Clearance Effects on Rotordynamic Performance of a Long Smooth Seal With Two-Phase, Mainly-Air Mixtures

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs ◽  
Dung L. Tran ◽  
Hari Shrestha
Keyword(s):  
Gas Turbines ◽  
Volume Fraction ◽  
Dynamic Stiffness ◽  
Test Fluid ◽  
Radial Clearance ◽  
Liquid Volume ◽  
Test Results ◽  
Stiffness Coefficients ◽  
Frequency Independent ◽  
The Impact

This paper experimentally studies the effects of changing radial clearance Cr on the performance of a long (length-to-diameter ratio L/D = 0.65) smooth seal under mainly-air (wet-gas) conditions. The test fluid is a mixture of air and silicone oil. Tests are conducted with Cr = 0.188, 0.163, and 0.140 mm, inlet pressure Pi = 62.1 bars, exit pressure Pe = 31 bars, inlet liquid volume fraction LVF = 0%, 2%, 5%, and 8%, and shaft speed ω = 10, 15, and 20 krpm. The seal's complex dynamic stiffness coefficients Hij are measured. The real parts of Hij cannot be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, frequency-dependent direct KΩ and cross-coupled kΩ stiffness coefficients are used. The imaginary parts of direct Hij produce frequency-independent direct damping C. Test results show that, for all pure- and mainly-air conditions, decreasing Cr decreases (as expected) the leakage mass flow rate m˙. Under mainly-air conditions, decreasing Cr decreases KΩ. This outcome is contrary to the test results at pure-air conditions, where KΩ increases as Cr decreases. Since an unstable centrifugal compressor rotor may precess at approximately 0.5ω, the effective damping Ceff at about 0.5ω is used as an indicator of the impact a seal would have on its associated compressor. For pure-air conditions, when Ω ≈ 0.5ω, decreasing Cr increases Ceff and makes the seal more stabilizing. This trend continues after the oil is added. A bulk-flow model developed by San Andrés (2011, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503) produces predictions to compare with test results. m˙ predictions correlate with measurements. Under pure-air conditions, the model correctly predicts the effects of changing Cr on KΩ and the Ceff value near 0.5ω. After the oil is added, as Cr decreases, predicted KΩ increases while measured KΩ decreases. Also, for mainly-air cases and Ω ≈ 0.5ω, decreasing Cr does not discernibly change predicted Ceff but increases the measured value.

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.

A Study on the Leakage and Rotordynamic Performance of a Long Labyrinth Seal Under Mainly Air Conditions

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Silicone Oil ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Labyrinth Seal ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
The Impact

Abstract This paper investigates the impact of liquid presence in air on the leakage and rotordynamic coefficients of a long (length-to-diameter ratio L/D = 0.747) teeth-on-stator labyrinth seal. The test fluid is a mixture of air and silicone oil (PSF-5cSt). Tests are carried out at inlet pressure Pi = 62.1 bars, three pressure ratios from 0.21 to 0.46, three speeds from 10 to 20 krpm, and six inlet liquid volume fractions (LVFs) from 0% to 15%. Complex dynamic-stiffness coefficients Hij are measured. The real parts of Hij are too frequency dependent to be fitted by frequency-independent stiffness and virtual-mass coefficients. Therefore, this paper presents frequency-dependent direct stiffness KΩ and cross-coupled stiffness kΩ. The imaginary parts of Hij produce frequency-independent direct damping C. Test results show that, under both pure- and mainly air conditions, the leakage mass flowrate m˙ of the test seal steadily increases as inlet LVF increases. KΩ is negative under all test conditions, and the magnitude of KΩ increases as inlet LVF increases, leading to a larger negative centering force on the associated compressor rotor. Under pure-air conditions, kΩ is a small negative value. Injecting oil into the air increases kΩ slightly and make the magnitude of kΩ closer to zero. Under mainly air conditions, increasing inlet LVF from 2% to 15% has little impact on kΩ. C normally increases as inlet LVF increases. The value of the effective damping Ceff = C − kΩ/Ω near 0.5ω is of significant interest to the system stability since an unstable centrifugal compressor may precess at approximately 0.5ω. Ω denotes the excitation frequency. The oil presence in the air has little impact on the value of Ceff near 0.5ω. Also, the liquid presence does not change the insensitiveness of m˙, KΩ, kΩ, C, and Ceff to change in ω; i.e., under both pure- and mainly air conditions, changes in ω has little impact on m˙, KΩ, kΩ, C, and Ceff.

Effects of Clearance on the Performance of a Labyrinth Seal Under Wet-Gas Conditions

2020 ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs ◽  
Dung L. Tran ◽  
Hari Shrestha
Keyword(s):  
Dynamic Stiffness ◽  
Labyrinth Seal ◽  
Test Fluid ◽  
Radial Clearance ◽  
Liquid Volume ◽  
Rotordynamic Coefficients ◽  
Whirling Motion ◽  
Wet Gas ◽  
Different Diameters ◽  
The Impact

Abstract The labyrinth seal is one of the most popular non-contact annular seals used in centrifugal compressors to improve machine efficiency by reducing the secondary flow leakage. Reducing the radial clearance Cr can effectively decrease the seal’s leakage and therefore increase the machine efficiency. However, reducing Cr can also introduce undesired effects on the machine’s vibration behaviors. This paper experimentally studies the impact of reducing Cr on the leakage and rotordynamic coefficients of a 16-tooth see-through labyrinth seal under wet-gas conditions. The test seal’s inner diameter is 89.256 mm. Two rotors with different diameters are used to obtain two radial clearances (0.102 mm and 0.178 mm). Tests are carried out at a supply pressure of 62 bars, three speeds from 10krpm to 20 krpm, three pressure ratios from 0.21 to 0.46, and six inlet liquid volume fractions (LVFs) from zero to 15%. The test fluid is a mixture comprised of air and silicon oil. Test results show that, for all pure-air and mainly-air conditions, decreasing Cr decreases (as expected) the test seal’s leakage mass flow rate. For all test cases, direct dynamic stiffness KΩ is negative, producing a negative centering force on the associated rotor. For inlet LVF ≤ 8%, the effects of decreasing Cr on KΩ are negligible. When inlet LVF = 12% and 15%, decreasing Cr increases KΩ (decreases the magnitude). In other words, when inlet LVF = 12% and 15%, decreasing Cr reduces the test seal’s negative centering force on the rotor, and would increase the critical speeds of the rotor. The value of the effective damping Ceff near 0.5ω represents the seal’s capability to suppress the rotor’s potential whirling motion at about 0.5ω. For all pure-air and mainly-air conditions, decreasing Cr generally increases the Ceff value near 0.5ω; i.e., decreasing Cr improves the test seal’s stabilizing capability against the rotor’s potential whirling motion at about 0.5ω.

Effects of Clearance on the Performance of a Labyrinth Seal Under Wet-Gas Conditions

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs ◽  
Dung L. Tran ◽  
Hari Shresth
Keyword(s):  
Dynamic Stiffness ◽  
Labyrinth Seal ◽  
Test Fluid ◽  
Radial Clearance ◽  
Liquid Volume ◽  
Rotordynamic Coefficients ◽  
Whirling Motion ◽  
Wet Gas ◽  
Different Diameters ◽  
The Impact

Abstract The labyrinth seal is one of the most popular noncontact annular seals used in centrifugal compressors to improve machine efficiency by reducing the secondary flow leakage. Reducing the radial clearance Cr can effectively decrease the seal's leakage and therefore increase the machine efficiency. However, reducing Cr can also introduce undesired effects on the machine's vibration behaviors. This paper experimentally studies the impact of reducing Cr on the leakage and rotordynamic coefficients of a 16-tooth see-through labyrinth seal under wet-gas conditions. The test seal's inner diameter is 89.256 mm. Two rotors with different diameters are used to obtain two radial clearances (0.102 mm and 0.178 mm). Tests are carried out at a supply pressure of 62 bars, three speeds from 10 krpm to 20 krpm, three pressure ratios from 0.21 to 0.46, and six inlet liquid volume fractions (LVFs) from zero to 15%. The test fluid is a mixture comprised of air and silicon oil. Test results show that, for all pure-air and mainly air conditions, decreasing Cr decreases (as expected) the test seal's leakage mass flowrate. For all test cases, direct dynamic stiffness KΩ is negative, producing a negative centering force on the associated rotor. For inlet LVF ≤ 8%, the effects of decreasing Cr on KΩ are negligible. When inlet LVF = 12% and 15%, decreasing Cr increases KΩ (decreases the magnitude). In other words, when inlet LVF = 12% and 15%, decreasing Cr reduces the test seal's negative centering force on the rotor, and would increase the critical speeds of the rotor. The value of the effective damping Ceff near 0.5ω represents the seal's capability to suppress the rotor's potential whirling motion at about 0.5ω. For all pure-air and mainly air conditions, decreasing Cr generally increases the Ceff value near 0.5ω; i.e., decreasing Cr improves the test seal's stabilizing capability against the rotor's potential whirling motion at about 0.5ω.

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.

A Study for Rotordynamic and Leakage Characteristics of a Long-Honeycomb Seal With Two-Phase, Mainly Air Mixtures

2019 ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Volume Fraction ◽  
Silicone Oil ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Liquid Volume Fraction ◽  
Honeycomb Seal ◽  
The Impact

Abstract This paper investigates the impact of the oil (silicone oil PSF-5cSt) presence in the air on the leakage and rotordynamic characteristics of a long-honeycomb seal with length-to-diameter ratio L/D = 0.748 and diameter D = 114.656 mm. Tests are carried out with inlet pressure Pi = 70.7 bars, pressure ratio PR = 0.35 and 0.25, inlet liquid volume fraction LVF = 0%, 3.5%, and 7%, and shaft speed ω = 10, 15, and 20 krpm. During the tests, the seal is centered. Test results show that leakage mass flow rate ṁ increases (as expected) as inlet LVF increases. Increasing inlet LVF makes direct stiffness K increase more rapidly with increasing excitation frequency Ω. Increasing inlet LVF has a negligible effect on K at low Ω values, but increases K at high Ω values. The value of effective damping Ceff at about 0.5ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5ω. Increasing inlet LVF increases the value of Ceff at about 0.5ω, reducing the possibility of sub-synchronous vibrations SSVs at about 0.5ω. San Andrés’s model is used to produce predictions. The model assumes that the test fluid in the seal clearance is an isothermal-homogenous mixture. The model adequately predicts ṁ, K, and the value of Ceff at about 0.5ω.

A Study for Rotordynamic and Leakage Characteristics of a Long-Honeycomb Seal With Two-Phase, Mainly Air Mixtures

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs
Keyword(s):  
Volume Fraction ◽  
Silicone Oil ◽  
Pressure Ratio ◽  
Excitation Frequency ◽  
System Stability ◽  
Test Fluid ◽  
Liquid Volume ◽  
Liquid Volume Fraction ◽  
Honeycomb Seal ◽  
The Impact

Abstract This paper investigates the impact of the oil (silicone oil PSF-5cSt) presence in the air on the leakage and rotordynamic characteristics of a long-honeycomb seal with length-to-diameter ratio L/D = 0.748 and diameter D = 114.656 mm. Tests are carried out with inlet pressure Pi = 70.7 bars, pressure ratio (PR) = 0.35 and 0.25, inlet liquid volume fraction (LVF) = 0%, 3.5%, and 7%, and shaft speed ω = 10, 15, and 20 krpm. During the tests, the seal is centered. Test results show that leakage mass flow rate m˙ increases (as expected) as inlet LVF increases. Increasing inlet LVF makes direct stiffness K increase more rapidly with increasing excitation frequency Ω. Increasing inlet LVF has a negligible effect on K at low Ω values, but increases K at high Ω values. The value of effective damping Ceff at about 0.5ω is an indicator to the system stability since an unstable centrifugal compressor rotor can precess at about 0.5ω. Increasing inlet LVF increases the value of Ceff at about 0.5ω, reducing the possibility of subsynchronous vibrations (SSVs) at about 0.5ω. San Andrés's model is used to produce predictions. The model assumes that the test fluid in the seal clearance is an isothermal-homogenous mixture. The model adequately predicts m˙, K, and the value of Ceff at about 0.5ω.

Test Results for the Static and Rotordynamic Characteristics of a Long (L/D = 0.75) Smooth Seal in Two-Phase (Mainly Gas) Conditions With a 62-Bar Inlet Pressure

2020 ◽  
Author(s):  
Dung L. Tran ◽  
Dara W. Childs ◽  
Hari Shrestha ◽  
Min Zhang
Keyword(s):  
Dynamic Characteristics ◽  
Gas Turbines ◽  
Flow Model ◽  
Dynamic Stiffness ◽  
Bulk Flow ◽  
Liquid Volume ◽  
Test Results ◽  
Two Phase ◽  
Static And Dynamic Characteristics ◽  
San Andres

Abstract Recent multiphase-pump developments encountered several rotordynamic issues with smooth balance-piston seals, creating a need to better understand the performance of annular seals under multiphase-flow operation. This paper presents measurements of static and dynamic characteristics of a long smooth seal (L/D = 0.75, D = 114.686 mm, and Cr = 0.200 mm) operating under pure- and mainly air condition in which air is mixed with silicone oil (PSF-5cSt). Tests are performed at a supply pressure of 62.1 bars-a, three rotation speeds (5, 10, 15 krpm), three pressure ratios (PRs) (0.6, 0.5, 0.4), for a range of inlet liquid volume fraction (LVFi) from 0% to 8%. The results are then compared to: (1) the previous test reported by Zhang et al. (2017, “Experimental Study of the Static and Dynamic Characteristics of a Long Smooth Seal with Two-Phase, Mainly-air Mixtures,” J. Eng. Gas Turbines Power, 139(12), p. 122504) with similar testing condition but a different seal geometry (L/D = 0.65, D = 89.306 mm, and Cr = 0.188 mm) and (2) the predictions from a bulk-flow model developed by San Andrés (2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbines Power, 134(2), p. 022503). Results show a significant increase of direct dynamic stiffness KΩ as LVFi increases, especially at low PR. Test results reported by Zhang et al. (2017) has an opposite tendency of KΩ as an impact of increasing LVFi. Concerning cross-coupled dynamic stiffness kΩ and cross-coupled damping c, the results from Zhang et al. (2017) and the present results agree to the effects of changing speed, PR, and LVFi under pure- and mainly air conditions. As LVFi increases, direct damping C increases while test results reported by Zhang et al. (2017) showed no significant increase. Except for the direct dynamic stiffness and the impact of changing LVFi on the cross-coupled dynamic stiffness, the bulk-flow model of San Andrés (2012) predicts decently the tendencies and magnitudes of the rotordynamic coefficients.

Rotordynamic Coefficients Measurements Versus Predictions for a High Speed Flexure-Pivot Tilting-Pad Bearing (Load-Between-Pad Configuration)

2005 ◽  
Author(s):  
Adnan Al-Ghasem ◽  
Dara Childs
Keyword(s):  
Dynamic Stiffness ◽  
Added Mass ◽  
Bulk Flow ◽  
Navier Stokes ◽  
Radial Clearance ◽  
Stiffness Coefficients ◽  
Tilting Pad ◽  
Model Predictions ◽  
Frequency Independent ◽  
Stiffness And Damping

Experimental dynamic force coefficients are presented for a flexure-pivot-tilting-pad (FPTP), bearing in load-between-pad (LBP) configuration for a range of rotor speeds and bearing unit loadings. The bearing has the following design parameters: 4 pads with pad arc angle 72° and 50% pivot offset, pad axial length 0.0762 m (3 in), pad radial clearance 0.254 mm (0.010 in), bearing radial clearance 0.1905 mm (0.0075 in), preload 0.25 and shaft nominal diameter of 116.84 mm (4.600 in). Measured dynamic coefficients have been compared with theoretical predictions using an isothermal analysis for a bulk-flow Navier-Stokes model. Predictions from two models — the Reynolds equation and a bulk-flow Navier-Stokes (NS) equation model are compared with experimental, complex dynamic stiffness coefficients (direct and cross-coupled) and show the following results: (i) The real part of the direct dynamic-stiffness coefficients is strongly frequency dependent because of pad inertia, support flexibility, and the effect of fluid inertia. This frequency dependency can be accurately modeled for by adding a direct added mass term to the conventional stiffness/damping matrix model. (ii) Both models underpredict the identified added-mass coefficient (∼32 kg), but the bulk-flow NS equations predictions are modestly closer. (iii) The imaginary part of the direct dynamic-stiffness coefficient (leading to direct damping) is a largely linear function of excitation frequency, leading to a constant (frequency independent) direct damping model. (iv) The real part of the cross-coupled dynamic-stiffness coefficients shows larger destabilizing forces than predicted by either model. The direct stiffness and damping coefficients increase with load, while increasing and decreasing with rotor speed, respectively. As expected, a small whirl frequency ratio (WFR) was found of about 0.15, and it decreases with increasing load and increases with increasing speed. The two model predictions for WFR are comparable and both underpredict the measured WFR values. Rotors supported by either conventional tilting PAD bearings or FPTP bearings are customarily modeled by frequency-dependent stiffness and damping matrices, necessitating an iterative calculation for rotordynamic stability. The present results show that adding a constant mass matrix to the FPTP bearing model produces an accurate frequency-independent model that eliminates the need for iterative rotordynamic stability calculations.

Experimental Study of the Leakage and Rotordynamic Coefficients of a Long Smooth Seal With Two-Phase, Mainly-Oil Mixtures

2018 ◽  
Author(s):  
Min Zhang ◽  
Dara W. Childs ◽  
James E. Mclean ◽  
Dung L. Tran ◽  
Hari Shrestha
Keyword(s):  
Natural Frequency ◽  
Volume Fraction ◽  
Dynamic Stiffness ◽  
Test Fluid ◽  
Inlet Temperature ◽  
Test Results ◽  
Virtual Mass ◽  
Annular Seal ◽  
Oil Flow ◽  
Oil Mixtures

Tests are conducted on a newly developed 2-phase annular seal stand (2PASS) at the Turbomachinery Laboratory of Texas A&M University. The test fluid is a mixture of silicone oil (PSF-5cSt) and air. Two spargers are used to produce mainly-oil mixtures by injecting air bubbles into the oil flow. The test seal is a smooth annular seal with inner diameter D = 89.306 mm, length-to-diameter ratio L/D = 0.65, and radial clearance Cr = 0.188 mm. Tests are performed with inlet gas-volume-fraction GVF = 0%, 2%, 4%, 6%, and 10%, rotor speed ω = 5, 7.5, 10, and 15 krpm, inlet temperature Ti = 39.4 °C, exit pressure Pe = 6.9 bars, and pressure drop PD = 31, 37.9, and 48.3 bars. The test seal is centered, and there is no intentional prerotation of the fluid at the seal inlet. The complex dynamic stiffness coefficients of the test seal are measured and fitted by the frequency-independent stiffness Kij, damping Cij, and virtual-mass Mij coefficients. Test results show that adding air into the oil flow does not change the seal’s mass flow leakage ṁ discernibly but significantly impacts the seal’s rotordynamic characteristics. Some planned 5 krpm cases with low inlet GVFs at PD = 31 and 37.9 bars are not accomplished due to stator instabilities, which are likely caused by negative stiffness of the test seals. For ω = 5 krpm when PD = 31 and 37.9 bars, direct stiffness K decreases from positive to negative as inlet GVF decreases. For all PDs and speeds, K increases as inlet GVF increases from zero to 10% except for 6% ≤ inlet GVF ≤ 10% when PD = 48.3 bars, where K decreases as inlet GVF increases. The K increment will increase a pump rotor’s natural frequency and critical speed. Increasing the rotor’s natural frequency would also increase the onset speed of instability (OSI) and improve the stability of the rotor. Adding air into the oil flow has little effect on cross-coupled stiffness k and direct damping C. Increasing inlet GVF has negligible effects on direct virtualmass M when ω ≤ 10 krpm and PD ≤ 37.9 bars, but generally decreases M when ω = 15 krpm or PD = 48.3 bars. Increasing inlet GVF has little effect on effective damping Ceff and does not change the seal’s resultant stabilizing force discernibly. Ceff = C − k/ω + mqω, where mq is the cross-coupled virtual-mass. Test results are compared to predictions from San Andrés’s [1] model. The model is based on a bulk-flow model and the Moody friction formula assuming that the liquid-gas mixture is isothermal and homogenous. The model reasonably predicts ṁ, C, and Ceff. All predicted K values are positive, while measured K values are negative for some test cases. Predicted k values are close to measurements when ω = 5 krpm and are larger than test results when 7.5 ≤ ω ≤ 15 krpm. M predictions are smaller than measurements, and the discrepancy between predicted and measured M values generally increases as inlet GVF increases.

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