Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based On the Applicability Analysis of Leakage Models Using Bulk-Flow Method

2021 ◽  
Author(s):  
Tianhao Wang ◽  
Zhigang LI ◽  
Jun LI
Keyword(s):  
Rotational Speed ◽  
Control Volume ◽  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Inlet Pressure ◽  
Flow Method ◽  
Leakage Model ◽  
Outlet Pressure ◽  
Prediction Approach

Abstract The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial for the analysis of the fluid excitation rotordynamics of the labyrinth seal. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of 72 leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

Rotordynamic Characteristics of the Straight-Through Labyrinth Seal Based On the Applicability Analysis of Leakage Models Using Bulk-Flow Method

2021 ◽  
Author(s):  
Tianhao Wang ◽  
Zhigang Li ◽  
Jun Li
Keyword(s):  
Rotational Speed ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Inlet Pressure ◽  
Leakage Flow ◽  
Flow Method ◽  
Leakage Model ◽  
Outlet Pressure ◽  
Prediction Approach

Abstract Labyrinth seals are widely applied in the turbomachinery to control the leakage flow through the clearance between the stationary and rotating components. The fluid excitation induced by the labyrinth seal would deteriorate the stability of turbomachinery shaft. Developing an accurate and rapid prediction approach is crucial for the analysis of the fluid excitation rotordynamics of the labyrinth seal. The objective of this study is to analyze the applicability of leakage models using Bulk-Flow method and investigate the factors affecting the rotordynamic characteristics of the labyrinth seal. An elliptical orbit for rotor whirling was assumed in the one-control-volume Bulk-Flow model considering an isentropic process to predict the frequency-dependent rotordynamic coefficients of the labyrinth seal. The optimal leakage model was determined by comprehensively analyzing the applicability of 72 leakage models. Employing the optimal leakage model in the Bulk-Flow method, the effects of sealing clearance, pressure ratio, preswirl ratio and rotational speed on the rotordynamic characteristics of the labyrinth seal were investigated. The conclusions show that the Bulk-Flow method has an average prediction error of around 10% for the leakage flow rate, cross-coupled stiffness and direct damping when equipped with the optimal leakage model. Increasing preswirl ratio has a significantly destabilizing effect on the rotor stability, while the influence of increasing rotational speed is strongly related to preswirl direction. The effective damping of the labyrinth seal is sensitive to the inlet pressure, but insensitive to the outlet pressure and sealing clearance. The crossover frequency is almost impervious to the inlet pressure, outlet pressure and sealing clearance.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals—Part I: Effects of Pressure Ratio, Rotational Speed, and Inlet Preswirl

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Rotational Speed ◽  
Pressure Ratio ◽  
Cross Coupling ◽  
Inlet Pressure ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Outlet Pressure ◽  
Swirl Velocity ◽  
Coupling Stiffness ◽  
Orbit Model

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.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals: Part I — Effects of Pressure Ratio, Rotational Speed and Inlet Preswirl

2014 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Rotational Speed ◽  
Pressure Ratio ◽  
Cross Coupling ◽  
Inlet Pressure ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Outlet Pressure ◽  
Swirl Velocity ◽  
Coupling Stiffness ◽  
Orbit Model

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.

Measured Comparison of Leakage and Rotordynamic Characteristics for a Slanted-Tooth and a Straight-Tooth Labyrinth Seal

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Naitik J. Mehta ◽  
Dara W. Childs
Keyword(s):  
Inclination Angle ◽  
Flow Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Inlet Pressure ◽  
Radial Clearance ◽  
Rotordynamic Coefficients ◽  
Seal Design ◽  
Number Of Teeth

Measured results are presented to compare rotordynamic coefficients and leakage of a slanted-tooth labyrinth seal and a straight-tooth labyrinth seal. Both seals had identical pitch, depth, and number of teeth. The teeth inclination angle of the teeth on the slanted-tooth labyrinth was 65 deg from the normal axis. Experiments were carried out at an inlet pressure of 70 bar-a (1015 psi-a), pressure ratios of 0.4, 0.5, and 0.6, rotor speeds of 10.2, 15.35, and 20.2 krpm, and a radial clearance of 0.2 mm (8 mils). One zero and two positive inlet preswirl ratios were used. The results show only minute difference in the rotordynamic coefficients between the two seals. The slanted-tooth labyrinth seal consistently leaked approximately 10% less at all conditions. Predictions were made using a one control volume bulk-flow model (1CVM) which was developed for a straight-tooth labyrinth seal design. 1CVM under-predicted the rotordynamic coefficients and the leakage.

Measured Comparison of Leakage and Rotordynamic Characteristics for a Slanted-Tooth and a Straight-Tooth Labyrinth Seal

2013 ◽  
Author(s):  
Naitik J. Mehta ◽  
Dara W. Childs
Keyword(s):  
Inclination Angle ◽  
Flow Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Bulk Flow ◽  
Inlet Pressure ◽  
Radial Clearance ◽  
Rotordynamic Coefficients ◽  
Seal Design ◽  
Number Of Teeth

Measured results are presented to compare rotordynamic coefficients and leakage of a slanted-tooth labyrinth seal and a straight-tooth labyrinth seal. Both seals had identical pitch, depth, and number of teeth. The teeth inclination angle of the teeth on the slanted-tooth labyrinth was 65° from the normal axis. Experiments were carried out at an inlet pressure of 70 bar-a (1015 psi-a), pressure ratios of 0.4, 0.5, and 0.6, rotor speeds of 10.2, 15.35, and 20.2 krpm, and a radial clearance of 0.2 mm (8 mils). One zero and two positive inlet preswirl ratios were used. The results show only minute difference in the rotordynamic coefficients between the two seals. The slanted-tooth labyrinth seal consistently leaked approximately 10% less at all conditions. Predictions were made using a one control volume bulk-flow model (1CVM) which was developed for a straight-tooth labyrinth seal design. 1CVM under-predicted the rotordynamic coefficients and the leakage.

Leakage and Cavity Pressures in an Interlocking Labyrinth Gas Seal: Measurements vs. Predictions

2019 ◽  
Author(s):  
Luis San Andrés ◽  
Tingcheng Wu ◽  
Jose Barajas-Rivera ◽  
Jiaxin Zhang ◽  
Rimpei Kawashita
Keyword(s):  
Mass Flow ◽  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Secondary Flows ◽  
Tip Clearance ◽  
Inlet Pressure ◽  
Steam Turbines ◽  
Rotor Speed ◽  
Labyrinth Seals ◽  
Gas Seals

Abstract Gas labyrinth seals (LS) restrict secondary flows (leakage) in turbomachinery and their impact on the efficiency and rotordynamic stability of high-pressure compressors and steam turbines can hardly be overstated. Amongst seal types, the interlocking labyrinth seal (ILS), having teeth on both the rotor and on the stator, is able to reduce leakage up to 30% compared to other LSs with either all teeth on the rotor or all teeth on the stator. This paper introduces a revamped facility to test gas seals for their rotordynamic performance and presents measurements of the leakage and cavity pressures in a five teeth ILS. The seal with overall length/diameter L/D = 0.3 and small tip clearance Cr/D = 0.00133 is supplied with air at T = 298 K and increasing inlet pressure Pin = 0.3 MPa ∼ 1.3 MPa, while the exit pressure/inlet pressure ratio PR = Pout/Pin is set to range from 0.3 to 0.8. The rotor speed varies from null to 10 krpm (79 m/s max. surface speed). During the tests, instrumentation records the seal mass flow (ṁ) and static pressure in each cavity. In parallel, a bulk-flow model (BFM) and a computational fluid dynamics (CFD) analysis predict the flow field and deliver the same performance characteristics, namely leakage and cavity pressures. Both measurements and predictions agree closely (within 5%) and demonstrate the seal mass flow rate is independent of rotor speed. A modified flow factor Φ¯=m.T/PinD1-PR2 characterizes best the seal mass flow with a unique magnitude for all pressure conditions, Pin and PR.

Effects of Pressure Ratio and Rotational Speed on Leakage Flow and Cavity Pressure in the Staggered Labyrinth Seal

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Xin Yan ◽  
Zhenping Feng
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Flow Coefficient ◽  
Leakage Flow ◽  
Cavity Pressure ◽  
Cavity Structure

Effects of pressure ratio and rotational speed on the leakage flow and cavity pressure characteristics of the rotating staggered labyrinth seal were investigated by means of experimental measurements and numerical simulations. The rotating seal test rig with turbine flowmeter and pressure measuring instruments was utilized to investigate the leakage flow of the staggered labyrinth seal at eight pressure ratios and five rotational speeds. The repeatability of the experimental data was demonstrated by three times measurements at different pressure ratios and fixed rotational speed. The three-dimensional Reynolds-averaged Navier–Stokes equations and standard k-ε turbulent model were also applied to study the leakage flow characteristics of the staggered labyrinth seal at the experimental conditions. The validation of the numerical approach was verified through comparison of the experimental data. The detailed flow field in the staggered labyrinth seal was illustrated according to the numerical simulations. The experimental and numerical results show that the leakage flow coefficient increases with increasing pressure ratio at the fixed rotational speed and is more sensitive to the smaller pressure ratio. The influence of rotational speed on the leakage flow coefficient is not obvious in the present rotational speed limitations. The cavity pressure coefficient in the staggered labyrinth seal decreases and is significantly influenced by the cavity structure along the flow direction.

Leakage and Dynamic Force Coefficients for Two Labyrinth Gas Seals: Teeth-on-Stator and Interlocking Teeth Configurations — A CFD Approach to Their Performance

2018 ◽  
Author(s):  
Luis San Andrés ◽  
Tingcheng Wu
Keyword(s):  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Inlet Pressure ◽  
Dynamic Force ◽  
Rotor Speed ◽  
Frequency Range ◽  
Force Coefficients ◽  
Supply Pressure ◽  
Exit Pressure ◽  
Gas Seals

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).

Sensitivity Analysis of the One-Control Volume Bulk-Flow Model for a 14 Teeth-on-Stator Straight-Through Labyrinth Seal

2017 ◽  
Author(s):  
Filippo Cangioli ◽  
Paolo Pennacchi ◽  
Giacomo Riboni ◽  
Giuseppe Vannini ◽  
Lorenzo Ciuchicchi ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Friction Factor ◽  
Flow Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Operating Conditions ◽  
Bulk Flow ◽  
Mathematical Treatment ◽  
Dynamic Coefficients ◽  
The One

Since the 80s, academic research in the rotordynamics field has developed mathematical treatment for the prediction of the dynamic coefficients of sealing components. Dealing with the straight-through labyrinth seal, Iwatsubo [1], at a first stage, and Childs [2], later on, have developed the one-control volume bulk flow model. The model allows evaluating the surrounding fluid forces acting on the rotor, analyzing the fluid dynamics within the seal: the continuity, circumferential momentum and energy equations are solved for each cavity. To consider axial fluid dynamics, correlations, aiming to estimate the leakage and the pressure distribution, are required. Several correlations have been proposed in the literature for the estimation of the leakage, of the kinetic energy carry-over coefficient (KE), of the discharge coefficient and of the friction factor. After decades of research in the field of seal dynamics, the bulk-flow model has been confirmed as the most popular code in the industries, however, it is not clear which is the best set of correlations for the prediction of seal dynamic coefficients. This paper allows identifying the most accurate combination of correlations to be implemented in the bulk-flow model. The correlations are related to: the leakage formula, the flow coefficient, the KE and the friction factor. Investigating the results of several models (32 models), which consider different sets of correlations, in comparison to the experimental data (performed by General Electric Oil & Gas), it is possible to observe the dependence, of the model correlations, on the operating conditions. The experimental results, performed using a 14 teeth-on-stator labyrinth seal, investigate several operating conditions of pressure drop.

Investigation on the Leakage Flow, Windage Heating and Swirl Development of Rotating Labyrinth Seal in a Compressor Stator Well

2016 ◽  
Author(s):  
Xiaozhi Kong ◽  
Gaowen Liu ◽  
Yuxin Liu ◽  
Qing Feng
Keyword(s):  
Mass Flow ◽  
Rotational Speed ◽  
Heat Dissipation ◽  
Pressure Ratio ◽  
Great Influence ◽  
Labyrinth Seal ◽  
Swirl Flow ◽  
Tip Clearance ◽  
Leakage Flow ◽  
Rotating Disc

What make the labyrinth seal in a compressor stator well different from the normal labyrinth seal are the inlet and outlet rotor-stator disc cavities. Due to the presence of rotating disc cavities, the windage heating and the swirl development are remarkable, which can have a great influence on the leakage characteristic. Besides, when compressor operates at different speeds, the rotor and stator grow differently owing to centrifugal expansion and thermal expansion. Hence the tip clearance which determines the leakage mass flow changes with the varying of rotational speed and temperature in the stator well. A rotating test rig with rotational speed 8100rpm and pressure ratio range 1.05∼1.3 was designed for the test of labyrinth seal in a compressor stator well. A cantilevered structure was used to entirely collect the mass flow for an accurate measurement. To know the working tip clearance precisely, the set up tip clearance was measured with plug gauges, while the radial displacements of rotating disc and stationary casing were measured separately with two high precision laser distance sensors. The total temperatures of airflow in the stator well were measured with thermocouples to analyze the proportion of windage heating among the inlet rotating disc cavity, outlet rotating disc cavity, and labyrinth seal segment. The disc and stator casing were manufactured with non-metallic materials to reduce heat dissipation. Furthermore, the circumferential velocity of the leakage flow was measured using probes to reveal the swirl development. Two-dimensional, axisymmetric swirl flow numerical simulations were carried out to provide insight into the flow field details, total temperature variation and swirl flow development in the stator well. The numerical results of discharge coefficient, windage heating and swirl ratio were compared with the experimental data. Of particular note is, the tip clearance of numerical model at a specific rotating speed was set to be the same with the actual working clearance which was measured in the experiment. The inlet and outlet parameters corresponded with the experimental conditions also.

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