Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Manish R. Thorat ◽  
Dara W. Childs
Keyword(s):  
Speed Of Sound ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Surface Velocity ◽  
Reduced Model ◽  
Running Speed ◽  
Frequency Dependent ◽  
Damping Coefficients ◽  
Rotor Surface ◽  
Stiffness And Damping

Prior one-control-volume (1CV) models for rotor-fluid interaction in labyrinth seals produce synchronously reduced (at running speed), frequency-independent stiffness and damping coefficients. The 1CV model, consisting of a leakage equation, a continuity equation, and a circumferential-momentum equation (for each cavity), was stated to be invalid for rotor surface speeds approaching the speed of sound. However, the present results show that while the 1CV fluid-mechanic model continues to be valid, the calculated rotordynamic coefficients become strongly dependent on the rotor’s precession frequency. A solution is developed for the reaction-force components for a range of precession frequencies, producing frequency-dependent stiffness and damping coefficients. They can be used to define a Laplace-domain transfer-function model for the reaction-force/rotor-motion components. Calculated results are presented for a simple Jeffcott rotor model acted on by a labyrinth seal. The model’s undamped natural frequency is 7.6 krpm. The fluid properties, seal radius Rs, and running speed ω cause the rotor surface velocity Rsω to equal the speed of sound c0 at ω=58 krpm. Calculated synchronous-response results due to imbalance coincide for the synchronously reduced and the frequency-dependent models. For an inlet preswirl ratio of 0.5, both models predict the same log-dec out to ω≈14.5 krpm. The synchronously reduced model predicts an onset speed of instability (OSI) at 10 krpm, but a return to stability at 48 krpm, with subsequent increases in log-dec out to 70 krpm. The frequency-dependent model predicts an OSI of 10 krpm and no return to stability out to 70 krpm. The frequency-dependent models predict small changes in the rotor’s damped natural frequencies. The synchronously reduced model predicts large changes. The stability-analysis results show that a frequency-dependent labyrinth seal model should be used if the rotor surface speed approaches a significant fraction of the speed of sound. For the present example, observable discrepancies arose when Rsω=0.26c0.

Predicted Rotordynamic Behavior of a Labyrinth Seal as Rotor Surface Speed Approaches Mach 1

2009 ◽  
Author(s):  
Manish R. Thorat ◽  
Dara W. Childs
Keyword(s):  
Speed Of Sound ◽  
Reaction Force ◽  
Labyrinth Seal ◽  
Surface Velocity ◽  
Reduced Model ◽  
Running Speed ◽  
Frequency Dependent ◽  
Damping Coefficients ◽  
Rotor Surface ◽  
Stiffness And Damping

Prior one-control-volume (1CV) models for rotor-fluid interaction in labyrinth seals produce synchronously-reduced (at running-speed), frequency-independent stiffness and damping coefficients. The 1CV model, consisting of a leakage equation, a continuity equation, and a circumferential-momentum equation (for each cavity) was stated to be invalid for rotor surface speeds approaching the speed of sound. However, the present results show that, while the 1CV fluid-mechanic model continues to be valid, the calculated rotordynamic coefficients become strongly frequency dependent. A solution is developed for the reaction-force components for a range of precession frequencies, producing frequency-dependent stiffness and damping coefficients. They can be used to define a Laplace-domain transfer-function model for the reaction-force/rotor-motion components. Calculated rotordynamic results are presented for a simple Jeffcott rotor acted on by a labyrinth seal. The seal radius Rs and running speed ω cause the rotor surface velocity Rsω to equal the speed of sound c0 at ω = 58 krpm. Calculated synchronous-response results due to imbalance coincide for the synchronously-reduced and the frequency-dependent models. For an inlet preswirl ratio of 0.5, both models predict the same log decs out to ω≈14.5 krpm. The synchronously-reduced model predicts an onset speed of instability (OSI) at 15 krpm, but a return to stability at 45 krpm, with subsequent increases in log dec out to 65 krpm. The frequency-dependent model predicts an OSI of 65 krpm. The frequency-dependent models predict small changes in the rotor’s damped natural frequencies. The synchronously-reduced model predicts large changes. The stability-analysis results show that a frequency-dependent labyrinth seal model should be used if the rotor surface speed approaches a significant fraction of the speed of sound. For the present example, observable discrepancies arose when Rsω = 0.26 c0.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

Segmentation Effects on Brush Seal Leakage and Rotordynamic Coefficients

2015 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Manuel Gaszner ◽  
Christos Georgakis ◽  
Paul Cooper
Keyword(s):  
Electrical Discharge ◽  
Electrical Discharge Machining ◽  
Labyrinth Seal ◽  
Performance Characteristics ◽  
Radial Clearance ◽  
Single Plane ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Stiffness And Damping

This paper studies the effect of brush seal segmentation on the seal performance characteristics. A brush-labyrinth sealing configuration arranged of one brush seal downstream and two labyrinth fins upstream is studied experimentally and theoretically. The studied brush seal is of welded design installed with zero cold radial clearance. The brush seal front and back rings as well as the bristle pack are segmented radially in a single plane using the electrical discharge machining technique. The segmentation procedure results in loss of bristles at the site of the cuts altering the leakage flow structure in the seal and its performance characteristics. Two test rigs are used to obtain leakage, as well as rotordynamic stiffness and damping coefficients of the seal at different pressure ratios. The CFD-based model is used to predict the seal performance and to study in detail local changes in the flow field due to the segmentation. A back-to-back comparison of the performance of non-segmented and segmented brush seals, as well as baseline labyrinth seal is provided. The obtained results demonstrate that the segmentation in general negatively affects the performance of the studied brush-labyrinth sealing configuration. However, the segmented brush seal shows increased direct damping coefficients.

scholarly journals Rotordynamic Coefficient and Leakage Test Results for Interlock and Tooth-on-Stator Labyrinth Seals

1988 ◽  
Author(s):  
Dara W. Childs ◽  
David A. Elrod ◽  
Keith Hale
Keyword(s):  
Labyrinth Seal ◽  
Damping Coefficient ◽  
Test Results ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Leakage Test ◽  
Stiffness And Damping ◽  
Rotordynamic Coefficient

Test results (leakage and rotordynamic coefficients) are presented for an interlock and tooth-on-stator labyrinth seals. Tests were carried out with air at speeds out to 16,000 cpm and supply pressures up to 7.5 bars. The rotordynamic coefficients consist of direct and cross-coupled stiffness and damping coefficients. Damping-coefficient data have not previously been presented for interlock seals. The test results support the following conclusions: (a) The interlock seal leaks substantially less than labyrinth seals. (b) Destabilizing forces are lower for the interlock seal. (c) The labyrinth seal has substantially greater direct damping values than the interlock seal. A complete rotordynamics analysis is needed to determine which type of seal would yield the best stability predictions for a given turbomachinery unit.

Experimental Rotordynamic Coefficient Results for: (a) A Labyrinth Seal With and Without Shunt Injection and (b) A Honeycomb Seal

1998 ◽  
Author(s):  
Elias A. Soto A. ◽  
Dara W. Childs
Keyword(s):  
Pressure Ratio ◽  
Injection Pressure ◽  
Labyrinth Seal ◽  
Surface Velocity ◽  
Labyrinth Seals ◽  
Honeycomb Seal ◽  
Radial Injection ◽  
Rotor Surface ◽  
Rotordynamic Coefficient ◽  
Better Than

Centrifugal compressors are increasingly required to operate at higher pressures, speeds, and fluid density. In these conditions, compressors are susceptible to rotordynamic instabilities. To remedy this situation, labyrinth seals have sometimes been modified by using shunt injection. In shunt injection, the gas is taken from the diffuser or discharge volute and injected into an upstream chamber of the balance-piston labyrinth seal. The injection direction can be radial or against rotation. This study contains the first measured rotordynamic data for labyrinth seals with shunt injection. A comparison has been made between conventional labyrinth seals, labyrinth seal with shunt injection (radial and against rotation), and a honeycomb seal. Labyrinth seals with injection against rotation are better able to control rotordynamic instabilities than labyrinth seals with radial injection; however, the leakage is slightly higher. The leakage comparison for all seals demonstrates that the honeycomb seal has the best flow control. Test data are presented for a top rotor surface velocity of 110 m/sec, a supply pressure of 13.7 bars, and IPr = 0.95 (injection pressure is 1.05 = 1/0.95 times the seal inlet pressure). For these conditions, and considering effective damping, the labyrinth seal with injection against rotation is better than the honeycomb seal when the pressure ratio across the seal PR<0.45. On the other hand, the honeycomb seal is better when PR>0.45. The effectiveness of the shunt-injection against rotation in developing effective damping is reduced with increasing rotor surface velocity.

Measured and Predicted Transfer Functions Between Rotor Motion and Pad Motion for a Rocker-Back Tilting-Pad Bearing in LOP Configuration

2011 ◽  
Author(s):  
Jason C. Wilkes
Keyword(s):  
Transfer Functions ◽  
Analytical Models ◽  
Single Frequency ◽  
Frequency Dependent ◽  
Damping Coefficients ◽  
Operating Region ◽  
Direct Measurements ◽  
Trailing Edges ◽  
Tilting Pad ◽  
Stiffness And Damping

Many researchers have compared predicted stiffness and damping coefficients for tilting-pad journal bearings (TPJBs) to measurements. Most have found that direct damping is consistently overpredicted. Continuing to test TBJBs in the same fashion is not likely to produce an explanation for the discrepancies between measured and predicted damping. Most analytical models for TPJBs are based on the assumption that explicit dependence on pad motion can be eliminated by assuming a solution for rotor motion such that the amplitude and phase of pad motions are predicted by rotor-pad transfer functions. Direct measurements of pad motion during test excitation are needed to produce measured transfer functions between rotor and pad motion, and a comparison between these measurements and predictions is needed to identify model discrepancies. A test setup was designed to fulfill these objectives. Motion probes were added to the loaded pad to obtain accurate measurement of pad radial and tangential motion, as well as tilt, yaw and pitch. For the remainder of this work, the loaded pad refers to the pad whose pivot sits on the static load line. Testing was performed primarily at low speeds and high loads, since this is the operating region for which predictions are most erroneous. Single frequency excitations were performed ranging from 10–350 Hz, producing rotor and pad motion, acceleration, and force vectors. This motion was used to determine frequency-dependent bearing impedances and rotor-pad transfer functions. A new pad perturbation model is proposed including the effects of pad angular, radial, and circumferential pad motion. This model was implemented in a Reynolds-based TPJB code to predict the frequency-dependent bearing impedances and rotor-pad transfer functions. These predictions are compared with measurements and discussed. Good agreement was found between the amplitude of the measured and predicted transfer functions concerning tilt and radial motions for low to moderate loads, but deviated in accuracy at the highest loaded case. Circumferential (sliding) pad motion was predicted and observed; however, the effect of this degree of freedom on dynamic bearing coefficients has not been quantitatively assessed. For the bearing investigated, radial motion accounted for more than 67% of total motion of the fluid-film height at the leading and trailing edges of the pad when operating at 4400 rpm under heavily loaded conditions. The measurements show that predicting TPJB stiffness and damping coefficients without accounting for pad pivot deformation will not produce satisfactory outcomes.

CFD Prediction and Test Results of Stiffness and Damping Coefficients for Brush-Labyrinth Gas Seals

2010 ◽  
Author(s):  
Alexander O. Pugachev ◽  
Martin Deckner
Keyword(s):  
Porous Medium ◽  
Three Dimensional ◽  
Great Influence ◽  
Dynamic Test ◽  
Labyrinth Seal ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Gas Seals ◽  
Stiffness And Damping

This paper presents ongoing investigations on calculation and measurement of rotordynamic coefficients for brush-labyrinth gas seals. The seals are tested on static and dynamic test rigs to measure leakage, pressure distribution, and seal specific forces. To predict seal performance a full three-dimensional eccentric CFD model is considered. Rotordynamic coefficients are calculated using the whirling rotor method. The bristle pack of the brush seal is modeled using the porous medium approach. The prediction results show some deviations in absolute values of stiffness and damping coefficients in comparison with the experimental values, but the trends are similar. Comparing with a staggered labyrinth seal, the brush seal improves rotordynamic characteristics in most cases. Position of the brush seal in sealing configuration has a great influence on the stiffness and damping coefficients, while leakage performance remains relatively unaffected. The capability of the brush seal model based on the porous medium approach to predict rotordynamic coefficients is discussed.

Application of Porous Materials to Annular Plain Seals: Part 2—Dynamic Characteristics

1990 ◽  
Vol 112 (4) ◽  
pp. 624-630 ◽  
Author(s):  
S. Kaneko
Keyword(s):  
Laminar Flow ◽  
Porous Materials ◽  
Dynamic Performance ◽  
Reaction Force ◽  
Mass Effect ◽  
Porous Matrix ◽  
Solid Surfaces ◽  
Damping Coefficients ◽  
Whirling Motion ◽  
Stiffness And Damping

For improving the dynamic performance of the annular plain seals employed in pumps, porous materials are applied to the seal surface by insertion into the inlet part of the seal. The linear stiffness and damping coefficients of the seal film are calculated in the laminar-flow regime, assuming the mass effect of the fluid to be negligibly small. Numerical results show that the annular plain seals with the porous materials have larger main stiffness terms and smaller cross-coupled stiffness terms and main damping terms than the conventional ones with the solid surfaces. This tendency is more marked with increasing the axial length of the porous matrix applied to the seal surface. The larger main stiffness terms for “the porous seal” yield larger radial reaction force acting on a rotor as a consequence of small whirling motion of shaft about a centered position, which would contribute to rotor stability.

Segmentation Effects on Brush Seal Leakage and Rotordynamic Coefficients

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Alexander O. Pugachev ◽  
Manuel Gaszner ◽  
Christos Georgakis ◽  
Paul Cooper
Keyword(s):  
Electrical Discharge Machining ◽  
Labyrinth Seal ◽  
Performance Characteristics ◽  
Radial Clearance ◽  
Single Plane ◽  
Rotordynamic Coefficients ◽  
Damping Coefficients ◽  
Brush Seal ◽  
Computational Fluid Dynamics Cfd ◽  
Stiffness And Damping

This paper studies the effect of brush seal segmentation on the seal performance characteristics. A brush–labyrinth sealing configuration arranged of one brush seal downstream and two labyrinth fins upstream is studied experimentally and theoretically. The studied brush seal is of welded design installed with zero cold radial clearance. The brush seal front and back rings as well as the bristle pack are segmented radially in a single plane using the electrical discharge machining (EDM) technique. The segmentation procedure results in loss of bristles at the site of the cuts altering the leakage flow structure in the seal and its performance characteristics. Two test rigs are used to obtain leakage, as well as rotordynamic stiffness and damping coefficients of the seal at different pressure ratios. The computational fluid dynamics (CFD)-based model is used to predict the seal performance and to study in detail local changes in the flow field due to the segmentation. A back-to-back comparison of the performance of nonsegmented and segmented brush seals as well as baseline labyrinth seal is provided. The obtained results demonstrate that the segmentation in general negatively affects the performance of the studied brush–labyrinth sealing configuration. However, the segmented brush seal shows increased direct damping coefficients.

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