The Effects of Converging and Diverging Axial Taper on the Rotordynamic Coefficients of Liquid Annular Pressure Seals: Theory Versus Experiment

1995 ◽  
Vol 122 (2) ◽  
pp. 126-131 ◽  
Author(s):  
W. Todd Lindsey ◽  
Dara W. Childs
Keyword(s):  
Turbulent Flow ◽  
Qualitative Agreement ◽  
Running Speed ◽  
Taper Angle ◽  
Rotordynamic Coefficients ◽  
Rotation Rates ◽  
Damping Coefficients ◽  
Theoretical Predictions ◽  
Theory Versus ◽  
Direct Stiffness

Experimental results are compared to predictions for turbulent flow, short (D=76.2mm,L/D=.17), smooth annular seals with converging and diverging axial taper. Results are presented for four geometries with the same minimum clearances: two convergent, two divergent, and a constant-clearance. Measurements were taken at seal pressure differentials and shaft rotation rates ranging from 1.34 to 3.54 MPa and 10,200 to 24,600 rpm, respectively. Measurements parameters include leakage, direct stiffness, cross-coupled stiffness, and direct damping coefficients. Results show that direct stiffness generally increases with converging axial taper and decreases with diverging axial taper; however, direct stiffness decreases in the first increase in the taper angle, contrary to predictions. Direct damping and cross-coupled stiffness were shown to decrease with increasing convergent or divergent taper. Measured damping values increase with increased running speed and decreasing average clearance. Theoretical predictions for rotordynamic coefficients are in reasonable qualitative agreement with measured results. The theory consistently underpredicts leakage by ranges of 10∼30 percent. The accuracy of predictions for leakage and rotordynamic coefficients was not influenced by running speed. [S0739-3717(00)70102-4]

The Effects of Converging and Diverging Axial Taper on the Rotordynamic Coefficients of Liquid Annular Pressure Seals: Theory Versus Experiment

1995 ◽  
Author(s):  
W. Todd Lindsey ◽  
Dara W. Childs
Keyword(s):  
Turbulent Flow ◽  
Experimental Results ◽  
Running Speed ◽  
Rotordynamic Coefficients ◽  
Rotation Rates ◽  
Damping Coefficients ◽  
Shaft Rotation ◽  
Theoretical Predictions ◽  
Theory Versus ◽  
Direct Stiffness

Abstract Experimental results are compared to predictions for turbulent flow, short (D = 76.2mm, L/D = .17), smooth annular seals with converging and diverging axial taper. Results are presented for four geometries: two convergent, two divergent, and a constant-clearance. Measurements were taken at seal pressure differentials and shaft rotation rates ranging from 1.34 to 3.54 MPa and 10,200 to 24,600 rpm, respectively. Measurements parameters include leakage, direct stiffness, cross-coupled stiffness, and direct damping coefficients. Results show that direct stiffness generally increases with converging axial taper and decreases with diverging axial taper. Direct damping and cross-coupled stiffness were shown to decrease with increasing convergent or divergent taper. Measured damping values increase with increased running speed and decreasing average clearance. Theoretical predictions for rotordynamic coefficients are in good overall agreement with measured results. The theory consistently underpredicts leakage by ranges of 10 ∼ 30%. The accuracy of predictions for leakage and rotordynamic coefficients was not influenced by running speed.

Theory Versus Experiment for Short (L/D = 1/6) Honeycomb and Smooth Annular Pressure Seals

1993 ◽  
Author(s):  
Dara W. Childs ◽  
George F. Kleynhans
Keyword(s):  
Pressure Ratio ◽  
Surface Friction ◽  
Computer Code ◽  
Cell Width ◽  
Rotordynamic Coefficients ◽  
Test Parameters ◽  
Theoretical Predictions ◽  
Theory Versus ◽  
Honeycomb Cell ◽  
Parameter Ranges

Abstract A study which compares theoretical predictions of experimental rotordynamic and leakage results is presented for short (L/D = 1/6) honeycomb and smooth annular pressure seals. A computer code used in this comparison has been developed from a theory that employs a perturbation analysis of the governing equations flow and uses Moody’s pipe friction relationship for the surface friction of the rotor and stator. This study was undertaken to investigate how well an existing code could predict these characteristics with input provided from recorded test data and independent flat-plate tests. The results examine the effect that the following independent test parameters have on the experimental measurements and theoretical predictions: inlet preswirl, rotor speed, inlet pressure, pressure ratio across seal, seal clearance, and honeycomb cell width. Experimental results show that leakage is reduced by decreasing the honeycomb cell width. Rotordynamically, the short seals are stabilizing over all test parameter ranges. However, the short seals did not perform as favorably as longer (L/D = 1/3) seals. In general, the theory overpredicts rotordynamic coefficients and leakage.

High-Pressure Pocket Damper Seals: Leakage Rates and Cavity Pressures

2006 ◽  
Vol 129 (4) ◽  
pp. 826-834 ◽  
Author(s):  
Ahmed M. Gamal ◽  
Bugra H. Ertas ◽  
John M. Vance
Keyword(s):  
High Pressures ◽  
Prediction Models ◽  
Working Fluid ◽  
Dual Purpose ◽  
Rotordynamic Coefficients ◽  
Numerical Predictions ◽  
Theoretical Predictions ◽  
Mass Flow Rates ◽  
Direct Stiffness ◽  
Stiffness And Damping

The turbomachinery component of interest in this paper, the pocket damper seal, has the dual purpose of limiting leakage and providing an additional source of damping at the seal location. The rotordynamic coefficients of these seals (primarily the direct stiffness and damping) are highly dependent on the leakage rates through the seals and the pressures in the seals’ cavities. This paper presents both numerical predictions and experimentally obtained results for the leakage and the cavity pressures of pocket damper seals operating at high pressures. The seals were tested with air, at pressures up to 1000psi(6.92MPa), as the working fluid. Earlier flow-prediction models were modified and used to obtain theoretical reference values for both mass flow rates and pressures. Leakage and static pressure measurements on straight-through and diverging-clearance configurations of eight-bladed and twelve-bladed seals were used for code validation and for calculation of seal discharge coefficients. Higher than expected leakage rates were measured in the case of the twelve-bladed seal, while the leakage rates for the eight-bladed seals were predicted with reasonable accuracy. Differences in the axial pitch lengths of the cavities and the blade profiles of the seals are used to explain the discrepancy in the case of the twelve-bladed seal. The analysis code used also predicted the static cavity pressures reasonably well. Tests conducted on a six-bladed pocket damper seal to further investigate the effect of blade profile supported the results of the eight-bladed and twelve-bladed seal tests and matched theoretical predictions with satisfactory accuracy.

Rotordynamic Characteristics of a Flexure Pivot Pad Bearing With an Active and Locked Integral Squeeze Film Damper

2012 ◽  
Author(s):  
Jeff Agnew ◽  
Dara Childs
Keyword(s):  
Added Mass ◽  
Squeeze Film ◽  
Test Results ◽  
Squeeze Film Damper ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Active Damper ◽  
Rotordynamic Coefficient

Measured rotordynamic coefficients are presented for a flexure-pivot-pad journal bearing (FPJB) in a load-between-pad configuration with: (1) an active, and (2) locked integral squeeze film damper (ISFD). Prior rotordynamic-coefficient test results have been presented for FPJBs (alone), and rotor-response results have been presented for rotors supported by FPJBS with ISFDs; however, these are the first rotordynamic-coefficient test results for FPJBs with ISFDs. A multi-frequency dynamic testing regime is employed. For both bearing configurations, quadratic curve fits provide good representation of the real portions of the dynamic-stiffness coefficients yielding a direct stiffness and a direct added-mass coefficient. The imaginary portions are well represented by linear curve fits, implying constant, frequency-independent direct-damping coefficients. Direct stiffness coefficients are ∼50% lower for the active-damper configuration, and direct damping coefficients are only modestly lower. The combination of ∼50% reduction in direct stiffness with a modest drop in direct damping indicates a very effective squeeze-film damper application. Added-mass coefficients are normally lower for the active-damper configuration, and all coefficient trends (for changes in loading and shaft speed) are “flatter” for the active flexure pivot-pad damper bearing. The measured rotordynamic coefficients are used to calculate the whirl frequency ratio and indicate high stability for both bearing configurations.

scholarly journals Theory Versus Experiment for the Rotordynamic Coefficients of Annular Gas Seals: Part 2—Constant-Clearance and Convergent-Tapered Geometry

1986 ◽  
Vol 108 (3) ◽  
pp. 433-437 ◽  
Author(s):  
C. C. Nelson ◽  
D. W. Childs ◽  
C. Nicks ◽  
D. Elrod
Keyword(s):  
Experimental Test ◽  
Experimental Results ◽  
Test Facility ◽  
Rotordynamic Coefficients ◽  
Theory Versus ◽  
Direct Stiffness ◽  
Gas Seals ◽  
Predicted Values

An experimental test facility is used to measure the leakage and rotordynamic coefficients of constant-clearance and convergent-tapered annular gas seals. The results are presented along with the theoretically predicted values. Of particular interest is the prediction that optimally tapered seals will have significantly larger direct stiffness than straight seals. The experimental results verify this prediction. Generally the theory does quite well, but fails to predict the large increase in direct stiffness when the fluid is prerotated.

High-Pressure Pocket Damper Seals: Leakage Rates and Cavity Pressures

2006 ◽  
Author(s):  
Ahmed M. Gamal ◽  
Bugra H. Ertas ◽  
John M. Vance
Keyword(s):  
High Pressures ◽  
Prediction Models ◽  
Working Fluid ◽  
Dual Purpose ◽  
Rotordynamic Coefficients ◽  
Numerical Predictions ◽  
Theoretical Predictions ◽  
Mass Flow Rates ◽  
Direct Stiffness ◽  
Stiffness And Damping

The turbomachinery component of interest in this paper, the pocket damper seal, has the dual purpose of limiting leakage and providing an additional source of damping at the seal location. The rotordynamic coefficients of these seals (primarily the direct stiffness and damping) are highly dependent on the leakage rates through the seals and the pressures in the seals’ cavities. This paper presents both numerical predictions and experimentally obtained results for the leakage and the cavity pressures of pocket damper seals operating at high pressures. The seals were tested with air, at pressures up to 1000 Psi (6.92 MPa), as the working fluid. Earlier flow-prediction models were modified and used to obtain theoretical reference values for both mass flow-rates and pressures. Leakage and static pressure measurements on straight-through and diverging-clearance configurations of eight-bladed and twelve-bladed seals were used for code validation and for calculation of seal discharge coefficients. Higher than expected leakage rates were measured in the case of the twelve-bladed seal, while the leakage rates for the eight-bladed seals were predicted with reasonable accuracy. Differences in the axial pitch lengths of the cavities and the blade profiles of the seals are used to explain the discrepancy in the case of the twelve-bladed seal. The analysis code used also predicted the static cavity pressures reasonably well. Tests conducted on a six-bladed pocket damper seal to further investigate the effect of blade profile supported the results of the eight-bladed and twelve-bladed seal tests and matched theoretical predictions with satisfactory accuracy.

Theory Versus Experiment for the Rotordynamic Characteristics of a Smooth Annular Gas Seal at Eccentric Positions

1995 ◽  
Vol 117 (1) ◽  
pp. 148-152 ◽  
Author(s):  
C. R. Alexander ◽  
D. W. Childs ◽  
Z. Yang
Keyword(s):  
Frequency Ratio ◽  
Pressure Ratio ◽  
Experimental Results ◽  
Test Results ◽  
Eccentricity Ratio ◽  
Rotordynamic Coefficients ◽  
Theory Versus ◽  
Direct Stiffness ◽  
Static Eccentricity ◽  
Independent Model

Experimental results are presented for the rotordynamic coefficients of a smooth gas seal at eccentricity ratios out to 0.5. The effects of speed, inlet pressure, pressure ratio, fluid prerotation, and eccentricity are investigated. The experimental results show that direct stiffness KXX decreases significantly, while direct damping and cross-coupled stiffness increase with increasing eccentricity. The whirl-frequency ratio, which is a measure of rotordynamic instability, increases with increasing eccentricity at 5000 rpm with fluid prerotation. At 16,000 rpm, the whirl-frequency ratio is insensitive to changes in the eccentricity. Hence, the results show that eccentric operation of a gas seal tends to destabilize a rotor operating at low speeds with preswirled flow. At higher speeds, eccentric operation has no significant impact on rotordynamic stability. The test results show that the customary, eccentricity-independent, model for rotordynamic coefficients is only valid out to an eccentricity ratio of 0.2~0.3. For larger eccentricity ratios, the dependency of rotordynamic coefficients on the static eccentricity ratio needs to be accounted for. Experimental results are compared to predictions for static and dynamic characteristics based on an analysis by Yang (1993). In general, the theoretical results reasonably predict these results; however, theory overpredicts direct stiffness, fails to indicate the decrease in KXX that occurs with increasing eccentricity, and incorrectly predicts the direction of change in KXX with changing pressure ratio. Also, direct damping is substantially underpredicted for low preswirl values and low supply pressures, but the predictions improve as either of these parameters increase.

Measured Static and Rotordynamic Characteristics of a Smooth-Stator/Grooved-Rotor Liquid Annular Seal

2017 ◽  
Author(s):  
J. Alex Moreland ◽  
Dara W. Childs ◽  
Joshua T. Bullock
Keyword(s):  
Frequency Ratio ◽  
Dynamic Performance ◽  
Radial Clearance ◽  
Test Results ◽  
Axial Pressure ◽  
Pressure Drops ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Annular Seal ◽  
Direct Stiffness

Electric submersible pumps utilize grooved-rotor seals to reduce leakage and break up contaminants within the pumped fluid. Additionally, due to their decreased surface area (when compared to a smooth seal), grooved seals decrease the chance of seizure in the case of rotor-stator rubs. Despite their use in industry, the literature does not contain measurements for smooth-stator/circumferentially-grooved-rotor liquid annular seals. This paper presents test results consisting of leakage measurements and rotordynamic coefficients for a smooth-stator/circumferentially-grooved-rotor liquid annular seal. Both static and dynamic performance for the grooved seal are investigated for various imposed pre-swirl ratios, static eccentricities, axial pressure drops, and running speeds. The grooved seals′ static and dynamic performance are compared to those of a smooth seal with identical length, diameter, and radial clearance. Results show that adding grooves reduces leakage at lower speeds (less than 5 krpm) and higher axial pressure drops, but does little at higher speeds. The grooved seal’s direct stiffness is generally negative, which would be detrimental to pump rotordynamics. Furthermore, increasing pre-swirl increases the magnitude of cross-coupled stiffness and increases the whirl frequency ratio. When compared to the smooth seal, the grooved seal has smaller effective damping coefficients, indicative of worse stability characteristics.

scholarly journals Theory Versus Experiment for the Rotordynamic Coefficients of an Interlocking Labyrinth Gas Seal

1995 ◽  
Author(s):  
David A. Elrod ◽  
Joseph M. Pelletti ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Labyrinth Seal ◽  
Back Pressure ◽  
Experimental Results ◽  
Rotordynamic Coefficients ◽  
Inlet Guide Vanes ◽  
Stabilizing Effect ◽  
Theory Versus ◽  
High Fluid ◽  
Direct Stiffness

Experimental results for the rotordynamic coefficients of an interlocking, compressible flow, labyrinth seal are presented. Tests were conducted at supply pressures out to 18.3 bars and rotor speeds out to 16,000 rpm. Seal back pressure was controlled to provide four pressure ratios at all supply pressures. Inlet guide vanes were used to provide fluid prerotation at the seal inlet. The experimental results are compared to the predictions of the bulk-flow, turbulent, one-control-volume, perturbation analysis of Scharrer (1988). The results show that the direct stiffness is negative but small, and is predicted well by theory. At high rotor speeds, the experimental cross-coupled stiffness is negative (stabilizing for forward whirl) for all values of fluid prerotation. Theory predicts positive (destabilizing for forward whirl) cross-coupled stiffness for high fluid prerotation, and overpredicts the direct damping of the seal. In general, the net stabilizing effect of the seal, as indicated by the whirl frequency ratio, is predicted well.

Measured Static and Rotordynamic Coefficient Results for a Rocker-Pivot, Tilting-Pad Bearing With 50 and 60% Offsets

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Chris D. Kulhanek ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Mass Matrix ◽  
Excitation Frequency ◽  
Quadratic Function ◽  
Added Mass ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Frequency Independent ◽  
Direct Stiffness

Static and rotordynamic coefficients are measured for a rocker-pivot, tilting-pad journal bearing (TPJB) with 50 and 60% offset pads in a load-between-pad (LBP) configuration. The bearing uses leading-edge-groove direct lubrication and has the following characteristics: 5-pads, 101.6 mm (4.0 in) nominal diameter,0.0814 -0.0837 mm (0.0032–0.0033 in) radial bearing clearance, 0.25 to 0.27 preload, and 60.325 mm (2.375 in) axial pad length. Tests were performed on a floating bearing test rig with unit loads from 0 to 3101 kPa (450 psi) and speeds from 7 to 16 krpm. Dynamic tests were conducted over a range of frequencies (20 to 320 Hz) to obtain complex dynamic stiffness coefficients as functions of excitation frequency. For most test conditions, the real dynamic stiffness functions were well fitted with a quadratic function with respect to frequency. This curve fit allowed for the stiffness frequency dependency to be captured by including an added mass matrix [M] to a conventional [K][C] model, yielding a frequency independent [K][C][M] model. The imaginary dynamic stiffness coefficients increased linearly with frequency, producing frequency-independent direct damping coefficients. Direct stiffness coefficients were larger for the 60% offset bearing at light unit loads. At high loads, the 50% offset configuration had a larger stiffness in the loaded direction, while the unloaded direct stiffness was approximately the same for both pivot offsets. Cross-coupled stiffness coefficients were positive and significantly smaller than direct stiffness coefficients. Negative direct added-mass coefficients were obtained for both offsets, especially in the unloaded direction. Cross-coupled added-mass coefficients are generally positive and of the same sign. Direct damping coefficients were mostly independent of load and speed, showing no appreciable difference between pivot offsets. Cross-coupled damping coefficients had the same sign and were much smaller than direct coefficients. Measured static eccentricities suggested cross coupling stiffness exists for both pivot offsets, agreeing with dynamic measurements. Static stiffness measurements showed good agreement with the loaded, direct dynamic stiffness coefficients.

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