Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor: Part 1 — Measurement

2019 ◽  
Author(s):  
Jieun Song ◽  
Suyong Kim ◽  
Tae Choon Park ◽  
Bong-Jun Cha ◽  
Dong Hun Lim ◽  
...  
Keyword(s):  
Centrifugal Compressor ◽  
System Level ◽  
Labyrinth Seals ◽  
Stiffness Coefficients ◽  
Pressure Distributions ◽  
Order Of Magnitude ◽  
Direct Stiffness ◽  
The Cross ◽  
Rotordynamic Forces ◽  
Pressure Perturbations

Abstract Centrifugal compressors can suffer from rotordynamic instability. While individual components (e.g., seals, shrouds) have been previously investigated, an integrated experimental or analytical study at the compressor system level is scarce. For the first time, non-axisymmetric pressure distributions in a statically eccentric shrouded centrifugal compressor with eye-labyrinth seals have been measured for various eccentricities. From the pressure measurements, direct and cross-coupled stiffness coefficients in the shrouded centrifugal compressor have been determined. Thus, the contributions of the pressure perturbations in the shroud cavity and labyrinth seals have been simultaneously investigated. The cross-coupled stiffness coefficients in the shroud and labyrinth seals are both positive and one order of magnitude larger than the direct stiffness coefficients. Furthermore, in the tested compressor, contrary to the common assumption, the cross-coupled stiffness in the shroud is 2.5 times larger than that in the labyrinth seals. Thus, the shroud contributes more to rotordynamic instability than the eye-labyrinth seals.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 1: Measurement

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Jieun Song ◽  
Suyong Kim ◽  
Tae Choon Park ◽  
Bong-Jun Cha ◽  
Dong Hun Lim ◽  
...  
Keyword(s):  
Centrifugal Compressor ◽  
System Level ◽  
Labyrinth Seals ◽  
Stiffness Coefficients ◽  
Pressure Distributions ◽  
Order Of Magnitude ◽  
Direct Stiffness ◽  
The Cross ◽  
Rotordynamic Forces ◽  
Pressure Perturbations

Abstract Centrifugal compressors can suffer from rotordynamic instability. While individual components (e.g., seals, shrouds) have been previously investigated, an integrated experimental or analytical study at the compressor system level is scarce. For the first time, non-axisymmetric pressure distributions in a statically eccentric shrouded centrifugal compressor with eye-labyrinth seals have been measured for various eccentricities. From the pressure measurements, direct and cross-coupled stiffness coefficients have been determined. Thus, the contributions of the pressure perturbations in the shroud cavity and labyrinth seals have been simultaneously investigated. The cross-coupled stiffness coefficients in the shroud and labyrinth seals are both positive and one order of magnitude larger than the direct stiffness coefficients. Furthermore, in the tested compressor, contrary to the common assumption, the cross-coupled stiffness in the shroud is 2.5 times larger than that in the labyrinth seals. Thus, not only eye-labyrinth seals but also shrouds need to be considered in rotordynamic analysis.

Rotordynamic Performance of a Negative-Swirl Brake for a Tooth-on-Stator Labyrinth Seal

2014 ◽  
Author(s):  
Dara W. Childs ◽  
James E. Mclean ◽  
Min Zhang ◽  
Stephen P. Arthur
Keyword(s):  
Labyrinth Seal ◽  
Test Results ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Shaft Rotation ◽  
Direct Stiffness ◽  
The Cross ◽  
Inlet Conditions ◽  
The Stability

In the late 1970’s, Benckert and Wachter (Technical University Stuttgart) tested labyrinth seals using air as the test media and measured direct and cross-coupled stiffness coefficients. They reported the following results: (1) Fluid pre-swirl in the direction of shaft rotation creates destabilizing cross-coupled stiffness coefficients, and (2) Effective swirl brakes at the inlet to the seal can markedly reduce the cross-coupled stiffness coefficients, in many cases reducing them to zero. In recent years, “negative-swirl” swirl brakes have been employed that attempt to reverse the circumferential direction of inlet flow, changing the sign of the cross-coupled stiffness coefficients and creating stabilizing stiffness forces. This study presents test results for a 16-tooth labyrinth seal with positive inlet preswirl (in the direction of shaft rotation) for the following inlet conditions: (1) No swirl brakes, (2) Straight, conventional swirl brakes, and (3) Negative-swirl swirl brakes. The negative-swirl swirl-brake designs were developed based on CFD predictions. Tests were conducted at 10.2, 15.35, and 20.2 krpm with 70 bars of inlet pressure for pressure ratios of 0.3, 0.4, 0.5. Test results include leakage and rotordynamic coefficients. In terms of leakage, the negative-swirl brake configuration leaked the least, followed by the conventional brake, followed by the no-brake design. Normalized to the negative-swirl brake configuration, the conventional-brake and no-brake configurations mass flow rate were greater, respectively, by factors of 1.04 and 1.09. The direct stiffness coefficients are negative but small, consistent with past experience. The conventional swirl brake drops the destabilizing cross-coupled stiffness coefficients k by a factor of about 0.8 as compared to the no-brake results. The negative-swirl brake produces a change in sign of k with an appreciable magnitude; hence, the stability of forwardly-precessing modes would be enhanced. In descending order, the direct damping coefficients C are: no-swirl, negative-swirl, conventional-swirl. Normalized in terms of the no-swirl case, C for the negative and conventional brake designs are, respectively, 0.7 and 0.6 smaller. The effective damping Ceff combines the effect of k and C. Ceff is large and positive for the negative-swirl configuration and near zero for the no-brake and conventional-brake designs. The present results for a negative-brake design are very encouraging for both eye-packing seals (where conventional swirl brakes have been previously employed) and division-wall and balance-piston seals where negative shunt injection has been employed.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor—Part 2: Analysis

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Jieun Song ◽  
Seung Jin Song
Keyword(s):  
Pressure Distribution ◽  
Centrifugal Compressor ◽  
Axisymmetric Flow ◽  
Mass Conservation ◽  
Labyrinth Seal ◽  
Operating Conditions ◽  
New Model ◽  
Flow Coupling ◽  
Order Of Magnitude ◽  
Rotordynamic Forces

AbstractAn integrated analytical model to predict non-axisymmetric flow fields and rotordynamic forces in a shrouded centrifugal compressor has been newly developed and validated. The model is composed of coupled, conservation law-based, bulk-flow submodels, and the model takes into account the flow coupling among the blades, labyrinth seals, and shroud cavity. Thus, the model predicts the entire flow field in the shrouded compressor when given compressor geometry, operating conditions, and eccentricity. When compared against the experimental data from part 1, the new model accurately predicts the evolution of the pressure perturbations along the shroud and labyrinth seal cavities as well as the corresponding rotordynamic stiffness coefficients. For the test compressor, the cross-coupled stiffness rotordynamic excitation is positive; the contribution of the shroud is the highest; the contribution of the seals is less than but on the same order of magnitude as that of the shroud; and contribution of impeller blades is insignificant. The new model also enables insight into the physical mechanism for pressure perturbation development. The labyrinth seal pressure distribution becomes non-axisymmetric to satisfy mass conservation in the seal cavity, and this non-axisymmetry, in turn, serves as the influential boundary condition for the pressure distribution in the shroud cavity. Therefore, for accurate flow and rotordynamic force predictions, it is important to model the flow coupling among the components (e.g., impeller, shroud, labyrinth seal, etc.), which determines the non-axisymmetric boundary conditions for the components.

scholarly journals Static and Rotordynamic Analysis of a Plain Annular (Liquid) Seal in the Laminar Regime With a Swirl Brake for Three Clearances

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Ovais Ahmed Bin Najeeb ◽  
Dara W. Childs
Keyword(s):  
Dynamic Force ◽  
Laminar Regime ◽  
Dynamic Measurements ◽  
Stiffness Coefficients ◽  
Stationary Coordinate System ◽  
Liquid Seal ◽  
Direct Stiffness ◽  
The Cross ◽  
Positive Direct ◽  
San Andres

Tests are reported for a smooth seal with radial clearances 127 μm, 254 μm, 381 μm (1×, 2×, and 3×); length 45.72 mm, diameter 101.6 mm. An insert induced upstream preswirl. Swirl brakes (SBs), comprising 36 square cuts with axial depth 5.08 mm, radial height 6.35 mm, and circumferential width 6.35 mm each. Static and rotordynamic data were produced at ω = 2, 4, 6, 8 krpm, ΔP = 2.07, 4.14, 6.21, 8.27 bar, and eccentricity ratios ε0 = e0/Cr = 0.00, 0.27, 0.53, and 0.80. ISO VG 46 oil at a range of 46–49 °C was used, netting laminar flow (total Re ≤ 650). Dynamic measurements included components of the following vectors: (a) stator–rotor relative displacements, (b) acceleration, and (c) applied dynamic force in a stationary coordinate system. SBs were effective at the 3× clearance only. With the 3× seal, the cross-coupled stiffness coefficients have the same sign (not destabilizing). However, the seal has a negative direct stiffness K that could potentially “suck” the rotor into contact with the stator wall, along with dropping the pump rotor's natural frequency, further reducing its dynamic stability. Measurements were compared to predictions from a code by Zirkelback and San Andrés. Most predictions agree well with test data. Notable exceptions are the direct and cross-coupled stiffness coefficients for the 3× clearance. Predictions showed positive direct stiffness and opposite signs for the cross-coupled stiffness coefficients.

Qualitative Characterization of Anti-Swirl Gas Dampers

1999 ◽  
Vol 121 (2) ◽  
pp. 342-348 ◽  
Author(s):  
N. L. Zirkelback
Keyword(s):  
Rotor Vibration ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Model Predictions ◽  
Backward Whirl ◽  
Rotor Surface ◽  
Direct Stiffness ◽  
The Cross

Anti-swirl gas dampers have applications in high-temperature turbomachinery. Nozzles comprising the circumference of the damper inject air against the direction of shaft rotation, providing a force tangential to the rotor surface that acts to damp rotor vibration. The present work involves prediction of experiments by using direct damping and cross-coupled stiffness coefficients given in Vance and Handy (1997) that characterize the rotordynamic performance of an anti-swirl damper. Direct stiffness added at the damper location is vital to representing the changes in critical speeds and the onset and cease of backward whirl given in the experiments. This direct stiffness arises due to the release of air axially across the annulus of the damper. With the addition of this significant direct stiffness, experimental results compare well with the present rotordynamic model. Predictions using the experimentally obtained damping coefficients adequately reproduce the reduction in vibration amplitudes at the critical speeds. However, applying the cross-coupled stiffness coefficients in predictions fails to show increases in the speed at which backward whirl begins and does not reproduce the wrecking instability experienced in the tests. A further study investigates the magnitude of the cross-coupled stiffness coefficient necessary to cause instability in the rotor-damper system.

Measurements Versus Predictions for Rotordynamic and Leakage Characteristics of a Convergent-Tapered, Honeycomb-Stator/Smooth-Rotor Annular Gas Seal

2008 ◽  
Author(s):  
Daniel E. van der Velde ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Excitation Frequency ◽  
Test Fluid ◽  
Low Frequencies ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Honeycomb Seals ◽  
Excitation Frequencies ◽  
The Cross

Measured results are presented for rotordynamic coefficients and leakage rates for two honeycomb-stator seal geometries, a convergent-tapered honeycomb seals (CTHC) and a constant-clearance honeycomb seals (CCHC) tested by Sprowl and Childs in 2007. The rotor diameter was 114.3 mm (4.500 in). The CTHC seals had inlet and exit clearances of 0.334 and 0.204 mm, respectively. The CCHC seal had a constant clearance of 0.204 mm. Honeycomb cells had depths of 3.175 mm (0.125 in) and widths of 0.79 mm (0.031 in). Measurements are reported with air as the test fluid, zero preswirl, ω = 20,200 rpm, a supply pressure of 69 bar (1,000 psi) and supply temperature of 18°C (64.4°F) for both seal geometries. The test pressure ratios are 0.5 for the CCHC seal, and 0.46 for the CTHC seal. The tapered seal leaks about 20% more than the constant-clearance seal. Measured and predicted dynamic coefficients are strong functions of excitation frequency. The measured direct stiffness coefficient was higher for the tapered seal at all excitation frequencies, including a projection to zero frequency, where the CCHC seal was on the order of −2MN/m versus roughly +13MN/m for the tapered seal. The CTHC seal had higher cross-coupled stiffness coefficients than the CCHC seal at all excitation frequencies. The CCHC and CTHC seals had comparable direct damping out to ∼80 Hz. For higher excitation frequencies, the CTHC seal had larger direct damping values. The effective damping Ceff combines the positive effect of direct damping and the destabilizing effect of cross-coupled-stiffness coefficients. It is negative at low frequencies and becomes positive for higher frequencies. The frequency at which it changes sign is called the cross-over frequency. The CCHC had a lower cross-over frequency (better from a stability viewpoint) and higher Ceff values out to ∼80 Hz. At higher excitation frequencies from ∼120Hz onward, the tapered seal has higher effective damping values. Kleynhans and Childs’ 1997 two-control-volume model did a generally good job of predicting the direct stiffness coefficients of both seals. It closely predicted the cross-coupled stiffness coefficients for the CCHC seal but substantially under predicted the values for the CTHC seal. It under predicted the direct damping for the CCHC seal at frequencies below ∼120Hz, but did a good job for higher frequencies. It under predicted direct damping for the CTHC seal at all frequencies. For the CCHC seal, the model did a good job of predicting Ceff at all frequencies and also accurately predicted the cross-over frequency. For the CTHC seal, the model accurately predicted the cross-over frequency but over predicted Ceff below the cross-over frequency (the seal was more destabilizing than predicted) and under predicted Ceff at higher frequencies.

Non-Axisymmetric Flows and Rotordynamic Forces in an Eccentric Shrouded Centrifugal Compressor: Part 2 — Analysis

2019 ◽  
Author(s):  
Jieun Song ◽  
Seung Jin Song
Keyword(s):  
Pressure Distribution ◽  
Centrifugal Compressor ◽  
Axisymmetric Flow ◽  
Mass Conservation ◽  
Labyrinth Seal ◽  
Operating Conditions ◽  
New Model ◽  
Order Of Magnitude ◽  
Entire Flow ◽  
Rotordynamic Forces

Abstract An integrated analytical model to predict non-axisymmetric flow fields and rotordynamic forces in a shrouded centrifugal compressor has been newly developed and validated. The model is composed of coupled, conservation law-based, bulk-flow sub-models, and the model takes into account the flow coupling among the blades, labyrinth seals, and shroud cavity. Thus, the model predicts the entire flow field in the shrouded compressor when given compressor geometry, operating conditions, and eccentricity. When compared against the experimental data from Part 1, the new model accurately predicts the evolution of the pressure perturbations along the shroud and labyrinth seal cavities as well as the corresponding rotordynamic stiffness coefficients. For the test compressor, the cross stiffness rotordynamic excitation is positive — the contribution of the shroud is the highest; the contribution of the seals is less than but on the same order of magnitude as that of the shroud; and contribution of impeller blades is insignificant. For accurate flow and rotordynamic force predictions, it is critical to model the coupling among the components (e.g., impeller, shroud, labyrinth seal, etc.) which determines the non-axisymmetric boundary conditions for the components. The new model also enables insight into the physical mechanism for pressure perturbation development. The labyrinth seal pressure distribution becomes non-axisymmetric to satisfy mass conservation in the seal cavity, and this non-axisymmetry, in turn, serves as the influential boundary condition for the pressure distribution in the shroud cavity.

Rotordynamic Performance of a Negative-Swirl Brake for a Tooth-on-Stator Labyrinth Seal

2015 ◽  
Vol 138 (6) ◽  
Author(s):  
Dara W. Childs ◽  
James E. Mclean ◽  
Min Zhang ◽  
Stephen P. Arthur
Keyword(s):  
Labyrinth Seal ◽  
Test Results ◽  
Labyrinth Seals ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Shaft Rotation ◽  
Computational Fluid Dynamics Cfd ◽  
The Cross ◽  
Inlet Conditions ◽  
The Stability

In the late 1970s, Benckert and Wachter (Technical University Stuttgart) tested labyrinth seals using air as the test media and measured direct and cross-coupled stiffness coefficients. They reported the following results: (1) fluid preswirl in the direction of shaft rotation creates destabilizing cross-coupled stiffness coefficients and (2) effective swirl brakes at the inlet to the seal can markedly reduce the cross-coupled stiffness coefficients, in many cases reducing them to zero. In recent years, “negative-swirl” swirl brakes have been employed, which attempt to reverse the circumferential direction of inlet flow, changing the sign of the cross-coupled stiffness coefficients and creating stabilizing stiffness forces. This study presents test results for a 16-tooth labyrinth seal with positive inlet preswirl (in the direction of shaft rotation) for the following inlet conditions: (1) no swirl brakes, (2) straight, conventional swirl brakes, and (3) negative-swirl swirl brakes. The negative-swirl swirl-brake designs were developed based on computational fluid dynamics (CFD) predictions. Tests were conducted at 10.2, 15.35, and 20.2 krpm with 70 bar of inlet pressure for pressure ratios of 0.3, 0.4, and 0.5. Test results include leakage and rotordynamic coefficients. In terms of leakage, the negative-swirl brake configuration leaked the least, followed by the conventional brake, followed by the no-brake design. Normalized to the negative-swirl brake configuration, the conventional-brake and no-brake configurations mass flow rate was greater, respectively, by factors of 1.04 and 1.09. The direct-stiffness coefficients are negative but small, consistent with past experience. The conventional swirl brake drops the destabilizing cross-coupled stiffness coefficients k by a factor of about 0.8 as compared to the no-brake results. The negative-swirl brake produces a change in sign of k with an appreciable magnitude; hence, the stability of forward precessing modes would be enhanced. In descending order, the direct-damping coefficients C are: no-swirl, negative-swirl, and conventional-swirl. Normalized in terms of the no-swirl case, C for the negative and conventional brake designs is, respectively, 0.7 and 0.6 smaller. The effective damping Ceff combines the effect of k and C. Ceff is large and positive for the negative-swirl configuration and near zero for the no-brake and conventional-brake designs. The present results for a negative-brake design are very encouraging for both eye-packing seals (where conventional swirl brakes have been previously employed) and division-wall and balance-piston seals, where negative shunt injection has been employed.

scholarly journals Qualitative Characterization of Anti-Swirl Gas Dampers

1998 ◽  
Author(s):  
Nicole L. Zirkelback
Keyword(s):  
Rotor Vibration ◽  
Critical Speeds ◽  
Damping Coefficients ◽  
Stiffness Coefficients ◽  
Model Predictions ◽  
Backward Whirl ◽  
Rotor Surface ◽  
Direct Stiffness ◽  
The Cross

Anti-swirl gas dampers have applications in high-temperature turbomachinery. Nozzles comprising the circumference of the damper inject air against the direction of shaft rotation, providing a force tangential to the rotor surface that acts to damp rotor vibration. The present work involves prediction of experiments by using direct damping and cross-coupled stiffness coefficients given in Vance and Handy (1997) that characterize the rotordynamic performance of an anti-swirl damper. Direct stiffness added at the damper location is vital to representing the changes in critical speeds and the onset and cease of backward whirl given in the experiments. This direct stiffness arises due to the release of air axially across the annulus of the damper. With the addition of this significant direct stiffness, experimental results compare well with the present rotordynamic model. Predictions using the experimentally obtained damping coefficients adequately reproduce the reduction in vibration amplitudes at the critical speeds. However, applying the cross-coupled stiffness coefficients in predictions fails to show increases in the speed at which backward whirl begins and does not reproduce the wrecking instability experienced in the tests. A further study investigates the magnitude of the cross-coupled stiffness coefficient necessary to cause instability in the rotor-damper system.

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