Experimental Force Coefficients for a Two-Bladed Labyrinth Seal and a Four-Pocket Damper Seal

1999 ◽  
Vol 121 (2) ◽  
pp. 370-376 ◽  
Author(s):  
David Ransom ◽  
Jiming Li ◽  
Luis San Andre´s ◽  
John Vance
Keyword(s):  
Labyrinth Seal ◽  
Supported Housing ◽  
Impact Loads ◽  
Damping Force ◽  
Frequency Spectra ◽  
Force Coefficients ◽  
Direct Stiffness ◽  
Gas Damper ◽  
Positive Direct ◽  
The Impact

Experiments are presented to identify the stiffness and damping force coefficients of a two-blade, teeth on stator labyrinth seal with diverging clearance and its modified version as a four-pocket gas damper seal. The seals were tested without journal rotation and at rotor speeds of 1500 rpm and 3000 rpm for seal supply to ambient pressure ratios ranging from 1 to 3. Calibrated impact loads excite a flexibly supported housing holding rigidly the test seal. The impact loads and seal displacement and acceleration time responses are measured and recorded as frequency spectra. The instrumental variable filter method is used to identify the seal dynamic force coefficients from the measured transfer functions over a frequency range. The experiments demonstrate the four pocket gas damper seal has large (positive) direct damping coefficients and relatively small (negative) direct stiffness coefficients. The two bladed labyrinth seal exhibits positive direct stiffness and negative damping force coefficients. The leakage performance of both seals is nearly identical. The four pocket damper seal clearly outperforms the labyrinth seal in terms of rotordynamic forces. Both seals show a minimal amount of cross-coupling force effects, well within the experimental uncertainty.

Comparison of Predictions With Test Results for Rotordynamic Coefficients of a Four-Pocket Gas Damper Seal

1999 ◽  
Vol 121 (2) ◽  
pp. 363-369 ◽  
Author(s):  
Jiming Li ◽  
David Ransom ◽  
Luis San Andre´s ◽  
John Vance
Keyword(s):  
Flow Model ◽  
Control Volume ◽  
Current Model ◽  
Excitation Frequency ◽  
Bulk Flow ◽  
Damping Force ◽  
Force Coefficients ◽  
Numerical Predictions ◽  
Direct Stiffness ◽  
Gas Damper

Experiments and field applications have demonstrated that multiple-pocket gas damper seals effectively eliminate subsynchronous vibration and attenuate imbalance response at the critical speeds in turbomachinery. A one-control volume, turbulent bulk-flow model for the prediction of the seal leakage and rotordynamic force coefficients of centered multiple-pocket damper seals is hereby detailed. Comparisons of numerical predictions with experimental force coefficients for a four-pocket damper seal are presented. The bulk-flow model and experiments indicate the seal direct stiffness and damping force coefficients are insensitive to journal speed while the cross-coupled stiffnesses increase slightly. However, the current model overpredicts the direct damping coefficient and underpredicts the direct stiffness coefficient for increasing test pressure ratios. Computed results show that the force coefficients of multiple-pocket gas damper seals are also functions of the rotor excitation frequency.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals—Part II: Effects of Partition Wall Type, Partition Wall Number, and Cavity Depth

2014 ◽  
Vol 137 (3) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Flow Rate ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Cavity Depth ◽  
Partition Wall ◽  
Leakage Flow Rate ◽  
Direct Stiffness ◽  
Cfd Method ◽  
Positive Direct ◽  
Orbit Model

Effects of partition wall type, partition wall number and cavity depth on the leakage and rotordynamic characteristics of the pocket damper seal (PDS) were numerically investigated using a presented 3D transient computational fluid dynamics (CFD) method based on the multifrequency elliptical whirling orbit model. The accuracy and availability of this transient CFD method and the multifrequency elliptical whirling orbit model were demonstrated with the experimental data of the experimental eight-bladed fully partitioned pocket damper seal (FPDS). The leakage flow rates and frequency-dependent rotordynamic coefficients of PDS were computed for two types of partition wall (namely conventional PDS and fully partitioned PDS), four partition wall numbers including the labyrinth seal (no partition wall) and six cavity depths including the plain smooth seal (zero cavity depth) at operational conditions with or without inlet preswirl and 15,000 rpm rotational speed. The numerical results show that the FPDS has the similar leakage performance and more superior stability capacity than the conventional PDS. The FPDS possesses slightly larger leakage flow rate (∼2.6–4.0% larger) compared to the labyrinth seal. Eight is a preferable value for the partition wall number to gain the best leakage performance of the FPDS with the least manufacturing cost. The FPDS possesses significantly larger stiffness and damping than the labyrinth seal. Increasing partition wall number results in a significant increase in the direct stiffness but limited desirable effect on the effective damping. The FPDS possesses the lowest leakage flow rate when the cavity depth is about 2.0 mm. Compared to the plain smooth seal, the FPDS possesses larger positive direct stiffness and significantly less direct damping and effective damping. Increasing cavity depth results in a significant decrease in the stabilizing direct damping and the magnitude of the destabilizing cross-coupling stiffness. H= 3.175 mm is a preferable value of the cavity depth for which the effective damping of the FPDS is largest, especially for the concerned frequencies (80–120 Hz) where most multistage high-pressure centrifugal compressors have stability problem.

scholarly journals Rotordynamic Force Coefficients of Pocket Damper Seals

2006 ◽  
Author(s):  
B. Ertas ◽  
A. Gamal ◽  
J. Vance
Keyword(s):  
Dynamic Pressure ◽  
Mechanical Impedance ◽  
Impedance Method ◽  
Force Density ◽  
Frequency Dependent ◽  
Force Coefficients ◽  
Direct Stiffness ◽  
Cross Axis ◽  
Positive Direct ◽  
Stiffness And Damping

This paper presents measured frequency dependent stiffness and damping coefficients for 12 and 8 bladed pocket damper seals (PDS) subdivided into 4 different seal configurations. Rotating experimental test are presented for inlet pressures at 69 bar (1,000 psi), a frequency excitation range of 20–300 Hz, and rotor speeds up to 20,200 rpm. The testing method used to determine direct and cross-coupled force coefficients was the mechanical impedance method, which required the measurement of external shaker forces, system accelerations, and motion in two orthogonal directions. In addition to the impedance measurements, dynamic pressure responses were measured for individual seal cavities of the 8 bladed PDS. Results of the frequency dependent force coefficients for the 4 PDS designs are compared. The conclusions of the test show that the 8 bladed PDS possessed significantly more positive direct damping and negative direct stiffness than the 12 bladed seal. The results from the dynamic pressure response tests show that the diverging clearance design strongly influences the dynamic pressure phase and force density of the seal cavities. The tests also revealed the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for all seals, which indicate that the seals do not produce a de-stabilizing influence on rotor-bearing systems.

Rotordynamic Behavior of Leaf Seals: Measurement of Frequency-Dependent Force Coefficients for Varying Inlet Parameters

2020 ◽  
Author(s):  
Clemens Griebel
Keyword(s):  
Dynamic Test ◽  
Operating Parameter ◽  
Labyrinth Seal ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Impedance Method ◽  
Force Coefficients ◽  
Leaf Pack ◽  
Dynamics Simulations ◽  
Positive Direct

Abstract While brush seals can be found in various applications for turbomachines today, leaf seals are a further development in compliant seal technology and have a lower level of maturity. Among the purported advantages are greater axial rigidity when subject to higher pressure differences and the potential for non-contacting operation due to lift-up. However, especially their rotordynamic behavior is little investigated in the literature so far. In this paper, measured rotordynamic force coefficients of a leaf seal are presented for varying inlet pressures, preswirl velocities and excitation frequencies. The leaf pack of the tested leaf seal has zero rotor cold clearance and its coverplates are designed for facilitating a lift-up effect when pressurizing the seal. Experiments were performed on a dynamic test rig with whirling rotor using active magnetic bearing technology and evaluated in the frequency domain based on the impedance method. Test results for the leaf seal reveal positive direct stiffness and an advantageous rotordynamic behavior due to significant levels of direct damping and negative cross-coupled stiffness throughout the operating parameter range. Leaf seal results are compared to brush and labyrinth seal data from previous studies for varying inlet pressures and preswirl velocities. Additional computational fluid dynamics simulations were carried out to predict the leaf deflection moment, which support the findings regarding hydrostatic lift-up from the experimental results.

Rotordynamic Force Coefficients for a New Damper Seal Design

2006 ◽  
Vol 129 (2) ◽  
pp. 365-374 ◽  
Author(s):  
Bugra H. Ertas ◽  
John M. Vance
Keyword(s):  
Dynamic Pressure ◽  
Mechanical Impedance ◽  
Experimental Tests ◽  
Impedance Method ◽  
Frequency Dependent ◽  
Force Coefficients ◽  
Seal Design ◽  
Cross Axis ◽  
Gas Damper ◽  
Positive Direct

The objective of the following work was to determine frequency-dependent rotordynamic force coefficients for a new annular gas damper seal design. Both rotating and nonrotating experimental tests are presented for inlet pressures at 1000psig(69bar), a frequency excitation range of 20-300Hz, and rotor speeds up to 15,200rpm. Two different testing methods were used for determining coefficients: (1) dynamic pressure response method and (2) mechanical impedance method. The dynamic pressure method required the measurement of internal seal cavity pressure modulations in combination with the vibratory motion, whereas the mechanical impedance method used the measurement of external shaker forces, accelerations, and motion of the mechanical system. In addition to the new fully partitioned damper seal (FPDS) tests, the same experiments were conducted for a conventional pocket damper seal (PDS) design. Results of the frequency-dependent force coefficients and the internal seal dynamics for the two different gas damper seals are compared. The conclusions of the tests show that the FPDS design possesses significantly more positive direct damping and direct stiffness compared to the conventional PDS. The experiments also show the measurement of same-sign cross-coupled (cross-axis) stiffness coefficients for both seals, which indicate that the seals do not produce a destabilizing influence on rotor-bearing systems.

Numerical Investigations on the Leakage and Rotordynamic Characteristics of Pocket Damper Seals: Part II — Effects of Partition Wall Type, Partition Wall Number and Cavity Depth

2014 ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Zhenping Feng
Keyword(s):  
Flow Rate ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Cavity Depth ◽  
Partition Wall ◽  
Leakage Flow Rate ◽  
Direct Stiffness ◽  
Cfd Method ◽  
Positive Direct ◽  
Orbit Model

Effects of partition wall type, partition wall number and cavity depth on the leakage and rotordynamic characteristics of the pocket damper seal (PDS) were numerically investigated using a presented 3D transient CFD method based on the multi-frequency elliptical whirling orbit model. The accuracy and availability of this transient CFD method and the multi-frequency elliptical whirling orbit model were demonstrated with the experimental data of the experimental eight-bladed fully-partitioned pocket damper seal (FPDS). The leakage flow rates and frequency-dependent rotordynamic coefficients of PDS were computed for two types of partition wall (namely conventional PDS and fully-partitioned PDS), four partition wall numbers including the labyrinth seal (no partition wall) and six cavity depths including the plain smooth seal (zero cavity depth) at operational conditions with or without inlet preswirl and 15000rpm rotational speed. The numerical results show that the FPDS has the similar leakage performance and more superior stability capacity than the conventional PDS. The FPDS possesses slightly larger leakage flow rate (∼2.6–4.0% larger) compared to the labyrinth seal. Eight is a preferable value for the partition wall number to gain the best leakage performance of the FPDS with the least manufacturing cost. The FPDS possesses significantly larger stiffness and damping than the labyrinth seal. Increasing partition wall number results in a significant increase in the direct stiffness but limited desirable effect on the effective damping. The FPDS possesses the lowest leakage flow rate when the cavity depth is about 2.0mm. Compared to the plain smooth seal, the FPDS possesses larger positive direct stiffness and significantly less direct damping and effective damping. Increasing cavity depth results in a significant decrease in the stabilizing direct damping and the magnitude of the destabilizing cross-coupling stiffness. H = 3.175mm is a preferable value of the cavity depth for which the effective damping of the FPDS is largest, especially for the concerned frequencies (80–120Hz) where most multistage high-pressure centrifugal compressors have stability problem.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals in Wet Gas Conditions

2018 ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Flow Rates ◽  
Force Coefficients ◽  
Wet Gas ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Gas Seals

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.

Numerical Investigation on the Leakage and Rotordynamic Characteristics for Three Types of Annular Gas Seals in Wet Gas Conditions

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Zhigang Li ◽  
Zhi Fang ◽  
Jun Li
Keyword(s):  
Liquid Phase ◽  
Gas Phase ◽  
Labyrinth Seal ◽  
Leakage Flow ◽  
Flow Rates ◽  
Force Coefficients ◽  
Wet Gas ◽  
Annular Seal ◽  
Direct Stiffness ◽  
Gas Seals

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.

scholarly journals The Impact of Managers and Network Interactions on the Integration of Circularity in Business Strategy

2021 ◽  
pp. 108602662199463
Author(s):  
Manon Eikelenboom ◽  
Gjalt de Jong
Keyword(s):  
The Netherlands ◽  
Survey Data ◽  
Empirical Research ◽  
Indirect Effect ◽  
Business Strategy ◽  
Business Processes ◽  
Core Business ◽  
Organizational Attributes ◽  
Positive Direct ◽  
The Impact

Integrating circularity in business strategy is difficult to achieve for companies as it requires impactful changes in core business processes. While research has focused on identifying key barriers, little is known about the organizational attributes that can assist businesses in integrating circularity in their strategies. The purpose of this study is to investigate the implications of organizational managers and network interactions for the integration of circularity in business strategy. Through using survey data from 627 SMEs (small- and medium-sized enterprises) in the Netherlands, this study shows that managers who interpret circularity as an opportunity can have a positive direct and indirect effect on the integration of circularity in a company’s strategy. The results furthermore highlight the importance of circular network interactions for the integration of circularity in business strategy. This article contributes to recent calls for more empirical research into the integration of circularity and offers relevant insights for companies aiming to integrate circularity.

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