Theory Versus Experiment for the Rotordynamic Characteristics of a High Pressure Honeycomb Annular Gas Seal at Eccentric Positions

2003 ◽  
Vol 125 (2) ◽  
pp. 422-429 ◽  
Author(s):  
Mark Weatherwax ◽  
Dara W. Childs
Keyword(s):  
Back Pressure ◽  
Test Fluid ◽  
Test Results ◽  
Eccentricity Ratio ◽  
Cell Width ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Theory Versus ◽  
A Cell ◽  
San Andres

Test results for leakage and rotordynamic coefficients are presented for a honeycomb-stator/smooth-rotor annular seal for eccentricity ratios out to 0.5 using air as the test fluid. Tests were conducted at supply pressures up to 70 bars and running speeds up to 20200 rpm. The seal has a diameter of 115 mm, a cell width of 0.79 mm, and a cell depth of 3.10 mm. Tests were conducted for the back-pressure ratios of 0.35, and 0.5. Comparisons are made to predictions from an analysis due to San Andres. The test results show a minimal sensitivity of either leakage or rotordynamic coefficients to changes in the eccentricity ratio. The predictions generally agree well with measurements.

Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal With Two-Phase, Mainly Air Mixtures

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Min Zhang ◽  
James E. Mclean ◽  
Dara W. Childs
Keyword(s):  
Gas Turbines ◽  
Dynamic Stiffness ◽  
Test Fluid ◽  
Liquid Volume ◽  
Test Cases ◽  
Test Results ◽  
Two Phase ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Annular Seal

A two-phase annular seal stand (2PASS) has been developed at the Turbomachinery Laboratory of Texas A&M University to measure the leakage and rotordynamic coefficients of division wall or balance-piston annular seals in centrifugal compressors. 2PASS was modified from an existing pure-air annular seal test rig. A special mixer has been designed to inject the oil into the compressed air, aiming to make a homogenous air-rich mixture. Test results are presented for a smooth seal with an inner diameter D of 89.306 mm, a radial clearance Cr of 0.188 mm, and a length-to-diameter ratio (L/D) of 0.65. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are conducted with inlet liquid volume fraction (LVF) = 0%, 2%, 5%, and 8%, shaft speed ω = 10, 15, and 20 krpm, and pressure ratio (PR) = 0.43, 0.5, and 0.57. The test seal is concentric with the shaft (centered), and the inlet pressure is 62.1 bar. Complex dynamic-stiffness coefficients are measured for the seal. The real parts are generally too dependent on excitation frequency Ω to be modeled by constant stiffness and virtual-mass coefficients. The direct real dynamic-stiffness coefficients are denoted as KΩ; the cross-coupled real dynamic-stiffness coefficients are denoted as kΩ. The imaginary parts of the dynamic-stiffness coefficients are modeled by frequency-independent direct C and cross-coupled c damping coefficients. Test results show that the leakage and rotordynamic coefficients are remarkable impacted by changes in inlet LVF. Leakage mass flow rate m˙ drops slightly as inlet LVF increases from zero to 2% and then increases with further increasing inlet LVF to 8%. As inlet LVF increases from zero to 8%, KΩ generally decreases except it increases as inlet LVF increases from zero to 2% when PR = 0.43. kΩ increases virtually with increasing inlet LVF from zero to 2%. As inlet LVF further increases to 8%, kΩ decreases or remains unchanged. C increases as inlet LVF increases; however, its rate of increase drops significantly at inlet LVF = 2%. Effective damping Ceff combines the stabilizing impact of C and the destabilizing impact of kΩ. Ceff is negative (destabilizing) for lower Ω values and becomes more destabilizing as inlet LVF increases from zero to 2%. It then becomes less destabilizing as inlet LVF is further increased to 8%. Measured m˙ and rotordynamic coefficients are compared with predictions from XLHseal_mix, a program developed by San Andrés (2011, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503) based on a bulk-flow model, using the Moody wall-friction model while assuming constant temperature and a homogenous mixture. Predicted m˙ values are close to measurements when inlet LVF = 0% and 2% and are smaller than test results by about 17% when inlet LVF = 5% and 8%. As with measurements, predicted m˙ drops slightly as inlet LVF increases from zero to 2% and then increases with increasing inlet LVF further to 8%. However, in the inlet LVF range of 2–8%, the predicted effects of inlet LVF on m˙ are weaker than measurements. XLHseal_mix poorly predicts KΩ in most test cases. For all test cases, predicted KΩ decreases as inlet LVF increases from zero to 8%. The increase of KΩ induced by increasing inlet LVF from zero to 2% at PR = 0.43 is not predicted. C is reasonably predicted, and predicted C values are consistently smaller than measured results by 14–34%. Both predicted and measured C increase as inlet LVF increases. kΩ and Ceff are predicted adequately at pure-air conditions, but not at most mainly air conditions. The significant increase of kΩ induced by changing inlet LVF from zero to 2% is predicted. As inlet LVF increases from 2% to 8%, predicted kΩ continues increasing versus that measured kΩ typically decreases. As with measurements, increasing inlet LVF from zero to 2% decreases the predicted negative values of Ceff, making the test seal more destabilizing. However, as inlet LVF increases further to 8%, the predicted negative values of Ceff drop versus measured values increase. For high inlet LVF values (5% and 8%), the predicted negative values of Ceff are smaller than measurements. So, the seal is more stabilizing than predicted for high inlet LVF cases.

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.

Static and Rotordynamic Characteristics of Liquid Annular Seals With a Circumferentially-Grooved Stator and Smooth Rotor Using Three Levels of Circumferential Inlet-Fluid Rotation

2018 ◽  
Author(s):  
Dara W. Childs ◽  
Jose M. Torres ◽  
Joshua T. Bullock
Keyword(s):  
Oil Recovery ◽  
Operating Conditions ◽  
Test Fluid ◽  
Radial Clearance ◽  
Test Results ◽  
Pressure Drops ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Electrical Submersible Pumps ◽  
Lower Magnitude

Test results are presented for a smooth-rotor/circumferentially-grooved, annular pump seal. The seal’s geometry and operating conditions are representative of electrical submersible pumps (ESPs) as used for oil recovery; however, most ESPs use grooved rotors instead of grooved stators. Test results include static and rotordynamic data at speeds ω of 2, 4, 6 krpm, axial pressure drops ΔP of 2.1, 4.1, 6.2, 8.3 bars. The grooved seal has a length-to-diameter ratio L/D of 0.5 and a minimum radial clearance Cr of 203 μm. It employs 15 circumferential grooves with a length Gl, and depth Gd of 1.52 mm, which are equally-spaced by a land length of 1.52 mm. Tests are conducted for eccentricity ratios ϵ0 of 0.00, 0.27, 0.53, 0.80. Three different inlet-fluid prerotation inserts are used upstream of the test seals to create a range of inlet preswirl ratios. Pitot tubes are used to measure the circumferential velocity at one location immediately upstream of the test seal and one downstream location near the seal exit. The test fluid is ISOVG2 oil @ 46 °C. Test results for the grooved seal are compared to test results for a smooth annular seal with the same L, D, and minimum Cr. The grooved-seal’s leakage rate Q̇, ranges from a low 15.64 LPM at ω = 6 krpm, and ΔP = 2 bar, to a high 56.36 LPM at ω = 2 krpm, and ΔP = 8 bar. When compared to the smooth seal, the grooved seal provides a 20% Q̇ reduction at ω = 2 krpm, and a 6% reduction at ω = 6 krpm. The grooved seal’s rotordynamic coefficients are generally not sensitive to changes in ϵ0. The smooth seal’s stiffness and damping coefficients are not very sensitive to changes in ϵ0 in moving from ϵ0 = 0 to 0.5, but typically increase dramatically in magnitude in moving from ϵ0 = 0.5 to 0.8. From a rotordynamic viewpoint, the major difference between the two seals concerns the direct stiffness coefficients, with the grooved seal having near zero to negative values and the smooth seal having larger positive values, particularly at increased ϵ0 values. The grooved seal generally produces lower-magnitude cross-coupled stiffness and direct damping coefficient values than the smooth seal.

Theoretical and Experimental Comparisons for Rotordynamic Coefficients of a High-Speed, High-Pressure, Orifice-Compensated Hybrid Bearing

1995 ◽  
Vol 117 (2) ◽  
pp. 285-290 ◽  
Author(s):  
Nancy M. Franchek ◽  
Dara W. Childs ◽  
Luis San Andres
Keyword(s):  
High Pressure ◽  
High Speed ◽  
Discharge Coefficient ◽  
Test Fluid ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Hybrid Bearing ◽  
San Andres ◽  
Experimental Comparisons ◽  
Good Agreement

Comparisons are presented between measurements and predictions for a 76.2 mm diameter, high-speed (24,600 rpm), high-pressure (7.0 MPa), hybrid bearings using warm (54°C) water as a test fluid. “Hybrid” refers to combined hydrostatic and hydrodynamic action. Test results are presented for an orifice-fed, square-recess configuration with five recesses. Data are provided for rotordynamic coefficients including direct and cross-coupled stiffness, direct damping, direct added-mass coefficients, and the whirl-frequency ratio. Experimental results are compared to predictions from an analysis by San Andres (1990a), which accounts for both temporal and convective acceleration terms in the fluid film. San Andres’ development uses an orifice discharge coefficient to model the pressure drop from supply pressure to recess pressure. With experimentally determined discharge-coefficient values as input, good agreement is obtained between theory and experiment. However, predictions are sensitive to changes in the orifice discharge coefficients.

Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal With Two-Phase, Mainly-Air Mixtures

2017 ◽  
Author(s):  
Min Zhang ◽  
James E. Mclean ◽  
Dara W. Childs
Keyword(s):  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Test Fluid ◽  
Radial Clearance ◽  
Test Cases ◽  
Test Results ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Rate Of Increase ◽  
Annular Seal

A 2-phase annular seal stand (2PASS) has been developed at the Turbomachinery Laboratory of Texas A&M University to measure the leakage and rotordynamic coefficients of division wall or balance-piston annular seals in centrifugal compressors. 2PASS was modified from an existing pure-air annular seal test rig. A special mixer has been designed to inject the oil into the compressed air, aiming to make a homogenous air-rich mixture. Test results are presented for a smooth seal with an inner diameter D of 89.306 mm, a radial clearance Cr of 0.188 mm, and a length-to-diameter ratio L/D of 0.65. The test fluid is a mixture of air and Silicone oil (PSF-5cSt). Tests are conducted with inlet LVF = 0%, 2%, 5%, and 8%, shaft speed ω = 10, 15, and 20 krpm, and pressure ratio PR = 0.43, 0.5, and 0.57. The test seal is concentric with the shaft (centered), and the inlet pressure is 62.1 bars. Complex dynamic stiffness coefficients are measured for the seal. The real parts are generally too dependent on excitation frequency Ω to be modeled by constant stiffness and virtual mass coefficients. The direct real dynamic stiffness coefficients are denoted as KΩ; the cross-coupled real dynamic stiffness coefficients are denoted as kΩ. The imaginary parts of the dynamic stiffness coefficients are modeled by frequency-independent direct C and cross-coupled c damping coefficients. Test results show that the leakage and rotordynamic coefficients are remarkable impacted by changes in inlet LVF. Leakage mass flow rate ṁ drops slightly as inlet LVF increases from zero to 2%, and then increases with further increasing inlet LVF to 8%. As inlet LVF increases from zero to 8%, KΩ generally decreases except it increases as inlet LVF increases from zero to 2% when PR = 0.43. kΩ increases virtually with increasing inlet LVF from zero to 2%. As inlet LVF further increases to 8%, kΩ decreases or remains unchanged. C increases as inlet LVF increases; however, its rate of increase drops significantly at inlet LVF = 2%. Effective damping Ceff combines the stabilizing impact of C and the destabilizing impact of kΩ. Ceff is negative (destabilizing) for lower Ω values and becomes more destabilizing as inlet LVF increases from zero to 2%. It then becomes less destabilizing as inlet LVF is further increased to 8%. Measured ṁ and rotordynamic coefficients are compared with predictions from XLHseal_mix, a program developed by San Andrés [1] based on a bulk-flow model, using the Moody wall-friction model while assuming constant temperature and a homogenous mixture. Predicted ṁ values are close to measurements when inlet LVF = 0 and 2%, and are larger than measured values when inlet LVF = 5% and 8%. As with measurements, predicted ṁ drops slightly as inlet LVF increases from zero to 2%, and then increases with increasing inlet LVF further to 8%. However, in the inlet LVF range of 2∼8%, the predicted effects of inlet LVF on ṁ are weaker than measurements. XLHseal_mix poorly predicts KΩ in most test cases. For all test cases, predicted KΩ decreases as inlet LVF increases from zero to 8%. The increase of KΩ induced by increasing inlet LVF from zero to 2% at PR = 0.43 is not predicted. C is reasonably predicted, and predicted C values are consistently smaller than measured results by 14∼34%. Both predicted and measured C increase as inlet LVF increases. kΩ and Ceff are predicted adequately at pure-air conditions, but not at most mainly-air conditions. The significant increase of kΩ induced by changing inlet LVF from zero to 2% is predicted. As inlet LVF increases 2% to 8%, predicted kΩ continue increasing versus that measured kΩ typically decreases. As with measurements, increasing inlet LVF from zero to 2% decreases the predicted negative values of Ceff, making the test seal more destabilizing. However, as inlet LVF increases further to 8%, the predicted negative values of Ceff drops versus measured values increase. For high inlet LVF values (5% and 8%), the predicted negative values of Ceff are smaller than measurements. So, the seal is actually more stable than predicted for high inlet LVF cases.

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.

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

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
J. Alex Moreland ◽  
Dara W. Childs ◽  
Joshua T. Bullock
Keyword(s):  
Radial Clearance ◽  
Test Results ◽  
Dynamic Features ◽  
Axial Pressure ◽  
Pressure Drops ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Static Eccentricity ◽  
Dynamic Variables

Electric submersible pumps (ESPs) utilize grooved-rotor/smooth-stator (SS/GR) 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 rotordynamic measurements for smooth-stator/circumferentially grooved-rotor liquid annular seals. This paper presents test results consisting of leakage measurements and rotordynamic coefficients for a SS/GR liquid annular sdeal. Both static and dynamic variables are investigated for various imposed preswirl ratios (PSRs), static eccentricity ratios (0–0.8), axial pressure drops (2–8 bars), and running speeds (2–8 krpm). The seals' static and dynamic features are compared to those of a smooth seal with the same length, diameter, and minimum radial clearance. Results show that the grooves reduce 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. As expected, increasing preswirl increases the magnitude of cross-coupled stiffness and increases the whirl frequency ratio (WFR). When compared to the smooth seal, the grooved seal has smaller effective damping coefficients, indicative of poorer stability characteristics.

Eccentricity Effects on the Rotordynamic Coefficients of Plain Annular Seals: Theory Versus Experiment

1997 ◽  
Vol 119 (3) ◽  
pp. 443-447 ◽  
Author(s):  
O. R. Marquette ◽  
D. W. Childs ◽  
L. San Andres
Keyword(s):  
High Speed ◽  
Small Motion ◽  
Rotordynamic Coefficients ◽  
Annular Seal ◽  
Theory Versus ◽  
High Speed Data ◽  
Static Eccentricity ◽  
Good Signal ◽  
Good Agreement ◽  
Annular Seals

Reliable high-speed data are presented for leakage and rotordynamic coefficients of a plain annular seal at centered and eccentric positions. A seal with L/D = 0.45 was tested, and measured results have good signal-to-noise ratios. The influence on rotordynamic coefficients of pressure drop, running speed, and static eccentricity was investigated. There is an excellent agreement between experimental and theoretical results in the centered position, even for direct inertia terms, which have not shown good agreement with predictions in past studies. However, the rotordynamic coefficients are more sensitive to changes in eccentricity than predicted. These results suggest that, in some cases, annular seals for pumps may need to be treated more like hydrodynamic bearings, with rotordynamic coefficients which are valid for small motion about a static equilibrium position versus the present eccentricity-independent coefficients.

Theory Versus Experiment for the Rotordynamic Impedances of Two Hole-Pattern-Stator Gas Annular Seals

2001 ◽  
Vol 124 (1) ◽  
pp. 137-143 ◽  
Author(s):  
Christopher G. Holt ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Pressure Ratio ◽  
Effective Stiffness ◽  
Cell Diameter ◽  
Rotordynamic Coefficients ◽  
Hole Area ◽  
Theory Versus ◽  
Density Factor ◽  
A Cell ◽  
Exit Temperature

Measured rotordynamic impedances are presented for two hole-pattern-stator seals and one smooth bore seal. These measured results are compared to predictions from a two-control-volume model and realized in the code ISOTSEAL (constant-temperature seal code). The hole-pattern seals have cell depths of 2.03 mm and 3.18 mm with a cell diameter of 1.59 mm. The hole-area density factor for both hole-pattern seals is 43 percent. The seal diameter is 114.71 mm with an L/D ratio of 0.75. Measured results for radial impedances and leakage were obtained. Test conditions involved three speeds out to 20,200 rpm, three inlet pressures out to 17.2 bar, and two exit-to-inlet pressure ratios of 40 percent and 54 percent. As predicted, the hole-pattern seals exhibit frequency-dependent rotordynamic coefficients K(Ω), k(Ω), C(Ω), c(Ω). Results of the tests show that the 3.18 mm hole-pattern seal has the highest average effective stiffness and lowest effective damping. Direct and effective stiffness were under-predicted in all cases; however, measured direct and effective damping are reasonably well predicted. Impedance predictions improve with increasing pressure ratio. Comparisons of leakage correlate extremely well with predictions; worse case deviations never exceed 10 percent. Results show that leakage decreases as cell depth increases. Results also show that the exit temperature increases substantially with increasing rotational speed.

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