Oil Seal Added Mass

10,000 rpm, 70 bar

Figure 13

Test data shows large added mass coefficients. Predictions correlate well with experimental results.

MXX

Grooved Seal

Added mass coefficients are larger for grooved seal

Smooth Seal

Classical theory (*) predicts ~ 1/10 of test value

(ch = 7c)

(cg= 15c)

[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.

slide27
Good correlation for direct force coefficients for the lower journal eccentricities (e/c=0,0.3) and moderate to good correlation for e/c=0.5.

Cross-coupled stiffnesses also predicted accurately for the smaller eccentricities. FE model accurately predicts the reduction of the direct stiffness, direct damping, and cross-coupled stiffness coefficients when adding a circumferential groove to the seal land.

Added mass coefficients for both seals (smooth and grooved) are also predicted accurately (within 20 %). Both analysis and test results show a grooved seal has larger direct added mass coefficient than a smooth seal.

Conclusions:

slide28
Discrepancies between test results and predictions for large journal eccentricities (e/c)~0.70. Discrepancies due to (unknown) changes in seal clearance and oil viscosity induced by thermal effects.

Current model is a significant improvement over prevailing predictive tools to analyze grooved oil seals.

Deep grooves do not fully uncouple parallel film lands!!

Model applied successfully to grooved SFDs (+ additional experimental verifications)

Conclusions:

slide29

http://rotorlab.tamu.edu

Learn more at

Acknowledgments

Thanks to TAMU Turbomachinery Research Consortium

Questions (?)

© 2011 Luis San Andres

slide30

Prediction: pressure fields for oil seal without inner groove

Journal whirl motion with r=5 mm, w=200 Hz)

  • Classical:central groove dyn. pressure = 0

(b) Current – central groove interacts with film lands

slide31

Prediction: pressure fields for oil seal with inner groove

Journal whirl motions with r=5 mm, w=200 Hz)

  • Classical:central groove dyn. pressure = 0inner land dyn. pressure = 0

(b) Current – central groove and inner groove interacts with film lands