Numerical Comparison of Rotordynamic Characteristics for a Fully-Partitioned Pocket Damper Seal and a Labyrinth Seal With High Positive and Negative Inlet Preswirl

Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng

Pocket damper seals are used as replacements for labyrinth seals in high-pressure centrifugal compressors at the balance piston location or center seal location to enhance rotordynamic stability. A concern exists that this enhanced stability will be lost at high positive inlet preswirl. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for a fully-partitioned pocket damper seal (FPDS) and a labyrinth seal at high positive and negative inlet preswirl, using a proposed transient CFD method based on the multi-frequency elliptical orbit whirling model. The negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation at seal inlet. Both seals have identical diameter and sealing clearance. The full 3D concentric CFD model and mesh were built for the labyrinth seal and FPDS, respectively. The accuracy and availability of the present transient CFD numerical method were demonstrated with the experiment data of frequency-dependent rotordynamic coefficients of the labyrinth seal and FPDS at zero and high positive preswirl conditions. The numerical boundary conditions include two high positive preswirl, two high negative preswirl and a zero preswirl. Numerical results show that the effect of inlet preswirl on the direct force coefficients is weak, but the effect on the cross-coupling stiffness and effective damping is dramatic. Both two seals possess negative effective damping at lower excitation frequencies due to positive preswirl, and the crossover frequency of effective damping term increases with increasing positive preswirl. Negative preswirl produces negative cross-coupling stiffness and positive effective damping over the whole excitation frequency range. Increasing negative preswirl is a stabilizing factor for annular gas seals which results in a significant increase in the effective damping and a decrease in the crossover frequency. It is desirable to reduce the inlet preswirl to zero or even negative through applications of negative-swirl brakes and negative injection devices.

Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng

Pocket damper seals (PDSs) are used as replacements for labyrinth seals in high-pressure centrifugal compressors at the balance-piston location or center seal location to enhance rotordynamic stability. A concern exists that this enhanced stability will be lost at high positive inlet preswirl. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for a fully partitioned PDS (FPDS) and a labyrinth seal at high positive and negative inlet preswirl, using a proposed transient computational fluid dynamics (CFD) method based on the multifrequency elliptical orbit whirling model. The negative preswirl indicates a fluid swirl in a direction opposite to rotor rotation at seal inlet. Both seals have identical diameter and sealing clearance. The full 3D concentric CFD model and mesh were built for the labyrinth seal and FPDS, respectively. The accuracy and availability of the present transient CFD numerical method were demonstrated with the experiment data of frequency-dependent rotordynamic coefficients of the labyrinth seal and FPDS at zero and high positive preswirl conditions. The numerical boundary conditions include two high positive preswirl, two high negative preswirl, and a zero preswirl. Numerical results show that the effect of inlet preswirl on the direct force coefficients is weak, but the effect on the cross-coupling stiffness and effective damping is dramatic. Both seals possess negative effective damping at lower excitation frequencies due to positive preswirl, and the crossover frequency of effective damping term increases with increasing positive preswirl. Negative preswirl produces negative cross-coupling stiffness and positive effective damping over the whole excitation frequency range. Increasing negative preswirl is a stabilizing factor for annular gas seals, which results in a significant increase in the effective damping and a decrease in the crossover frequency. It is desirable to reduce the inlet preswirl to zero or even negative through applications of negative-swirl brakes and negative injection devices.


Author(s):  
Min Zhang ◽  
Dara W. Childs

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.


Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng

Effects of pressure ratio, rotational speed and inlet preswirl on the leakage and rotordynamic characteristics of a eight-bladed fully partitioned pocket damper seal (FPDS) were numerically investigated using proposed three-dimensional (3D) transient computational fluid dynamics (CFD) methods based on the multifrequency elliptical whirling orbit model. The accuracy and availability of the multifrequency elliptical whirling orbit model and the transient CFD numerical methods were demonstrated with the experimental data of frequency-dependent rotordynamic coefficients of the FPDS at two rotational speeds with high preswirl conditions. The frequency-dependent rotordynamic coefficients of the FPDS at three pressure ratios (three inlet pressures and three outlet pressures), three rotational speeds, three inlet preswirls were computed. The numerical results show that changes in outlet pressure have only weak effects on most rotordynamic coefficients. The direct damping and effective damping slightly increase in magnitude with decreasing outlet pressure at the frequency range of 20–200 Hz. The effect of inlet pressure is most prominent, and increasing inlet pressure for the FPDS results in a significant increase in the magnitudes of all rotordynamic coefficients. The magnitudes of the seal response force and effective damping are proportional to pressure drop through the seal. Increasing rotational speed and increasing inlet preswirl velocity both result in a significant decrease in the effective damping term due to the obvious increase in the magnitude of the destabilizing cross-coupling stiffness with increasing rotational speed or increasing preswirl velocity. The crossover frequency of effective damping significantly increases and the peak magnitude of effective damping decreases with increasing rotational speed or increasing preswirl velocity. The destabilizing cross-coupling stiffness is mainly caused by the circumferential swirl velocity generating from high rotational speed and inlet preswirl. Reducing swirl velocity (such as swirl brake) can greatly enhance the stabilizing capacity of the FPDS.


Author(s):  
Luis San Andrés ◽  
Tingcheng Wu

Labyrinth gas seals (LS) commonly used in turbomachines reduce secondary flow leakage. Conventional see-through labyrinth seal designs include either all Teeth-On-Stator (TOS) or all Teeth-On-Rotor (TOR). Experience shows that an interlocking labyrinth seal (ILS), with teeth on both stator and rotor, reduces gas leakage by up to 30% compared to the conventional see-through designs. However, field data for ILS rotordynamic characteristics is still vague and scarce in the literature. This work presents flow predictions for an ILS and a TOS LS, both seals share identical design features, namely radial clearance Cr = 0.2 mm, rotor diameter D = 150 mm, tooth pitch Li = 3.75 mm, and tooth height B = 3 mm. Air enters the seal at supply pressure Pin = 3.8, 6.9 bar (absolute) and temperature of 25 °C. The ratio of gas exit pressure to supply pressure ranges from 0.5 to 0.8, and the rotor speed is fixed at 10 krpm (surface speed of 79 m/s). The analysis implements a computational fluid dynamics (CFD) method with a multi-frequency-orbit rotor whirl model. The CFD predicted mass flow rate for the ILS is ∼21% lower than that of the TOS LS, thus making the ILS a more efficient choice. Integration of the dynamic pressure fields in the seal cavities, obtained for excitation frequency (ω) ranging from 12% to 168% of rotor speed (sub and super synchronous whirl), allows an accurate estimation of the seal dynamic force coefficients. For all the considered operating conditions, at low frequency range the TOS LS shows a negative direct stiffness (K < 0), frequency independent; whereas the ILS has K > 0 that increases with both frequency and supply pressure. For both seals, the magnitude of K decreases when the exit pressure/inlet pressure ratio increases. On the other hand, the cross-coupled stiffness (k) from both seals is frequency dependent, its magnitude increases with gas supply pressure, and the k for the ILS is more sensitive to a change in the exit/inlet pressure ratio. Notably, k turns negative for subsynchronous frequencies below rotor speed (Ω) for both the TOS LS and ILS. The direct damping (C) for the TOS LS remains constant for ω > ½ Ω and has a larger magnitude than the damping for the ILS over the frequency range up to 1.5Ω. An increase in exit/inlet pressure ratio decreases the direct damping for both seals. The effective damping coefficient, Ceff = (C-k/ω) whenever positive aids to damp vibrations, whereas Ceff < 0 is a potential source for an instability. For frequencies ω /Ω < 1.3, Ceff for the TOS LS is higher in magnitude than that for the ILS. From a rotordynamics point of view, the ILS is not a sound selection albeit it reduces leakage. Comparison of the CFD predicted force coefficients against those from a bulk flow model demonstrate the later simple model delivers poor results, often contradictory and largely indifferent to the type of seal, ILS or TOS LS. In addition, CFD model predictions are benchmarked against experimental dynamic force coefficients for two TOS LSs published by Ertas et al. (2012) and Vannini et al. (2014).


Author(s):  
Luis San Andre´s

As oil fields deplete, in particular in deep sea reservoirs, pump and compression systems work under more strenuous conditions with gas in liquid and liquid in gas mixtures, mostly inhomogeneous. Off-design operation affects system overall efficiency and reliability, including penalties in leakage and rotordynamic performance of secondary flow components, namely seals. The paper details a bulk-flow model for annular damper seals operating with gas in liquid mixtures. The analysis encompasses all-liquid and all-gas seals, as well as seals lubricated with homogenous (bubbly) mixtures, and predicts the static and dynamic force response of mixture lubricated seals; namely: leakage, power loss, reaction forces and rotordynamic force coefficients, etc., as a function of the mixture volume fraction (βS), supply and discharge pressures, rotor speed, whirl frequency, etc. A seal example with a Nitrogen gas mixed with light oil is analyzed. The large pressure drop (70 bar) causes a large expansion of the gas within the seal even for (very) small gas volume fractions (βS). Predictions show leakage and power loss decrease as β → 1; albeit at low βS (<0.3) (re)laminarization of the flow and an apparent increase in mixture viscosity, produce a hump in power loss. Cross-coupled stiffnesses and direct damping coefficients decrease steadily with increases in the gas volume fraction; however some anomalies are apparent when the flow turns laminar. Mixture lubricated seals show frequency dependent force coefficients. The equivalent damping decreases above and below βS∼0.10. The direct stiffness coefficients show atypical behavior: a low βS = 0.1 produces stiffness hardening as the excitation frequency increases. Recall that an all liquid seal has a dynamic stiffness softening as frequency increases due to the apparent fluid mass. The predictions call for an experimental program to quantify the static and dynamic forced performance of annular seals operating with (bubbly) mixtures and to validate the current predictive model results.


1999 ◽  
Vol 121 (4) ◽  
pp. 853-861 ◽  
Author(s):  
Nicole Zirkelback ◽  
Luis San Andre´s

An analysis for compressible fluid spiral groove thrust bearings (SGTBs) and face seals (SGFSs) is presented. Zeroth- and first-order equations rendering the static and dynamic performance of SGFSs, respectively, are solved using the finite element method with a successive approximation scheme. Comparison of the present isothermal compressible fluid model for static and dynamic SGTB and SGFS performance validates previous narrow groove theory, finite difference, and finite element analyses. A discussion follows to indicate the importance of using a small number of grooves to prevent instabilities from negative damping in SGTBs and SGFSs when pressurization is lost. Force coefficients are shown to reach asymptotic limits as the axial excitation frequency increases.


Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng

Effects of pressure ratio, rotational speed and inlet preswirl on the leakage and rotordynamic characteristics of a eight-bladed fully-partitioned pocket damper seal (FPDS) were numerically investigated using proposed 3D transient CFD methods based on the multi-frequency elliptical whirling orbit model. The accuracy and availability of the multi-frequency elliptical whirling orbit model and the transient CFD numerical methods were demonstrated with the experimental data of frequency-dependent rotordynamic coefficients of the FPDS at two rotational speeds with high preswirl conditions. The frequency-dependent rotordynamic coefficients of the FPDS at three pressure ratios (three inlet pressures and three outlet pressures), three rotational speeds, three inlet preswirls were computed. The numerical results show that changes in outlet pressure have only weak effects on most rotordynamic coefficients. The direct damping and effective damping slightly increase in magnitude with decreasing outlet pressure at the frequency range of 20–200Hz. The effect of inlet pressure is most prominent, and increasing inlet pressure for the FPDS results in a significant increase in the magnitudes of all rotordynamic coefficients. The magnitudes of the seal response force and effective damping are proportional to pressure drop through the seal. Increasing rotational speed and increasing inlet preswirl velocity both result in a significant decrease in the effective damping term due to the obvious increase in the magnitude of the destabilizing cross-coupling stiffness with increasing rotational speed or increasing preswirl velocity. The crossover frequency of effective damping significantly increases and the peak magnitude of effective damping decreases with increasing rotational speed or increasing preswirl velocity. The destabilizing cross-coupling stiffness is mainly caused by the circumferential swirl velocity generating from high rotational speed and inlet preswirl. Reducing swirl velocity (such as swirl brake) can greatly enhance the stabilizing capacity of the FPDS.


Author(s):  
Tingcheng Wu ◽  
Luis San Andrés

Labyrinth gas seals (LSs) commonly used in turbomachines reduce secondary flow leakage. Conventional see-through labyrinth seal designs include either all teeth-on-stator (TOS) or all teeth-on-rotor (TOR). Experience shows that an interlocking labyrinth seal (ILS), with teeth on both stator and rotor, reduces gas leakage by up to 30% compared to the conventional see-through designs. However, field data for ILS rotordynamic characteristics are still vague and scarce in the literature. This work presents flow predictions for an ILS and a TOS LS, both seals share identical design features, namely radial clearance Cr = 0.2 mm, rotor diameter D = 150 mm, tooth pitch Li = 3.75 mm, and tooth height B = 3 mm. Air enters the seal at supply pressure Pin = 3.8, 6.9 bar (absolute) and temperature of 25 °C. The ratio of gas exit pressure to supply pressure ranges from 0.5 to 0.8, and the rotor speed is fixed at 10 krpm (surface speed of 79 m/s). The analysis implements a computational fluid dynamics (CFD) method with a multi-frequency-orbit rotor whirl model. The CFD predicted mass flow rate for the ILS is ∼ 21% lower than that of the TOS LS, thus making the ILS a more efficient choice. Integration of the dynamic pressure fields in the seal cavities, obtained for excitation frequency (ω) ranging from 12% to 168% of rotor speed (sub and super synchronous whirl), allows an accurate estimation of the seal dynamic force coefficients. For all the considered operating conditions, at low frequency range, the TOS LS shows a negative direct stiffness (K < 0), frequency independent; whereas the ILS has K > 0 that increases with both frequency and supply pressure. For both seals, the magnitude of K decreases when the exit pressure/inlet pressure ratio increases. On the other hand, the cross-coupled stiffness (k) from both seals is frequency dependent, its magnitude increases with gas supply pressure, and k for the ILS is more sensitive to a change in the exit/inlet pressure ratio. Notably, k turns negative for subsynchronous frequencies below rotor speed (Ω) for both the TOS LS and the ILS. The direct damping (C) for the TOS LS remains constant for ω > ½ Ω and has a larger magnitude than the damping for the ILS over the frequency range up to 1.5 Ω. An increase in exit/inlet pressure ratio decreases the direct damping for both seals. The effective damping coefficient, Ceff = (C-k/ω), whenever positive aids to damp vibrations, whereas Ceff < 0 is a potential source for an instability. For frequencies ω/Ω < 1.3, Ceff for the TOS LS is higher in magnitude than that for the ILS. From a rotordynamics point of view, the ILS is not a sound selection albeit it reduces leakage. Comparison of the CFD predicted force coefficients against those from a bulk flow model demonstrates that the later simple model delivers poor results, often contradictory and largely indifferent to the type of seal, ILS or TOS LS. In addition, CFD model predictions are benchmarked against experimental dynamic force coefficients for two TOS LSs published by Ertas et al. (2012, “Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbines Power, 134(4), pp. 04250301–04250312) and Vannini et al. (2014, “Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data,” ASME J. Eng. Gas Turbines Power, 136(2), pp. 022501–022509.)


Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration. To improve the annular seal behavior and increase rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique and the multi-frequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of non-contact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth seal (LABY) and a fully-partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance and axial length. The accuracy and availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVF) of 0%, 2%, 5% and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15 000 rpm and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and fourteen subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.


Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li

The modern compressor operation is challenged by the liquid presence in wet gas operating conditions. The liquid phase may affect the compressor stability by partially flooding the internal annular gas seals and inducing subsynchronous vibration (SSV). To improve the annular seal behavior and increase the rotor stability, high-precision results of leakage flow rates and rotordynamic force coefficients are needed for annular gas seals in wet gas conditions. In order to better understand the leakage and rotordynamic characteristics of the annular gas seal in wet gas conditions, a 3D transient CFD-based perturbation method was proposed for computations of leakage flow rates and rotordynamic force coefficients of annular gas seals with liquid phase in main gas phase, based on inhomogeneous Eulerian-Eulerian multiphase flow model, mesh deformation technique, and the multifrequency rotor whirling orbit model. Numerical results of frequency-dependent rotordynamic force coefficients and leakage flow rates were presented and compared for three types of noncontact annular gas seals, which include a smooth plain annular seal (SPAS), a labyrinth (LABY) seal, and a fully partitioned pocket damper seal (FPDS). These three seals were designed to have the identical rotor diameter, sealing clearance, and axial length. The accuracy and the availability of the present transient CFD numerical method were demonstrated with the experiment data of leakage flow rates and frequency-dependent rotordynamic force coefficients of the smooth plain seal with four inlet liquid volume fractions (LVFs) of 0%, 2%, 5%, and 8%. Steady and transient numerical simulations were conducted at inlet air pressure of 62.1 bar, pressure ratio of 0.5, rotational speed of 15,000 rpm, and inlet preswirl ratio of 0.3 for four inlet LVFs varying from 0% to 8% and 14 subsynchronous and synchronous whirling frequencies up to 280 Hz. The numerical results show that the inlet liquid phase has a significant influence on the leakage and rotordynamic coefficients for all three types of annular gas seals. The mixture leakage flow rate increases with the increasing inlet LVF, combining the decreasing gas-phase and linearly increasing liquid-phase leakage flow rates. The smooth plain seal leaks the most gas phase and liquid phase, followed by the pocket damper seal (PDS) and then the labyrinth seal. Increasing inlet LVF significantly decreases the direct stiffness and slightly increases the effective damping of the smooth plain seal. The labyrinth seal possesses evident negative direct stiffness and shows a noticeable decreasing effective damping with the increasing inlet LVF at the subsynchronous frequency range. Increasing inlet LVF obviously increases all the force coefficients of the pocket damper seal including the positive effective damping. From a rotordynamic viewpoint, the FPDS possesses a better liquid tolerant capability and so is a better sealing scheme for the balance piston seals and center seals of the centrifugal compressor in wet gas operating condition.


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