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

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

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

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

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]

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.

- - 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)

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

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.

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

- 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

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

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

Finite Element for solution of Reynolds Eqn.

Assemble system of equations, impose boundary conditions and solve

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 frequencyand small amplitude motions(eX, eY)about the equilibrium position. Hence

Small amplitude journal motions about an equilibrium position

- 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)

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

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

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)

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

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

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

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

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

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

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

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

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

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.

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:

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:

Learn more at

Acknowledgments

Thanks to TAMU Turbomachinery Research Consortium

Questions (?)

© 2011 Luis San Andres

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

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

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